EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2016-166 LHCb-PAPER-2016-017

Measurement of the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
lifetime

The LHCb collaboration†††Authors are listed at the end of this paper.

This paper is dedicated to the memory of our friend and colleague Ailsa
Sparkes.

Using a data set corresponding to an integrated luminosity of
$3\mbox{\,fb}^{-1}$, collected by the LHCb experiment in $pp$ collisions at
centre-of-mass energies of 7 and 8 TeV, the effective lifetime in the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
decay mode, $\tau_{\textrm{eff}}$, is measured to be

$\tau_{\textrm{eff}}=1.479\pm 0.034~{}\textrm{(stat)}\pm
0.011~{}\textrm{(syst)}{\mathrm{\,ps}}.$

Assuming $C\\!P$ conservation, $\tau_{\textrm{eff}}$ corresponds to the
lifetime of the light ${{B}^{0}_{s}}$ mass eigenstate. This is the first
measurement of the effective lifetime in this decay mode.

Accepted by Phys. Lett. B.

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

Studies of $B^{0}_{s}-\overline{B}^{0}_{s}$ mixing provide important tests of
the Standard Model (SM) of particle physics. In the SM, mixing occurs via box
diagrams. Extensions to the SM may introduce additional $C\\!P$-violating
phases that alter the value of the ${{B}^{0}_{s}}-{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ mixing weak phase,
$\phi_{s}$, from that of the SM [1]. The ${{B}^{0}_{s}}$ system exhibits a
sizeable difference in the decay widths $\Gamma_{\rm L}$ and $\Gamma_{\rm H}$,
where $\rm L$ and $\rm H$ refer to the light and heavy ${{B}^{0}_{s}}$ mass
eigenstates, respectively. The effective lifetime, $\tau_{\textrm{eff}}$, of a
${{B}^{0}_{s}}$ meson decay mode is measured by approximating the decay time
distribution, determined in the ${{B}^{0}_{s}}$ rest system, by a single
exponential function. For final states that can be accessed by both
${{B}^{0}_{s}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ mesons the effective
lifetime depends on their $C\\!P$ components and is also sensitive to
$\phi_{s}$ [2, 3].

In this analysis $\tau_{\textrm{eff}}$ is determined for the $C\\!P$-even
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$ decay
mode. As ${\phi_{{s}}}$ is measured to be small [4, 5] the mass eigenstates
are also $C\\!P$ eigenstates to better than per mille level and
$\tau_{\textrm{eff}}$ measured in
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
decays is equal, to good approximation, to the lifetime of the light
${{B}^{0}_{s}}$ mass eigenstate, $\tau_{\rm L}\propto\Gamma_{\rm L}^{-1}$. In
the SM $\tau_{\rm L}$ is predicted to be $1.43\pm 0.03{\mathrm{\,ps}}$ [6].
Measurements of $\tau_{\rm L}$ have previously been reported by LHCb in the
${{B}^{0}_{s}}\rightarrow{{D}^{+}_{s}}{{D}^{-}_{s}}$ and
${{B}^{0}_{s}}\rightarrow K^{+}K^{-}$ decay modes [7, 8]. The latter is
dominated by penguin diagrams, which could arise within and beyond the SM and
gives rise to direct $C\\!P$ violation. This then leads to a different
$\tau_{\textrm{eff}}$, when compared to measurements in the
${{B}^{0}_{s}}\rightarrow{{D}^{+}_{s}}{{D}^{-}_{s}}$ and
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
decays which are mediated by tree diagrams. Improved precision on the
effective lifetimes $\tau_{\rm L}$ and $\tau_{\rm H}$ will enable more
stringent tests of the consistency between direct measurements of the decay
width difference $\Delta\Gamma_{s}=\Gamma_{\rm L}-\Gamma_{\rm H}$ measured in
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$
decays and those inferred using effective lifetimes.

The measurement of the effective
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
lifetime presented in this Letter uses 3 $\mbox{\,fb}^{-1}$ of data collected
in $pp$ collisions at centre-of-mass energies of 7 TeV and 8 TeV during 2011
and 2012 using the LHCb detector. The ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ meson is reconstructed via the dimuon decay mode and the $\eta$ meson
via the diphoton decay mode. The presence of only two charged particles in the
final state minimizes systematic uncertainties related to the tracking system.

##  2 Detector and simulation

The LHCb detector [9, 10] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector (TT) located upstream
of a dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5 % at low
momentum to 1.0 % at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Large samples
of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}}{\mu^{-}}$ and
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$ decays,
collected concurrently with the data set used here, were used to calibrate the
momentum scale of the spectrometer to a precision of $0.03\,\%$ [11]. The
minimum distance of a track to a primary vertex (PV), the impact parameter
(IP), is measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

Different types of charged hadrons are distinguished using information from
two ring-imaging Cherenkov detectors. Photons, electrons and hadrons are
identified by a calorimeter system consisting of scintillating-pad and
preshower detectors, an electromagnetic calorimeter and a hadronic
calorimeter. The calorimeter response is calibrated using samples of
$\pi^{0}\rightarrow\gamma\gamma$ decays. For this analysis a further
calibration was made using the decay $\eta\rightarrow\gamma\gamma$, which
results in a precision of $0.07\,\%$ on the neutral energy scale. 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 [12], which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, where a full event reconstruction is made.
Candidate events are required to pass the hardware trigger, which selects muon
and dimuon candidates with high $p_{\mathrm{T}}$ based upon muon system
information. The subsequent software trigger is composed of two stages. The
first performs a partial event reconstruction and requires events to have two
well-identified oppositely charged muons with an invariant mass larger than
$2.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The second stage performs a
full event reconstruction. Events are retained for further processing if they
contain a displaced ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-}$ candidate. The decay vertex is required to
be well separated from each reconstructed PV of the proton-proton interaction
by requiring the distance between the PV and the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ decay vertex divided by its
uncertainty to be greater than three. This introduces a non-uniform efficiency
for ${b}$-hadron candidates that have a decay time less than
$0.1{\mathrm{\,ps}}$.

Simulated $pp$ collisions are generated using Pythia [13, *Sjostrand:2007gs]
with a specific LHCb configuration [15]. Decays of hadronic particles are
described by EvtGen [16], in which final-state radiation is generated using
Photos [17]. The interaction of the generated particles with the detector, and
its response, are implemented using the Geant4 toolkit [18,
*Agostinelli:2002hh] as described in Ref. [20].

##  3 Selection

A two-step procedure, is used to optimize the selection of
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
decay candidates. These studies use simulated data samples together with the
high mass sideband of the data ($5650<m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\eta)<5850{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$), which is not used
in the subsequent determination of $\tau_{\textrm{eff}}$. In a first step,
loose selection criteria are applied that reduce background significantly
whilst retaining high signal efficiency. Subsequently, a multivariate
selection (MVA) is used to reduce further the combinatorial background. This
is optimized using pseudoexperiments to obtain the best precision on the
measured ${{B}^{0}_{s}}$ lifetime.

The selection starts from a pair of oppositely charged particles, identified
as muons, that form a common decay vertex. Combinatorial background is
suppressed by requiring that $\chi^{2}_{\text{IP}}$ of the muon
candidates111The quantity $\chi^{2}_{\text{IP}}$ is defined as the difference
between the $\chi^{2}$ of the PV reconstructed with and without the considered
particle. to all reconstructed PVs to be larger than four. To ensure a high
reconstruction efficiency the muon candidates are required to have a
pseudorapidity between 2.0 and 4.5. The invariant mass of the dimuon candidate
must be within $50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ mass [21]. In addition, the
trigger requirement that the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$
decay length divided by its uncertainty is greater than three is reapplied.

Photons are selected from neutral clusters reconstructed in the
electromagnetic calorimeter [10] that have a transverse energy in excess of
$300~{}\mathrm{MeV}$ and a confidence level to be a photon,
$\mathcal{P}_{\gamma}$, greater than 0.009. The latter requirement has an
efficiency of $98\,\%$ for the simulated signal sample whilst removing
$23\,\%$ of the background in the high mass sideband. To suppress
combinatorial background, if either of the photons when combined with any
other photon candidate in the event has an invariant mass within
$25~{}\mathrm{MeV}/c^{2}$ of the known $\pi^{0}$ meson mass [21] the candidate
is rejected.

Candidate $\eta\rightarrow\gamma\gamma$ decays are selected from diphoton
combinations with an invariant mass within $70~{}\mathrm{MeV}/c^{2}$ of the
known $\eta$ mass [21] and with a transverse momentum larger than
$2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The decay angle between the photon
momentum in the $\eta$ rest frame and the direction of Lorentz boost from the
laboratory frame to the $\eta$ rest frame, $\theta^{*}_{\eta}$, is required to
satisfy $\left|\cos\theta^{*}_{\eta}\right|<0.8$.

The ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and $\eta$ candidates are
combined to form candidate ${B}^{0}_{(s)}$ mesons. The average number of PVs
in each event is 1.8 (2.0) for the 2011 (2012) dataset. When multiple PVs are
reconstructed, the one with the minimum $\chi^{2}_{\text{IP}}$ to the
$B^{0}_{({s})}$ candidate is chosen. A kinematic fit is performed to improve
the invariant mass resolution [22]. In this fit the momentum vector of the
${B}^{0}_{(s)}$ candidate is constrained to point to the PV and the
intermediate resonance masses are constrained to their known values. The
reduced $\chi^{2}$ of this fit, $\chi^{2}/\mathrm{ndf}$, is required to be
less than five. The measured ${B}^{0}_{({s})}$ decay time must be larger than
$0.3{\mathrm{\,ps}}$ and less than $10{\mathrm{\,ps}}$. If more than one PV is
reconstructed in an event the properties of the unassociated vertices are
studied. Any candidate for which there is a second PV with
$\chi^{2}_{\text{IP}}<50$ is rejected. This requirement has an efficiency of
$98\%$ that is almost flat as a function of the decay time and reduces
background due to incorrect association of the ${B}^{0}_{({s})}$ candidate to
a PV. Finally, as in Ref. [23], the position of the PV along the beam-line is
required to be within $10$ cm of the nominal interaction point, where the
standard deviation of this variable is approximately $5\,$cm. This criterion
leads to a 10 % reduction in signal yield but defines a fiducial region where
the reconstruction efficiency is uniform.

The second step of the selection process is based on a neural network [24],
which is trained using the simulated signal sample and the high-mass sideband
of the data for background. Seven variables that show good agreement between
data and simulation and that do not significantly bias the ${B}^{0}_{({s})}$
decay time distribution are used to train the neural net: the $\chi^{2}$/ndf
of the kinematic fit; the $p_{\mathrm{T}}$ of the $B^{0}_{({s})}$ and $\eta$
mesons; the minimum $p_{\mathrm{T}}$ of the two photons;
$\left|\cos\theta^{*}_{\eta}\right|$; the minimum $\mathcal{P}_{\gamma}$ of
the two photons and the total hit multiplicity in the TT sub-detector.

The requirement on the MVA output was chosen to minimize the statistical
uncertainty on the fitted $\tau_{\textrm{eff}}$ using a sample of 100
pseudoexperiments. The chosen value removes $94\,\%$ of background candidates
whilst retaining $69\,\%$ of the signal candidates. After applying these
requirements $2\,\%$ of events contain multiple candidates from which only
one, chosen at random, is kept.

##  4 Fit model

The effective lifetime is determined by performing a two-dimensional maximum
likelihood fit to the unbinned distributions of the ${B}^{0}_{(s)}$ candidate
invariant mass and decay time

$t=\frac{m\cdot l}{p},$

where $l$ is the candidate decay length, $p$ the candidate momentum and $m$
the reconstructed invariant mass of the candidate. The fit is performed for
candidates with $5050<m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\eta)<5650{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
$0.3<t<10{\mathrm{\,ps}}$. The fit model has four components: the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
signal, background from the
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
decay, background from partially reconstructed
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta X$
decays, and combinatorial background.

In the fit, the decay-time distribution of each component is convolved with a
Gaussian resolution function whose width is fixed to the standard deviation of
the decay-time resolution in simulated data. A decay-time acceptance function
accounts for the dependence of the signal efficiency on several effects. The
procedure used to model the decay-time acceptance is described in detail in
Ref. [23]. The overall acceptance, $A_{\textrm{tot}}$, is factorised into the
product of the selection ($A_{\textrm{sel}}$), trigger ($A_{\textrm{trig}}$)
and vertex ($A_{\beta}$) acceptance functions, determined as described below.
The effect of the selection requirements, dominated by the cut on the
displacement of the muons from the PV, is studied using simulation and
parameterised with the form

$A_{\textrm{sel}}=\frac{1-c_{0}t}{1+(c_{1}t)^{-c_{2}}},$

where $t$ is the decay time, and $c_{0},c_{1}$ and $c_{2}$ are parameters
determined from the simulation and summarized in Table 1.

Table 1: Acceptance parameters due to the selection requirements ($A_{\textrm{sel}}$). The correlation coefficients are $\rho_{c_{0}c_{1}}=0.51$, $\rho_{c_{0}c_{2}}=0.62$ and $\rho_{c_{1}c_{2}}=0.95$. Parameter | Value
---|---
$c_{0}$ | $(6.5\pm 0.4)\times 10^{-3}{\mathrm{\,ps}}^{-1}$
$c_{1}$ | $(6.6\pm 0.3){\mathrm{\,ps}}^{-1}$
$c_{2}$ | $1.50\pm 0.04$

In the second level of the software trigger a cut is applied on the decay
length significance of the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$
candidate, which biases the decay time distribution. The trigger efficiency,
$A_{\textrm{trig}}$, is measured separately for the 2011 and 2012 datasets
using events that are selected by a dedicated prescaled trigger in which this
requirement is removed. It increases approximately linearly from $98\%$ at
$t=0.3{\mathrm{\,ps}}$ to $100\%$ $4{\mathrm{\,ps}}$. The resulting acceptance
shape is parameterised in bins of decay time with linear interpolation between
the bins. Finally, the reconstruction efficiency of the vertex detector
decreases as the distance of closest approach of the decay products to the
$pp$ beam-line increases. This effect is studied using
${{{B}^{+}}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$
decays where the kaon is reconstructed without using vertex detector
information [23] and parameterised with the form

$A_{\beta}=1-\beta t-\gamma t^{2},$

where the parameters $\beta$ and $\gamma$ are determined separately for the
2011 and 2012 data. The obtained values are summarized in Table 2.

Table 2: Values of the $\beta$ and $\gamma$ factor fitting the quadratic form. The first uncertainty is statistical and the second from the propagation of the uncertainty on the efficiency versus the distance of closest approach obtained with the ${{{B}^{+}}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$ calibration sample. The correlation coefficienct between $\beta$ and $\gamma$ is 0.8.  Sample |  $\beta$ [%] |  $\gamma$ [%]
---|---|---
2011 data | $0.39\pm 0.06^{-0.01}_{+0.07}$ | $0.115\pm 0.021^{-0.004}_{+0.001}$
2012 | $0.93\pm 0.080^{+0.001}_{-0.01}$ | $0.051\pm 0.023^{-0.006}_{+0.006}$

Figure 1 shows the overall acceptance curves obtained for the 2011 and 2012
datasets. The shape of $A_{\textrm{tot}}$ is mainly determined by
$A_{\textrm{sel}}$, whose uncertainty is dominated by the size of the
simulation sample. The overall acceptance correction is relatively small.
Fitting the simulated data with and without the correction
$\tau_{\textrm{eff}}$ changes by $13\mathrm{\,fs}$.

Figure 1: Total acceptance function, $A_{\textrm{tot}}$ for 2011 data (black
dashed line) and 2012 data (solid red).

The invariant mass distribution for the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
signal is parameterised by a Student’s t-distribution. The Bukin [25] and
JohnsonSU [26] functions are considered for systematic variations. In the fit
to the data, the shape parameters of this distribution are fixed to the
simulation values. The decay time distribution for this component is modelled
with an exponential function convolved with the detector resolution and
multiplied by the detector acceptance, as discussed above.

The second component in the fit accounts for the
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
decay. As the invariant mass resolution is approximately
$48{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ this overlaps with the
${{B}^{0}_{s}}$ signal mode. Its mass distribution is modelled, analogously to
the ${{B}^{0}_{s}}$ component, with a Student’s t-distribution, with
resolution parameters fixed to values determined in the simulation. The mass
difference between the ${{B}^{0}_{s}}$ and ${{B}^{0}}$ mesons, and the
${{B}^{0}}$ lifetime, are fixed to their known central values:
$m({{B}^{0}_{s}})-m({{B}^{0}})=87.29\pm
0.26{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ [27] and
$\tau({{B}^{0}})=1.519\pm 0.005{\mathrm{\,ps}}$ [21] and the uncertainty
propagated to the systematic error. Similarly, the relative yield of the
${{B}^{0}}$ and ${{B}^{0}_{s}}$ components, $f_{r}$, is fixed to $(7.3\pm
0.8)\,\%$ calculated from the average of the branching fractions measurements
made by the Belle [28, 29] and LHCb collaborations [30], and the measured
fragmentation fractions [31, 32, 33].

Combinatorial background is modelled by a first order Chebyshev polynomial in
mass and the sum of two exponentials in decay time. In the fit to the data the
lifetime of the shorter lived component is fixed to the value found in the fit
to the sideband. As a systematic variation of the mass model, an exponential
function is considered.

Background from partially reconstructed decays of ${b}$ hadrons is studied
using a simulated ${b}\overline{{b}}$ sample. Using this sample an additional
background component, due to partially reconstructed
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta X$
decays, is identified. Background from this source lies at invariant masses
below $5100{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and has a lifetime of
$1.33\pm 0.10{\mathrm{\,ps}}$. This component is modelled by a Novosibirsk
function [34] in mass and an exponential in time. All parameters for this
component apart from the yield are fixed to the simulation values in the fit
to the data.

The fit has eight free parameters: the yield of the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$
component ($N^{{{B}^{0}_{s}}}$), the combinatorial background yield
($N^{\textrm{comb}}$), the partially reconstructed background yield
($N^{\textrm{partial}}$), the ${{B}^{0}_{s}}$ mass, the lifetime of the signal
component ($\tau_{\textrm{{eff}}}$), the coefficient of the combinatorial
background component in mass ($a_{\textrm{comb}}$), the longer lived
background lifetime ($\tau_{\textrm{comb}}$) and the fraction of the short-
lived background ($f_{\textrm{comb}}$). Independent fits are performed for the
2011 and 2012 data and a weighted average of the two lifetime values is made.
The correctness of the fit procedure is validated using the full simulation
and pseudoexperiments. No significant bias is found and the uncertainties
estimated by the fit are found to be accurate.

##  5 Results

Figure 2 shows the fit projections in mass and decay time for the 2011 and
2012 data. The corresponding fit results are summarized in Table 3. The fitted
signal yields of the two years scale according to the known integrated
luminosity and ${b}$-hadron production cross-section. There is some tension in
the relative yield of the partially reconstructed background between the two
years. However, this parameter is almost uncorrelated with
$\tau_{\textrm{eff}}$ and this tension has no impact on the result. The
average of the fitted values of $\tau_{\textrm{eff}}$ is

$\tau_{\textrm{eff}}=1.479\pm 0.034{\mathrm{\,ps}},$

where the uncertainty is statistical.

Figure 2: Mass and decay time distributions for the 2011 dataset (top row) and 2012 dataset (bottom row). The fit model described in the text is superimposed (red line). The partially reconstructed component is shown in solid yellow (dark grey), the combinatorial background in solid green (light grey) and the ${{B}^{0}}$ component as open blue. The pull, i.e. the difference between the observed and fitted value divided by the uncertainty, is shown below each of the plots.  Table 3: Parameters of the fit to $B^{0}_{(s)}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$ candidates for the 2011 and 2012 datasets. Uncertainties are statistical only. | Fitted value
---|---
Fit parameter | 2011 | 2012
$N^{{{B}^{0}_{s}}}$ |  960$\,\pm\,\,$ | 42 |  2061$\,\pm\,\,$ | 60
$m_{{{B}^{0}_{s}}}$ [${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$ ] |  5365.6$\,\pm\,\,$ | 1.8 |  5369.6$\,\pm\,\,$ | 1.3
$\tau_{\textrm{eff}}$ [ps] |  1.485$\,\pm\,\,$ | 0.060 |  1.476$\,\pm\,\,$ | 0.041
$N^{\textrm{comb}}$ |  1898$\,\pm\,\,$ | 64 |  3643$\,\pm\,\,$ | 89
$N^{\textrm{partial}}$ |  81$\,\pm\,\,$ | 26 |  345$\,\pm\,\,$ | 39
$a_{\textrm{comb}}$ |  $-0.37$$\,\pm\,\,$ | 0.05 |  $-0.31$$\,\pm\,\,$ | 0.03
$f_{\textrm{comb}}$ |  0.52$\,\pm\,\,$ | 0.03 |  0.49$\,\pm\,\,$ | 0.02
$\tau_{\textrm{comb}}$ [ps] |  0.97$\,\pm\,\,$ | $0.06$ |  0.82$\,\pm\,\,$ | $0.04$

The main source of systematic uncertainty is due to the modelling of the decay
time acceptance function (Section 4). Varying the parameters of the acceptance
function within their correlated uncertainties, a variation of the fitted
lifetime of 10 fs is found, which is assigned as a systematic uncertainty.
Uncertainties on $A_{\textrm{sel}}$ due to the parameterisation of this effect
are evaluated to be negligible by replacing the functional form with a
histogram. The statistical and systematic uncertainties on $A_{\beta}$ are
evaluated by repeating the fit and varying the parameterisation within its
uncertainties. The statistical uncertainty on $A_{\textrm{trig}}$ is
propagated by generating an ensemble of histograms with each bin varied within
its statistical uncertainty. Systematic uncertainties on $A_{\textrm{trig}}$
are estimated to be small by varying the binning of the histogram and
considering an alternative analytic form. In simulation studies the efficiency
of the MVA is found to be independent of the decay time within uncertainties.
Conservatively, allowing for a linear dependence, an uncertainty of
$1.7\mathrm{\,fs}$ is assigned.

The influence of the decay time resolution is estimated by increasing its
value from 51 to $70\mathrm{\,fs}$. This variation covers the variation of the
resolution with decay time and any possible discrepancy in the resolution
between data and simulation. The change in $\tau_{\textrm{eff}}$ from this
variation is negligible. The impact of the uncertainties in $f_{r}$, the
${{B}^{0}_{s}}-{{B}^{0}}$ mass splitting, and the ${{B}^{0}}$ lifetime are
evaluated by repeating the fit procedure varying these parameters within their
quoted uncertainties.

Further uncertainties arise from the modelling of the time distributions of
the background components. In the default fit the lifetime of the short-lived
component is fixed to the value found in a fit to the mass sideband. Removing
this constraint changes the result by $4\mathrm{\,fs}$, which is assigned as a
systematic uncertainty. The uncertainty due to the fixed lifetime of the
partially reconstructed component is found to be negligible.

Uncertainties arising from the modelling of the signal and background mass
distributions are evaluated using the discrete profiling method described in
Ref. [35] and found to be negligible. Further small uncertainties arise due to
the limited knowledge of the length scale of the detector along the beam axis
($z-$scale), the charged particle momentum scale and the neutral particle
energy scale.

The stability of the result has been tested against a number of possible
variations, such as the fitted invariant mass range, the requirement on the IP
of the muons, the MVA requirement and analysing the sample according to the
number of reconstructed PVs. No significant change in the final result is
found and hence no further systematic uncertainty is assigned.

All the uncertainties are summarized in Table 4. Adding them in quadrature
leads to a total systematic uncertainty of $11.1\mathrm{\,fs}$ which is
dominated by the size of the simulation sample used to determine the
acceptance and to validate the analysis procedure.

Table 4: Systematic uncertainties on the lifetime measurement. Uncertainties less than $0.1\mathrm{\,fs}$ are indicated by a dash. Source |  Uncertainty [$\mathrm{\,fs}$]
---|---
$A_{\textrm{sel}}$ | 10.0
$A_{\beta}$ (stat) | 2.0
$A_{\beta}$ (syst) | 0.1
$A_{\textrm{trig}}$ (stat) | 0.6
$A_{\textrm{trig}}$ (syst) | 0.6
MVA | 1.7
Time resolution | –
$f_{r}$ | 1.2
${{B}^{0}_{s}}-{{B}^{0}}$ mass difference | –
${{B}^{0}}$ lifetime | 0.2
Releasing $\tau_{\textrm{back}}$ | 4.0
Varying $\tau_{\textrm{partial}}$ | –
Mass model | –
Momentum scale | –
$z$-scale | 0.3
Total | 11.1

##  6 Summary

Using data collected by LHCb, the effective lifetime in the
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\eta$ decay
mode is measured to be

$\tau_{\textrm{eff}}=1.479\pm 0.034~{}\textrm{(stat)}\pm
0.011~{}\textrm{(syst)}{\mathrm{\,ps}}.$

In the limit of ${C\\!P}$ conservation, $\tau_{\textrm{eff}}$ is equal to the
lifetime of the light ${{B}^{0}_{s}}$ mass eigenstate $\tau_{L}$. The present
measurement is consistent with, and has similar precision to, the effective
lifetime determined using the
${{B}^{0}_{s}}\rightarrow{{D}^{+}_{s}}{{D}^{-}_{s}}$ decay mode [7],
$\tau_{\textrm{eff}}({{D}^{+}_{s}}{{D}^{-}_{s}})=1.379\pm
0.026\mathrm{\,(stat)}\pm 0.017\mathrm{\,(syst)}$${\mathrm{\,ps}}$ and also
with the value measured in the ${{B}^{0}_{s}}\rightarrow K^{+}K^{-}$ mode [8],
$\tau_{\textrm{eff}}(K^{+}K^{-})=1.407\pm 0.016\mathrm{\,(stat)}\pm
0.007\mathrm{\,(syst)}$${\mathrm{\,ps}}$, where penguin diagrams are expected
to be more important. Averaging the tree level measurements gives $\tau_{\rm
eff}=1.42\pm 0.02{\mathrm{\,ps}}$ in good agreement with the expectations of
the Standard Model [6], $\tau_{\rm L}=1.43\pm 0.03{\mathrm{\,ps}}$ and the
value quoted by HFAG [36] from measurements made in the
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ mode,
$\tau_{\rm L}=1.420\pm 0.006{\mathrm{\,ps}}$. The values from these different
measurements are compared in Fig. 3.

Figure 3: Summary of measurements of $\tau_{\rm L}$. The yellow band
corresponds to the 2015 HFAG central value and uncertainty.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOM
and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES
and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine);
STFC (United Kingdom); NSF (USA). We acknowledge the computing resources that
are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy),
SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex
LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID
(Poland) and OSC (USA). We are indebted to the communities behind the multiple
open source software packages on which we depend. Individual groups or members
have received support from AvH Foundation (Germany), EPLANET, Marie
Skłodowska-Curie Actions and ERC (European Union), Conseil Général de Haute-
Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR and Yandex
LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal
Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust
(United Kingdom).

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LHCb collaboration

R. Aaij39, B. Adeva38, M. Adinolfi47, Z. Ajaltouni5, S. Akar6, J. Albrecht10,
F. Alessio39, M. Alexander52, S. Ali42, G. Alkhazov31, P. Alvarez Cartelle54,
A.A. Alves Jr58, S. Amato2, S. Amerio23, Y. Amhis7, L. An40, L. Anderlini18,
G. Andreassi40, M. Andreotti17,g, J.E. Andrews59, R.B. Appleby55, O. Aquines
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I. Bediaga1, L.J. Bel42, V. Bellee40, N. Belloli21,i, K. Belous36, I.
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A. Bizzeti18,u, T. Blake49, F. Blanc40, J. Blouw11, S. Blusk60, V. Bocci26, T.
Boettcher57, A. Bondar35, N. Bondar31,39, W. Bonivento16, A. Borgheresi21,i,
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J. Brodzicka55, E. Buchanan47, C. Burr55, A. Bursche2, J. Buytaert39, S.
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Swientek28, V. Syropoulos43, M. Szczekowski29, T. Szumlak28, S. T’Jampens4, A.
Tayduganov6, T. Tekampe10, G. Tellarini17,g, F. Teubert39, C. Thomas56, E.
Thomas39, J. van Tilburg42, V. Tisserand4, M. Tobin40, S. Tolk48, L.
Tomassetti17,g, D. Tonelli39, S. Topp-Joergensen56, F. Toriello60, E.
Tournefier4, S. Tourneur40, K. Trabelsi40, M. Traill52, M.T. Tran40, M.
Tresch41, A. Trisovic39, A. Tsaregorodtsev6, P. Tsopelas42, A. Tully48, N.
Tuning42, A. Ukleja29, A. Ustyuzhanin67,66, U. Uwer12, C. Vacca16,39,f, V.
Vagnoni15,39, S. Valat39, G. Valenti15, A. Vallier7, R. Vazquez Gomez19, P.
Vazquez Regueiro38, S. Vecchi17, M. van Veghel42, J.J. Velthuis47, M.
Veltri18,r, G. Veneziano40, A. Venkateswaran60, M. Vernet5, M. Vesterinen12,
B. Viaud7, D. Vieira1, M. Vieites Diaz38, X. Vilasis-Cardona37,m, V. Volkov33,
A. Vollhardt41, B. Voneki39, D. Voong47, A. Vorobyev31, V. Vorobyev35, C.
Voß65, J.A. de Vries42, C. Vázquez Sierra38, R. Waldi65, C. Wallace49, R.
Wallace13, J. Walsh24, J. Wang60, D.R. Ward48, H.M. Wark53, N.K. Watson46, D.
Websdale54, A. Weiden41, M. Whitehead39, J. Wicht49, G. Wilkinson56,39, M.
Wilkinson60, M. Williams39, M.P. Williams46, M. Williams57, T. Williams46,
F.F. Wilson50, J. Wimberley59, J. Wishahi10, W. Wislicki29, M. Witek27, G.
Wormser7, S.A. Wotton48, K. Wraight52, S. Wright48, K. Wyllie39, Y. Xie63, Z.
Xing60, Z. Xu40, Z. Yang3, H. Yin63, J. Yu63, X. Yuan35, O. Yushchenko36, M.
Zangoli15, K.A. Zarebski46, M. Zavertyaev11,c, L. Zhang3, Y. Zhang7, Y.
Zhang62, A. Zhelezov12, Y. Zheng62, A. Zhokhov32, V. Zhukov9, S. Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Sezione INFN di Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione INFN di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
36Institute for High Energy Physics (IHEP), Protvino, Russia
37ICCUB, Universitat de Barcelona, Barcelona, Spain
38Universidad de Santiago de Compostela, Santiago de Compostela, Spain
39European Organization for Nuclear Research (CERN), Geneva, Switzerland
40Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
41Physik-Institut, Universität Zürich, Zürich, Switzerland
42Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
43Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
44NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
45Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
46University of Birmingham, Birmingham, United Kingdom
47H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
48Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
49Department of Physics, University of Warwick, Coventry, United Kingdom
50STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
51School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
52School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
53Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
54Imperial College London, London, United Kingdom
55School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
56Department of Physics, University of Oxford, Oxford, United Kingdom
57Massachusetts Institute of Technology, Cambridge, MA, United States
58University of Cincinnati, Cincinnati, OH, United States
59University of Maryland, College Park, MD, United States
60Syracuse University, Syracuse, NY, United States
61Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
62University of Chinese Academy of Sciences, Beijing, China, associated to 3
63Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
64Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
65Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
66National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
67Yandex School of Data Analysis, Moscow, Russia, associated to 32
68Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 37
69Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 42

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Viet Nam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines