Precision physics with heavy-flavoured hadrons

Patrick Koppenburg

Nikhef National Institute for Subatomic Physics
PO box 41882, 1009 DB Amsterdam,The Netherlands
European Organization for Nuclear Research (CERN)
CH-1211 Geneva 23, Switzerland
<EMAIL_ADDRESS>

Vincenzo Vagnoni

Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Bologna
via Irnerio 46, 40126 Bologna, Italy
<EMAIL_ADDRESS>
The understanding of flavour dynamics is one of the key aims of elementary
particle physics. The last 15 years have witnessed the triumph of the
Kobayashi-Maskawa mechanism, which describes all flavour changing transitions
of quarks in the Standard Model. This important milestone has been reached
owing to a series of experiments, in particular to those operating at the so-
called $B$ factories, at the Tevatron, and now at the LHC. We briefly review
status and perspectives of flavour physics, highlighting the results where the
LHC has given the most significant contributions, notably including the recent
observation of the $B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$ decay.

Published in 60 Years of CERN Experiments and Discoveries
Advanced Series on Directions in High Energy Physics, Vol. 23, World
Scientific Publishing

##  1 Introduction

Flavour physics has played a central rôle in the development of the Standard
Model (SM), which represents the state of the art of the fundamental theory of
elementary physics interactions. The SM is able to describe with excellent
accuracy all of the fundamental physics phenomena related to the
electromagnetic, weak and strong forces, observed to date. Yet, it fails with
some key aspects, notably including the fact that it does not provide an
answer to one of the most fundamental questions: why is antimatter absent from
the observed universe? Owing to the work of Andrei Sakharov in 1967 [1], the
phenomenon of $C\\!P$ violation, _i.e._ the non-invariance of the laws of
nature under the combined application of charge ($C$) and parity ($P$)
transformations, is known to be one of the ingredients needed to dynamically
generate a baryon asymmetry starting from an initially symmetric universe.
However, it is also known that the size of $C\\!P$ violation in the SM is too
small, by several orders of magnitude, to explain the observed baryon
asymmetry of the universe [2, 3, 4]. As a consequence, other sources of
$C\\!P$ violation beyond the SM (BSM), which should produce observable effects
in the form of deviations from the SM predictions of certain $C\\!P$-violating
quantities, must exist. Rare decays that are strongly suppressed in the SM are
of particular interest, since BSM amplitudes could be relatively sizable with
respect to those of the SM.

The first run of the Large Hadron Collider (LHC), with 7 and 8
$\mathrm{\,Te\kern-1.00006ptV}$ $pp$ collisions, has led to the discovery of
the Higgs boson [5, 6], but no hint of the existence of other new particles
has been found. Neither supersymmetry nor any other direct sign of BSM physics
has popped out of the data. Besides the Higgs discovery, analyses from the
first years of running have also firmly established the great impact of the
ATLAS [7], CMS [8] and LHCb [9] experiments in the field of $C\\!P$ violation
and rare decays of heavy-flavoured hadrons. In particular, LHCb has produced a
plethora of results on a broad range of flavour observables in the $c$\- and
$b$-quark sectors, and ATLAS and CMS have given significant contributions to
the $b$-quark sector, mainly using final states containing muon pairs. Also
these measurements do not provide hints of BSM physics.

Nevertheless, it is of fundamental importance for future developments of
elementary particle physics to keep improving the theoretical and experimental
fields of flavour physics. On the one hand, such improvements increase the
reach of indirect searches for BSM physics, probing higher and higher mass
scales in the event that no BSM effects were discovered by direct detection.
On the other hand, they would enable the BSM Lagrangian to be precisely
determined, if any new particle were detected in direct searches. Starting
with a brief historical perspective on the development of heavy flavour
physics, we review the present status, highlighting some of the results where
the LHC has given the most significant contributions.

##  2 An historical perspective

###  2.1 The origin of the KM mechanism

As already mentioned, flavour physics has played a prominent rôle in the
development of the SM. As an example, one of the most notable predictions made
in this context was that of the existence of a third quark generation, in a
famous paper of 1973 by Makoto Kobayashi and Toshihide Maskawa [10]. In that
work, which won them the Nobel Price in Physics in 2008 “for the discovery of
the origin of the broken symmetry which predicts the existence of at least
three families of quarks in nature”, Kobayashi and Maskawa extended the
Cabibbo [11] (with only $u$, $d$, and $s$ quarks) and the Glashow-Iliopoulos-
Maiani [12] (GIM, including also the $c$ quark) mechanisms, pointing out that
$C\\!P$ violation could be incorporated into the emerging picture of the SM if
six quarks were present. This is commonly referred to as the Kobayashi-Maskawa
(KM) mechanism. It must be emphasised that at that time only hadrons made of
the three lighter quarks had been observed. An experimental revolution took
place in 1974, when a new state containing the $c$ quark was discovered almost
simultaneously at Brookhaven [13] and SLAC [14]. Then, the experimental
observations of the $b$ [15] and $t$ [16] quarks were made at FNAL in 1977 and
1995, respectively.

The idea of Kobayashi and Maskawa, formalised in the so-called Cabibbo-
Kobayashi-Maskawa (CKM) quark mixing matrix, was then included in the SM by
the beginning of the 1980’s. The phenomenon of $C\\!P$ violation, first
revealed in 1964 using decays of neutral kaons [17], was elegantly accounted
for as an irreducible complex phase within the CKM matrix. The experimental
proof of the validity of the KM mechanism and the precise measurement of the
value of the $C\\!P$-violating phase soon became questions of paramount
importance.

###  2.2 The rise of $B$ physics

Due to the nature of the CKM matrix, an accurate test of the KM mechanism
required an extension of the physics programme to heavy-flavoured hadrons.
Pioneering steps in the $b$-quark flavour sector were moved at the beginning
of the 1980’s by the CLEO experiment at CESR [18]. At the same time, Ikaros
Bigi, Ashton Carter and Tony Sanda published papers exploring the possibility
that large $C\\!P$-violating effects could be present in the decay rates of
$B^{0}$ mesons decaying to the $J/\psi K^{0}_{S}$ $C\\!P$ eigenstate [19, 20].
In addition, they also pointed out that such a measurement could be
interpreted in terms of the $C\\!P$-violating phase without relevant
theoretical uncertainties due to strong interaction effects. However, there
were two formidable obstacles to overcome: first, an experimental observation
required an enormous amount of $B^{0}$ mesons, well beyond what was
conceivable to produce and collect at the time; second, a precise measurement
of the decay time was required, together with the knowledge of the flavour of
the $B^{0}$ meson at production.

Few years later, in 1987, the ARGUS experiment at DESY measured for the first
time the mixing rate of $B^{0}$ and $\bar{B}^{0}$ mesons [21], whose knowledge
was an important ingredient to understand the feasibility of measuring $C\\!P$
violation with $B^{0}\rightarrow J/\psi K^{0}_{S}$ decays. Another crucial
ingredient came along due to tremendous developments in the performance of
$e^{+}e^{-}$ storage rings. By the late 1980’s, many different possible
designs for new machines were being explored. A novel idea was put forward by
Pier Oddone in 1987: a high-luminosity asymmetrical $e^{+}e^{-}$ circular
collider operating at the centre-of-mass energy of the $\Upsilon(4S)$ meson
[22]. Owing to the beam-energy asymmetry, $B$ mesons would be produced with a
boost in the laboratory frame towards the direction of the most energetic
beam. The consequent nonzero decay length, measured by means of state-of-the-
art silicon vertex detectors, would enable precise measurements of the decay
time to be achieved. Two machines based on Oddone’s concept, so-called $B$
factories, were eventually built: PEP-II at SLAC in the United States and KEKB
at KEK in Japan. The associated detectors, BaBar [23] at PEP-II and Belle [24]
at KEKB, were approved in 1993 and in 1994, respectively. If CESR was
initially able to produce few tens of $b\bar{b}$ pairs per day, PEP-II and
KEKB were capable of producing order of one million $b\bar{b}$ pairs per day.

Meanwhile, during the course of the 1990’s, many $b$-physics measurements were
being performed at the $Z^{0}$ factories, _i.e._ the LEP experiments [25, 26,
27, 28] at CERN, and the SLD [29] experiment at SLAC. Despite the relatively
small statistics, $b$ hadrons produced in $Z^{0}$ decays were naturally
characterised by a large boost, enabling measurements of lifetimes of all
$b$-hadron species and of oscillation frequencies of neutral $B$ mesons to be
performed. In particular, for the first time it was possible to study samples
of $B^{0}_{s}$-meson, $b$-baryon and even a handful of $B^{+}_{c}$-meson
decays [30, 31]. Similar pioneering measurements were also made at the
Tevatron with Run I data, using hadronic collisions as a source of $b$ quarks
[32].

Soon after PEP-II and KEKB were turned on, the two machines broke any existing
record of instantaneous and integrated luminosity of previous particle
colliders. By the end of their research programmes, BaBar and Belle measured
$C\\!P$ violation in $B^{0}\rightarrow J/\psi K^{0}_{S}$ decays with a
relative precision of about 3% [33, 34]. The large sample of $B$-meson decays
collected at BaBar and Belle enabled a series of further measurements in the
flavour sector to be performed, well beyond the initial expectations. In the
same years, a major step forward in these topics was also made at the Tevatron
with Run II data. Although with a somewhat limited scope if compared to $B$
factories, the CDF and D0 experiments at FNAL collected large amounts of
heavy-flavoured-hadron decays, performing some high precision measurements
[35], notably including the first observation of $B^{0}_{s}$-meson mixing in
2006 [36].

###  2.3 The LHC era

When the constructions of the BaBar and Belle detectors were being scrutinised
for approval, three distinct proposals for a dedicated $b$-physics experiment
at the LHC were put forward, so-called COBEX, GAJET, and LHB. GAJET and LHB
were both based on fixed targets, the former working with a gas target placed
inside the LHC beam pipe and the latter exploiting an extracted LHC beam.
COBEX was instead proposed to work in proton-proton collider mode. The three
groups of proponents were asked to join together and submit to the LHC
Experiments Committee (LHCC) a proposal for a single collider-mode experiment,
namely LHCb [9]. LHCb was then designed to exploit the potential for heavy-
flavour physics at the LHC by instrumenting the forward region of proton-
proton collisions, in order to take advantage of the large $b\bar{b}$ cross
section in the forward (or backward) LHC beam direction. The LHCb experiment
was approved in 1998, and started taking data with the start-up of LHC in
2009.

Figure 1: Sketch of the LHCb detector.

The LHCb detector [9, 37], shown in Fig. 1, includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream of the
magnet. The tracking system provides a measurement of momentum of charged
particles with a relative uncertainty that varies from 0.5% at low momentum to
1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The silicon sensors of the
vertex detector come as close as 8 $\rm\,mm$ to the LHC beam. This allows for
a very precise measurement of the track trajectory close to the interaction
point, which is crucial to separate decays of beauty and charm hadrons, with
typical flight distances of a few millimetres in the laboratory frame, from
the background. The distance of a track to a primary vertex, the impact
parameter, is measured with a resolution of 15–30 $\mu$m.

One distinctive feature of LHCb, when compared to the ATLAS and CMS detectors,
is its particle identification capability for charged hadrons. This is mainly
achieved by means of two ring-imaging Cherenkov (“RICH”) detectors placed on
either side of the tracking stations. Once particle momenta are measured, the
two RICH detectors enable the identification of protons, kaons and pions to be
obtained. An electromagnetic calorimeter, complemented with scintillating-pad
and preshower detectors, provides energy and position of photons and
electrons, and allow for their identification in conjunction with information
from the tracking system. The electromagnetic calorimeter is followed by a
hadronic calorimeter that also gives some information to identify hadrons.
Finally, muons are identified by a system composed of alternating layers of
iron and multiwire proportional chambers. The online event selection is
performed by a trigger [38] which consists of a hardware stage, based on
information from the calorimeter and muon systems, followed by a software
stage, which applies full event reconstruction.

LHCb operates at a much lower instantaneous luminosity than the peak
luminosity made available by the LHC. This is necessary to better distinguish
charged particles resulting from $b$\- and $c$-hadron decays from particles
produced in other $pp$ collisions, in the forward region covered by the
detector acceptance. During the first run of the LHC, the average number of
$pp$ collisions per bunch crossing at the LHCb intersection was kept at about
$1.7$, corresponding to a luminosity of $4\times
10^{32}\rm\rm\,cm^{-2}s^{-1}$. This was achieved by a dynamical adjustment of
the transverse offset between the LHC beams during the fill, enabling constant
luminosity to be kept throughout.

Besides LHCb, the general purpose ATLAS and CMS detectors were also designed
with the aim of performing $b$-physics measurements, mainly using final states
containing muon pairs due to constraints dictated by the trigger and to the
absence of sub-detectors with strong particle identification capabilities for
charged hadrons.

##  3 The CKM matrix

###  3.1 Definition

In the SM, charged-current interactions of quarks are described by the
Lagrangian

$\mathcal{L}_{W^{\pm}}=-\frac{g}{\sqrt{2}}\overline{U}_{i}\gamma^{\mu}\frac{1-\gamma^{5}}{2}\left(V_{\rm
CKM}\right)_{ij}D_{j}W_{\mu}^{+}+h.c.,$

where $g$ is the electroweak coupling constant and $V_{\rm CKM}$ is the CKM
matrix

$V_{\rm CKM}=\left(\begin{array}[]{lcr}V_{ud}&V_{us}&V_{ub}\\\
V_{cd}&V_{cs}&V_{cb}\\\ V_{td}&V_{ts}&V_{tb}\end{array}\right),$

originating from the misalignment in flavour space of the up and down
components of the $SU(2)_{L}$ quark doublet of the SM. The $V_{ij}$ matrix
elements represent the couplings between up-type quarks $U_{i}=(u,\,c,\,t)$
and down-type quarks $D_{j}=(d,\,s,\,b)$.

An important feature of the CKM matrix is its unitarity. Such a condition
determines the number of free parameters of the matrix. A generic $N\times N$
unitary matrix depends on $N\left(N-1\right)/2$ mixing angles and
$N\left(N+1\right)/2$ complex phases. In the CKM case, dealing with a mixing
matrix between the quark flavour eigenstates, the Lagrangian enables the phase
of each quark field to be redefined, such that $2N-1$ unphysical phases cancel
out. As a consequence, any $N\times N$ complex matrix describing mixing
between $N$ generations of quarks has

$\underbrace{\frac{1}{2}N\left(N-1\right)}_{\mbox{mixing
angles}}\,\,\,\,\,\,+\underbrace{\frac{1}{2}\left(N-1\right)\left(N-2\right)}_{\mbox{physical
complex phases}}=\,\,\,\,\,\,\left(N-1\right)^{2}$

free parameters. The interesting case $N=2$ leads to the GIM mixing matrix
with only one free parameter, namely the Cabibbo angle $\theta_{C}$ [11]

$V_{\rm
GIM}=\left(\begin{array}[]{lcr}\phantom{-}\cos{\theta_{C}}&\phantom{-}\sin{\theta_{C}}\\\
-\sin{\theta_{C}}&\phantom{-}\cos{\theta_{C}}\end{array}\right).$

When formalised in 1970, the nature of $V_{\rm GIM}$ was invoked to explain
the suppression of flavour changing neutral current (FCNC) processes, and put
the basis for the discovery of the charm quark [12, 13, 14]. In the case
$N=3$, the resulting number of free parameters is four: three mixing angles
and one complex phase. This phase alone is responsible for $C\\!P$ violation
in the weak interactions of the SM.

###  3.2 Standard parametrisation

Among the various possible conventions, a standard choice to parametrise
$V_{\rm CKM}$ is given by

$V_{\rm
CKM}=\left(\begin{array}[]{ccc}c_{12}c_{13}&s_{12}c_{13}&s_{13}e^{-i\delta}\\\
-s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\delta}&c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\delta}&s_{23}c_{13}\\\
s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\delta}&-c_{12}s_{23}-s_{12}c_{23}s_{13}e^{i\delta}&c_{23}c_{13}\end{array}\right),$

where $s_{ij}=\sin{\theta_{ij}}$, $c_{ij}=\cos{\theta_{ij}}$ and $\delta$ is
the $C\\!P$-violating phase. All the $\theta_{ij}$ angles can be chosen to lie
in the first quadrant, thus $s_{ij},c_{ij}\geq 0$. The coupling between quark
generations $i$ and $j$ vanishes if the corresponding $\theta_{ij}$ is equal
to zero. In the case where $\theta_{13}=\theta_{23}=0$, the third generation
would decouple and the CKM matrix would take the form of $V_{\rm GIM}$. The
presence of a complex phase in the mixing matrix is a necessary condition for
$C\\!P$ violation, although not sufficient. As pointed out in Ref. [39],
another key condition is

$\left(m_{t}^{2}-m_{c}^{2}\right)\left(m_{t}^{2}-m_{u}^{2}\right)\left(m_{c}^{2}-m_{u}^{2}\right)\left(m_{b}^{2}-m_{s}^{2}\right)\left(m_{b}^{2}-m_{d}^{2}\right)\left(m_{s}^{2}-m_{d}^{2}\right)\times
J_{C\\!P}\neq 0,$

where

$J_{C\\!P}=\left|\Im\left(V_{i\alpha}V_{j\beta}V_{i\beta}^{*}V_{j\alpha}^{*}\right)\right|\qquad\left(i\neq
j,\alpha\neq\beta\right)$

is the so-called Jarlskog parameter. This condition is related to the fact
that the CKM phase could be eliminated if any of two quarks with the same
charge were degenerate in mass. As a consequence, the origin of $C\\!P$
violation in the SM is deeply connected to the origin of the quark mass
hierarchy and to the number of fermion generations.

The Jarlskog parameter can be interpreted as a measure of the size of $C\\!P$
violation in the SM. Its value does not depend on the phase convention of the
quark fields, and adopting the standard parametrisation it can be written as

$J_{C\\!P}=s_{12}s_{13}s_{23}c_{12}c_{23}c_{13}^{2}\sin{\delta}.$

Experimentally one has $J_{C\\!P}=\mathcal{O}\left(10^{-5}\right)$, which
quantifies how small $C\\!P$ violation is in the SM.

###  3.3 Wolfenstein parametrisation

Experimental information leads to the evidence that transitions within the
same generation are characterised by $V_{\rm CKM}$ elements of
$\mathcal{O}(1)$. Instead, those between the first and second generations are
suppressed by a factor $\mathcal{O}(10^{-1})$; those between the second and
third generations by a factor $\mathcal{O}(10^{-2})$; and those between the
first and third generations by a factor $\mathcal{O}(10^{-3})$. It can be
stated that

$s_{12}\simeq 0.22\gg s_{23}=\mathcal{O}(10^{-2})\gg
s_{13}=\mathcal{O}(10^{-3}).$

It is useful to introduce a parametrisation of the CKM matrix, whose original
formulation was due to Wolfenstein [40], defining

$\displaystyle s_{12}$
$\displaystyle=\lambda=\frac{\left|V_{us}\right|}{\sqrt{\left|V_{ud}\right|^{2}+\left|V_{us}\right|^{2}}},$
$\displaystyle s_{23}$
$\displaystyle=A\lambda^{2}=\lambda\left|\frac{V_{cb}}{V_{us}}\right|,$
$\displaystyle s_{13}e^{-i\delta}$
$\displaystyle=A\lambda^{3}\left(\rho-i\eta\right)=V_{ub}.$

The CKM matrix can be re-written as a power expansion of the parameter
$\lambda$ (which corresponds to $\sin{\theta_{C}}$)

$V_{\rm
CKM}=\left(\begin{array}[]{ccc}1-\frac{1}{2}\lambda^{2}-\frac{1}{8}\lambda^{4}&\lambda&A\lambda^{3}\left(\rho-i\eta\right)\\\
-\lambda+\frac{1}{2}A^{2}\lambda^{5}\left[1-2(\rho+i\eta)\right]&1-\frac{1}{2}\lambda^{2}-\frac{1}{8}\lambda^{4}(1+4A^{2})&A\lambda^{2}\\\
A\lambda^{3}\left[1-(\rho+i\eta)\left(1-\frac{1}{2}\lambda^{2}\right)\right]{}&~{}-A\lambda^{2}+\frac{1}{2}A\lambda^{4}\left[1-2(\rho+i\eta)\right]{}&~{}1-\frac{1}{2}A^{2}\lambda^{4}\end{array}\right),$

which is valid up to $\mathcal{O}\left(\lambda^{6}\right)$. With this
parametrisation, the CKM matrix is complex, and hence $C\\!P$ violation is
allowed for, if and only if $\eta$ differs from zero. To lowest order the
Jarlskog parameter becomes

$J_{C\\!P}=\lambda^{6}A^{2}\eta,$

and, as expected, is directly related to the $C\\!P$-violating parameter
$\eta$.

###  3.4 The unitarity triangle

The unitarity condition of the CKM matrix, $V_{\rm CKM}V_{\rm
CKM}^{\dagger}=V_{\rm CKM}^{\dagger}V_{\rm CKM}=\mathbb{I}$, leads to a set of
12 equations: 6 for diagonal terms and 6 for off-diagonal terms. In
particular, the equations for the off-diagonal terms can be represented as
triangles in the complex plane, all characterised by the same area
$J_{C\\!P}/2$

$\displaystyle\underbrace{V_{ud}V_{us}^{*}}_{\mathcal{O}(\lambda)}+\underbrace{V_{cd}V_{cs}^{*}}_{\mathcal{O}(\lambda)}+\underbrace{V_{td}V_{ts}^{*}}_{\mathcal{O}(\lambda^{5})}$
$\displaystyle=$ $\displaystyle 0,$
$\displaystyle\underbrace{V_{us}V_{ub}^{*}}_{\mathcal{O}(\lambda^{4})}+\underbrace{V_{cs}V_{cb}^{*}}_{\mathcal{O}(\lambda^{2})}+\underbrace{V_{ts}V_{tb}^{*}}_{\mathcal{O}(\lambda^{2})}$
$\displaystyle=$ $\displaystyle 0,$
$\displaystyle\underbrace{V_{ud}V_{ub}^{*}}_{\mathcal{O}(\lambda^{3})}+\underbrace{V_{cd}V_{cb}^{*}}_{\mathcal{O}(\lambda^{3})}+\underbrace{V_{td}V_{tb}^{*}}_{\mathcal{O}(\lambda^{3})}$
$\displaystyle=$ $\displaystyle 0,$
$\displaystyle\underbrace{V_{ud}V_{cd}^{*}}_{\mathcal{O}(\lambda)}+\underbrace{V_{us}V_{cs}^{*}}_{\mathcal{O}(\lambda)}+\underbrace{V_{ub}V_{cb}^{*}}_{\mathcal{O}(\lambda^{5})}$
$\displaystyle=$ $\displaystyle 0,$
$\displaystyle\underbrace{V_{cd}V_{td}^{*}}_{\mathcal{O}(\lambda^{4})}+\underbrace{V_{cs}V_{ts}^{*}}_{\mathcal{O}(\lambda^{2})}+\underbrace{V_{cb}V_{tb}^{*}}_{\mathcal{O}(\lambda^{2})}$
$\displaystyle=$ $\displaystyle 0,$
$\displaystyle\underbrace{V_{ud}V_{td}^{*}}_{\mathcal{O}(\lambda^{3})}+\underbrace{V_{us}V_{ts}^{*}}_{\mathcal{O}(\lambda^{3})}+\underbrace{V_{ub}V_{tb}^{*}}_{\mathcal{O}(\lambda^{3})}$
$\displaystyle=$ $\displaystyle 0.$

Only two out of these six triangles have sides of the same order of magnitude,
$\mathcal{O}(\lambda^{3})$. In terms of the Wolfenstein parametrisation, up to
$\mathcal{O}(\lambda^{7})$ the corresponding equations can be written as

$A\lambda^{3}\\{(1-\lambda^{2}/2)(\rho+i\eta)+[1-(1-\lambda^{2}/2)(\rho+i\eta)]+(-1)\\}=0,$
$A\lambda^{3}\\{(\rho+i\eta)+[1-\rho-i\eta-\lambda^{2}(1/2-\rho-i\eta)]+[-1+\lambda^{2}(1/2-\rho-i\eta)]\\}=0.$

Eliminating the common factor $A\lambda^{3}$ from both equations, the two
triangles in the complex plane represented in Fig. 2 are obtained. In
particular, the triangle defined by the former equation is commonly referred
to as the unitarity triangle (UT).

Figure 2: Representation in the complex plane of the non-squashed triangles
obtained from the off-diagonal unitarity relations of the CKM matrix.

The sides of the UT are given by

$R_{u}\equiv\left|\frac{V_{ud}V_{ub}^{*}}{V_{cd}V_{cb}^{*}}\right|=\sqrt{\bar{\rho}^{2}+\bar{\eta}^{2}},$
$R_{t}\equiv\left|\frac{V_{td}V_{tb}^{*}}{V_{cd}V_{cb}^{*}}\right|=\sqrt{\left(1-\bar{\rho}\right)^{2}+\bar{\eta}^{2}},$

where to simplify the notation the parameters $\bar{\rho}$ and $\bar{\eta}$,
namely the coordinates in the complex plane of the only non-trivial apex of
the UT, the others being (0, 0) and (1, 0), have been introduced. The exact
relation between $\bar{\rho}$ and $\bar{\eta}$ and the Wolfenstein parameters
is defined by

$\rho+i\eta=\sqrt{\frac{1-A^{2}\lambda^{4}}{1-\lambda^{2}}}\frac{\bar{\rho}+i\bar{\eta}}{1-A^{2}\lambda^{4}(\bar{\rho}+i\bar{\eta})},$

which, at the lowest non-trivial order in $\lambda$, yields

$\rho=\left(1+\frac{\lambda^{2}}{2}\right)\bar{\rho}+\mathcal{O}(\lambda^{4}),\qquad\eta=\left(1+\frac{\lambda^{2}}{2}\right)\bar{\eta}+\mathcal{O}(\lambda^{4}).$

The angles of the UT are related to the CKM matrix elements as

$\alpha\equiv\arg{\left(-\frac{V_{td}V_{tb}^{*}}{V_{ud}V_{ub}^{*}}\right)}=\arg{\left(-\frac{1-\bar{\rho}-i\bar{\eta}}{\bar{\rho}+i\bar{\eta}}\right)},$
$\beta\equiv\arg{\left(-\frac{V_{cd}V_{cb}^{*}}{V_{td}V_{tb}^{*}}\right)}=\arg{\left(\frac{1}{1-\bar{\rho}-i\bar{\eta}}\right)},$
$\gamma\equiv\arg{\left(-\frac{V_{ud}V_{ub}^{*}}{V_{cd}V_{cb}^{*}}\right)}=\arg{\left(\bar{\rho}+i\bar{\eta}\right)}.$

The second non-squashed triangle has similar characteristics with respect to
the UT. The apex is placed in the point $(\rho,~{}\eta)$ and is tilted by an
angle

$\beta_{s}\equiv\arg{\left(-\frac{V_{ts}V_{tb}^{*}}{V_{cs}V_{cb}^{*}}\right)}=\lambda^{2}\eta+\mathcal{O}(\lambda^{4}).$

###  3.5 Phenomenology of $C\\!P$ violation

The phenomenon of $C\\!P$ violation has been observed at a level above five
standard deviations in a dozen of processes involving charged and neutral
$B$-meson decays, as well as in a couple of neutral kaon decays [41]. In this
section we focus in particular on the phenomenology of $C\\!P$ violation in
the $b$-quark sector.

Three types of $C\\!P$ violation can occur in the quark sector: $C\\!P$
violation in the decay (also known as direct $C\\!P$ violation), $C\\!P$
violation in the mixing of neutral mesons, and $C\\!P$ violation in the
interference between mixing and decay.

Defining the amplitude of a $B$ meson decaying to the final state $f$ as
$A_{f}$, and that of its $C\\!P$ conjugate $\bar{B}$ to the $C\\!P$ conjugate
final state $\bar{f}$ as $\bar{A}_{\bar{f}}$, direct $C\\!P$ violation occurs
when $\left|A_{f}\right|\neq\left|\bar{A}_{\bar{f}}\right|$. This is the only
possible type of $C\\!P$ violation that can be observed in the decays of
charged mesons and baryons, where mixing is not allowed for. If for example
there are two distinct processes contributing to the decay amplitude, one can
write

$\displaystyle A_{f}$ $\displaystyle=$ $\displaystyle
e^{i\varphi_{1}}\left|A_{1}\right|e^{i\delta_{1}}+e^{i\varphi_{2}}\left|A_{2}\right|e^{i\delta_{2}}$
$\displaystyle\bar{A}_{\bar{f}}$ $\displaystyle=$ $\displaystyle
e^{-i\varphi_{1}}\left|A_{1}\right|e^{i\delta_{1}}+e^{-i\varphi_{2}}\left|A_{2}\right|e^{i\delta_{2}},$

where $\varphi_{1,2}$ denotes $C\\!P$-violating weak phases and
$\left|A_{1,2}\right|e^{i\delta_{1,2}}$ $C\\!P$-conserving strong amplitudes
of the two processes, labelled by the subscripts 1 and 2. The
$C\\!P$-violating asymmetry is given by

$\begin{split}A_{C\\!P}&\equiv\frac{\Gamma_{\bar{B}\rightarrow\bar{f}}-\Gamma_{B\rightarrow
f}}{\Gamma_{\bar{B}\rightarrow\bar{f}}+\Gamma_{B\rightarrow
f}}=\frac{\left|\bar{A}_{\bar{f}}\right|^{2}-\left|A_{f}\right|^{2}}{\left|\bar{A}_{\bar{f}}\right|^{2}+\left|A_{f}\right|^{2}}=\\\
&=\frac{2\left|A_{1}\right|\left|A_{2}\right|\sin{\left(\delta_{2}-\delta_{1}\right)}\sin{\left(\varphi_{2}-\varphi_{1}\right)}}{\left|A_{1}\right|^{2}+2\left|A_{1}\right|\left|A_{2}\right|\cos{\left(\delta_{2}-\delta_{1}\right)}\cos{\left(\varphi_{2}-\varphi_{1}\right)}+\left|A_{2}\right|^{2}}.\end{split}$
(1)

A nonzero value of the asymmetry $A_{C\\!P}$ arises from the interference
between the two processes, and requires both a nonzero weak phase difference
$\varphi_{2}-\varphi_{1}$ and a nonzero strong phase difference
$\delta_{2}-\delta_{1}$. The presence of (at least) two interfering processes
is a distinctive feature to observe $C\\!P$ violation.

When neutral heavy mesons are involved, the phenomenon of mixing between
opposite flavours takes place. In the case of $B^{0}$ and $B^{0}_{s}$ mesons,
due to the diagrams sketched in Fig. 3, an initial $\left|B\right\rangle$
state will evolve as a superposition of $\left|B\right\rangle$ and
$\left|\overline{B}\right\rangle$ states.

Figure 3: Box diagrams contributing to $\bar{B}^{0}-B^{0}$ and
$\bar{B}_{s}^{0}-B_{s}^{0}$ mixing.

Hence the mass eigenstates do not coincide with the flavour eigenstates, but
are related to them by

$\left|B_{\mathrm{H}}\right\rangle=\frac{p\left|B\right\rangle+q\left|\bar{B}\right\rangle}{\sqrt{\left|p\right|^{2}+\left|q\right|^{2}}},\qquad\left|B_{\mathrm{L}}\right\rangle=\frac{p\left|B\right\rangle-q\left|\bar{B}\right\rangle}{\sqrt{\left|p\right|^{2}+\left|q\right|^{2}}},$

where $p$ and $q$ are two complex parameters, and
$\left|B_{\mathrm{H}}\right\rangle$ and $\left|B_{\mathrm{L}}\right\rangle$
denote the two eigenstates of the $B^{0}_{(s)}$–${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}^{0}_{(s)}$ system. These two
eigenstates are split in mass and lifetime, and we can define the mass and
width differences $\Delta m_{d(s)}\equiv
m_{{d(s)},\,\mathrm{H}}-m_{{d(s)},\,\mathrm{L}}$ and
$\Delta\Gamma_{d(s)}\equiv\Gamma_{{d(s)},\,\mathrm{L}}-\Gamma_{{d(s)},\,\mathrm{H}}$.
The subscripts $\mathrm{H}$ and $\mathrm{L}$ denote the heavy and light
eigenstates. With this convention, the values of $\Delta m_{d}$ and $\Delta
m_{s}$ are positive by definition. The present knowledge of $B^{0}$\- and
$B^{0}_{s}$-mixing processes is obtained from flavour-tagged time-dependent
studies of semileptonic decays and of other decays involving flavour-specific
final states, such as $B^{0}_{s}\rightarrow D_{s}^{-}\pi^{+}$. The world
averages of the mass differences are $\Delta m_{d}=0.510\pm
0.003\,\mathrm{ps}^{-1}$ and $\Delta m_{s}=17.757\pm 0.021\,\mathrm{ps}^{-1}$
[42]. The value of $\Delta\Gamma_{s}$ is measured to be positive [43, 44],
$\Delta\Gamma_{s}=0.106\pm 0.011\,(\mathrm{stat})\pm
0.007\,(\mathrm{syst}){\rm\,ps^{-1}}$ [44]. The value of $\Delta\Gamma_{d}$ is
also positive in the SM and is expected to be much smaller than that of
$\Delta\Gamma_{s}$, $\Delta\Gamma_{d}\simeq 3\times 10^{-3}{\rm\,ps^{-1}}$
[45].

$C\\!P$ violation in the mixing of neutral mesons arises when the rate of
_e.g._ $B^{0}_{(s)}$ mesons transforming into ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}^{0}_{(s)}$ mesons differs from the
rate of ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}}^{0}_{(s)}$ mesons
transforming into $B^{0}_{(s)}$ mesons. The condition to have $C\\!P$
violation in the mixing is given by $|q/p|\neq 1$. However, to a very good
approximation the SM predicts $|q/p|\simeq 1$, _i.e._ $C\\!P$ violation in the
mixing is very small, as also confirmed by experimental determinations [42,
46]. For neutral $B^{0}$ and $B^{0}_{s}$ mesons, the value of $|q/p|$ can be
measured by means of the so-called semileptonic asymmetry

$A^{d(s)}_{\mathrm{sl}}\equiv\frac{\Gamma_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}}^{0}_{(s)}\rightarrow\ell^{+}X}(t)-\Gamma_{{B^{0}_{(s)}\rightarrow\ell^{-}X}}(t)}{\Gamma_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}}^{0}_{(s)}\rightarrow\ell^{+}X}(t)+\Gamma_{{B^{0}_{(s)}\rightarrow\ell^{-}X}}(t)}=\frac{1-|q/p|_{d(s)}^{4}}{1+|q/p|_{d(s)}^{4}},$

which actually turns out to be not dependent on time.

Finally, $C\\!P$ violation may arise in the interference between decay and
mixing processes. Assuming $C\\!PT$ invariance, the $C\\!P$ asymmetry as a
function of decay time for a neutral $B^{0}$ or $B^{0}_{s}$ meson decaying to
a self-conjugate final state $f$, is given by

$A(t)\equiv\frac{\Gamma_{{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}}}^{0}_{(s)}\rightarrow
f}(t)-\Gamma_{B^{0}_{(s)}\rightarrow f}(t)}{\Gamma_{{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}}}^{0}_{(s)}\rightarrow
f}(t)+\Gamma_{B^{0}_{(s)}\rightarrow f}(t)}=\frac{-C_{f}\cos\left(\Delta
m_{d(s)}t\right)+S_{f}\sin\left(\Delta
m_{d(s)}t\right)}{\cosh\left(\frac{\Delta\Gamma_{d(s)}}{2}t\right)+A^{\Delta\Gamma}_{f}\sinh\left(\frac{\Delta\Gamma_{d(s)}}{2}t\right)}.$

The quantities $C_{f}$, $S_{f}$ and $A^{\Delta\Gamma}_{f}$ are

$\begin{split}C_{f}\equiv\frac{1-|\lambda_{f}|^{2}}{1+|\lambda_{f}|^{2}},\,\,\,\,\,\,\,\,\,\,\,S_{f}\equiv\frac{2\Im\lambda_{f}}{1+|\lambda_{f}|^{2}}\,\,\,\,\,\mathrm{and}\,\,\,\,\,\,A^{\Delta\Gamma}_{f}\equiv-\frac{2\Re\lambda_{f}}{1+|\lambda_{f}|^{2}},\end{split}$

where $\lambda_{f}$ is given by

$\lambda_{f}\equiv\frac{q}{p}\frac{\bar{A}_{f}}{A_{f}}.$

The parameter $\lambda_{f}$ is thus related to $B^{0}_{(s)}$–${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}^{0}_{(s)}$ mixing (via $q/p$) and to
the decay amplitudes of the $B^{0}_{(s)}\rightarrow f$ decay ($A_{f}$) and of
the ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}}^{0}_{(s)}\rightarrow f$
decay ($\bar{A}_{f}$). With negligible $C\\!P$ violation in the mixing
($|q/p|=1$), the terms $C_{f}$ and $S_{f}$ parametrise $C\\!P$ violation in
the decay and in the interference between mixing and decay, respectively. The
following relation between $C_{f}$, $S_{f}$ and $A^{\Delta\Gamma}_{f}$ holds

$\left(C_{f}\right)^{2}+\left(S_{f}\right)^{2}+\left(A^{\Delta\Gamma}_{f}\right)^{2}=1.$

Notably, one has direct $C\\!P$ violation ($\bar{A}_{f}\neq A_{f}$) when
$C_{f}\neq 0$. But even in the case of suppressed $C\\!P$ violation in the
decay, it is still possible to observe $C\\!P$ violation if a relative phase
between $q/p$ and $\bar{A}_{f}/A_{f}$ exists. In such a case, one has
$S_{f}=\Im(q/p\times\bar{A}_{f}/A_{f})$. For example, for the
$B^{0}\rightarrow J/\psi K^{0}_{S}$ decay, to an approximation that is valid
in the SM at the percent level or below, one has $S_{B^{0}\rightarrow J/\psi
K^{0}_{S}}=\sin(\phi_{d})$ and $C_{B^{0}\rightarrow J/\psi K^{0}_{S}}=0$, with
$\phi_{d}=2\beta$. Similarly, for the $B^{0}_{s}\rightarrow J/\psi\phi$ decay,
$C\\!P$ violation in the interference between mixing and decay gives access to
$\phi_{s}=-2\beta_{s}$.

###  3.6 Experimental determination of the unitarity triangle

The experimental determination of the UT is here presented in brief. Many
excellent reviews are available in the literature [42, 47, 48, 49, 50], where
detailed discussions on the various topics can be found. Several pieces of
information must be combined by means of sophisticated fits in order to
determine the apex of the UT with the highest possible precision. Relevant
inputs to the fits are

  * •

$|\varepsilon_{K}|$: This parameter is determined by measuring indirect
$C\\!P$ violation in the neutral kaon mixing, using $K\rightarrow\pi\pi$,
$K\rightarrow\pi l\nu$, and $K^{0}_{L}\rightarrow\pi^{+}\pi^{-}e^{+}e^{-}$
decays, and provides a very important constraint on the position of the UT
apex.

  * •

$\left|V_{ub}\right|/\left|V_{cb}\right|$: The measurements of branching
fractions of semileptonic decays governed by $b\rightarrow ul\bar{\nu}$ and
$b\rightarrow cl\bar{\nu}$ transitions give information about the magnitudes
of $V_{ub}$ and $V_{cb}$, respectively. The ratio between these two quantities
constrains the side of the UT between the $\gamma$ and $\alpha$ angles.

  * •

$\Delta m_{d}$: This parameter represents the frequency of $B^{0}-\bar{B}^{0}$
mixing. It is proportional to the magnitude of $V_{td}$ and thus constrains
the side of the UT between the $\beta$ and $\alpha$ angles.

  * •

$\Delta m_{s}/\Delta m_{d}$: $\Delta m_{s}$ is the analogue of $\Delta m_{d}$
in the case of $B_{s}^{0}-\bar{B}_{s}^{0}$ mixing and its value is
proportional to the magnitude $V_{ts}$. However, in order to reduce
theoretical uncertainties on hadronic parameters determined using Lattice QCD
calculations, the use of the ratio $\Delta m_{s}/\Delta m_{d}$ is more
effective. This also provides a constraint on the side of the UT between the
$\beta$ and $\alpha$ angles.

  * •

$\sin(2\beta)$: This quantity is mainly determined from time-dependent
$C\\!P$-violation measurements of $B^{0}\rightarrow J/\psi K^{0}_{S}$ decays,
and provides a powerful constraint on the angle $\beta$ of the UT.

  * •

$\alpha$: This UT angle is determined from the measurements of
$C\\!P$-violating asymmetries and branching fractions in $B\rightarrow\pi\pi$,
$B\rightarrow\rho\rho$ and $B\rightarrow\rho\pi$ decays.

  * •

$\gamma$: The determination of this angle is performed by measuring time-
integrated $C\\!P$-violating asymmetries and branching fractions of
$B\rightarrow D^{(*)}K^{(*)}$ decays, and time-dependent $C\\!P$ violation in
$B^{0}_{s}\rightarrow D_{s}^{\pm}K^{\mp}$ decays.

Figure 4: Results of global CKM fits performed by the (left) CKMfitter [51] and (right) UTfit [45] groups. The 95% probability regions corresponding to each of the experimental measurements are indicated by filled areas of different colours. The various areas intersect in the position of the UT apex. Table 1: Results of global CKM fits by the CKMfitter [51] and UTfit [45] groups. Group | $A$ | $\lambda$ | $\bar{\rho}$ | $\bar{\eta}$
---|---|---|---|---
CKMfitter  | $0.810^{\>+\>0.018}_{\>-\>0.024}$ | $0.22548^{\>+\>0.00068}_{\>-\>0.00034}$ | $0.1453^{\>+\>0.0133}_{\>-\>0.0073}$ | $0.343^{\>+\>0.011}_{\>-\>0.012}$
UTfit | $0.821\pm 0.012$ | $0.22534\pm 0.00065$ | $0.132\pm 0.023$ | $0.352\pm 0.014$

World averages of the various experimental measurements are kept up to date by
the Heavy Flavour Averaging Group [42]. Each of these measurements yields a
constraint on the position of the UT apex, _i.e._ on the values of the
$\bar{\rho}$ and $\bar{\eta}$ parameters. Two independent groups, namely
CKMfitter [51] and UTfit [45], regularly perform global CKM fits starting from
the same set of experimental and theoretical inputs, but using different
statistical approaches. In particular, CKMfitter performs a frequentist
analysis, whereas UTfit follows a Bayesian method. Their latest results are
displayed in Fig. 4. Each of the experimental constraints is represented as a
95% probability region by a filled area of different colour. The intersection
of all regions identifies the position of the UT apex. The level of agreement
amongst the various regions in pinpointing the UT apex is also a measure of
the level of consistency of the KM mechanism with data. If (at least) one of
the areas were not in agreement with the others, that would be an indication
of the existence of BSM physics. At present, no striking evidence of any
disagreement is found. The latest values of $A$, $\lambda$, $\bar{\rho}$ and
$\bar{\eta}$ obtained by the CKMfitter and UTfit groups are reported in Table
1. Besides small fluctuations, also stemming from slightly different
theoretical inputs and statistical procedures, the two sets of results are in
good agreement.

##  4 Overview of beauty physics at the LHC

###  4.1 $C\\!P$ violation

Owing to the legacy of the $B$ factories [52], we have entered the era of
precision tests of CKM physics, where ultimate sensitivity is needed to search
for new sources of $C\\!P$ violation beyond the single phase of the CKM
matrix.

The LHC is often considered as a ${B}^{0}_{s}$-meson factory, due to the large
production cross-section and to the excellent capabilities of the LHC
experiments to precisely resolve ${B}^{0}_{s}$ oscillations. This has opened
the door to precision measurements of the $C\\!P$-violating phase
$\varphi_{s}^{{c}{\overline{c}}{s}}$, which is equal to $-2\beta_{s}$ in the
SM, neglecting sub-leading penguin contributions. It has been measured at the
LHC by ATLAS, CMS and LHCb using the flavour eigenstate decays
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}{{K}^{-}}$ [53, 54, 55] and
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ [56]. Recently LHCb has used the decay
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}{{K}^{-}}$ for the first time in a polarisation-dependent way
[57]. The quantity $\varphi_{s}^{{c}{\overline{c}}{s}}$ has also been measured
with a fully hadronic final state using the decay
${{B}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{-}_{s}}$ with
${{D}^{\pm}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{\pm}}$, yielding
$0.02\pm 0.17\pm 0.02$ rad [58]. Combining all determinations, LHCb obtains
$\varphi_{s}^{{c}{\overline{c}}{s}}=-0.010\pm 0.039$ rad. Including also other
results, and in particular those from ATLAS and CMS, the uncertainty is
further reduced, obtaining $\varphi_{s}^{{c}{\overline{c}}{s}}=-0.015\pm
0.035$ rad. The constraints on $\varphi_{s}^{{c}{\overline{c}}{s}}$ and on the
decay width difference $\Delta\Gamma_{s}$ are shown in Fig. 5, together with
the corresponding SM expectations.

Figure 5: Constraints on $\Delta\Gamma_{s}$ and
$\varphi_{s}^{{c}{\overline{c}}{s}}$ from various experiments.

With the precision reaching the degree level, the effects of suppressed
penguin topologies cannot be neglected anymore [59, 60, 61, 62, 63, 64]. Such
effects may lead to a shift $\delta\varphi_{s}$ in the measured value of
$\varphi_{s}^{{c}{\overline{c}}{s}}$, which can be constrained using Cabibbo-
suppressed decay modes, where penguin topologies are relatively more
prominent. This programme has started with studies of the decays
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ [65, 66],
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ [67] and more
recently ${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ [68]. These studies enable a constraint on
$\delta\varphi_{s}$ to be placed in the range $[-0.018,0.021]$ rad at 68% CL.
Considering the present uncertainty of $0.039$ rad, such a shift needs to be
to constrained further.

Another interesting test of the SM is provided by the measurement of the
mixing phase $\varphi_{s}^{{s}{\overline{s}}{s}}$ with a penguin-dominated
mode as ${{B}^{0}_{s}}\\!\rightarrow\phi\phi$. In this case the measured value
is $-0.17\pm 0.15\pm 0.03$ rad [69], which is compatible with the SM
expectation.

Similarly, the decays ${B}\\!\rightarrow hh$ with $h={\pi},{K}$ receive large
contributions from penguin topologies, and are sensitive to $\gamma$ and
$\beta_{s}$. LHCb for the first time measured time-dependent $C\\!P$-violating
observables in ${B}^{0}_{s}$ decays using the decay
${{B}^{0}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}$ [70]. Using methods outlined
in Refs. [71, 72, 64], a combination of this and other results from
$B\rightarrow\pi\pi$ modes enables the determination
$-2\beta_{s}=-0.12{\>}^{+{\>}0.14}_{-{\>}0.16}$ $\rm\,rad$ using as input the
angle $\gamma$ from tree-level decays (see below), or
$\gamma=(63.5{\>}^{+{\>}7.2}_{-{\>}6.7})^{\circ}$ relating $-2\beta_{s}$ to
the SM expectation [73]. These values are in principle sensitive to the amount
of U-spin (a subgroup of $SU(3)$ analogous to isospin, but involving $d$ and
$s$ quarks instead of $d$ and $u$ quarks) breaking in the involved decay
amplitudes and are given here for a maximum allowed breaking of 50%. This
value of $\gamma$ can be compared to that obtained from tree-dominated
${B}\\!\rightarrow{D}{K}$ decays, where the $C\\!P$-violating phase appears in
the interference of the ${b}\\!\rightarrow{c}$ and ${b}\\!\rightarrow{u}$
topologies. The determination of $\gamma$ from tree decays is considered free
from contributions beyond the SM and unaffected by hadronic uncertainties.
Yet, its precise measurement is important to test the consistency of the KM
mechanism, also allowing for comparisons with measurements from modes
dominated by penguin topologies.

The most precise determination of $\gamma$ from a single tree-level decay mode
is achieved with the decay ${{{B}^{+}}}\\!\rightarrow D{{K}^{+}}$ followed by
$D\\!\rightarrow{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{-}$ with
$h={\pi},{K}$ [74], yielding $\gamma=(62{\>}^{+{\>}15}_{-{\>}14})^{\circ}$.
Here the interference of the ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ decays to
${{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{-}$ is exploited to measure
$C\\!P$ asymmetries [75]. The method needs external input in the form of a
measurement of the strong phase over the Dalitz plane of the $D$ decay, coming
from CLEO-c data [76]. The same decay mode is also used in a model-dependent
measurement [77].

A different way for determining $\gamma$ is provided by the decay
${{B}^{0}_{s}}\\!\rightarrow D_{s}^{\pm}{K}^{\mp}$ [78, 79, 80, 81]. In this
case the phase is measured in a time-dependent tagged $C\\!P$-violation
analysis. Using a dataset corresponding to 1 $\mbox{\,fb}^{-1}$, LHCb
determines $\gamma=(115{\>}^{+{\>}28}_{-{\>}43})^{\circ}$, which is not yet
competitive with other methods but will provide important cross-checks with
more data.

The $\gamma$ measurements of Refs. [74, 81, 82, 83, 84, 85] are then combined
in an LHCb average [86]. Using all ${B}\\!\rightarrow D{K}$ decay modes one
finds $\gamma=(73{\>}^{+{\>}9}_{-{\>}10})^{\circ}$, which is more precise than
the corresponding combination of measurements from the $B$ factories [52]. The
LHCb likelihood profile is shown in Fig. 6.

Figure 6: LHCb combination of ${B}\\!\rightarrow D{K}$ decays measuring
$\gamma$ [86].

The same-sign dimuon asymmetry measured by the D0 collaboration [87] and
interpreted as a combination of the semileptonic asymmetries
$A_{\text{sl}}^{d}$ and $A_{\text{sl}}^{s}$ in ${B}^{0}$ and ${B}^{0}_{s}$
decays, respectively, differs from the SM expectation by $3\sigma$. So far
LHCb has not been able to confirm or disprove this result. The measurement
from LHCb looks at the $C\\!P$ asymmetry between partially reconstructed
${B}\\!\rightarrow{D}\mu\nu$ decays, where the flavour of the $D$ meson
identifies that of the $B$. The measured value of $A_{\text{sl}}^{s}$ [46] and
the newly reported $A_{\text{sl}}^{d}$ [88] are both consistent with the SM
and the D0 values. The world average including measurements from the $B$
factories and D0 is not more conclusive, as shown in Fig. 7.

Figure 7: Experimental constraints on $A_{\text{sl}}^{d}$ and
$A_{\text{sl}}^{s}$ from various experiments. The symbol $\ell$ stands for
electron or muon. The horizontal and vertical bands represent the
uncertainties on the averages of the experimental measurements. The elliptic
contour represents the measurement of the same-sign dimuon asymmetry by the D0
experiment.

Large $C\\!P$ violation has been found in charmless $b$-hadron decays like
${{{B}^{+}}}\\!\rightarrow h^{+}h^{-}h^{+}$ [89] ($h={\pi},{K}$) and
${{{B}^{+}}}\\!\rightarrow{p}{\overline{p}}h^{+}$ [90]. Particularly striking
features of these decays are the very large asymmetries observed in small
regions of the phase-space not related to any resonance, which are opposite in
sign for ${{B}^{\pm}}\\!\rightarrow h^{\pm}{{K}^{+}}{{K}^{-}}$ and
${{B}^{\pm}}\\!\rightarrow h^{\pm}{{\pi}^{+}}{{\pi}^{-}}$ decays. This
observation could be a sign of long-distance
${{\pi}^{+}}{{\pi}^{-}}\leftrightarrow{{K}^{+}}{{K}^{-}}$ rescattering.

Another important field is the study of $C\\!P$ violation in beauty baryons.
The probability that a $b$ quark hadronises to a ${\mathchar
28931\relax}^{0}_{b}$ baryon is measured to be surprisingly large at the LHC
in the forward region [91], almost half of that to a ${B}^{0}$ meson. These
baryons can be used for measurements of $C\\!P$ violation with better
precision than ${B}^{0}_{s}$ mesons. Searches have been performed by LHCb with
the decays ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{p}{{\pi}^{-}}$ [92], ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{{K}^{0}}{p}{{\pi}^{-}}$ [93], and by CDF
with ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}\pi^{-}$ and
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}K^{-}$ [94]. It is worth
noting that no evidence for $C\\!P$ violation in any decay of a baryon has
ever been reported to date.

###  4.2 Rare electroweak decays

The family of decays ${b}\\!\rightarrow{s}{\ell^{+}}{\ell^{-}}$ is a
laboratory for BSM-physics searches on its own. In particular the exclusive
decay ${{B}^{0}}\\!\rightarrow{{K}^{*0}}{\ell^{+}}{\ell^{-}}$ ($\ell=e,\mu$)
provides a very rich set of observables with different sensitivities to BSM
physics and for which the available SM predictions are affected by varying
levels of hadronic uncertainties. For some ratios of such observables, most of
the theoretical uncertainties cancel out, thus providing a clean test of the
SM [95, 96, 97, 98, 99, 100].

The differential decay width with respect to the dilepton mass squared
$q^{2}$, the forward-backward asymmetry $A_{\text{FB}}$, and the longitudinal
polarisation fraction $F_{\text{L}}$ of the ${K}^{*}$ resonance have been
measured by many experiments [101, 102, 103, 104, 105, 106] with no
significant sign of deviations from the SM expectation.

In a second analysis of the already published 2011 data [106], LHCb has
published another set of angular observables [107] suggested by Ref. [100]. In
particular a $3.7\sigma$ local deviation from the SM expectation of one of
these observables has been found in one bin of $q^{2}$. This measurement has
triggered a lot of interest in the theoretical community, with interpretation
articles being submitted very quickly to journals. See Refs. [108, 109, 110,
111, 112] for a small subset. It is not clear whether this discrepancy is an
experimental fluctuation, is due to under-estimated form factor uncertainties
(see Ref. [113]), or is the manifestation of a heavy $Z^{\prime}$ boson, among
many other suggested explanations. The contribution of $c$$\overline{c}$
resonances is also being questioned [114] after the LHCb observation of
${{{B}^{+}}}\\!\rightarrow\psi(4160){{K}^{+}}$ with
$\psi(4160)\\!\rightarrow{\mu^{+}\mu^{-}}$ [115], where the $\psi(4160)$ and
its interference with the non-resonant component accounts for 20% of the rate
for dimuon masses above 3770 ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Such
a large contribution was not expected.

Given a hint of abnormal angular distributions, LHCb tried to look for other
deviations in several asymmetry measurements. The $C\\!P$ asymmetry in
${{B}^{0}}\\!\rightarrow K^{(*)0}{\mu^{+}\mu^{-}}$ and
${{B}^{\pm}}\\!\rightarrow{{K}^{\pm}}{\mu^{+}\mu^{-}}$ decays turns out to be
compatible with zero as expected [116], as does the isospin asymmetry between
${{B}^{0}}\\!\rightarrow K^{(*)0}{\mu^{+}\mu^{-}}$ and
${{B}^{+}}\\!\rightarrow K^{(*)+}{\mu^{+}\mu^{-}}$ decays [117]. The lepton
universality factor $R_{K}=\frac{{\cal
B}({{{B}^{+}}}\\!\rightarrow{{K}^{+}}{\mu^{+}\mu^{-}})}{{\cal
B}({{{B}^{+}}}\\!\rightarrow{{K}^{+}}{e^{+}e^{-}})}$ is measured to be
$0.745{\>}^{+{\>}0.090}_{-{\>}0.074}\pm 0.036$ [118] in the
$1<q^{2}<6\>{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ range, which
indicates a $2.6\sigma$ deviation from unity. This result can be interpreted
as a possible indication of a new vector particle that would couple more
strongly to muons and interfere destructively with the SM vector current [119,
120, 121, 122, 123].

###  4.3 Observation of the $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ decay

The measurement of the branching fractions of the rare
$B^{0}\rightarrow\mu^{+}\mu^{-}$ and $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$
decays is considered amongst the most promising avenues to search for BSM
effects at the LHC. These decays proceed via FCNC processes and are highly
suppressed in the SM. Moreover, the helicity suppression of axial vector terms
makes them sensitive to scalar and pseudoscalar BSM contributions that can
alter their branching fractions with respect to SM expectations. The untagged
time-integrated SM predictions for the branching fractions of these decays are
[124]

$\displaystyle\mathcal{B}(B_{s}^{0}\rightarrow\mu^{+}\mu^{-})_{SM}=(3.66\pm
0.23)\times 10^{-9}\,,$
$\displaystyle\mathcal{B}(B^{0}\rightarrow\mu^{+}\mu^{-})_{SM}=(1.06\pm
0.09)\times 10^{-10}\,,$

which are obtained using the latest combination of values for the top-quark
mass from LHC and Tevatron experiments [125]. The ratio ${\mathcal{R}}$
between these two branching fractions is also a powerful tool to discriminate
amongst BSM models. In the SM it is predicted to be

$\displaystyle{\mathcal{R}}=\frac{{\cal
B}(B^{0}\rightarrow\mu^{+}\mu^{-})}{{\cal
B}(B_{s}^{0}\rightarrow\mu^{+}\mu^{-})}=\frac{\tau_{B^{0}}}{1/\Gamma_{H}^{s}}\left(\frac{f_{B^{0}}}{f_{B_{s}^{0}}}\right)^{2}\left|\frac{V_{td}}{V_{ts}}\right|^{2}\frac{M_{B^{0}}\sqrt{1-\tfrac{4m_{\mu}^{2}}{M_{B^{0}}^{2}}}}{M_{B_{s}^{0}}\sqrt{1-\tfrac{4m_{\mu}^{2}}{M_{B_{s}^{0}}^{2}}}}=0.0295^{\>+\>0.0028}_{\>-\>0.0025}\,,$

where $\tau_{B^{0}}$ and $1/\Gamma_{H}^{s}$ are the lifetimes of the $B^{0}$
and of the heavy mass eigenstate of the $B^{0}_{s}$–${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}^{0}_{s}$ system, $M_{B_{(s)}^{0}}$ is
the mass and $f_{B_{(s)}^{0}}$ is the decay constant of the $B_{(s)}^{0}$
meson, $V_{td}$ and $V_{ts}$ are the elements of the CKM matrix and $m_{\mu}$
is the mass of the muon. In minimal flavour-violating BSM scenarios, the
branching fractions of both decays can change, but their ratio is predicted to
be equal to that of the SM.

The LHCb collaboration reported the first evidence of the
$B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$ decay with a $3.5\,\sigma$ significance
in 2012 using 2$\,\mathrm{fb}^{-1}$ of data [126]. One year later, CMS and
LHCb presented their updated results based on 25$\,\mathrm{fb}^{-1}$ and
3$\,\mathrm{fb}^{-1}$, respectively [127, 128]. The two measurements resulted
in good agreement with comparable precisions. However, none of them was
precise enough to claim the first observation of the
$B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$ decay. A naïve combination of CMS and
LHCb results was presented in 2013 [129], but no attempt was made to take into
account all correlations stemming from common physical quantities, and no
statistical significance for the existence of the signals was provided.

More recently, a combination of the CMS and LHCb results based on a
simultaneous fit to the two datasets has been performed. This fit correctly
takes into account correlations between the input parameters. The CMS and LHCb
experiments have very similar analysis strategies.
$B_{(s)}^{0}\rightarrow\mu^{+}\mu^{-}$ candidates are selected as two
oppositely charged tracks. A soft first selection is applied in order to
reduce the background while keeping high the efficiency on the signal. After
this selection, the remaining backgrounds are mainly due to random
combinations of muons from semileptonic $B$ decays (combinatorial background),
semileptonic decays, such as $B\rightarrow h\mu\nu$, $B\rightarrow h\mu\mu$
and $\Lambda^{0}_{b}\rightarrow p\mu^{-}\bar{\nu}$, and
$B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ decays (peaking background)
where hadrons are misidentified as muons. Further separation between signal
and background is achieved exploiting the power of a multivariate classifier.
The classification of the events is done using the dimuon invariant mass
$m_{\mu\mu}$ and the multivariate classifier output. The multivariate
classifier is trained using kinematic and geometrical variables. The
calibration of the dimuon mass $m_{\mu\mu}$ is performed using the dimuon
resonances and, for LHCb, also by using $B^{0}_{(s)}\rightarrow
h^{+}h^{{}^{\prime}-}$ decays. For both analyses the
$B_{(s)}^{0}\rightarrow\mu^{+}\mu^{-}$ yield is normalised with respect to the
$B^{+}\rightarrow J/\psi K^{+}$ yield, taking into account the hadronisation
fractions of a $b$ quark to $B_{s}^{0}$ and $B^{0}$ mesons measured by the
LHCb experiment [130, 131, 132]. LHCb also uses the $B^{0}\rightarrow
K^{+}\pi^{-}$ decay as a normalisation channel.

A simultaneous fit is performed to evaluate the branching fractions of the
$B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$ and $B^{0}\rightarrow\mu^{+}\mu^{-}$
decays. The CMS and LHCb datasets are used together as in a single combined
experiment. A simultaneous unbinned extended maximum likelihood fit is
performed to the invariant mass spectrum in 20 categories of multivariate
classifier output for the two experiments: 8 categories for LHCb and 12
categories for CMS. The various categories are characterised by construction
by different values of signal purity. In each category the mass spectrum is
described as the sum of each background source and the two signals. The
parameters shared between the two experiments are the branching fractions of
the two signal decays being looked for, ${\cal
B}(B_{s}^{0}\rightarrow\mu^{+}\mu^{-})$ and ${\cal
B}(B^{0}\rightarrow\mu^{+}\mu^{-})$, the already measured branching fraction
of the common normalisation channel ${\cal B}(B^{+}\rightarrow J/\psi K^{+})$,
and the ratio of the hadronisation fractions $f_{s}/f_{d}$. Assuming the SM,
$94\pm 7$ $B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$ events and $10.5\pm 0.6$
$B^{0}\rightarrow\mu^{+}\mu^{-}$ events are expected in the full dataset. For
illustrative purposes, Fig. 8 shows the dimuon mass distribution for the
events corresponding to the six multivariate categories with highest
$B^{0}_{s}$ signal purity. The results of the simultaneous fit are [133]

$\displaystyle\mathcal{B}(B_{s}^{0}\rightarrow\mu^{+}\mu^{-})=\left(2.8^{\>+\>0.7}_{\>-\>0.6}\right)\times
10^{-9}\,,$
$\displaystyle\mathcal{B}(B^{0}\rightarrow\mu^{+}\mu^{-})=\left(3.9^{\>+\>1.6}_{\>-\>1.4}\right)\times
10^{-10}\,.$

The statistical significances, evaluated using the Wilks’ theorem [134], are
$6.2\,\sigma$ and $3.2\,\sigma$ for $B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$ and
$B^{0}\rightarrow\mu^{+}\mu^{-}$, respectively. The expected significances
assuming the SM branching fractions are $7.4\,\sigma$ and $0.8\,\sigma$ for
$B_{s}^{0}$ and $B^{0}$ channels, respectively.

Figure 8: Dimuon mass distribution for the six multivariate-classifier
categories with highest $B_{s}^{0}$ signal purity. The result of the
simultaneous fit is overlaid.

Since the Wilks’ theorem shows a $B^{0}\rightarrow\mu^{+}\mu^{-}$ signal
significance slightly above the $3\,\sigma$ level, a more refined method based
on the Feldman-Cousins construction [135] is also used for the
$B^{0}\rightarrow\mu^{+}\mu^{-}$ mode. A statistical significance of
$3.0\,\sigma$ is obtained in this case. The Feldman-Cousins confidence
intervals at $\pm 1\,\sigma$ and $\pm 2\,\sigma$ are $[2.5,5.6]\times
10^{-10}$ and $[1.4,7.4]\times 10^{-10}$, respectively. In Fig. 9 the
likelihood contours in the ${\cal
B}(B_{s}^{0}\rightarrow\mu^{+}\mu^{-})$–${\cal
B}(B^{0}\rightarrow\mu^{+}\mu^{-})$ plane are shown. In the same figure, the
likelihood profile for each signal mode is displayed.

Figure 9: (left) Likelihood contours in the ${\cal
B}(B_{s}^{0}\rightarrow\mu^{+}\mu^{-})$–${\cal
B}(B^{0}\rightarrow\mu^{+}\mu^{-})$ plane. Likelihood profile for (top-right)
${\cal B}(B_{s}^{0}\rightarrow\mu^{+}\mu^{-})$ and (bottom-right) ${\cal
B}(B^{0}\rightarrow\mu^{+}\mu^{-})$. The dark and light areas define the $\pm
1\,\sigma$ and $\pm 2\,\sigma$ confidence intervals, respectively. The SM
expectations are indicated with vertical bands.

The compatibility of ${\cal B}(B_{s}^{0}\rightarrow\mu^{+}\mu^{-})$ and ${\cal
B}(B^{0}\rightarrow\mu^{+}\mu^{-})$ with the SM is evaluated at the
$1.2\,\sigma$ and $2.2\,\sigma$ levels, respectively. A separate fit to the
ratio of $B^{0}$ to $B_{s}^{0}$ gives
${\mathcal{R}}=0.14^{\>+\>0.08}_{\>-\>0.06}$, which is compatible with the SM
at the $2.3\,\sigma$ level. The likelihood profile for ${\mathcal{R}}$ is
shown in Fig. 10.

Figure 10: Likelihood profile for ${\mathcal{R}}$. The dark and light areas
define the $\pm 1\,\sigma$ and $\pm 2\,\sigma$ confidence intervals,
respectively. The SM expectation is indicated with a vertical band.

##  5 Conclusions

The LHC is the new $b$-hadron factory. The ATLAS, CMS and LHCb experiments
will be dominating heavy-flavour physics in the next decade, together with the
forthcoming Belle II experiment, and even beyond with the high luminosity LHC
phase. During Run I, ATLAS, CMS and LHCb have performed fundamental
measurements in the field of $C\\!P$ violation and rare decays of $B$ mesons.
In this paper we have discussed some of these measurements, notably including
that of the $B^{0}_{s}$-meson mixing phase from $b\rightarrow c\bar{c}s$
decays, $\varphi_{s}^{c\bar{c}s}$; of the UT angle $\gamma$ from tree-level
decays; of $B^{0}$ and $B^{0}_{s}$ semileptonic asymmetries; of angular
observables in $b\rightarrow s{\ell^{+}}{\ell^{-}}$ transitions; and of the
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ branching fraction, with the first
observation of this decay at more than five standard deviations. No striking
evidences of deviations from SM expectations have emerged from any of these
measurements so far. However, they have enabled strong constraints to be set
on many BSM models. The upcoming Run II, with its higher centre-of-mass energy
translating into a higher $b$$\overline{b}$ cross-section, will witness
substantial improvements in the study of $B$ physics, and will hopefully lead
to the observation of new physics phenomena not accounted for in the SM.

Heavy flavour physics in the quark sector is not limited to beauty hadrons
alone. The LHC is also an abundant source of charmed hadrons, which provide
another interesting laboratory for BSM-physics searches. The recent
experimental improvements in the measurement of mixing-related observables of
$D^{0}$ mesons at LHCb have raised the interest for $C\\!P$-violation
measurements in this sector. Belle II and LHCb, with its upgraded detector
that will be operational in the third LHC run, will probe $C\\!P$ violation in
charm mixing with ultimate precision. The top quark is also another excellent
tool for seeking BSM physics. The unprecedented samples collected by the ATLAS
and CMS experiments will enable relevant studies of $C\\!P$ violation in top-
quark production and decays to be carried out.

## References

  * [1] A. D. Sakharov, _Violation of $C\\!P$ invariance, $C$ asymmetry, and baryon asymmetry of the universe_, Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32
  * [2] A. G. Cohen, D. B. Kaplan, and A. E. Nelson, _Progress in electroweak baryogenesis_ , Ann. Rev. Nucl. Part. Sci. 43 (1993) 27, arXiv:hep-ph/9302210
  * [3] A. Riotto and M. Trodden, _Recent progress in baryogenesis_ , Ann. Rev. Nucl. Part. Sci. 49 (1999) 35, arXiv:hep-ph/9901362
  * [4] W.-S. Hou, _Source of $C\\!P$ violation for the baryon asymmetry of the universe_, Chin. J. Phys. 47 (2009) 134, arXiv:0803.1234
  * [5] ATLAS collaboration, G. Aad et al., _Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC_ , Phys. Lett. B716 (2012) 1, arXiv:1207.7214
  * [6] CMS collaboration, S. Chatrchyan et al., _Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC_ , Phys. Lett. B716 (2012) 30, arXiv:1207.7235
  * [7] ATLAS collaboration, G. Aad et al., _The ATLAS Experiment at the CERN Large Hadron Collider_ , JINST 3 (2008) S08003
  * [8] CMS collaboration, S. Chatrchyan et al., _The CMS experiment at the CERN LHC_ , JINST 3 (2008) S08004
  * [9] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_ , JINST 3 (2008) S08005
  * [10] M. Kobayashi and T. Maskawa, _$C\\!P$ violation in the renormalizable theory of weak interaction_, Prog. Theor. Phys. 49 (1973) 652
  * [11] N. Cabibbo, _Unitary symmetry and leptonic decays_ , Phys. Rev. Lett. 10 (1963) 531
  * [12] S. L. Glashow, J. Iliopoulos, and L. Maiani, _Weak interactions with lepton-hadron symmetry_ , Phys. Rev. D2 (1970) 1285
  * [13] J. J. Aubert et al., _Experimental observation of a heavy particle J_ , Phys. Rev. Lett. 33 (1974) 1404
  * [14] J. E. Augustin et al., _Discovery of a narrow resonance in $e^{+}e^{-}$ annihilation_, Phys. Rev. Lett. 33 (1974) 1406
  * [15] S. W. Herb et al., _Observation of a Dimuon Resonance at 9.5-GeV in 400-GeV Proton-Nucleus Collisions_ , Phys. Rev. Lett. 39 (1977) 252
  * [16] CDF collaboration, F. Abe et al., _Observation of top quark production in $\bar{p}p$ collisions_, Phys. Rev. Lett. 74 (1995) 2626, arXiv:hep-ex/9503002
  * [17] J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, _Evidence for the $2{\pi}$ Decay of the $\rm K_{2}^{0}$ Meson_, Phys. Rev. Lett. 13 (1964) 138
  * [18] CLEO collaboration, D. Andrews et al., _The CLEO detector_ , Nucl. Instrum. Meth. 211 (1983) 47
  * [19] A. B. Carter and A. I. Sanda, _$C\\!P$ violation in $B$ meson decays_, Phys. Rev. D23 (1981) 1567
  * [20] I. I. Y. Bigi and A. I. Sanda, _On ${B}^{0}$–${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mixing and violations of $C\\!P$ symmetry_, Phys. Rev. D29 (1984) 1393
  * [21] ARGUS collaboration, H. Albrecht et al., _ARGUS: A universal detector at DORIS-II_ , Nucl. Instrum. Meth. A275 (1989) 1
  * [22] P. Oddone, _Detector considerations_ , eConf C870126 (1987) 423
  * [23] BaBar collaboration, B. Aubert et al., _The BaBar detector_ , Nucl. Instrum. Meth. A479 (2002) 1, arXiv:hep-ex/0105044
  * [24] A. Abashian et al., _The Belle detector_ , Nucl. Instrum. Meth. A479 (2002) 117
  * [25] ALEPH collaboration, D. Decamp et al., _ALEPH: A detector for electron-positron annnihilations at LEP_ , Nucl. Instrum. Meth. A294 (1990) 121
  * [26] DELPHI collaboration, P. A. Aarnio et al., _The DELPHI detector at LEP_ , Nucl. Instrum. Meth. A303 (1991) 233
  * [27] L3 collaboration, _The Construction of the L3 Experiment_ , Nucl. Instrum. Meth. A289 (1990) 35
  * [28] OPAL collaboration, K. Ahmet et al., _The OPAL detector at LEP_ , Nucl. Instrum. Meth. A305 (1991) 275
  * [29] SLD collaboration, _SLD design report_ , , SLAC Report-273
  * [30] G. J. Barker, _b-physics at LEP_ , Springer Tracts Mod. Phys. 236 (2010) 1
  * [31] P. C. Rowson, D. Su, and S. Willocq, _Highlights of the SLD physics program at the SLAC linear collider_ , Ann. Rev. Nucl. Part. Sci. 51 (2001) 345, arXiv:hep-ph/0110168
  * [32] M. Paulini, _$B$ lifetimes, mixing and $C\\!P$ violation at CDF_, Int. J. Mod. Phys. A14 (1999) 2791, arXiv:hep-ex/9903002
  * [33] BaBar collaboration, B. Aubert et al., _Measurement of time-dependent $C\\!P$ asymmetry in $B^{0}\rightarrow c\bar{c}K^{(*)0}$ decays_, Phys. Rev. D79 (2009) 072009, arXiv:0902.1708
  * [34] I. Adachi et al., _Precise measurement of the $C\\!P$ violation parameter $\sin 2\phi_{1}$ in $B^{0}\rightarrow(c\bar{c})K^{0}$ decays_, Phys. Rev. Lett. 108 (2012) 171802, arXiv:1201.4643
  * [35] T. Kuhr, _Flavor physics at the Tevatron_ , Springer Tracts Mod. Phys. 249 (2013) 1
  * [36] CDF collaboration, A. Abulencia et al., _Observation of ${B}^{0}_{s}$–${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ Oscillations_, Phys. Rev. Lett. 97 (2006) 242003, arXiv:hep-ex/0609040
  * [37] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [38] R. Aaij et al., _The LHCb trigger and its performance in 2011_ , JINST 8 (2013) P04022, arXiv:1211.3055
  * [39] C. Jarlskog, _Commutator of the quark mass matrices in the Standard Electroweak Model and a measure of maximal $C\\!P$ violation_, Phys. Rev. Lett. 55 (1985) 1039
  * [40] L. Wolfenstein, _Parametrization of the Kobayashi-Maskawa matrix_ , Phys. Rev. Lett. 51 (1983) 1945
  * [41] Particle Data Group, K. A. Olive et al., _Review of particle physics_ , Chin. Phys. C38 (2014) 090001
  * [42] Heavy Flavor Averaging Group, Y. Amhis et al., _Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2014_, arXiv:1412.7515, updated results and plots available at http://www.slac.stanford.edu/xorg/hfag/
  * [43] Y. Xie, P. Clarke, G. Cowan, and F. Muheim, _Determination of $2\beta_{s}$ in ${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}{{K}^{-}}$ decays in the presence of a ${{K}^{+}}{{K}^{-}}$ S-wave contribution_, JHEP 0909 (2009) 074, arXiv:0908.3627
  * [44] LHCb collaboration, R. Aaij et al., _Determination of the sign of the decay width difference in the $B^{0}_{s}$ system_, Phys. Rev. Lett. 108 (2012) 241801, arXiv:1202.4717
  * [45] UTfit collaboration, M. Bona et al., _The unitarity triangle fit in the Standard Model and hadronic parameters from Lattice QCD: a reappraisal after the measurements of $\Delta m_{s}$ and BR$(B\rightarrow\tau\nu)$_, JHEP 0610 (2006) 081, arXiv:hep-ph/0606167
  * [46] LHCb collaboration, R. Aaij et al., _Measurement of the flavour-specific $C\\!P$-violating asymmetry $a_{\mathrm{sl}}^{s}$ in $B_{s}^{0}$ decays_, Phys. Lett. B728 (2014) 607, arXiv:1308.1048
  * [47] M. Ciuchini and A. Stocchi, _Physics Opportunities at the Next Generation of Precision Flavor Physics_ , Ann. Rev. Nucl. Part. Sci. 61 (2011) 491, arXiv:1110.3920
  * [48] Particle Data Group, K. A. Olive et al., _Review of Particle Physics_ , Chin. Phys. C38 (2014) 090001
  * [49] LHCb collaboration, R. Aaij et al., _Implications of LHCb measurements and future prospects_ , Eur. Phys. J. C73 (2013), no. 4 2373, arXiv:1208.3355
  * [50] R. Fleischer, _$C\\!P$ violation in the $B$ system and relations to $K\rightarrow\pi\nu\bar{\nu}$ decays_, Phys. Rept. 370 (2002) 537, arXiv:hep-ph/0207108
  * [51] J. Charles et al., _Current status of the Standard Model CKM fit and constraints on $\Delta F=2$ new physics_, arXiv:1501.05013
  * [52] BaBar collaboration, Belle collaboration, A. J. Bevan et al., _The physics of the $B$ factories_, arXiv:1406.6311
  * [53] ATLAS collaboration, G. Aad et al., _Flavour tagged time dependent angular analysis of the $B_{s}^{0}\rightarrow J/\psi\phi$ decay and extraction of $\Delta\Gamma$ and the weak phase $\phi_{s}$ in ATLAS_, Phys. Rev. D90 (2014) 052007, arXiv:1407.1796
  * [54] CMS collaboration, _Measurement of the $C\\!P$-violating weak phase $\phi_{s}$ and the decay width difference $\Delta\Gamma_{s}$ using the $B_{s}^{0}\rightarrow J/\psi\phi(1020)$ decay channel_, 2014\.  CMS-PAS-BPH-13-012
  * [55] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ violation and the $B^{0}_{s}$ meson decay width difference with $B_{s}^{0}\rightarrow J/\psi K^{+}K^{-}$ and $B_{s}^{0}\rightarrow J/\psi\pi^{+}\pi^{-}$ decays_, Phys. Rev. D87 (2013) 112010, arXiv:1304.2600
  * [56] LHCb collaboration, R. Aaij et al., _Measurement of the $C\\!P$-violating phase $\phi_{s}$ in $\overline{B}^{0}_{s}\rightarrow J/\psi\pi^{+}\pi^{-}$ decays_, Phys. Lett. B736 (2014) 186, arXiv:1405.4140
  * [57] LHCb collaboration, R. Aaij et al., _Precision measurement of $C\\!P$ violation in $B_{s}^{0}\rightarrow J/\psi K^{+}K^{-}$ decays_, Phys. Rev. Lett. 114 (2015) 041801, arXiv:1411.3104
  * [58] LHCb collaboration, R. Aaij et al., _Measurement of the $C\\!P$-violating phase $\phi_{s}$ in $\overline{B}^{0}_{s}\rightarrow D_{s}^{+}D_{s}^{-}$ decays_, Phys. Rev. Lett. 113 (2014) 211801, arXiv:1409.4619
  * [59] R. Fleischer, _Extracting $\gamma$ from $B_{s(d)}\rightarrow J/\psi K_{S}$ and $B_{d(s)}\rightarrow D^{+}_{(d/s)}D^{-}_{(d/s)}$_, Eur. Phys. J. C10 (1999) 299, arXiv:hep-ph/9903455
  * [60] R. Fleischer, _Extracting CKM phases from angular distributions of $B_{(d,s)}$ decays into admixtures of $C\\!P$ eigenstates_, Phys. Rev. D60 (1999) 073008, arXiv:hep-ph/9903540
  * [61] R. Fleischer, _Recent theoretical developments in $C\\!P$ violation in the $B$ system_, Nucl. Instrum. Meth. A446 (2000) 1, arXiv:hep-ph/9908340
  * [62] S. Faller, M. Jung, R. Fleischer, and T. Mannel, _The golden modes ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K_{(S,L)}$ in the era of precision flavour physics_, Phys. Rev. D79 (2009) 014030, arXiv:0809.0842
  * [63] K. De Bruyn, R. Fleischer, and P. Koppenburg, _Extracting $\gamma$ and penguin topologies through $C\\!P$ violation in ${B}^{0}_{s}$ $\rightarrow$ ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$${K}^{0}_{\rm\scriptscriptstyle S}$_, Eur. Phys. J. C70 (2010) 1025, arXiv:1010.0089
  * [64] M. Ciuchini, M. Pierini, and L. Silvestrini, _The Effect of penguins in the ${{B}^{0}}\rightarrow J/\psi{{K}^{0}}$ $C\\!P$ asymmetry_, Phys. Rev. Lett. 95 (2005) 221804, arXiv:hep-ph/0507290
  * [65] LHCb collaboration, R. Aaij et al., _Measurement of the effective $B^{0}_{s}\rightarrow J/\psi K^{0}_{S}$ lifetime_, Nucl. Phys. B873 (2013) 275, arXiv:1304.4500
  * [66] LHCb collaboration, R. Aaij et al., _Measurement of the time-dependent $C\\!P$ asymmetries in $B_{s}^{0}\rightarrow J/\psi K_{S}^{0}$_, JHEP 06 (2015) 131, arXiv:1503.07055
  * [67] LHCb collaboration, R. Aaij et al., _Measurement of the $B^{0}_{s}\rightarrow J/\psi\overline{K}^{*0}$ branching fraction and angular amplitudes_, Phys. Rev. D86 (2012) 071102(R), arXiv:1208.0738
  * [68] LHCb collaboration, R. Aaij et al., _Measurement of the $C\\!P$-violating phase $\beta$ in $\overline{B}^{0}\rightarrow J/\psi\pi^{+}\pi^{-}$ decays and limits on penguin effects_, Phys. Lett. B742 (2015) 38, arXiv:1411.1634
  * [69] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ violation in $B_{s}^{0}\rightarrow\phi\phi$ decays_, Phys. Rev. D90 (2014) 052011, arXiv:1407.2222
  * [70] LHCb collaboration, R. Aaij et al., _First measurement of time-dependent $C\\!P$ violation in $B_{s}^{0}\rightarrow K^{+}K^{-}$ decays_, JHEP 10 (2013) 183, arXiv:1308.1428
  * [71] R. Fleischer, _New strategies to extract $\beta$ and $\gamma$ from ${{B}^{0}}\rightarrow\pi^{+}\pi^{-}$ and ${{B}^{0}_{s}}\rightarrow K^{+}K^{-}$_, Phys. Lett. B459 (1999) 306, arXiv:hep-ph/9903456
  * [72] R. Fleischer, _$B_{s,d}^{0}\rightarrow\pi\pi,\pi K,KK$ : Status and Prospects_, Eur. Phys. J. C52 (2007) 267, arXiv:0705.1121
  * [73] LHCb collaboration, R. Aaij et al., _First observation of $\overline{B}^{0}\rightarrow J/\psi K^{+}K^{-}$ and search for $\overline{B}^{0}\rightarrow J/\psi\phi$ decays_, Phys. Rev. D88 (2013) 072005, arXiv:1308.5916
  * [74] LHCb collaboration, R. Aaij et al., _Measurement of the CKM angle $\gamma$ using $B^{\pm}\rightarrow DK^{\pm}$ with $D\rightarrow K_{S}^{0}\pi^{+}\pi^{-}$, $K_{S}^{0}K^{+}K^{-}$ decays_, JHEP 10 (2014) 097, arXiv:1408.2748
  * [75] A. Giri, Y. Grossman, A. Soffer, and J. Zupan, _Determining $\gamma$ using ${{B}^{\pm}}\rightarrow D{{K}^{\pm}}$ with multibody $D$ decays_, Phys. Rev. D68 (2003) 054018, arXiv:hep-ph/0303187
  * [76] CLEO collaboration, J. Libby et al., _Model-independent determination of the strong-phase difference between $D^{0}$ and $\bar{D}^{0}\rightarrow K^{0}_{S,L}h^{+}h^{-}$ ($h=\pi,K$) and its impact on the measurement of the CKM angle $\gamma/\phi_{3}$_, Phys. Rev. D82 (2010) 112006, arXiv:1010.2817
  * [77] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ violation and constraints on the CKM angle $\gamma$ in $B^{\pm}\rightarrow DK^{\pm}$ with $D\rightarrow K_{S}^{0}\pi^{+}\pi^{-}$ decays_, Nucl. Phys. B888 (2014) 169, arXiv:1407.6211
  * [78] I. Dunietz and R. G. Sachs, _Asymmetry between inclusive charmed and anticharmed modes in ${B}^{0}$, ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decay as a measure of $C\\!P$ violation_, Phys. Rev. D37 (1988) 3186
  * [79] R. Aleksan, I. Dunietz, and B. Kayser, _Determining the $C\\!P$ violating phase gamma_, Z. Phys. C54 (1992) 653
  * [80] R. Fleischer, _New strategies to obtain insights into $C\\!P$ violation through ${{B}^{0}_{s}}\rightarrow{{D}^{\pm}_{s}}{{K}^{\mp}},D_{s}^{*\pm}{{K}^{\mp}}$, …and ${{B}^{0}}\rightarrow D^{\pm}\pi^{\mp},{D}^{*\pm}\pi^{\mp}$, …decays_, Nucl. Phys. B671 (2003) 459, arXiv:hep-ph/0304027
  * [81] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ asymmetry in $B^{0}_{s}\rightarrow D^{\mp}_{s}K^{\pm}$ decays_, JHEP 11 (2014) 060, arXiv:1407.6127
  * [82] LHCb collaboration, R. Aaij et al., _Observation of $C\\!P$ violation in $B^{\pm}\rightarrow DK^{\pm}$ decays_, Phys. Lett. B712 (2012) 203, Erratum ibid. B713 (2012) 351, arXiv:1203.3662
  * [83] LHCb collaboration, R. Aaij et al., _Observation of the suppressed ADS modes $B^{\pm}\rightarrow[\pi^{\pm}K^{\mp}\pi^{+}\pi^{-}]_{D}K^{\pm}$ and $B^{\pm}\rightarrow[\pi^{\pm}K^{\mp}\pi^{+}\pi^{-}]_{D}\pi^{\pm}$_, Phys. Lett. B723 (2013) 44, arXiv:1303.4646
  * [84] LHCb collaboration, R. Aaij et al., _A study of $C\\!P$ violation in $B^{\pm}\rightarrow DK^{\pm}$ and $B^{\pm}\rightarrow D\pi^{\pm}$ decays with $D\rightarrow K^{0}_{S}K^{\pm}\pi^{\mp}$ final states_, Phys. Lett. B733 (2014) 36, arXiv:1402.2982
  * [85] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ violation parameters in $B^{0}\rightarrow DK^{*0}$ decays_, Phys. Rev. D90 (2014) 112002, arXiv:1407.8136
  * [86] LHCb collaboration, _Improved constraints on $\gamma$: CKM2014 update_, Sep, 2014.  LHCb-CONF-2014-004
  * [87] D0 collaboration, V. M. Abazov et al., _Study of $C\\!P$-violating charge asymmetries of single muons and like-sign dimuons in $p\bar{p}$ collisions_, Phys. Rev. D89 (2014), no. 1 012002, arXiv:1310.0447
  * [88] LHCb collaboration, R. Aaij et al., _Measurement of the semileptonic $C\\!P$ asymmetry in $B^{0}$–$\overline{B}^{0}$ mixing_, Phys. Rev. Lett. 114 (2015) 041601, arXiv:1409.8586
  * [89] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ violation in the three-body phase space of charmless $B^{\pm}$ decays_, Phys. Rev. D90 (2014) 112004, arXiv:1408.5373
  * [90] LHCb collaboration, R. Aaij et al., _Evidence for $C\\!P$ violation in $B^{+}\rightarrow p\overline{p}K^{+}$ decays_, Phys. Rev. Lett. 113 (2014) 141801, arXiv:1407.5907
  * [91] LHCb collaboration, R. Aaij et al., _Study of the kinematic dependences of $\Lambda_{b}^{0}$ production in $pp$ collisions and a measurement of the $\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$ branching fraction_, JHEP 08 (2014) 143, arXiv:1405.6842
  * [92] LHCb collaboration, R. Aaij et al., _Observation of the $\Lambda_{b}^{0}\rightarrow J/\psi p\pi^{-}$ decay_, JHEP 07 (2014) 103, arXiv:1406.0755
  * [93] LHCb collaboration, R. Aaij et al., _Searches for $\Lambda^{0}_{b}$ and $\Xi^{0}_{b}$ decays to $K^{0}_{S}p\pi^{-}$ and $K^{0}_{S}pK^{-}$ final states with first observation of the $\Lambda^{0}_{b}\rightarrow K^{0}_{S}p\pi^{-}$ decay_, JHEP 04 (2014) 087, arXiv:1402.0770
  * [94] CDF collaboration, T. Aaltonen et al., _Measurements of direct $C\\!P$ violating asymmetries in charmless decays of strange bottom mesons and bottom baryons_, Phys. Rev. Lett. 106 (2011) 181802, arXiv:1103.5762
  * [95] A. Ali, P. Ball, L. Handoko, and G. Hiller, _A comparative study of the decays ${B}\rightarrow({K},{{K}^{*}}){\ell^{+}}{}{\ell^{-}}$ in the Standard Model and supersymmetric theories_, Phys. Rev. D61 (2000) 074024, arXiv:hep-ph/9910221
  * [96] Frank Krüger and Joaquim Matias, _Probing new physics via the transverse amplitudes of ${B}{}\rightarrow{{K}^{*}}{}({K}{}{{\pi}^{+}}{})\ell{}\ell$ at large recoil_, Phys. Rev. D71 (2005) 094009, arXiv:hep-ph/0502060
  * [97] W. Altmannshofer et al., _Symmetries and asymmetries of $B\rightarrow K^{*}\mu^{+}\mu^{-}$ decays in the Standard Model and beyond_, JHEP 0901 (2009) 019, arXiv:0811.1214
  * [98] U. Egede et al., _New observables in the decay mode $\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ $\rightarrow$ ${\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*}$$\ell^{+}$$\ell^{-}$_, JHEP 0811 (2008) 032, arXiv:0807.2589
  * [99] C. Bobeth, G. Hiller, and G. Piranishvili, _$C\\!P$ asymmetries in $\bar{B}\rightarrow\bar{K}^{*}(\rightarrow\bar{K}\pi)\bar{\ell}\ell$ and untagged $\bar{B}_{s}$, $B_{s}\rightarrow\phi(\rightarrow K^{+}K^{-})\bar{\ell}\ell$ decays at NLO_, JHEP 0807 (2008) 106, arXiv:0805.2525
  * [100] S. Descotes-Genon, T. Hurth, J. Matias, and J. Virto, _Optimizing the basis of ${B}\rightarrow{K}^{*}\ell^{+}\ell^{-}$ observables in the full kinematic range_, JHEP 1305 (2013) 137, arXiv:1303.5794
  * [101] BaBar collaboration, B. Aubert et al., _Measurements of branching fractions, rate asymmetries, and angular distributions in the rare decays $B\rightarrow K\ell^{+}\ell^{-}$ and $B\rightarrow K^{*}\ell^{+}\ell^{-}$_, Phys. Rev. D73 (2006) 092001, arXiv:hep-ex/0604007
  * [102] Belle collaboration, J.-T. Wei et al., _Measurement of the Differential Branching Fraction and Forward-Backward Asymmetry for $B\rightarrow{{K}^{*}}\ell^{+}\ell^{-}$_, Phys. Rev. Lett. 103 (2009) 171801, arXiv:0904.0770
  * [103] CDF collaboration, T. Aaltonen et al., _Measurements of the Angular Distributions in the Decays $B\rightarrow K^{(*)}\mu^{+}\mu^{-}$ at CDF_, Phys. Rev. Lett. 108 (2012) 081807, arXiv:1108.0695
  * [104] CMS collaboration, S. Chatrchyan et al., _Angular analysis and branching fraction measurement of the decay $B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$_, Phys. Lett. B727 (2013) 77, arXiv:1308.3409
  * [105] ATLAS collaboration, _Angular analysis of $B_{d}\rightarrow K^{\ast 0}\mu^{+}\mu^{-}$ with the ATLAS experiment_, Apr, 2013.  ATLAS-CONF-2013-038
  * [106] LHCb collaboration, R. Aaij et al., _Differential branching fraction and angular analysis of the decay $B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$_, JHEP 08 (2013) 131, arXiv:1304.6325
  * [107] LHCb collaboration, R. Aaij et al., _Measurement of form-factor-independent observables in the decay $B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$_, Phys. Rev. Lett. 111 (2013) 191801, arXiv:1308.1707
  * [108] R. Gauld, F. Goertz, and U. Haisch, _An explicit $Z^{\prime}$-boson explanation of the $B\rightarrow K^{*}\mu^{+}\mu^{-}$ anomaly_, JHEP 1401 (2014) 069, arXiv:1310.1082
  * [109] S. Descotes-Genon, J. Matias, and J. Virto, _Understanding the $B\rightarrow K^{*}\mu^{+}\mu^{-}$ anomaly_, Phys. Rev. D88 (2013), no. 7 074002, arXiv:1307.5683
  * [110] W. Altmannshofer and D. M. Straub, _New physics in $B\rightarrow K^{*}\mu\mu$?_, Eur. Phys. J. C73 (2013) 2646, arXiv:1308.1501
  * [111] A. Datta, M. Duraisamy, and D. Ghosh, _Explaining the $B\rightarrow K^{\ast}\mu^{+}\mu^{-}$ data with scalar interactions_, Phys. Rev. D89 (2014), no. 7 071501, arXiv:1310.1937
  * [112] F. Mahmoudi, S. Neshatpour, and J. Virto, _$B\rightarrow K^{*}\mu^{+}\mu^{-}$ optimised observables in the MSSM_, Eur. Phys. J. C74 (2014) 2927, arXiv:1401.2145
  * [113] F. Beaujean, C. Bobeth, and D. van Dyk, _Comprehensive Bayesian analysis of rare (semi)leptonic and radiative $B$ decays_, Eur. Phys. J. C74 (2014) 2897, arXiv:1310.2478
  * [114] J. Lyon and R. Zwicky, _Resonances gone topsy turvy - the charm of QCD or new physics in $b\rightarrow s\ell^{+}\ell^{-}$?_, arXiv:1406.0566
  * [115] LHCb collaboration, R. Aaij et al., _Observation of a resonance in $B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}$ decays at low recoil_, Phys. Rev. Lett. 111 (2013) 112003, arXiv:1307.7595
  * [116] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ asymmetries in the decays $B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$ and $B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}$_, JHEP 09 (2014) 177, arXiv:1408.0978
  * [117] LHCb collaboration, R. Aaij et al., _Differential branching fractions and isospin asymmetries of $B\rightarrow K^{(*)}\mu^{+}\mu^{-}$ decays_, JHEP 06 (2014) 133, arXiv:1403.8044
  * [118] LHCb collaboration, R. Aaij et al., _Test of lepton universality using $B^{+}\rightarrow K^{+}\ell^{+}\ell^{-}$ decays_, Phys. Rev. Lett. 113 (2014) 151601, arXiv:1406.6482
  * [119] G. Hiller and M. Schmaltz, _$R_{K}$ and future $b\rightarrow s\ell\ell$ physics beyond the standard model opportunities_, Phys. Rev. D90 (2014) 054014, arXiv:1408.1627
  * [120] D. Ghosh, M. Nardecchia, and S. A. Renner, _Hint of lepton flavour non-universality in $B$ meson decays_, JHEP 1412 (2014) 131, arXiv:1408.4097
  * [121] W. Altmannshofer and D. M. Straub, _New physics in $b\rightarrow s$ transitions after LHC run 1_, Eur. Phys. J. C75 (2015), no. 8 382, arXiv:1411.3161
  * [122] A. Crivellin, G. D’Ambrosio, and J. Heeck, _Explaining $h\rightarrow\mu^{\pm}\tau^{\mp}$, $B\rightarrow K^{*}\mu^{+}\mu^{-}$ and $B\rightarrow K\mu^{+}\mu^{-}/B\rightarrow Ke^{+}e^{-}$ in a two-Higgs-doublet model with gauged $L_{\mu}-L_{\tau}$_, Phys. Rev. Lett. 114 (2015) 151801, arXiv:1501.00993
  * [123] S. L. Glashow, D. Guadagnoli, and K. Lane, _Lepton Flavor Violation in $B$ Decays?_, Phys. Rev. Lett. 114 (2015) 091801, arXiv:1411.0565
  * [124] C. Bobeth et al., _$B_{s,d}\rightarrow l^{+}l^{-}$ in the Standard Model with reduced theoretical uncertainty_, Phys. Rev. Lett. 112 (2014) 101801, arXiv:1311.0903
  * [125] ATLAS collaboration, CDF collaboration, CMS collaboration and D0 collaboration, _First combination of Tevatron and LHC measurements of the top-quark mass_ , arXiv:1403.4427
  * [126] LHCb collaboration, R. Aaij et al., _First evidence for the decay $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$_, Phys. Rev. Lett. 110 (2013) 021801, arXiv:1211.2674
  * [127] LHCb collaboration, R. Aaij et al., _Measurement of the $B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$ branching fraction and search for $B^{0}\rightarrow\mu^{+}\mu^{-}$ decays at the LHCb experiment_, Phys. Rev. Lett. 111 (2013) 101805, arXiv:1307.5024
  * [128] CMS collaboration, S. Chatrchyan et al., _Measurement of the ${{B}^{0}_{s}}\\!\rightarrow{\mu^{+}\mu^{-}}$ branching fraction and search for ${{B}^{0}}\\!\rightarrow{\mu^{+}\mu^{-}}$ with the CMS Experiment_, Phys. Rev. Lett. 111 (2013) 101804, arXiv:1307.5025
  * [129] CMS and LHCb collaborations, _Combination of results on the rare decays ${B}^{0}_{(s)}\rightarrow{\mu^{+}\mu^{-}}$ from the CMS and LHCb experiments_, Jul, 2013.  CMS-PAS-BPH-13-007, LHCb-CONF-2013-012
  * [130] LHCb collaboration, R. Aaij et al., _Determination of $f_{s}/f_{d}$ for 7 TeV $pp$ collisions and measurement of the $B^{0}\rightarrow D^{-}K^{+}$ branching fraction_, Phys. Rev. Lett. 107 (2011) 211801, arXiv:1106.4435
  * [131] LHCb collaboration, R. Aaij et al., _Measurement of $b$ hadron production fractions in 7 TeV $pp$ collisions_, Phys. Rev. D85 (2012) 032008, arXiv:1111.2357
  * [132] LHCb collaboration, _Updated average $f_{s}/f_{d}$ $b$-hadron production fraction ratio for $7~{}T\kern-0.50003pteV$ $pp$ collisions_, LHCb-CONF-2013-011
  * [133] CMS and LHCb collaborations, V. Khachatryan et al., _Observation of the rare $B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$ decay from the combined analysis of CMS and LHCb data_, Nature 522 (2015) 68, arXiv:1411.4413
  * [134] S. S. Wilks, _The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses_ , Annals Math. Statist. 9 (1938), no. 1 60
  * [135] G. J. Feldman and R. D. Cousins, _A Unified approach to the classical statistical analysis of small signals_ , Phys. Rev. D57 (1998) 3873, arXiv:physics/9711021