5(0,0) bordeau  1(0.6,9)

1(0.6,3) 1(6,0.1) white

1(11,0.1) white  10.3(5.4,3) white

A $b$-baryon sonata

Habilitation à diriger des recherches de l’Université Paris-Saclay

présentée et soutenue à IJCLab, le 20 Mai 2020, par
Yasmine Sara Amhis

Composition du Jury :

Prof Tulika Bose |
---|---
University of Wisconsin-Madison | Rapportrice
Prof Gino Isidori |
University of Zürich | Examinateur
Prof François Le Diberder |
Université de Paris, IJCLab Orsay | Examinateur
Prof Achille Stocchi |
Université Paris-Saclay, IJCLab Orsay | Examinateur
Prof Guy Wilkinson |
University of Oxford | Rapporteur
Dr Isabelle Wingerter-Seez |
Laboratoire d’Annecy de Physique des Particules | Rapportrice

###### Abstract

This manuscript summarises a selection of my research activities from the past
ten years. I obtained my PhD in 2009 at LAL under the supervision of Marie-
Hélène Schune and Jacques Lefrançois. Afterwards I moved to EPFL as a
postdoctoral researcher, where I worked for three years in the group of
Olivier Schneider. In 2012, I obtained a CNRS position at LAL now IJCLab.
Three physics analyses based on the LHCb data, focusing on properties of
$b$-baryons such as masses, lifetimes and a lepton universality test are
discussed in this manuscript. For each topic, I cherry picked key experimental
points that will be developed in the text. The papers corresponding to these
analyses can be found at the end of the document. Specific contributions to
the scintillator fibre tracker and the calorimeters of the LHCb detector are
also described. The object that you are holding in your hands is not meant to
be pedagogical nor an exhaustive review, however, I hope that it contains
enough information and references to guide any curiosity that it triggers.

###### Contents

  1. 1 Allegro non troppo
    1. 1 A powerful yet incomplete theory
    2. 2 Handling multi-scale problems
    3. 3 What can we learn from mass measurements?
    4. 4 What can we learn from lifetime measurements?
    5. 5 What can we learn from Lepton Universality tests?
    6. 6 What is emerging in the Loch Ness?
  2. 2 Allegretto
    1. 7 The LHCb detector
    2. 8 Pattern recognition
    3. 9 Calorimeters
  3. 3 Allegro
    1. 10 Dear $b$-baryons
    2. 11 Mass measurements
    3. 12 Lifetime measurements
    4. 13 Lepton universality test
  4. 4 Conclusion
  5. Apprentices
    1. Anja Beck - 2019/M2

Pour un kilo de Loulou

Orsay, August 30${}^{th}~{}2019$

I am writing this foreword from an odd place. $R_{{p}{K}}^{-1}$ is still blind
and hopefully will be unblinded in a few weeks. The expected statistical
uncertainty is quite large, about 16%. However, this measurement will say
“something” about the ${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ anomalies. I am
lucky to witness a peculiar time, where saying that we might have signs,
indications or hints of New Physics in our LHCb data is not a complete
fantasy. Some of the global flavour fits to the Wilson coefficients do report
up to five standard deviations with respect to the Standard Model predictions.
How exciting is that? Can these anomalies be only a misunderstanding of
hadronic uncertainties? That would be rubbish. What do we think of the
Leptoquarks? What about the somewhat resilient $U_{1}\equiv({\bf 3},{\bf
1})_{2/3}$?
It goes without saying that flavour physics analyses are not just about New
Physics searches, far from it, and this humble document aims at demonstrating
so. Part of me though, always envied my peers who were “there” when new or
unexpected particles were discovered. Without further ado, let us dive in.
Trois, quatre…

##  Chapter 1 Allegro non troppo

> A Bird, came down the Walk -
> He did not know I saw -
> He bit an Angle Worm in halves
> And ate the fellow, raw
>
> Emily Dickinson

###  1 A powerful yet incomplete theory

The Standard Model (SM) of particle physics was invented in the late 60’s, it
is a quantum gauge theory. Similarly to a lego game, there are only a few
different kinds of fundamental particles describing visible matter as we know
it. The SM is structured in three families or generations of fermions named
quarks and leptons. There are six types of quarks up, down, charm, strange,
top and bottom. The bottom quark ($b$), is also referred to as $beauty$-quark.
There are three charged leptons $e^{-},\mu^{-},\tau^{-}$ and three associated
neutral leptons $\nu_{e},\nu_{\mu},\nu_{\tau}$ [1]. By construction in the SM,
three interactions i.e.: the electromagnetic, weak and strong interactions are
responsible for the transitions between these particles. These interactions
are mediated by particles called gauge bosons, $\gamma$, $Z$ and $W$, the
gluons, they are described by a gauge group $SU(3)_{c}\times SU(2)_{L}\times
U(1)_{Y}$. This group is spontaneously broken down to $SU(3)_{c}\times
U(1)_{em}$, $i.e:$ QCD and QED, through the non-vanishing vacuum expectation
value of the Higgs field. Depending on the properties of the fermions and
bosons at play, such as electric charge and other quantum numbers, particles
will be affected by the interactions in different ways. For example, given
that they carry a charge of “colour” only quarks are affected by the strong
interaction. The SM of particles physics has often been described as an
elegant theory; this is partly due to its precise predictive power. The SM is
also appealing since it offers a wide class of physics observables that can be
confronted with experimental measurements, a few examples of which will be
discussed in this habilitation. This being said, the SM fails to describe some
fairly fundamental aspects of nature. The SM does not accommodate gravity, nor
can it explain the mass hierarchy of many orders of magnitude observed between
particles. For instance, the mass of an electron is 0.511 MeV/$c^{2}$ and the
mass of the top quark is 173 GeV/$c^{2}$ [1]. Furthermore, satellite
experiments such as Planck show that visible matter only comprises 5 % of the
universe, the rest is attributed to dark energy (68%) and dark matter (27 %)
[2]. In other words, the SM is excellent at describing what seems to be the
tip of an iceberg. Both the theory and experimental physics communities share
the viewpoint that there must exist sources of New Physics (NP), new theories
able to propose a more complete description of nature.

One of the main purposes of the experiments located at the Large Hadron
Collider at CERN, is to search for new particles. Experimentally, there are
two strategies to search for these unknown particles. The first approach is to
“hunt” directly for new particles in the decay products of the proton-proton
collisions. This is how the Higgs boson was discovered in 2012 by the ATLAS
and CMS collaborations [3]. A second approach is to demonstrate the presence
of new particles in an indirect way. The heart of indirect searches relies on
a class of physics observables that may differ from SM predictions in the
presence of NP. This method is heavily exploited by the LHCb experiment. If
one assumes that NP lies at a scale $\Lambda_{\textrm{NP}}$ higher than the
mass of the weak interaction bosons, then one can write a Lagrangian as
follows:

${\cal L}_{\textrm{ \tiny NP}}={\cal L}_{\textrm{ \tiny
SM}}+\sum_{d>4}\sum_{n=1}^{N_{d}}\frac{c_{n}^{(d)}}{\Lambda_{\textrm{\tiny
NP}}^{d-4}}{\cal O}_{n}^{(d)},$ (1)

where the NP is described by higher order operators suppressed by a scale
$\Lambda_{\textrm{NP}}$. The rule of the game of flavour physics is twofold.
On the one hand it is essential to understand and constrain as precisely as
possible SM processes, where no NP is expected. These class of processes are
sometimes called “standard candles”, they can be probed using dedicated
observables such as mass or lifetime measurements. The second aspect is to
search for deviations from SM predictions using “theoretically clean” probes,
for instance angular observables, lepton universality tests, etc.

This chapter is organised as follow, after a discussion of the theoretical
framework employed to make predictions, three observables, namely, masses,
lifetimes, and lepton universality tests be will described. They serve as
illustrations of how one can poke at different aspects of the physics that we
care about. As will be later discussed in Chapter 2 and 3, the LHCb detector
is specialised in the analysis of decays of hadrons containing a $b$-quark.
Following the hadronisation which occurs after the production of pairs of
$b$-quarks (for instance in gluon-gluon fusion processes) all types of
$b$-hadrons are produced and in particular $b$-baryons. Their organisation
within a quark model is shown in Figure 1. $b$-baryons have emerged as a
pattern in the research that I have conducted in the past years. Their
properties and the observables that they allow to reach are used as a “fil
conducteur” throughout the work documented in this habilitation.

Figure 1: SU(4) multiplets of baryons made of $u$, $d$, $s$ and $b$ quarks.
Left: the multiplet with an SU(3) octet on the lowest level. Right: the
multiplet with an SU(3) decuplet on the lowest level. Observed states are
shown in red, while predicted unobserved states are in blue [1].

###  2 Handling multi-scale problems

Effective Field Theories (EFTs) are powerful tools to describe high energy NP
phenomena and their effect on precision observables. Their strength lies in
their ability to separate and treat multi-scale problems such as for example
${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ transitions. At each scale, all the
degrees of freedom with properties higher than the value of the scale will be
integrated out. For instance, let us consider tree-level $b$ $\rightarrow$ $c$
decay, in the SM at the lowest order it mediated by the exchange of $W$ boson,
these transitions are referred to a Flavour Changing Charged Current (FCCC).
For this type of decay, the momentum transfer from the $W$ is very small in
comparison to its mass, one can write:

$\frac{-g_{\mu\nu}+q_{\mu}q_{\nu}/M_{W}^{2}}{q^{2}-M_{W}^{2}}\xrightarrow[]{q^{2}\ll
M_{W}^{2}}\frac{g_{\mu\nu}}{M_{W}^{2}},$ (2)

The charged current can be reduced to a point-like four fermion interaction by
”integrating-out” the $W$ boson. This is illustrated in Figure: 2.

Figure 2: Example of ”integrating-out” a $W$ boson in a FCCC.

Different models can be adopted depending on the scale where one is trying to
address a specific problem or make a prediction for a physics observable.
Examples of models which will be later discussed in this document as a
function of energy are illustrated in Figure 3. What makes EFTs powerful to
describe NP is that they can be used to study processes, where one does not
know a priori the underlying ultra violet (UV) theory [4, 5]. Another usage of
EFT is the study of low energy properties of the strong interaction, for
example Chiral Perturbative Theory or Heavy Quark Expansion Theory [6, 7]
which do not rely on fully perturbative computations.

Figure 3: Sketch of relevant energy scale (first line), New Physics ETFs and
QCD ones.

In the EFT framework, the phenomenology of $b$-decays can be described in a
convenient way, with an Effective Hamiltonian formalism [6, 8, 9]. For a given
initial state $I$ going to a final state $F$, the amplitude can be written as
:

${\cal A}(I\rightarrow F)=\langle F|{\cal H}_{\textrm{eff}}|I\rangle,$ (3)

where the ${\cal H}_{\textrm{eff}}$ describes both the low energy dynamics
(long distance) and high energy ones (short distance).

###  3 What can we learn from mass measurements?

A hadron can be thought of as a bound state of constituent quarks. It can
either form a meson ($q\bar{q}$), a baryon ($qqq$, $\bar{q}\bar{q}\bar{q}$) or
more exotic combinations such as tetra- or pentaquarks [10]. This
classification was first proposed by Gell-Mann and Nishijima in 1958. The
generalised Gell-Mann-Nishijima formula relating the various hadron quantum
numbers is given by:

$Q=I_{z}+\frac{{\cal B}+S+C+B+T}{2}$ (4)

where $Q$ is the charge, $\cal{B}$ is the baryon number, $I_{z}$ is the $z$
projection of the Isopsin and $S,C,B$ and $T$ are the flavour of the quark.
While, we know today that there are six types of quarks, up, down, strange,
charm, top and beauty, one should remember that at that time, Gell-Mann and
Nishijima, nor any other physicists, were not aware of the existence of
neither the charm, beauty nor the top quark. Nevertheless, they were able to
predict the existence of the $\Omega^{-}$(sss) baryon discovered in 1964 in a
hydrogen bubble chamber. The masses, which are one of the most fundamental
properties of all hadrons, are a pure QCD effect. One could write in a
simplified way:

$m_{\textrm{hadron}}=\sum_{i}m^{i}_{\textrm{quark}}+E_{\textrm{Binding}}$ (5)

Except for the top quark, there are not free quarks in nature. This makes the
information about their mass difficult to access. Furthermore, the binding
energy is completely driven by QCD effects. Therefore, relatively large
uncertainties in the theoretical description of hadron masses are expected,
see for example those predictions listed in Table 1. Given that baryons are
three-body systems, the theory describing their dynamics within quark models
is much more complicated than that for mesons. There are many approaches used
within QCD to predict their properties. For example non-relativistic
formulations of QCD, quark models [1] or light-cone sum rules [11] allow us to
investigate the dependence of the baryon mass splittings on the heavy and
light quark masses. In lattice QCD, the correlation functions used to compute
the action for baryons are more difficult to determine than those for mesons,
therefore it is comparatively harder to extract a reliable mass spectrum for
heavy baryons [12]. The predictions of the CQM [13] method for example, rely
on the knowledge of the charm baryonic counter part. The spread of the
predictions and their uncertainties in Table 1 demonstrate that precise
measurements of many heavy hadron and in particular $b$-baryon masses help to
either exclude some of the theoretical approaches or contribute to refining
them. Furthermore, a better understanding of the dynamics of quarks inside the
hadrons can help to understand and characterize the nature of exotic
particles, such as the pentaquarks, the $X(3872)$ or the $Z(4140)$, etc. which
have been observed in the past years at the $B$-factories and at the LHC [1].

Prediction |  ${\mathchar 28931\relax}^{0}_{b}$ mass |  ${\mathchar 28932\relax}^{-}_{b}$ mass |  ${\mathchar 28938\relax}^{-}_{b}$ mass
---|---|---|---
CQM [13] | Used as input | 5790-5800 | 6052.1 $\pm$ 5.6
$1/N_{c}$ expansion [14] | Used as input | Used as input | 6039.1 $\pm$ 8.3
RCQM [15] | 5211$\pm$ 100 | 5812 $\pm$ 100 | 6065 $\pm$ 100
HQET + QCD sum rule [16] | $5637^{+68}_{-56}$ | $5780^{+73}_{-68}$ | $6036\pm 81$
QCD sum rule [17] | $5690\pm 130$ |  | $5890\pm 180$
Lattice QCD [18] | $5641\pm 21^{+15}_{-33}$ | $5781\pm 17^{+17}_{-16}$ | $6006\pm 10^{+20}_{-19}$
Table 1: Mass predictions in ${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$ for
${\mathchar 28931\relax}^{0}_{b}$, ${\mathchar 28932\relax}^{-}_{b}$ and
${\mathchar 28938\relax}^{-}_{b}$ baryons.

###  4 What can we learn from lifetime measurements?

Another fundamental property of particles is their lifetime. While at first
order all $b$-hadron lifetimes are expected to be the same, the presence of
the spectator quark displayed in Figure 4 can not be ignored in accurate
numerical computations. Non-perturbative effects to heavy-flavour decays can
be expressed through an expansion in inverse powers of $m_{{b}}$. The decay
rate of the transition of a $b$-hadron, $H_{{b}}$, to an inclusive final state
$X$, can be expressed in terms of a phase-space integral (PS) of the square of
the matrix element, summed over all final state $X$ with the same quantum
numbers

$\Gamma(H_{b}\rightarrow
X)=\frac{1}{2m_{H_{{b}}}}\sum_{X}\int_{\textrm{PS}}(2\pi)^{4}\delta^{(4)}(p_{H_{{b}}}-p_{X})|\langle
X|H_{\textrm{eff}}|H_{{b}}\rangle|^{2}$ (6)

Explicitly calculating the integral, one arrives at the Heavy Quark Expansion
[7] of decay rates of heavy hadrons:

$\Gamma(H_{b}\rightarrow
X)=\Gamma_{0}+\frac{\Lambda^{2}}{m_{{b}}^{2}}\Gamma_{2}+\frac{\Lambda^{3}}{m_{{b}}^{3}}\Gamma_{3}+\frac{\Lambda^{4}}{m_{{b}}^{4}}\Gamma_{4}+...,$
(7)

where the expansion parameter is denoted ${\Lambda}/{m_{{b}}}$, where the
typical scale of $\Lambda$ is $\sim$ 1 GeV.

Each of the $\Gamma_{i}$ terms of the expansion describes different aspects of
the possible effects inside the hadrons.

  * •

$\Gamma_{0}$ spectator model all $b$-hadrons have the same lifetime.

  * •

There are no corrections in $1/m_{b}$.

  * •

$\Gamma_{2}$ Fermi motion and chromomagnetic interaction, first corrections
due to the strong interaction, isospin, at this order one would expect :
$\tau_{{B}^{+}}/\tau_{{B}^{0}}-1\approx 0$ and $\tau_{{\mathchar
28931\relax}^{0}_{b}}/\tau_{{B}^{0}}-1\approx 2\%$.

  * •

$\Gamma_{3}$ Weak annihilation and Pauli interference, the spectator quark is
involved only at $1/{m_{{b}}^{3}}$ order.

The measurement of the lifetime differences of $b$-hadrons allows therefore to
test HQET at the third order.

Figure 4: Feynman diagram of ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{\mathchar 28931\relax}^{(*)}$

One important assumption behind the heavy quark expansion is the so-called
quark-hadron duality. It can be translated as follows: rates computed at the
quark-gluon level are equal to the corresponding observables involving
hadrons. Extensive discussions can be found in the literature regarding this
assumption. One of the best ways to test this is to confront HQET computations
to experimental measurements. A detailed review and summary of HQET principles
can be found in Ref. [19] and useful references can be found in Refs.
[20],[21], [22].

###  5 What can we learn from Lepton Universality tests?

Within the SM, there are no Flavour Changing Neutral Currents (FCNC) at tree
level, as a consequence ${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ transitions can
only occur through loops. Therefore, NP contributions can compete with the SM
ones, which makes ${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ transitions a
particularly interesting laboratory. For instance, in Figure: 5 the SM gauge
boson $Z$ could be replaced by a new particle, such as a heavier gauge boson,
for example the $Z^{\prime}$ or Leptoquarks.

Figure 5: Feynman diagram of a ${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$
transition.

For these decays, the effective Hamiltonian, ${\cal H}_{\textrm{eff}}$ is
defined as:

${\cal
H}_{\textrm{eff}}=\frac{G_{F}}{\sqrt{2}}\lambda^{\textrm{CKM}}\sum_{i}C_{i}{\cal
O}_{i},$ (8)

where $G_{F}$ is the Fermi constant and $\lambda^{\textrm{CKM}}$ are the
Cabibbo-Kobayashi-Maskawa terms describing the coupling between the $W^{\pm}$
bosons and the quarks [1]. In this formalism, the hard contributions generated
by the electromagnetic, weak, and strong interactions can be factorised
depending on their energy scale at leading order. The low energy part of the
transition, typically lower than the mass of the $b$-quark, mediated for
example by soft gluons, is encoded in what are called hadronic matrix
elements, ${\cal O}_{i}$. These elements can be evaluated using “numerical”
techniques such as Lattice QCD [23]. The Wilson coefficients $C_{i}$, on the
other hand describe short distance contributions to the transition occurring
at high energy, typically $\cal{O}$($m_{W}$). These coefficients can be
calculated using perturbative methods [24].

As shown in Equation 8, with EFTs one can factorise long distance from short
distance components. The short distances parts, which are sensitive to NP, are
encoded in the Wilson coefficients. The dominant operators relevant for
${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ transitions are:

${\cal
O}_{7}=\frac{e}{16\pi^{2}}m_{{b}}(\bar{s}\sigma_{\mu\nu}P_{R}{b})F^{\mu\nu};$
(9) ${\cal
O}_{9}=\frac{e^{2}}{16\pi^{2}}(\bar{s}\gamma_{\mu}P_{L}{b})(\bar{{\ell}}\gamma^{\mu}{\ell});$
(10) ${\cal
O}_{10}=\frac{e^{2}}{16\pi^{2}}(\bar{s}\gamma_{\mu}P_{L}{b})(\bar{{\ell}}\gamma^{\mu}\gamma_{5}{\ell});$
(11)

where $P_{L,R}=(1\mp\gamma_{5})/2$ are the projectors for left-(right-)handed
chirality. $P_{L}$ corresponds to the $V-A$ structure of the weak interaction
in the SM. Due to the universality of lepton couplings for the three
generations, the SM Wilson coefficients have the same value for all three
lepton generations. The determination of the Wilson coefficients requires a
matching of the high-energy theory (in this case the SM) and at the
electroweak scale and a running from this scale down to the low-energy one
close to the mass of the $b$ quark. NP can manifest itself as shifts to the
Wilson coefficients or enhancements of new operators which are either absent
or strongly suppressed in the SM.

One interesting feature of ${b}\rightarrow{s}{\ell}^{+}{\ell}^{-}$ decays is
shown in Figure: 6. It displays the variation of the differential rate i.e.
the probability of a ${b}\rightarrow{s}{\ell}^{+}{\ell}^{-}$ decay to occur as
a function of $q^{2}$, where $q^{2}$ is the sum square of the di-lepton system
invariant mass. In particular, it is worth noting that Wilson coefficients
($C_{7}^{(\prime)},C_{9}^{(\prime)},C_{10}^{(\prime)}$) contribute differently
to the different $q^{2}$ regions. For example, the very low $q^{2}$ region is
dominated by the Wilson coefficient $C_{7}^{(\prime)}$ corresponding to a
Feynman diagram where a photon is produced as illustrated in Figure: 6.
Therefore, to fully exploit the rich phenomenology of these decays,
experimental measurements, such as branching fractions, forward-backward
asymmetry, etc. are performed as a function of $q^{2}$.

Figure 6: Differential rate as a function of $q^{2}$ in
${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ transitions.

In order to constrain the values of the Wilson coefficients, the LHCb
collaboration has conducted many measurements of
${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ transitions, such as differential
branching fraction of ${{B}^{+}}\\!\rightarrow{{K}^{+}}{\mu^{+}\mu^{-}}$,
${{B}^{0}}\\!\rightarrow{{K}^{*0}}{\mu^{+}}{\mu^{-}}$, as well as
${{B}^{0}_{s}}\rightarrow\phi\mu^{+}\mu^{-}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{\mathchar 28931\relax}\mu^{+}\mu^{-}$. A few
deviations have been observed with respect to the SM predictions. Similar
patterns have been observed in angular analyses, where optimised observables,
for example $P^{\prime}_{5}$ , have been designed and employed to minimize the
impact of hadronic uncertainties, as shown in Figure: 7.

Figure 7: Measurements of $P^{\prime}_{5}$ by different experiments, compared
to the theoretical predictions.

Lepton Universality (LU) is an “accidental” property of the SM. It predicts
equal coupling of the SM gauge bosons to all three families of leptons at
tree-level. Lepton universality tests form some of the “cleanest” observables,
since all the hadronic uncertainties in these decays cancel in the ratios
leaving only differences due to QED corrections, which are expected to be very
small [25]. This property can be tested in many sectors and in particular in
loop-induced decays such as ${b}\rightarrow{s}{\ell}^{+}{\ell}^{-}$
transitions, but also tree-level decays such as
${b}\rightarrow{c}\ell\nu_{\ell}$ decays. For this latter process, the ratios
$R_{D}=0.299~{}\pm~{}0.003$ and $R_{D^{*}}=0.258~{}\pm~{}0.005$ were measured
at the $B$-factories and LHCb and lie 3.5 standard deviations above the SM
predictions. The current world average agrees with the SM at only three
standard deviations [26]. For ${b}\rightarrow{s}{\ell}^{+}{\ell}^{-}$
transitions, the LU ratios are defined as as:

$\displaystyle R_{H}\equiv\frac{\bigintssss\frac{d\Gamma(B\rightarrow
H{\mu^{+}\mu^{-}})}{d{q^{2}}}\,d{q^{2}}}{\bigintssss\frac{d\Gamma(B\rightarrow
H{e^{+}e^{-}})}{d{q^{2}}}\,d{q^{2}}}\,.$ (12)

LU in ${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ decays has been tested until now
in $B$ meson decays by the LHCb experiment [27], [28], and the results as a
function of $q^{2}$ are :

$R_{{K}}=0.846^{+0.060}_{-0.054}\mbox{ }^{+0.016}_{-0.014},\mbox{
}{q^{2}}\in[1,6]{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}},$ (13)
$R_{{{K}^{*0}}}=\left\\{\begin{array}[]{ll}0.66^{+0.11}_{-0.07}\pm 0.03,\mbox{
}{q^{2}}\in[0.045,1.1]{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}},\\\
0.69^{+0.11}_{-0.07}\pm 0.05,\mbox{
}{q^{2}}\in[1.1,6.0]{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}.\end{array}\right.$

While these results are still statistically limited, it is important to extend
the scope of these measurements to verify if the pattern of a “deficit” of
muons emerging from the LU tests together with the branching fraction
measurements in the muonic decays [29, 30], holds or not.

Recently, Ref.[4] argued that if NP has a $V-A$ structure, i.e.
$C_{9}=-C_{10}$, then one expects in the SM that the electron-muon LU ratios
across all species of $b$-hadrons should be the same:

$R_{{K}}\approx R_{{{K}^{*0}}}\approx R_{K\pi\pi}\approx R_{K_{S}}\approx
R_{\phi}\approx R_{\Lambda}\approx R_{{p}{K}}.$ (14)

The first test of lepton universality with a $b$-baryon is discussed in this
habilitation in Chapter 3.

###  6 What is emerging in the Loch Ness?

As of today there are a few phenomenological attempts to fits the Wilson
coefficients. While some of these approaches differ in their treatment of the
hadronic uncertainties [31], which can manifest themselves in the size of the
uncertainties on form factors for instance, most of them seem to draw a
similar picture.

Figure 8: Likelihood contours from neutral current LFU observables and the
global fit in the the plane of a lepton flavour universal contribution to
$C_{9}^{\textrm{univ}}$ Figure taken from Ref.[32].

An example of such a phenomenological study [32] is shown in Figure 8. The
selected result displays one of the phenomenological global fits, with a
lepton flavour universal $C_{9}^{\textrm{univ}}$ Wilson coefficient shown as a
function of a scenario linking a purely muonic contribution to $C_{9}$ and a
$C_{9}^{~{}bs\mu\mu}=-C_{10}^{~{}bs\mu\mu}$ hypothesis, before and after the
inclusion of the latest $R_{{K}}$ result from LHCb. This pattern of Wilson
coefficients can be found in several NP models with tree-level mediators, such
as Leptoquarks.

While there has been a myriad of theory developments in the past few years to
interpret the flavour anomalies in a consistent and coherent way, Leptoquarks,
which are tree-level mediators, have received particular attention. Given the
experimental constraints from both loop-induced currents and tree-level
decays, there are today three viable options for Leptoquarks models summarised
in Table 2. The first option is based on models which predict a $U_{1}$
Leptoquark and necessitate UV completion [33, 34, 35, 36]. The other two make
use of two scalar Leptoquarks $S_{1}+S_{3}$ [37, 38, 39] or $S_{3}+R_{2}$ [5].
It will be most interesting to see in the next few years which scenarios
survive the additional experimental constrains.

Model | $R_{K^{(*)}}$ | $R_{D^{(*)}}$ |  $R_{K^{(*)}}$ & $R_{D^{(*)}}$
---|---|---|---
$S_{1}=(3,1)_{-1/3}$ | ✖ | ✔ | ✖
$R_{2}=(3,2)_{~{}7/6}$ | ✖ | ✔ | ✖
$\widetilde{R}_{2}=(3,2)_{~{}1/6}$ | ✖ | ✖ | ✖
$S_{3}=(3,3)_{-1/3}$ | ✔ | ✖ | ✖
$U_{1}=(3,1)_{~{}2/3}$ | ✔ | ✔ | ✔
$U_{3}=(3,3)_{~{}2/3}$ | ✔ | ✖ | ✖
Table 2: Summary of Leptoquark models which can accommodate $R_{K^{(*)}}$ ,
$R_{D^{(*)}}$ and both. Table based work from Ref. [40]. The SM quantum
numbers are denoted by $(SU(3)_{c},SU(2)_{L})_{Y}$.

Pick your horse in Figure 9, the bets are open !

Figure 9: Example of NP Feynman diagrams [41],[42],[43].

##  Chapter 2 Allegretto

> “Don’t you know that Rome wasn’t built in a day”
>
> Morcheeba

###  7 The LHCb detector

The LHCb detector [44], shown in Figure 10, was designed to study the
asymmetry between matter and anti-matter, and search for physics beyond the SM
in $b$-hadron decays. It turned out that the excellent performance of the
detector was such that the physics program was extended very rapidly to
explore also charm, electroweak, and, more recently, heavy ion physics.

Figure 10: The LHCb detector [44].

LHCb is a single-arm spectrometer located at the interaction point (IP) 8 of
the LHC. The choice of detector geometry is justified by the fact that both
$b$ and $\bar{b}$ hadrons are predominantly produced in the same forward or
backward cone. If our collaboration had the budget of the ministry of defence
we would probably have built two LHCb detectors, to catch both the forward and
backward pairs. Charged tracks are detected by a vertex locator near to the
IP, and their momenta and charge are subsequently determined with tracking
stations (TT, T1, T2 and T3) either side of a magnet providing an integrated
field of 4 Tm. The tracking efficiencies were found to be $\sim 96\%$ for
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow{\mu^{+}}\mu^{-}$ in
the momentum range
$5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}<p<200{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.
Ring imaging Cherenkov (RICH) counters are used to distinguish kaons, pions
and protons. An excellent hadron identification is crucial for a flavour
experiment111For instance, for a requirement on the $K$-$\pi$ separation,
$\Delta log{\cal L}({K}-{\pi})>0$, when averaging over the momentum range
2-100 GeV/c one finds the kaon efficiency to be $\sim 95\%$ with a pion
misidentification rate of $\sim 10\%$., for example the measurement of
${C\\!P}$ asymmetries in $B_{d,s}^{0}\rightarrow\pi\pi,{K}{K},{\pi}{\pi}$
decays. Electromagnetic and hadronic calorimeters (ECAL and HCAL), together
with an instrumented preshower (SPD/PS) system, provide measurements of the
energies of neutral particles as well as electrons. Finally, muons are
identified with a dedicated detection system (M1-M5). The vertex locator
provides precise information on the origin of the tracks and the tracking
stations are essential to measure the momenta of the particles involved in the
decay of the particles of interest. This gives extremely powerful information
to reject background, since signal tracks i.e. secondary particles produced by
the particles of interest, must originate from common vertices that are
displaced from the primary vertex of the LHC proton-proton collision, due to
the non-negligible lifetimes of the decaying bottom hadrons (${\cal O}(1)$
ps), whereas the largest potential source of background is from random
combinations of tracks that originate from the primary vertex. The LHCb
trigger is a key to the success of the experiment. It operates in two stages.
A hardware trigger based on the information provided by the calorimeters and
the muon chambers reduces the frequency of events from the LHC beam crossing
rate of up to 40 MHz to a rate of 1 MHz at which the entire detector can be
read out. The subsequent high-level software trigger stage was responsible for
reducing the output rate to a level at which data can be written to permanent
storage. This rate evolved significantly between Run 1 and Run 2, reaching
12.5 kHz at the end of Run 2. Detailed discussion of the performances of the
LHCb detector can be found in Ref. [45]. The Run naming convention and the
schedule of the LHC are defined in Table 3.

Run 1 | LS1 | Run 2 | LS2 | Run 3 | LS3 | Run 4…
---|---|---|---|---|---|---
2010-2012 | 2013-2015 | 2015-2018 | 2018 - 2020 | 2021-2024 | 2025 - 2027 | 2027 - ….
Table 3: LHC schedule. The data taking period are highlighted in blue, the
technical stops are highlighted in yellow.

The LHCb detector is currently undergoing its first major upgrade to allow for
data taking at $2\times 10^{33}$cm-2s-1 in 2021, a factor five increase
compared to earlier runs. All the tracking system will be replaced [46]. The
vertex locator strips will be replaced by pixel detectors [47], and the TT
will be upgraded to an Upstream Tracker (UT) with a larger acceptance around
the beam pipe. The central trackers will be replaced with a scintillating
fibre tracker (SciFi). Furthermore, the entire electronics will be replaced to
allow the detector to be read out at the proton-proton collision rate, and to
send the data to be processed online in the high level trigger. In order to
maximise the physics output of the experiment, the philosophy of the
collaboration has been to perform full track reconstruction, including
particle identification and track fitting, as early as possible in the data
processing.

I have been involved in two upgrade projects. With my former PhD student
Renato Quagliani [48], whom I co-supervised with Patrick Robbe and colleagues
from LPNHE in Paris, Pierre Billoir and Francesco Polci, we developed a
pattern recognition algorithm that we baptised Hybrid Seeding. The aim of this
tracking algorithm is to reconstruct track segments using only in the
information of the SciFi, enabling later the reconstruction of long-lived
particles such as ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$, $\mathchar
28931\relax$ or more exotic ones, like dark photon candidates. This algorithm
and its performance are discussed in Section 8. I am also involved in a
hardware project for the calorimeter, where I am responsible for a control
board designed by O.Duarte and A.Saussac. The purpose of this board is to
distribute information from the central LHCb system such as the 40 MHz clock
and propagate it to the calorimeter front-end boards. The design of this board
is described Section 9.

###  8 Pattern recognition

The LHCb upgrade tracking algorithms rely on three detectors: the vertex
locator, the upstream tracker and the scintillating fibre tracker. Figure 11
shows the different types of tracks produced by the reconstruction; their
somewhat jargonic classification can be found in Table 4.

Figure 11: Track types in the LHCb Upgrade.

The SciFi tracker [49] is composed of three tracking stations, T1, T2, T3.
Each station is composed of four layers, separated by air-filled gap of 50
$\mathrm{\,mm}$, oriented in the so called stereo configuration (x-u-v-x). The
fibre mats in the first and fourth x-layer (within the same station) are
vertically oriented, i.e. the fibre mats are parallel to the y axis of the
laboratory frame. Therefore, the read-out of a x-layer provides the direct
measurement of the $x^{track}(z_{layer})$ position. But no information at all
about the y can be directly extracted. The second (u) and the third (v) layers
are identical to the x-layer, but their fibre mats are tilted with respect to
the x-layer by $+5^{\circ}$ and $-5^{\circ}$ respectively. The read-out of the
u/v-layers provides the u and v stereo coordinates, which are used to extract
the information on the y-z plane motion of the particles.

The SciFi tracker benefits from a good uniformity whereas the former central
tracking system, was based on different technologies, mechanical supports
etc.. This ensures that the fraction of particles that survive the passage
through the SciFi Tracker is quite high. The fraction was found to be 96.9%
for hadrons, 93.9% for electrons and 95.2% for photons. With the SciFi, a
difficulty was introduced by the absence of a $y$\- segmentation in the
tracker. This feature makes the track finding close to the beam pipe, where
the detector occupancy is the highest, quite challenging, and the impact of
the loss of light propagation in the fibres, a particular problem. Renato
worked out a way around this. From the expected $y$-position of a traversing
track based on the information from the x-layers and the stereo ones, he
figured out a way to tune the hit requirements of the tracks according to the
expected light attenuation in the SciFi fibres, which reduced significantly
the fake (or ghost) rate.

The decay rates and topologies considered for the LHCb Upgrade are very broad
[46]. They vary from rare decays, such as the very rare
$B_{s}^{0}\rightarrow{\mu^{+}}\mu^{-}$ mode or the radiative mode ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{\mathchar 28931\relax}\gamma$, to multi-track
final states such as $B_{s}^{0}\rightarrow
D_{s}^{+}(\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}})D_{s}^{-}(\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{-}})$.
One has also to take into account from the spread of the momentum ranges of
these particles, from the very soft tracks like the pions from $D^{*}$ decays
all the way to the hard ones from $W$ and $Z$ decays. With this in mind, the
algorithm was designed to reach a good compromise in the holy tracking
trinity: high tracking efficiencies and low fake rate and small processing
time.

The main idea behind the Hybrid Seeding is to progressively clean the tracking
environment by first finding the tracks which are easier to reconstruct, and
then searching for those with more complicated trajectories or signatures
using the left-over hits.

Some of the improvements reached were achieved thanks to an update of the
track parametrisation, an optimisation of the search windows and a redesign of
the loops over the hit containers. The rethinking of recovery routines
permitted to improve the low momentum track efficiency and the robustness of
the algorithm.

Name | Property
---|---
hasT |  reconstructible in Scintillating Fiber Tracker
UT \+ Scintillating Fiber Tracker |  reconstructible in Scintillating Fiber Tracker and UT
noVelo | not reconstructible in the VELO
long |  reconstructible in VELO and Scintillating Fiber Tracker
strange | daughter of a strange particle ( ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$, $\mathchar 28931\relax$, ..)
from B | belong to the decay chain of a $b$ hadron
from D | belong to the decay chain of a $c$ hadron

Table 4: Sub-selections used by the performances indicators.

The results obtained from these studies are summarised in Table 5 and Figure
12. They make clear that the Hybrid Seeding performs significantly better than
the first implementation of the prototype algorithm referred to in this text
as TDR Seeding. A significant improvement is achieved in all the fields:

  * •

The ghost rate is reduced by a factor two with respect to the old seeding
version (even when averaged for the events), and the efficiencies are
significantly larger.

  * •

The tracking efficiencies are significantly improved for all the track
categories, especially for lower $p$ and $p_{T}$ tracks ($\sim$20 %), while
for higher $p$ a gain of 4-6 % is achieved.

  * •

The clone killing which allows to remove duplicate candidates is more
efficient than the previous algorithm. This is achieved thanks to a more
accurate track comparison and to the internal sorting of the hits, which
allows a better track-to-track comparison.

  * •

The timing of the Hybrid Seeding is significantly improved with respect to TDR
Seeding, by almost a factor 3-4 on average (depending on the detector
occupancy level), as shown in Table 5.

In other words, Hybrid Seeding is more robust against busy events with respect
to the TDR Seeding. Timing comparisons have been achieved running both the
algorithms on the same machine (a standard lxplus machine SLC6 in 64-bit mode)
and we also quote the timing of the forward tracking algorithm (as a reference
value) in the so called best tracking sequence stage, i.e., the configuration
aiming to find all long tracks in the event.

Machine speed |  | Algorithm | Avg. time | Min. time | Max. time
---|---|---|---|---|---
$n\cdot$ 2.8 GHz Xenon |  |  | [$\frac{ms}{evt.}$] | [$\frac{ms}{evt.}$] | [$\frac{ms}{evt.}$]
2.79 |  | Forward Tracking Best | 48.62 | 0.30 | 1271.4
TDR Seeding | 150.95 | 1.86 | 6069.0
Hybrid Seeding | 46.80 | 0.70 | 1239.1

Table 5: Average, maximum and minimum timing of the algorithms for the
different samples. Timing performances are also quoted with respect to the
forward tracking used for the upgrade.

Track type | Sample 2
---|---
TDR Seeding | Hybrid Seeding
|  $\epsilon$ (clone rate) |  $\epsilon$ (clone rate)
hasT | (53.5 $\pm$ 0.1)(3.5) $\%$ | (66.6 $\pm$ 0.1)(0.0) $\%$
long | (78.4 $\pm$ 0.1)(3.3) $\%$ | (92.1 $\pm$ 0.1)(0.0) $\%$
long $P>5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ | (87.5 $\pm$ 0.1)(2.6) $\%$ | (95.4 $\pm$ 0.4)(0.0) $\%$
long from B | (80.4 $\pm$ 0.6)(2.7) $\%$ | (93.0 $\pm$ 0.3)(0.0) $\%$
long from B $P>5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ | (88.5 $\pm$ 0.5)(2.3) $\%$ | (95.9 $\pm$ 0.1)(0.0) $\%$
long from B or D | (80.7 $\pm$ 0.2)(2.7) $\%$ | (93.3 $\pm$ 0.1)(0.0) $\%$
long from B or D $P>5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ | (89.3 $\pm$ 0.2)(2.3) $\%$ | (95.9 $\pm$ 0.1)(0.0) $\%$
UT +Scintillating Fiber Tracker strange | (76.3 $\pm$ 0.1)(3.3) $\%$ | (91.8 $\pm$ 0.1)(0.0) $\%$
UT +Scintillating Fiber Tracker strange $P>5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ | (88.8 $\pm$ 0.1)(2.5) $\%$ | (95.7 $\pm$ 0.1)(0.0) $\%$
noVELO +UT +Scintillating Fiber Tracker strange | (76.8 $\pm$ 0.2)(3.3) $\%$ | (91.3 $\pm$ 0.1)(0.0) $\%$
noVELO +UT +Scintillating Fiber Tracker strange $P>5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ | (88.7 $\pm$ 0.2)(2.7) $\%$ | (95.6 $\pm$ 0.1)(0.0) $\%$
ghost rate | (37.3 $\pm$ 0.1)$\%$ | (19.4 $\pm$ 0.1) $\%$
ghost rate (evt.avg) | 21.6 $\%$ | 11.2 $\%$
hit purity | 98.9 $\%$ | 99.6 $\%$
hit efficiency | 93.6 $\%$ | 95.4 $\%$

Table 6: Tracking performance comparison between the TDR Seeding and the
Hybrid Seeding algorithms. Figure 12: Tracking efficiency distributions,
selecting tracks having hits in the UT and the Scintillating Fiber Tracker and
being daughters of long-lived strange particles, such as $K^{0}_{S}$ or
$\Lambda^{0}$. The efficiencies obtained with the Hybrid Seeding (blue)
algorithm are on average $\simeq$12$\%$ better than the ones from the TDR
Seeding.

The performance quoted in this section have been obtained with a description
of the SciFi geometry which was not final. However, even with more refined
versions of the geometry, which were later made available, the overall
conclusions of this work remain unchanged. The Hybrid Seeding algorithm has
continued to evolve, and further improvements have been achieved. More
recently, the focus of the efforts has been towards improving the
reconstruction electrons at low momenta.

###  9 Calorimeters

As part of the first phase of the LHCb upgrade and the calorimeters upgrade in
particular, both the SPD and PS detectors have been removed and the entire
electronics of the system will be replaced. There will no longer be a hardware
trigger and the aim is to process all the subdetectors at 40 MHz. The
electromagnetic (ECAL) and hadronic (HCAL) calorimeters will remain in place.
They are both based on a “shashlik” technology of lead/iron and scintillators,
and the light is collected by wave length shifting fibres [50]. The ECAL
energy resolution is $10\%/\sqrt{E}\oplus 1\%$ where the energy is expressed
in GeV. The information provided by this sub-detector is used as input to the
particle identifications algorithms and flags photons, neutral pions or
electrons. The HCAL energy resolution is significantly worse being
$80\%/\sqrt{E}$, however this was enough to provide information for the
hardware trigger (L0) during Run 1 and 2.

The new acquisition systems of both the ECAL and HCAL calorimeters will be
driven by a control board (3CU). The purpose of this board is to process and
send critical information (the clock, the slow control signals and the fast
and synchronous command) received through optical fibres from the main LHCb
system to the front-end boards. A total of 23 control boards including spares
are needed for both the electromagnetic and hadronic calorimeters.

The LHCb operational master clock for data taking and the entire precise
timing and synchronisation of the sub-detectors rely on the LHC bunch clock
and the LHC orbit signal. The orbit signal marks each turn of the full LHC
circulating bunch scheme (3563 steps). The readout supervisor system receives
directly these two clocks from the RF-system of the LHC via an LHC Interface
card located on the readout supervisor card. The LHC bunch clock is
distributed to the front-end and readout boards with sufficiently low jitter
(assumed for the moment to be ${\cal O}$(10 ps)), and constant and
reproducible phase. To ensure this low jitter requirement, a great care was
needed in the design of the clock tree distribution within the board. The
readout supervisor card distributes the clock and the Fast Control commands to
the readout board, and the interface readout board distribute the clock and
the Fast Control command to the control board.

Figure 13: Schematic of a calorimeter crate.

The calorimeter crate mechanics are a standard 9U frame. They have two custom
backplanes mounted in the back. The lower 3U backplane provides the power
supplies, the Time Fast Control commands and the clock distribution. The upper
6U backplane is dedicated for the exchange of signals between the boards
inside the crate and with the other crates. A calorimeter front-end crate
contains up to 16 front-end boards which perform the acquisition of the
detector channels, and in the middle of the crate, a reserved slot for the
control board.

The main role of the control board is to receive the GBT (GigaBit Transceiver)
frame through the optical link and to extract the information which is needed
by the front end boards inside a same crate: the 40 MHz clock, the Time Fast
Control (TFC) commands and Experiment Control System (ECS). Figure 14 shows a
picture of the control board (3CU). The various parts of the board are clearly
identified. The board contains :

Figure 14: 3CU board.

  * •

A Versatile Link Transceiver-Receiver (VTRx), for the reception and
transmission to the SOL40 which an interface board that allows is to interface
the fast and the slow control to the front-end boards.

  * •

A radiation tolerant chip that can be used to implement multipurpose high
speed (3.2-4.48 Gb/s user bandwidth) bidirectional optical links (GBTX).

  * •

A GBT-SCA ASIC, part of the GBT chip-set, to distribute control and monitoring
signals to the on-detector front-end electronics and perform monitoring
operations of detector environmental parameters.

  * •

A Microsemi FPGA (IGLOO2 family) which is in charge of the processing on the
3CU.

Except for the commercial FPGA, the components listed above were designed at
CERN and are shared across various sub-detectors in the LHCb upgrade.
Following the clock and TFC command (or from left to right on the picture),
first the 3CU receives the clock and the TFC command through the optical
transmitter (VTRx) and decoding inside the GBTX. After processing inside the
FPGA, the board transmits through the 3U backplane these signals to all the
front-end boards inside the same crate.

A challenging aspect of the board was the design of the schematic for the PCB
(Printer Circuit Board) especially around the GBTX component, where the
density of extracted links is very high, about 300 out of the 400 of the GBTX
pins.

Two prototypes of these boards are currently available in the lab in Orsay and
have been validated, the final production of the board has been submitted.

The next steps will be to start testing the whole setup in a crate at CERN
using the central acquisition system. Later, we will proceed to install and
commission the electronics and ramp up for data taking.

##  Chapter 3 Allegro

> ”Once you kill a cow,
> you gotta make a burger”
>
> Lady Gaga

###  10 Dear $b$-baryons

The first observed baryon with a $b$-quark was the ${\mathchar
28931\relax}^{0}_{b}$ baryon ($bud$). This isospin-zero particle was
discovered in ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ $\mathchar
28931\relax$ decays, at the UA1 detector in proton-antiproton collisions at
CERN [51] and was later confirmed and studied by several experiments.
${\mathchar 28931\relax}^{0}_{b}$ particles are produced abundantly in the
proton-proton collisions of the LHC, their production rate222In 13 TeV proton-
proton collisions. relative to $B$-mesons is $f_{{\mathchar
28931\relax}^{0}_{b}}/(f_{u}+f_{d})=0.259~{}\pm~{}0.018$ [52].

Figure 15: Most probably one of the first ${\mathchar 28931\relax}^{0}_{b}$
distributions seen at LHCb.

Figure 15 shows the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ $\mathchar
28931\relax$ invariant mass using 5 pb-1 from the 2010 dataset, when a
requirement on the decay time of the ${\mathchar 28931\relax}^{0}_{b}$
candidate to be higher than 0.3 ps is applied. I am particularly fond of this
plot, because it was one of the first distribution of ${\mathchar
28931\relax}^{0}_{b}$ decays seen at LHCb and it really marked the start of my
research activities with $b$-baryons. With more data, more $b$-baryons were
seen and discovered, in particular I was involved in the studies of the
${\mathchar 28932\relax}^{-}_{b}$ and ${\mathchar 28938\relax}^{-}_{b}$
baryons at LHCb. For what concerns NP searches, $b$-baryons allow to verify
the anomalies in a different hadronic environment. Furthermore, since they
carry half-integer spin, NP-sensitive observables which are not present in
$B$-mesons can be measured in ${\mathchar 28931\relax}^{0}_{b}$ decays. Table
7 summarises the current experimental knowledge on the lightest $b$-baryons.

Table 7: Properties of the lightest $b$-baryon states. Based on Ref. [1]. Name |  Quark content | Mass, ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ |  Lifetime or width | $J^{P}$ | ($I$,$I_{3}$) | $S$
---|---|---|---|---|---|---
${\mathchar 28931\relax}^{0}_{b}$ | $udb$ | $5619.60\pm 0.17$ |  $1.470\pm 0.010$ ps | $1/2^{+}$ | $(0,0)$ | $0$
${\mathchar 28932\relax}^{0}_{b}$ | $usb$ | $5791.9\pm 0.5$ |  $1.479\pm 0.031$ ps | $1/2^{+}$ | $(1/2,1/2)$ | $-1$
${\mathchar 28932\relax}^{-}_{b}$ | $dsb$ | $5797.0\pm 0.9$ |  $1.571\pm 0.040$ ps | $1/2^{+}$ | $(1/2,-1/2)$ | $-1$
${\mathchar 28934\relax}^{+}_{{b}}$ | $uub$ | $5810.55\pm 0.25$ |  $4.83\pm 0.48$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ | $1/2^{+}$ | $(1,1)$ | $0$
${\mathchar 28934\relax}^{0}_{{b}}$ | $udb$ | not yet observed | $1/2^{+}$ | $(1,0)$ | $0$
${\mathchar 28934\relax}^{-}_{{b}}$ | $ddb$ | $5815.64\pm 0.28$ |  $5.33\pm 0.56$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ | $1/2^{+}$ | $(1,-1)$ | $0$
${\mathchar 28932\relax}^{\prime 0}_{b}$ | $usb$ | not yet observed | $1/2^{+}$ | $(1/2,1/2)$ | $-1$
${\mathchar 28932\relax}^{\prime-}_{b}$ | $dsb$ | $5935.02\pm 0.05$ |  $<0.08$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ | $1/2^{+}$ | $(1/2,-1/2)$ | $-1$
${\mathchar 28938\relax}^{-}_{b}$ | $ssb$ | $6046.1\pm 1.7$ |  $1.64\pm 0.18$ ps | $1/2^{+}$ | $(0,0)$ | $-2$
${\mathchar 28934\relax}^{*+}_{{b}}$ | $uub$ | $5830.28\pm 0.28$ |  $9.34\pm 0.54$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ | $3/2^{+}$ | $(1,1)$ | $0$
${\mathchar 28934\relax}^{*0}_{{b}}$ | $udb$ | not yet observed | $3/2^{+}$ | $(1,0)$ | $0$
${\mathchar 28934\relax}^{*-}_{{b}}$ | $ddb$ | $5834.73\pm 0.30$ |  $10.68\pm 0.68$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ | $3/2^{+}$ | $(1,-1)$ | $0$
${\mathchar 28932\relax}^{*0}_{b}$ | $usb$ | $5949.8\pm 1.4$ |  $0.90\pm 0.18$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ | $3/2^{+}$ | $(1/2,1/2)$ | $-1$
${\mathchar 28932\relax}^{*-}_{b}$ | $dsb$ | $5955.33\pm 0.13$ |  $1.65\pm 0.33$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ | $3/2^{+}$ | $(1/2,-1/2)$ | $-1$
${\mathchar 28938\relax}^{*-}_{b}$ | $ssb$ | not yet observed | $3/2^{+}$ | $(0,0)$ | $-2$

###  11 Mass measurements

My main collaborators for the measurements [53] discussed in this section were
Sneha Malde and Matthew Needham. Within the SM of particle physics, mesons and
baryons are colourless objects composed of quarks and gluons as discussed in
Chapter 1. These systems are bound through the strong interaction, described
by QCD. A basic property of hadrons that can be compared to QCD theoretical
predictions is their masses. In 2008, there was the controversial discovery of
the $\Omega_{b}^{-}$ first claimed by the DØ experiment with
$M(\Omega_{b}^{-})=6165\pm 10(\textrm{stat})\pm 13(\textrm{syst})$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. A few months later the CDF
collaboration also reported a measurement of the mass of this baryon
$M(\Omega_{b}^{-})=6054.4\pm 6.8(\textrm{stat})\pm
0.9(\textrm{syst}){\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Assuming the
uncertainties to be uncorrelated across experiments, the difference between
these two measurements, $111\pm 12(\textrm{stat})\pm
13(\textrm{syst}){\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, represents a
discrepancy of more than six standard deviations. What was particularly
puzzling about the DØ measurement is that it was in disagreement with the
expectations of mass splittings inferred from quark model predictions of both
beauty and charm particles. For example, as shown in Chapter 1, the
theoretical predictions for the $\Omega_{b}^{-}$ mass are fairly broad, they
lie in the range of 5940 - 6120 ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

A key aspect of mass measurements is controlling the momentum scale of the
experiment. A time-dependent momentum scale calibration procedure was used to
“correct” the measured $b$-baryon masses [54].

Figure 16:  Measured ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$ mass (top) and resolution (bottom) as a
function of run number during the entire 2010 data-taking period. The steps
(indicated with vertical lines) correspond to the times when the TT operating
temperature was altered.

The principles behind the momentum scale calibration can be described as
follows. For a two-body decay $P\rightarrow c_{1}c_{2}$ relativistic mechanics
gives:

$m_{12}^{2}=(E_{1}+E_{2})^{2}-(\vec{p}_{1}+\vec{p}_{2}).(\vec{p}_{1}+\vec{p}_{2}).$
(15)

It can be shown that if the momentum scale is wrong by a factor (1-$\alpha$),
the the measured mass $m_{12}$ is given to first order in $m/p$ by:

$m_{12}=\frac{m_{P}^{2}-f}{(1-\alpha)^{2}}+f,$ (16)

where

$f=m_{1}^{2}+m_{2}^{2}+\frac{p_{2}}{p_{1}}m_{1}^{2}+\frac{p_{1}}{p_{2}}m_{2}^{2}.$
(17)

If $\alpha\ll 1$ this expression simplifies, to first order, to

$\Delta m=\alpha\frac{f-m_{P}^{2}}{m_{P}}$ (18)

where $\Delta m=m_{P}-m_{12}$. For decays of quarkonia or heavy hadrons where
the mass of the final state particles can be neglected with respect to the
parent particle, the correction needed can be written as:

$\Delta m=-\alpha~{}m_{P}.$ (19)

A set of two-body decay modes was considered for the calibration of the
momentum scale. The central value of the momentum scale is taken as the value
of $\alpha$ extracted using ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-}$ decays. An example of the trends is shown in
Figure: 16.

Figure 17: Average momentum scale bias $\alpha$ extracted from the
reconstructed mass of various decay modes after the momentum calibration
procedure. The ${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays are divided
into two categories: those where the two child tracks have hits in the vertex
detector (labelled L) and those without (labelled D). The black error bars
represent the statistical uncertainty whilst the (yellow) filled areas also
include contributions to the systematic uncertainty from the fitting
procedure, the effect of QED radiative corrections, and the uncertainty on the
mass of the decaying meson [1]. The (red) dashed line shows the assigned
uncertainty of $\pm 0.03\%$ on the momentum scale.

To understand the odd behaviour in the trends (around Run 500), we relied on
the log-books of the LHCb data shifter. We identified that it was due to a
temperature variation of the TT tracker. To evaluate the impact of these
variations, two versions of the detector alignment were tested, the standard
one and one were the hits from the TT are systematically excluded from the
track reconstruction. The whole exercise (track reconstruction, selection,
mass fits) was repeated. Finally, the impact of the TT temperature variation
was found not to be significant on the observables of interest, and no
additional systematic uncertainty was assigned.

The systematic uncertainty on the momentum scale was taken as the difference
between the values of $\alpha$ extracted form
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow\mu^{+}\mu^{-}$ and
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$ decays.
The calibration was cross-checked using other $b$-decay modes.

Figure 17 shows a summary of the momentum scale calibration. To measure the
impact of systematic effects, the overall momentum scale was shifted by
$\alpha=0.5\times 10^{-3}$ with little variation amongst the modes. The
momenta of all the tracks used to form the $b$-baryon candidates are
multiplied by $1-\alpha$ before any mass constraint is applied, the
uncertainty on the knowledge of $\alpha$ is later propagated to the final
measurement as a systematic uncertainty on the mass measurements.

The decay modes employed to measure the masses of the ${\mathchar
28931\relax}^{0}_{b}$, ${\mathchar 28932\relax}^{-}_{b}$ and ${\mathchar
28938\relax}^{-}_{b}$, were ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{\mathchar 28931\relax}$, ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\Xi(\rightarrow{\mathchar 28931\relax}\pi^{-})$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\Omega(\rightarrow{\mathchar
28931\relax}{K}^{-})$ respectively. The $\mathchar 28931\relax$ particle that
decays to a pion and a proton travels a relatively long distance in the LHCb
detector, $\cal O$(cm). The child tracks from the $\mathchar 28931\relax$
baryon are referred to as long tracks if they leave energy deposits in the
vertex locator or downstream tracks if they don’t. To improve the resolution
on the measured mass of the $b$-baryons by almost a factor two, a constraint
on the known masses of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
the $\mathchar 28931\relax$ particles was systematically applied.

For these measurements simple cut-based selections relying on the kinematic
properties of the final state particles and their identification probabilities
were sufficient to select clean signal samples. The values of the masses were
extracted from maximum likelihood fits to the invariant mass. The fit model
was based on a Gaussian function to describe the signal and an exponential
function to describe the combinatorial background. In the case of the
${\mathchar 28938\relax}^{-}_{b}$ baryon, given the discrepancy which was
observed between the previous measurements, the fitted value of the mass was
kept blind throughout the analysis process, although not the mass distribution
itself. The results are reported in Table 8.

Table 8: Comparison of the $b$-baryon mass measurements using the full LHCb 2011 data sample with the single most precise results from the ATLAS [55], CDF [56, 57] and D0 [58, 59] collaborations, and with the PDG averages [60]. The PDG averages (2014) contain the results from CDF and DØ as well as the $\Lambda_{b}^{0}$ measurement from LHCb performed with the 2010 data sample. The quoted errors include statistical and systematic uncertainties. All values are in ${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$. | $M(\Lambda_{b}^{0})$ | $M(\Xi_{b}^{-})$ | $M(\Omega_{b}^{-})$
---|---|---|---
ATLAS | $5619.7\pm 1.3~{}$ | – | –
CDF | $5619.7\pm 1.7~{}$ | $5790.9\pm 2.7$ | $6054.4\pm 6.9$
DØ | – | $5774~{}~{}\,\pm 19$ | $6165~{}~{}\,\pm 16$
PDG (2014) | $5619.4\pm 0.7~{}$ | $5791.1\pm 2.2$ | $6071~{}~{}\,\pm 40$
LHCb | $5619.5\pm 0.5~{}$ | $5795.8\pm 1.0$ | $6046.0\pm 2.3$

To take into account the “look elsewhere effect”, the significance of the
$\Omega_{b}^{-}$ signal was determined using a large number of pseudo-
experiments with background only. For each pseudo-experiment a sample of mass
values with the same size as the data sample is generated using the
exponential background distribution determined from the fit to the data
candidates. We determined the probability that, in these pseudo-experiments,
any signal seen in the mass range
5.8–6.3${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ would lead to a value of
$\ln({\cal L}_{\rm max}/{\cal L}_{0})$ larger than in the data, and interpret
it as the probability that the observed $\Omega_{b}^{-}$ peak in the data is
due to a statistical fluctuation of the background. The distribution of
$\ln({\cal L}_{\rm max}/{\cal L}_{0})$, determined with 2,500,000 pseudo-
experiments, is shown in Figure 18. The fact that no pseudo-experiment yields
a value larger than the data suggests a $p$-value smaller than 4$\times
10^{-7}$, which translates to a statistical significance consistent with
$6.8\,\sigma$.

The LHCb collaboration measured the $\Omega_{b}^{-}$ mass, using the hadronic
final state ${\mathchar 28938\relax}^{0}_{c}$ ($\rightarrow$ $p$ $K$ $K$
$\pi$)$\pi$ [61]. The result was found to be in agreement with the measurement
discussed in this section and the result from CDF. The measurement from the DØ
experiment is no longer taken into account in the PDG averages [1].
Spectroscopy and mass measurements have a bright future at LHCb, the first
observation of $\Omega_{b}^{-}$ baryon excited states was reported recently in
Ref. [62].

Figure 18: Distribution of the negative log-likelihood difference $\ln({\cal
L}_{\rm max}/{\cal L}_{0})$ in $2.5\times 10^{6}$ pseudo-experiments with
background only. The red arrow corresponds to the value observed in the data.

###  12 Lifetime measurements

My main collaborators on the lifetime measurements [63] were Francesca Dordei
and Greig Cowan. Lifetime measurements are often considered to be the “bread &
butter” of a flavour experiment. Whoever thinks this should be sent to jail.
The analysis discussed in this section grouped many $b$-hadrons. The decays of
these hadrons all shared $J/\psi X$ topologies displayed in Figure 19, where
$X$ was required to be ${K}^{+},{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}},{{K}^{*0}},\phi$ or a $\mathchar 28931\relax$.

Figure 19: Sketch of the decay of a $b$-hadron to a $J/\psi$ and an additional
particle X. The $b$-hadron is produced at the primary vertex (PV) and it
decays at the decay vertex (SV). The length $L$ is the spatial separation
between the two vertices.

Thanks to the clean dimuon signatures of these decays and the usage of mass
constraints on the known values mass of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$,
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ and $\mathchar 28931\relax$
particles, simple cut-based selections were found to be sufficient to select
all the signals. Furthermore, cut-based selections were even favoured to more
sophisticated multivariate ones, since we were trying to track down all the
possible sources of biases that might influence the measured lifetimes. The
decay time, $t$, of a particle in its rest frame, can be computed as follows:

$t=L~{}\frac{m}{|\,\vec{p}\,|}$ (20)

where $L$ is the flight distance travelled by the $b$-hadron, $p$ is the
reconstructed three-momentum and $m$ its reconstructed mass.

Two approaches were used to access the observable of interest. The first one
was based on a two-dimensional likelihood fit to the invariant mass and decay
time of the $b$-hadron. In the second approach, ${}_{s}\cal{W}$eights [64]
were extracted from a fit to the invariant mass distribution and exploited to
subtract the background components from the lifetime distributions, which were
then fitted. While doing the analysis it was thought to be very useful to have
two methods for cross-checks.

The signal probability density function used in the lifetime fit to extract
the observable of interest $\tau_{H_{b}}$ can be written as follows:

$[e^{(t^{\prime}/\tau_{H_{b}})}\otimes{\cal
R}(t,t^{\prime})]\times\textrm{Acc}(t)$ (21)

A sketch of a typical shape of the decay time resolution ($\cal{R}$) and the
decay time acceptance (Acc) are shown in Figure 20. Given that the expected
statistical uncertainty for these measurements was around a few femtoseconds,
it was mandatory to have a very good control of the acceptance effects in
particular. The decay-time resolution was measured using data. At the start of
the LHCb data taking, large samples of “prompt-$J/\psi$” decays were recorded
with dedicated trigger lines. Given that they were produced at zero lifetime,
the width of their decay time distribution was dominated by the decay time
resolution. Typical values of the decay time resolution for these decay modes
was about 50 fs.

Figure 20: Sketch of a decay-time distribution, decay-time resolution and
decay-time acceptance of a $b$-hadron ($x$-axes not to scale).

Understanding the decay-time acceptances turned out to be a tricky job. Figure
21 displays the breakdown of all the effects entering the decay-time
acceptance seen in ${\mathchar 28931\relax}^{0}_{b}$ decays. When we first
started to test the fitting procedure using simulated samples, on which the
full reconstruction and event selection was applied, biases up to 18 fs were
observed for the decay modes where all the tracks were decaying inside the
vertex locator. The biases were smaller $\sim$10 fs for decays with long-lived
particles (${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ and $\mathchar
28931\relax$). This observation allowed to point towards effects coming from
the vertex locator reconstruction. And indeed, an assumption that the tracks
were produced in a region close to the interaction region was used in the
pattern recognition algorithms. This assumption was the main cause for the
“upper lifetime” acceptance. Since this was the start of LHCb data taking and
the time-dependent analyses did not have the maturity that they have now, we
did not feel comfortable to simply plug whatever bias was measured from
simulation into the data fit. We developed a data-driven method to address
this point. A large sample of
${{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$
decays was used where the kaon was reconstructed without using the information
from the vertex locator333The $K$ was reconstructed using only the downstream
tracking.. For the purpose of these studies, we reprocessed both the data and
simulation samples using the downstream tracking on the kaon. The vertex
locator reconstruction efficiency was then computed using a tag-and-probe
technique.

A parametrisation based on the distance of closest approach of one of the
final state particles allowed to model the efficiency of this algorithm on
data. This parametrisation took into account the different tunings of the
reconstruction in the trigger and offline, as well as correlations between
tracks. Weights were extracted from the vertex locator reconstruction
efficiency distribution and applied to the signal candidates in data to
correct for this effect.

The remaining effects that contributed to the decay time acceptances were: the
position of the primary vertex, the vertex quality of the fit which was worse
for tracks with a small opening angle (for example
$\phi\rightarrow{{K}^{+}}{{K}^{-}}$), a requirement on the displacement of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ from the primary vertex in the
software trigger and in the stripping selection.

Figure 21: ${\mathchar 28931\relax}^{0}_{b}$ acceptance steps as a function of
the different reconstruction, selection and trigger requirements in the
analysis.

The absolute lifetimes of the $b$-hadrons are reported in Table 9. Besides the
${\mathchar 28931\relax}^{0}_{b}$ measurement all the others were the world’s
best measurements.

The early measurements of the ratio of ${\mathchar 28931\relax}^{0}_{b}$ to
${B}^{0}$ lifetimes were mainly driven by the Tevatron, and gave results which
were considerably smaller than the theoretical expectation [22, 65, 66]. It
was considered for a while by the theory community that additional operators
should be included in the description of the ${\mathchar 28931\relax}^{0}_{b}$
amplitude to account for these differences. However, today the combined
measurement of the ${\mathchar 28931\relax}^{0}_{b}$ lifetime from LHCb,
$1.468\pm 0.009\pm 0.008$ ps is in agreement with most of the predictions from
HQET [19]. With work, it is fair to say that we closed the ${\mathchar
28931\relax}^{0}_{b}$ lifetime saga.

Table 9: Fit results for the ${B}^{+}$, ${B}^{0}$, ${B}^{0}_{s}$ mesons and
${{\mathchar 28931\relax}^{0}_{b}}$ baryon lifetimes. The first uncertainty is
statistical and the second is systematic.

Lifetime Value [${\mathrm{\,ps}}$ ]
$\tau_{{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}}$ 1.637 $\pm$ 0.004 $\pm$ 0.003
$\tau_{{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*0}}}$ 1.524 $\pm$ 0.006 $\pm$ 0.004
$\tau_{{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}}$ 1.499 $\pm$ 0.013 $\pm$
0.005 $\tau_{{{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{\mathchar 28931\relax}}$ 1.415 $\pm$ 0.027 $\pm$ 0.006
$\tau_{{{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi}$ 1.480 $\pm$ 0.011 $\pm$ 0.005

The cherry on the cake from this analysis, was that the lifetimes of
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*0}}$ and
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays were used to measure
$\Delta\Gamma_{d}/\Gamma_{d}$ as suggested in Ref. [67]. Flavour-specific
final states such as
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*0}}$ have
$\mathcal{A}_{\Delta\Gamma_{d}}^{{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*0}}}=0$, while
$\mathcal{A}_{\Delta\Gamma_{d}}^{{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}}=\cos(2\beta)$ to a good
approximation in the SM, where for a given final state $f$:

$\mathcal{A}_{\Delta\Gamma_{d}}^{f}=\frac{2\textrm{Re}(\lambda_{f})}{1+|\lambda_{f}|^{2}},\mbox{
~{}and~{} }\lambda_{f}=\frac{q}{p}\frac{\bar{A}_{f}}{A_{f}}$ (22)

where, parameters ${\bar{A}_{f}}$ and ${A_{f}}$ are the complex amplitudes for
the decay of a $\bar{{{B}^{0}}}$ and ${B}^{0}$ to the final state $f$,
respectively, and
$\beta\equiv\arg\left[-(V_{cd}V^{*}_{cb})/(V_{td}V^{*}_{tb})\right]$ is one of
the CKM unitarity triangle angles [26]. Hence, the two effective lifetimes can
be expressed as

$\displaystyle\tau_{{{B}^{0}}\rightarrow J/\psi K^{*0}}$
$\displaystyle=\frac{1}{\Gamma_{d}}\frac{1}{1-y_{d}^{2}}\left(1+y_{d}^{2}\right),$
(23) $\displaystyle\tau_{{{B}^{0}}\rightarrow J/\psi K^{0}_{S}}$
$\displaystyle=\frac{1}{\Gamma_{d}}\frac{1}{1-y_{d}^{2}}\left(\frac{1+2\cos(2\beta)y_{d}+y_{d}^{2}}{1+\cos(2\beta)y_{d}}\right).$
(24)

Using the effective lifetimes reported in Table 9 and
$\beta=(21.5^{+0.8}_{-0.7})^{\circ}$ [26], a fit of $\Delta\Gamma_{d}$ and
$\Gamma_{d}$ to the expressions in Eq. (23) and Eq. (24) leads to

$\displaystyle\Gamma_{d}$ $\displaystyle=\phantom{+}0.656\pm 0.003\pm
0.002{\mathrm{\,ps^{-1}}},$ (25) $\displaystyle\Delta\Gamma_{d}$
$\displaystyle=-0.029\pm 0.016\pm 0.007{\mathrm{\,ps^{-1}}},$ (26)

where the first uncertainty is statistical and the second is systematic. The
correlation coefficient between $\Delta\Gamma_{d}$ and $\Gamma_{d}$ is $0.43$
when including statistical and systematic uncertainties. The combination gives

$\frac{\Delta\Gamma_{d}}{\Gamma_{d}}=-0.044\pm 0.025\pm 0.011,$ (27)

consistent with the SM expectation: $40.9^{+8.9}_{-9.9}\times 10^{-4}$ [68,
69] and the current world-average value [26].

###  13 Lepton universality test

In this section, I will discuss the first test of lepton universality
measurement with $b$-baryons from Ref.[70]. This measurement was the PhD
thesis of Vitalii Lisovskyi [71] whom I co-supervised together with Marie-
Hélène. We were then joined by Carla Marin Benito who is funded by the ANR
BACH project.

In the SM the couplings of the $W$ and $Z$ bosons to all charged lepton
species are identical and a large number of experiments where the electroweak
bosons are directly produced have tested this property. The LEP measurements
of the $Z\rightarrow{e^{+}e^{-}}$, $Z\rightarrow\mu^{+}\mu^{-}$ and
$Z\rightarrow\tau^{+}\tau^{-}$ partial widths are in very good agreement with
each other [72]:

$\frac{\Gamma(Z\rightarrow\mu^{+}\mu^{-})}{\Gamma(Z\rightarrow{e^{+}e^{-}})}=1.0009\pm
0.0028.$ (28)
$\frac{\Gamma(Z\rightarrow\tau^{+}\tau^{-})}{\Gamma(Z\rightarrow{e^{+}e^{-}})}=1.0019\pm
0.0032.$ (29)

In addition to the measurement at the $Z$ pole, a good agreement was also
found in the LHC measurements [73]. A detailed review of further LU tests with
$W$ bosons, as well as in light pseudo scalar mesons can be found in Ref.
[74]. Under the assumption of LU, all the decay widths of the $Z$ boson decay
to leptons are expected to be equal in the SM.

As it was shown in the previous sections, $\mathchar 28931\relax$ particles
have a rather long lifetime and a lower reconstruction efficiency in
comparison to particles produced close to the interaction point. Therefore,
the overall yields of ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\mathchar
28931\relax}\ell^{+}\ell^{-}$ decays were expected to be smaller than
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{\ell^{+}}{\ell^{-}}$
decays. This is what motivated the choice of this particular decay for the LU
test. Table 10 summarised the current experimental knowledge on ${\mathchar
28931\relax}^{0}_{b}$ baryon to $pKX$ final states. What can be seen is that
at the time when this analysis started only the branching fraction of the
decays to charmonia decays were known. The $pK$ resonant structure was
resolved only for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
mode444This analysis that led to the discovery of the states compatible with
pentaquark particles. , as shown in Figure 22.

Table 10: Status of the decay modes of interest of the ${\mathchar 28931\relax}^{0}_{b}$ baryon before the work discussed in this section. Decay mode | Observed | Published | BR measured | Refs.
---|---|---|---|---
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}\mu^{+}\mu^{-}$ | Yes | Yes | No | [75]
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{e^{+}e^{-}}$ | No | No | No | N/A
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ | Yes | Yes | $(3.17\pm 0.04^{+0.57}_{-0.45})\times 10^{-4}$ | [76]
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow p{K}{\psi{(2S)}}$ | Yes | Yes | $(6.6^{+1.2}_{-1.0})\times 10^{-5}$ | [77]
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow p{K}\gamma$ | (Yes) | No | No | N/A

Figure 22: Invariant mass of $m(pK)$ in ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ (left) and ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}\mu^{+}\mu^{-}$ (right) data. Figures
taken from and Ref. [78] Ref. [75] respectively.

The identification of electrons is peculiar with respect to the other charged
tracks in the LHCb detector. Electrons555The average transverse momentum of
electrons from $b$-decays is a couple of GeV.  emit bremsstrahlung radiation
when they interact with the material in the detector. This radiation is
emitted colinearly to the electron direction. This effect will have an impact
on the electron momentum estimate. If the bremsstrahlung photon is emitted
before the magnet, it will continue its path in the original direction of the
electron, while the electron will be bent in the magnet. Hence the electron
and the photon will not be absorbed in the same cells of the electromagnetic
calorimeter. The measured momentum of the electron is lower given that it lost
some of its energy to the photon. In this configuration the emitted
bremsstrahlung does not affect the measured ratio $E/p$ used in the electron
identification. If on the other hand the photon is emitted after the magnet,
but before the electromagnetic calorimeter, the momentum of the electron has
already been estimated. The photon and the electron end up in the same cell.
Hence their combined energy release provides the original electron energy and
here also $E/p$ is not affected.

In order to account for the bremsstrahlung effects, dedicated algorithms are
used inside the LHCb reconstruction algorithms to correct for them. One of the
main impacts of the bremsstrahlung radiation is the very striking and non-
trivial shape of the $b$-hadron invariant mass distribution. Typically,
three666One per bremsstrahlung category. bifurcated Crystal-Ball functions are
necessary to describe the shapes decays involving electrons like
${{B}^{+}}\\!\rightarrow{{K}^{+}}{e^{+}e^{-}}$,
${{B}^{0}}\\!\rightarrow{{K}^{*0}}{e^{+}e^{-}}$ or ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{e^{+}e^{-}}$. Furthermore, because
of the worse overall mass resolution with respect to muon modes, great care is
needed to model the partially reconstructed backgrounds which populate the
left hand side of the invariant mass distributions. These distributions were
quite a change of scenery to me, given that I was used to very clean dimuon
signatures.

Figure 23: Illustration of the bremsstrahlung photons emitted by an electron
before and after the magnet.

The observable of interest $R_{{p}{K}}^{-1}$ can be written as:

$R_{{p}{K}}^{-1}=\frac{BR({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{e^{+}e^{-}})}{BR({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}\mu^{+}\mu^{-})}\times\frac{BR({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\\!\rightarrow{\mu^{+}\mu^{-}}))}{BR({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{e^{+}e^{-}}))}.$ (30)

It is defined this way to ensure the best possible cancellation of effects
that can be introduced by the differences in the treatment of reconstruction
effects between muons and electrons. For example, the universality of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ decays which has been already
tested very precisely:

$\frac{\Gamma_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{e^{+}e^{-}}}}{\Gamma_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}\mu^{-}}}}=1.0016\pm 0.0031,$ (31)

is used to evaluate $R_{{p}{K}}^{-1}$ as a double ratio rather than a more
obvious single ratio.

One of the most frequent questions that the proponents of the analysis and
myself received since the publication of our results is: “Why did you measure
$R_{{p}{K}}^{-1}$ and not $R_{{p}{K}}$?”. The answer to this question is
illustrated in Figure 24 which indicates better behaviour of the log-
likelihood profile for $R_{{p}{K}}^{-1}$ with respect to $R_{{p}{K}}$. This
effect is driven by the fact that a log-likelihood profile will be more
Gaussian if the smaller number (the electron yield in our case) is at the
numerator rather than the denominator. The first $R_{{K}}$ and
$R_{{{K}^{*0}}}$ measurements were done at the $B$-factories where the overall
yields of the electron and muon rare modes were of about the same size and
this particular point was not as relevant for them.

The $R_{{p}{K}}^{-1}$ analysis was performed in trigger categories. Indeed it
was shown that the kinematics of the decay vary depending on whether the
candidates were triggered by the hardware trigger based on the electromagnetic
calorimeter or by the “other” particles in the event. In the jargon of LHCb,
this classification is called TIS for Triggered Independently of the Signal
and this was the prime category for the electron channel, or TOS for Trigger
On Signal and this was the second category. In our construction these two
categories were exclusive. For decays involving muons in the final state, only
one trigger category based on the information from the muon stations in the
hardware level was used.

To reduce the combinatorial background, multivariate approaches based on
boosted-decision trees were employed. The algorithms were trained on simulated
signal samples which were reweighed to account for differences between data
and simulation. The background samples were obtained from the upper side bands
of the invariant mass data distribution and $k$-folding was used to avoid
biases in the training phase.

Figure 24: Log-likelihood profile for $R_{{p}{K}}$ (left) and
$R_{{p}{K}}^{-1}$ (right) using “fake” efficiency to constrain the central
value to be equal to unity.

Requirements based on the particle identification probabilities were applied
to all the tracks to reduce the backgrounds originating from hadron mis-
identification. The remaining components were then later taken into account in
the fit to the invariant mass distributions.

Besides these sources of background, one has to take into account backgrounds
from cascade decays. The branching fraction of $b$ $\rightarrow$ $c$ $\ell\nu$
decays is typically three orders of magnitude larger than the $b$
$\rightarrow$ $s$ one. These types of backgrounds are not relevant in the
cases where the leptons decay via a resonance like the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$.

Dedicated vetoes were setup to suppress some of them, the remaining events are
then modelled in the fit or taken into account as part of the systematic
studies.

One of the most important aspects of a LU test is to ensure a good control of
the efficiencies; this was achieved as stated earlier thanks to the evaluation
of the ratio $r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}^{-1}$
computed as:

$\displaystyle r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}^{-1}=\frac{N({{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow
p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{e^{+}e^{-}}))}{N({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\\!\rightarrow{\mu^{+}\mu^{-}}))}\times\frac{\epsilon({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\\!\rightarrow{\mu^{+}\mu^{-}}))}{\epsilon({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{e^{+}e^{-}}))}.$ (32)

The aim of this stringent test is to make sure that this ratio is equal to
unity and flat across phase-space. The simulation is known not to be a perfect
description of the data. A set of “corrections” derived from data are applied
to the simulation to account for these differences. They are based on the
kinematics and decay model of the ${\mathchar 28931\relax}^{0}_{b}$ particle
but also on the multiplicity of the events. The
$r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}^{-1}$ test was performed
separately for each of the trigger categories and data taking periods.

Figure 25: Comparison of unblinded $r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}^{-1}$ values in different trigger categories and datasets, with total
and statistical-only uncertainties displayed.

The procedure described below to measure
$r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}^{-1}$ is identical between
the datasets, with the only difference arising from selection requirements and
weights applied to the simulation.

  1. 1.

The ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow
p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\\!\rightarrow{\mu^{+}\mu^{-}})$ generator-level simulation sample,
with the relevant weights applied, is used to extract the number of simulated
events at the generator stage.

  2. 2.

The ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow
p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\\!\rightarrow{\mu^{+}\mu^{-}})$ reconstructed-level simulation
sample, processed through the complete chain of selection requirements, and
having all the relevant weights applied, is used to extract the number of
simulated events after the final selection.

  3. 3.

The number of reconstructed-level events (step 2) is divided by the number of
generated-level events (step 1), and multiplied by the values of generating
and filtering efficiencies, to get the total efficiency.

  4. 4.

For Run I, the 2011 and 2012 datasets have to be merged. To do so, their
simulation samples are merged, having a dedicated weight applied ensuring the
correct ratio of integrated luminosity (1:2) between the two datasets. In
addition, the ratio of ${\mathchar 28931\relax}^{0}_{b}$ production cross-
sections at 8 and 7 TeV is taken to be $1.23$, as per the LHCb measurement
[76]. The relevant values of generation and filtering efficiencies are passed
to each of the two datasets. Steps 1 and 2 are performed with already merged
generator-level and reconstruction-level samples.

  5. 5.

The simulation samples of the specific backgrounds, with the final selection
applied, are used to extract their invariant mass shapes.

  6. 6.

The ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow
p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\\!\rightarrow{\mu^{+}\mu^{-}})$ simulation sample is used to extract
the signal invariant mass shape.

  7. 7.

The fit is performed to the ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow
p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\\!\rightarrow{\mu^{+}\mu^{-}})$ data, with the final selection
applied. The signal yield and its uncertainty are extracted from the fit.

  8. 8.

The signal yield is divided by the total efficiency (step 3) to obtain the
efficiency-corrected yield.

  9. 9.

All the previous steps are repeated for the ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{e^{+}e^{-}})$ mode.

  10. 10.

Efficiency-corrected yields of the ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{e^{+}e^{-}})$ are divided by the efficiency-corrected
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow
p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\\!\rightarrow{\mu^{+}\mu^{-}})$ yields to get the value of
$r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}^{-1}$.

Comparisons of $r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}^{-1}$
between trigger categories and datasets are shown in Fig. 25. The
uncertainties displayed are statistical uncertainties only. Getting
$r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}^{-1}$ “right” as a
function of phase-space, $r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}^{-1}=0.96\pm 0.05$, took the best part of a year of Vitalii’s PhD.

Finally, $R_{{p}{K}}^{-1}$ is measured using a simultaneous fit to both
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}\mu^{+}\mu^{-}$ and
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{e^{+}e^{-}}$ decay
modes, using all available data sets and trigger categories. The yields of the
control modes and the efficiencies are measured beforehand and are plugged as
Gaussian constrains in the fit. The fit has two observables, $R_{{p}{K}}^{-1}$
and $r_{{\mathcal{B}}}={\mathcal{B}}({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}\mu^{+}\mu^{-})/{\mathcal{B}}({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow p{K}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\\!\rightarrow{\mu^{+}\mu^{-}}))$. The branching fraction of the rare
electron mode is later derived as a byproduct of the simultaneous fit.

Figure 26: Measured value of $R_{{p}{K}}^{-1}$ in the range
$0.1<{q^{2}}<6{\mathrm{\,Ge\kern-0.90005ptV^{2}\\!/}c^{4}}$ and
$\mathrm{\,m}({p}{K}^{-})<2600{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$ (red
point), including statistical and systematic uncertainties, compared to unity
(dashed line).

The result of the test of LU in ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{\ell^{+}}{\ell^{-}}$ decays,
$R_{{p}{K}}^{-1}$, in the range
$0.1<q^{2}<6{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ and
$m({p}{K}^{-})<2600{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is

$\left.R_{{p}{K}}^{-1}\right|_{0.1<q^{2}<6{\mathrm{\,Ge\kern-0.70004ptV^{2}\\!/}c^{4}}}=1.17^{\,+\,0.18}_{\,-\,0.16}\pm
0.07,$

where the first uncertainty is statistical and the second systematic.

The first measurement of the branching fraction of the rare muonic decay mode
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}\mu^{+}\mu^{-}$ is also
performed and its value is found to be $\left.{{\mathcal{B}}({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}\mu^{+}\mu^{-})}\right|_{0.1<q^{2}<6{\mathrm{\,Ge\kern-0.70004ptV^{2}\\!/}c^{4}}}=\left(2.65\pm
0.14\pm 0.12\pm 0.29^{\,+\,0.38}_{\,-\,0.23}\right)\times 10^{-7}$.

The electron mode ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{e^{+}e^{-}}$ is observed for the
first time $\left.{{\mathcal{B}}({{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{e^{+}e^{-}})}\right|_{0.1<q^{2}<6{\mathrm{\,Ge\kern-0.70004ptV^{2}\\!/}c^{4}}}=\left(3.1\pm
0.4\pm 0.2\pm 0.3^{\,+\,0.4}_{\,-\,0.3}\right)\times 10^{-7}$, with a
significance larger than $7\sigma$ including systematic uncertainties.

To conclude, more data are needed to confirm or exclude the presence of NP
contributions in these decays. It should be noted that the current analysis is
sensitive to different experimental uncertainties than those of lepton-
universality tests performed with $B$ mesons, such as the backgrounds that
affect the extraction of the signal yields from data, or the control modes
which are used to calibrate the simulation and measure the double ratio.
Consequently, it provides an independent test of the SM.

Finally, the prospects for ${b}\rightarrow{s}{\ell}^{+}{\ell}^{-}$ decays with
the LHCb Upgrades are very exciting. The statistical uncertainties will be
significantly reduced, so that with 23 fb-1 we expect to reach about 0.025,
0.031 and 0.076 precision on $R_{{K}}$, $R_{{{K}^{*0}}}$ and $R_{{p}{K}}$
respectively [79]. It will also be possible to investigate new $b$-decay
modes, and especially to explore angular observables, to probe directly the
Wilson coefficients and who knows maybe discover New Physics ?

##  Chapter 4 Conclusion

> “Que mon conte soit beau et se déroule comme un long fil”
>
> Marie Louise Taous Amrouche Le grain magique

I had the good fortune to contribute to a few, yet very diverse facets of
flavour physics, as well to the LHCb detector and its first upgrade. The
months ahead of us are extremely important, as we are about to embark in the
commissioning of an almost whole new detector, while working on the analysis
of the legacy datasets and preparing LHCb upgrade II. Truly somedays, it seems
like a titanic work. However, the excitement and the myriad of possibilities
from flavour physics are such, that I believe all the efforts are worth it
(although to be honest, sometimes after sitting in four or five hours long
meetings, discussing the impact of the phases of the moon on our measurements
of detector designs, I do think that all of it should be tossed out a window).

The results presented in this habilitation explored different properties of
$b$-baryons. To achieve precise mass measurements of the ${\mathchar
28931\relax}^{0}_{b}$, ${\mathchar 28932\relax}_{b}$ and ${\mathchar
28938\relax}^{-}_{b}$ baryons, it was shown that a good control and
understanding of the momentum scale played an essential role. The ${\mathchar
28938\relax}^{-}_{b}$ measurement allowed to clarify the observed discrepancy
between the two previous measurements from the Tevatron. I then proceeded to
discuss lifetime measurements of the $b$-hadrons using decay modes with
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ in the final state. Given the
size of the statistical uncertainties, it was mandatory to have an excellent
handle on the systematic uncertainties. With this analysis, lifetime
acceptance effects were broken down as much as physically possible. Data-
driven methods were employed to estimate the impact of reconstruction effects.
The results were in good agreement with the theoretical prediction from HQET
and contributed to significantly reduce the uncertainty of the updated world
averages. Finally, I discussed the first test of lepton universality using
${\mathchar 28931\relax}^{0}_{b}$ decays, $R_{{p}{K}}^{-1}$. With this
analysis, the first observation of the rare mode ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{e^{+}e^{-}}$ was established as well
as the measurement of the branching fraction of ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{K}{e^{+}e^{-}}$ in ${q^{2}}\in[1,6]$
${\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ and $m_{pK}<$ 2600
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. A key aspect of this analysis
relies on the computation of the observable
$r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}^{-1}$ which gives
confidence in the good control of the reconstruction effects and expected
differences between electrons and muons. While this is statistically limited,
it follows the same trend observed in lepton universality tests performed with
other $B$-mesons. With this measurement, we did not close the window on the
anomalies, so let us see if they will remain and lead to the discovery of new
particles, or fade away with more data.

To conclude, the experimental measurements of $b$-baryon properties
contributed to the understanding or validation of theoretical computations.
However, there are still plenty of measurements to be done and phenomena to be
further investigated, and I am looking forward to doing so in LHCb in the next
few years.

## Apprentices

An HDR would make little to probably no sense without the participation of
students. I had the pleasure to supervise and co-supervise many bachelor (L3)
and master (M1 or M2) students since I started working at CNRS in 2012. I
don’t mention in this section the contribution of my PhD students Renato
Quagliani and Vitalii Lisovskyi as they each produced almost 300 pages of
material describing their work [48], [71]. They all played very different
roles and contributed to many areas of my research activities for example,
they helped me to kick-start physics analyses, learn new techniques, methods
or software, study the feasibility of a measurement, address a specific
analysis point. I would like to thank all of them for their enthusiasm and
energy. I would like also to thank Carla Marin Benito & Sébastien Descotes-
Genon who shared some of the supervision with me.

#### Kevin de Vasconcelos Corga 2013/M1

With Kevin we evaluated the expected statistical uncertainty on
$\Delta\Gamma_{d}$ and $\tau_{{B}^{0}}$ using LHCb 2011 and 2012 datasets.
Kevin wrote a new fitting program which permitted to access the observables of
interest in a simulatanous way from ${B}^{0}$ $\rightarrow$
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ and ${B}^{0}$ $\rightarrow$
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ ${K}^{*0}$ signal events. He
also made an extrapolation for the LHCb Upgrade. For this study, there was no
special treatment of the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ tracks,
both types of track categories were accounted for and each of them had their
own decay time acceptance.

#### Ilham Dami 2015/L3

With Ilham we stated the lepton universality analysis with ${\mathchar
28931\relax}^{0}_{b}$ decays. During her internship, Ilham studied the shape
of the rare electron mode using simulated samples of ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\Lambda(1520)e^{+}e^{-}$ decays. We also had a
look at multivariate selections for this decay mode, she used the scikit learn
software and we played with the various algorithms and optimisation techniques
[80].

#### Rabah Abdul Khalek 2016/M1

Rabah’s internship happened during a time where I was working on the software
of the scintillator fibre tracker for the LHCb Upgrade. Trying to reduce the
processing time and optimise the algorithms was a priority. Using dedicated
tools such as Valgrind, Rabah identified that a significant amount of
processing time was spent in the first loop making combinations from hits from
x-layers. He rewrote part of this code in a smarter way and this allowed to
reduce the processing time in this step by a factor two. Later on, he gave a
try to using a Neural Network in the suppression of the ghosts track
combinations inside the algorithm. With this improvement the ghost rate was
reduced by a factor two.

#### Florian Mercier - 2017/L3

Co-supervised with Sébastien Descotes-Genon.
During three years, I shared a course called ”introduction to particle
physics” for second year bachelor students. Amongst my students Florian was
probably the most curious one, and he asked me for advice. He wanted to do an
internship working on a ”theory” project but he was worried to end up only
reading papers and making photocopies. After discussing with S. Descotes-
Genon, we agreed to share his supervisor and investigate what would be the
impact of measuring properties of ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\Lambda(1520)\ell^{+}\ell^{-}$ decays in
global fits. Florian used flavio a python based package for global flavour
fits [81]. A few assumptions had to me made given that no form factors were
computed for this decay, he used approximations suggested in arXiv:1102.00897
based on quark models and Heavy Quark Effective theory and produced
constraints on the Wilson coefficients $C_{9}$ and $C_{10}$.

#### Mathieu Markovitch & Corentin van Den Broek D’obrenan - 2019/L3

Co-supervised with Carla Marin Benito.
The work of Mathieu and Corentin was based on arXiv:1807.01643. Mathieu
studied the impact of the radiative decay $B_{s}\rightarrow f_{1}(1420)\gamma$
on the Wilson coefficient $C_{7}^{\prime}$ associated with right-handed
currents in ${b}\rightarrow{s}$ transitions using the flavio package. The
final state $B_{s}\rightarrow f_{1}(1420)(\rightarrow KK{{\pi}^{0}})\gamma$ is
quite challenging to reconstruct at LHCb. Corentin used multivariate approches
from the scikit learn software to evaluate the possibility of seeing this
signal in the LHCb data.

#### Felicia Volle - 2019/M2

Co-supervised with Carla Marin Benito.
The $m({p}{K})$ spectrum from ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK\ell^{+}\ell^{-}$ decays has never been measured outside of the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ region, ultimately it will be
needed to know the resonant structure of the hadronic part of the rare modes
to be able to compare any result to theoretical predictions and this will be
possible when enough data will be analysed. One can use the region around
$q^{2}=0$, where the photon is produced on shell to perform such a study. As
part of her internship, Felicia worked on a selection using a multi-variable
method to isolate ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK\gamma$
decays. She showed that one can expect to have about 1’000 signal candidates
in 2012 data collected by LHCb.

#### Anja Beck - 2019/M2

Co-supervised with Carla Marin Benito.
Anja is enrolled at the University of Dortmund in Johannes Albrecht’s group.
She spent six months in our group at IJCLab as part of an Erasmus program.
Anja’s work is a follow up of Felicia’s one. She first investigated the shape
of the angular acceptance and resolution. Anja dived in the helicity formalism
needed to perform the amplitude analysis of ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK\gamma$. This work is now documented in
arXiv:2002.02692 and submitted to JHEP. The amplitude fit that she is
developing is based on the TensorFlow software. She already has a version of
the fit which gives sensible results of the fractions for the different
$\Lambda^{*}$ resonances, using the legacy Run 1/2 LHCb datasets.

See pages 1,7,8,9,10,11,12,13,14,15 of masses.pdf See pages
1,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29 of
lifetimes.pdf See pages 1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22
of RpK.pdf

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###### Acknowledgements.

Bagneux, March 20${}^{th}~{}2020$ Day 4 of confinement I will be honest, I am
writing these acknowledgements standing in my kitchen, while Loulou is
watching “Youhoo to the rescue”. What a strange situation we find ourselves
in. Nonetheless, I would like to use this precious time to acknowledge a few
people. I would like to first thank my referees, Tulika Bose, Guy Wilkinson
and Isabelle Wingerter-Seez for their comments and suggestions to improve this
manuscript. I would like to also thank Gino Isidori, François Lediberder and
Achille Stocchi for accepting to be in my habilitation Jury. Renato Quagliagni
for his robustness like a good pattern recognition algorithm, with whom I had
a great time figuring out the tricks of the LHCb tracking and for
investigating the properties of all the hits in the SciFi one by one. Vitalii
Lisovskyi for his mythical ”maybe”, for his curiosity, intelligence,
enthusiasm and ability to fish out every last single little bias and
background in the data. Carla Marin Benito, for “guarding the house” while I
was busy writing, for being sharp like a Japanese Samurai sword and for being
such a joy to work with. I would like to thank Anja Beck for making the
helicity formalism sound like a piece of vegan cake. I would like to thank
Marie-Hélène Schune for being the first one to open the door of LAL and
building 208 in particular to me. I am looking forward to many H2O
discussions. I would like to thank Jacques Lefrançois, we should all want to
be Jacques when we grow up, the world would be a much better place. I
appreciated during these years the interactions with all the PhD students in
the LHCb group, and I would like to thank them all. Alexandra Martín Sánchez
with whom I ended up sharing one of our bigger life experiments, Olga
Kochebina for her good spirits and knowledge about charm physics, Maksym
Teklishyn my office mate for a year, Alexis Vallier who’s good mood is
difficult to challenge, Martino Borsato and his “interesting” and very
specialised taste in music, Victor Daussy-Renaudin for recommending all the
podcasts popular to trendy left wing kids, Andrii Usachov for his weird
stories, Fabrice Desse for his unbeatable cool, and Elisabeth Niel for making
me smile even when I am grumpy and also for being so precise with ${}^{\bf
6}_{\bf 8}$ rythms. I would like to thank Francesco Bossu and Michael Winn,
for putting in a new light the heavy ions topic, that was not an easy task.
Sergey Barsuk for his odd ukrainian chocolate imports and upgrading our group
with a decent coffee machine. Patrick Robbe for his friendship, knowledge
about the of the gory details of the LHCb simulation, as well as harmony
rules. I would like to thank Olivier Schneider, Aurelio Bay, Tatsuya Nakada,
Raluca Muresan, Marc-Olivier Bettler, Géraldine Conti and Joel Bressieux for
the wonderful three years at EPFL. I would like to thank my theory colleagues,
Sébastien Descotes-Genon for the hours that he spared me to discuss EFTs,
Damir Bečirević, for his invaluable help and also for quizzing me like a
student about the dimensions of operators. I would like to thank Olcyr
Sumensari for proofreading the theory chapter and very precise comments on
Figure 1.3. I would also like to thank Danny van Dyk, Marzia Bordone,
Alexandre Lenz, Aoife Bharucha, Peter Stangl, Diego Guadagnoli, and Yossi Nir
for all the discussions. A special thank you to Tim Gershon, who’s always been
so very supportive throughout all the years, for his help reviewing all my
relevant documents. Thank you. Peter Clarke, for the great time we had as
conveners and discussing the lifetime agonies. I would like to thank my
collaborators of the lifetime and mass measurements Francesca Dordei, Sneha
Malde, Greig Cowan and Matthew Needham. Jaap Panman for the luminosity work,
Pierre Billoir and Manuel Schiller for the seeding discussions. Mark Tobin for
his help during the ST piquets. Sophie Redford for always correcting my
English, Tim Head for teaching us about PR and MR and all of that. Conor
Fitzpatrick for his general Irishness and everything that goes with it. Ben
Couturier for his help with the obscure part of the LHCb software. Evelina
Gersabeck for her support. Eluned Smith for her initiative and cello chats,
Paula Collins for building us a Velo. Simone Bifani for his help swinging an
epic EW talk, Stephanie Reichert for her feminism and careful readings. The
Oxbridge representatives of LHCb, Patrick Owen and Matthew Kenzie for the long
debates we had about the anomalies and other topics. Julian Wishahi for his
support during the early SciFi days. Jerko Merkel for the fun chats at CERN
and attempts to teach me German. My (loud) colleagues from building 208 and in
particular Nicolas Leroy for the book recommendations. Laurent Serin for
sharing the L2 class with me and Antoine Laudrain for his help preparing the
NPAC projects. Dimitris Varouchas for his Greekness, Marta Spinelli for her
energy. Francesco Polci, for his kindness, for being a great collaborator and
friend, thank you for the teas in R1, the music and all the complaining. Viola
Sordini, for sharing so many chapters of our lives together, for offering me
her couch when I moved to Geneva, for the hours and hours of talking and
everything else. Zaida Conesa del Valle for being such a great collaborator
throughout our various committees. I would like to thank Nathalie Grub,
Lalaine Barbon Strebel, Anu Liisa Saarelainen, Cindy Denis, Amélie Caillet,
Erika Luthi, Isabelle Vauleon, Dominique Bony, Catherine Bourge, Catherine
Zomer, and Sylvie Teulet for making my administrative duties an order of
magnitudes easier. Gregory Perrin, Thomas Roulet, Guillaume Philippon, Gerard
Marchal Duval for their help setting up the masterclasses every year. Outside
of the work environment I benefit from a very complex and sophisticated
architecture of humans and I would like to thank them all. Mathilde Daussy-
Renaudin, for being the best supportive petite chauve-souris and for her
infinite knowledge about medieval witches and snails. Emmanuelle Zagoria, who
helped me outline so many projects and hopefully many others to come, for
being such an inspiration and for somehow creating a little bit of New York
just for me. Blandine Huchet for making me discover so many string quartets
and the time spent in chamber music festivals. My cello teachers, Guillaume
Martigné, Domitille Sanyas, et Thalie Bonvallet Michalakakos who have been
through their teachings, the guardians of my sanity and curiosity. Ljubica and
Vladimir for their kindness and especially for looking after Loulou, taking
such great care of her during all the hours when I am working or travelling.
Julien Bouyssou et Aghiles Ziani, who stacked one on top of the other would
reach 4m. Thank you for being the brothers I never had. My sisters, Lili et
Nina, for their magnificent sense of humour and for their million jokes in all
circumstances, and by all circumstances I mean all circumstances, you two are
the pillars of my joy. My parents, for the eternal love and support, their
unshakable confidence, where would I be without you? Most probably nowhere. My
grand mother for being the first one to teach me about patriarchy and how we
should slowly and methodically dismantle it, thank you for being so stubborn
and an inspiration for finishing your eleventh book at age ninety two.
Finally, I would like to thank my ultimate partner in crime. I could make
things easy, but then again, why would I? *****

#### Audio support

While writing this document, or driving in the car thinking about it, I
listened to:

  * •

Johannes Sebastien Bach - Goldberg variations and Cello Suites.

  * •

Anoushka Shankar - Land of gold.

  * •

System of a Down - Toxicity.

  * •

Britney Spears - Everything.

  * •

Antonio Vivaldi - Double Cello Concerto 531.

  * •

Jeanne Added - Radiate.

  * •

Clara Lucia - La grenade.

for many, many hours.