Flavour tagged time dependent angular analysis of the $B_s \rightarrow J/\psi \phi$ decay and extraction of $\Delta\Gamma$ and the weak phase $\phi_s$ in ATLAS

A measurement of the $B_s \rightarrow J/\psi \phi$ decay parameters, updated to include flavour tagging is reported using $4.9 fb^{-1}$ of integrated luminosity collected by the ATLAS detector from $\sqrt{s}= 7$TeV $pp$ collisions recorded in 2011 at the LHC. The values measured for the physical parameters are: \begin{eqnarray*} \phi_s&=&0.12 \pm 0.25(stat.)\pm 0.05(syst.)rad \\ \Delta\Gamma&=&0.053 \pm 0.021(stat.) 0.010(syst.)ps^{-1} \\ \Gamma_s&=&0.677 \pm 0.007 (stat.)\pm 0.004 (syst.)ps^{-1}\\ |A_{\parallel}(0)|^2&=&0.220 \pm 0.008 (stat.)\pm 0.009(syst.)\\ |A_{0}(0)|^2&=&0.529 \pm 0.006 (stat.)\pm 0.012(syst.)\\ \delta_\perp&=&3.89 \pm 0.47(stat.) \pm 0.11(syst.)rad \end{eqnarray*} where the parameter $\Delta\Gamma$ is constrained to be positive. The $S$-wave contribution was measured and found to be compatible with zero. Results for $\phi_s$ and $\Delta\Gamma$ are also presented as $68\%$ and $95\%$ likelihood contours, which show agreement with the Standard Model expectations.

Flavour tagged time dependent angular analysis of the B 0 s → J/ψφ decay and extraction of ∆Γ s and the weak phase φ s in ATLAS The ATLAS Collaboration where the parameter ∆Γs is constrained to be positive. The S-wave contribution was measured and found to be compatible with zero. Results for φs and ∆Γs are also presented as 68% and 95% likelihood contours, which show agreement with the Standard Model expectations.

I. INTRODUCTION
New phenomena beyond the predictions of the Standard Model (SM) may alter CP violation in B-decays. A channel that is expected to be sensitive to new physics contributions is the decay B 0 s → J/ψφ. CP violation in the B 0 s → J/ψφ decay occurs due to interference between direct decays and decays with B 0 s − B 0 s mixing. The oscillation frequency of B 0 s meson mixing is characterized by the mass difference ∆m s of the heavy (B H ) and light (B L ) mass eigenstates. The CP violating phase φ s is defined as the weak phase difference between the B 0 s − B 0 s mixing amplitude and the b → ccs decay amplitude. In the absence of CP violation, the B H state would correspond to the CP odd state and the B L to the CP even state. In the SM the phase φ s is small and can be related to CKM quark mixing matrix elements via the relation φ s −2β s , with β s = arg[−(V ts V * tb )/(V cs V * cb )]; a value of φ s −2β s = −0.037 ± 0.002 rad [1] is predicted in the SM. Many new physics models predict large φ s values whilst satisfying all existing constraints, including the precisely measured value of ∆m s [2,3].
Another physical quantity involved in B 0 s − B 0 s mixing is the width difference ∆Γ s = Γ L −Γ H , which is predicted to be ∆Γ s = 0.087 ± 0.021 ps −1 [4]. Physics beyond the SM is not expected to affect ∆Γ s as significantly as φ s [5]. Extracting ∆Γ s from data is nevertheless useful as it allows theoretical predictions to be tested [5].
The decay of the pseudoscalar B 0 s to the vector-vector final-state J/ψφ results in an admixture of CP odd and CP even states, with orbital angular momentum L = 0, 1 or 2. The final states with orbital angular momentum L = 0 or 2 are CP even while the state with L = 1 is CP odd. Flavour tagging is used to distinguish between the initial B 0 s and B 0 s states. The CP states are separated statistically using an angular analysis of the final-state particles.
In this paper, an update to the previous measurement [6] with the addition of flavour tagging, is presented. Flavour tagging significantly reduces the uncertainty of the measured value of φ s while also allowing a measurement of one of the strong phases. Previous measurements of these quantities have been reported by the DØ, CDF and LHCb collaborations [7][8][9]. The analysis presented here uses 4.9 fb −1 of LHC pp data at √ s = 7 TeV collected by the ATLAS detector in 2011.

II. ATLAS DETECTOR AND MONTE CARLO SIMULATION
The ATLAS experiment [10] is a multipurpose particle physics detector with a forward-backward symmetric cylindrical geometry and near 4π coverage in solid angle. The inner tracking detector (ID) consists of a silicon pixel detector, a silicon microstrip detector and a transition radiation tracker. The ID is surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, and by a high granularity liquid-argon sampling electromagnetic calorimeter. A steel/scintillator tile calorimeter provides hadronic coverage in the central rapidity range. The end-cap and forward regions are instrumented with Liquid-argon calorimeters for both electromagnetic and hadronic measurements. The muon spectrometer (MS) surrounds the calorimeters and consists of three large superconducting toroids with eight coils each, a system of tracking chambers, and detectors for triggering.
The muon and tracking systems are of particular importance in the reconstruction of B meson candidates. Only data where both systems were operating correctly and where the LHC beams were declared to be stable are used. A muon identified using a combination of MS and ID track parameters is referred to as combined. A muon formed by track segments which are not associated with an MS track, but which are matched to ID tracks extrapolated to the MS is referred to as segment tagged.
The data were collected during a period of rising instantaneous luminosity, and the trigger conditions varied over this time. The triggers used to select events for this analysis are based on identification of a J/ψ → µ + µ − decay, with either a 4 GeV transverse momentum [11] (p T ) threshold for each muon or an asymmetric configuration that applies a p T threshold of 4 GeV to one of the muons while accepting a second muon with p T as low as 2 GeV.
Monte Carlo (MC) simulation is used to study the detector response, estimate backgrounds and model systematic effects. For this study, 12 million MC-simulated B 0 s → J/ψφ events were generated using Pythia 6 [12] tuned with recent ATLAS data [13]. No p T cuts were applied at the generator level. Detector responses for these events were simulated using the ATLAS simulation package based on GEANT4 [14,15]. Pile-up corresponding to the conditions during data taking was included. In order to take into account the varying trigger configurations during data-taking, the MC events were weighted to have the same trigger composition as the collected collision data. Additional samples of the background decay B 0 → J/ψK 0 * as well as the more general bb → J/ψX and pp → J/ψX backgrounds were also simulated using Pythia.

III. RECONSTRUCTION AND CANDIDATE SELECTION
Events passing the trigger and the data quality selections described in section II are required to pass the following additional criteria: the event must contain at least one reconstructed primary vertex, built from at least four ID tracks, and at least one pair of oppositely charged muon candidates that are reconstructed using information from the MS and the ID [16]. Both combined and segment tagged muons are used. In this analysis the muon track parameters are taken from the ID measurement alone, since the precision of the measured track parameters for muons in the p T range of interest for this analysis is dominated by the ID track reconstruction. The pairs of muon tracks are refitted to a common vertex and accepted for further consideration if the fit results in χ 2 /d.o.f. < 10. The invariant mass of the muon pair is calculated from the refitted track parameters. To account for varying mass resolution, the J/ψ candidates are divided into three subsets according to the pseudorapidity η of the muons. A maximum likelihood fit is used to extract the J/ψ mass and the corresponding resolution for these three subsets. When both muons have |η| < 1.05, the dimuon invariant mass must fall in the range (2.959-3.229) GeV to be accepted as a J/ψ candidate. When one muon has 1.05 < |η| < 2.5 and the other muon |η| < 1.05, the corresponding signal region is (2.913-3.273) GeV. For the third subset, where both muons have 1.05 < |η| < 2.5, the signal region is (2.852-3.332) GeV. In each case the signal region is defined so as to retain 99.8% of the J/ψ candidates identified in the fits.
The candidates for φ → K + K − are reconstructed from all pairs of oppositely charged particles with p T > 0.5 GeV and |η| < 2.5 that are not identified as muons. Candidates for B 0 s → J/ψ(µ + µ − )φ(K + K − ) are sought by fitting the tracks for each combination of J/ψ → µ + µ − and φ → K + K − to a common vertex. Each of the four tracks is required to have at least one hit in the pixel detector and at least four hits in the silicon microstrip detector. The fit is further constrained by fixing the invariant mass calculated from the two muon tracks to the J/ψ mass [17]. These quadruplets of tracks are accepted for further analysis if the vertex fit has a χ 2 /d.o.f. < 3, the fitted p T of each track from φ → K + K − is greater than 1 GeV and the invariant mass of the track pairs (under the assumption that they are kaons) falls within the interval 1.0085 GeV < m(K + K − ) < 1.0305 GeV. If there is more than one accepted candidate in the event, the candidate with the lowest χ 2 /d.o.f. is selected. In total 131513 B 0 s candidates are collected within a mass range of 5.15 < m(B 0 s ) < 5.65 GeV. For each B 0 s meson candidate the proper decay time t is estimated by the expression: where p T B is the reconstructed transverse momentum of the B 0 s meson candidate and M B denotes the world average mass value [17] of the B 0 s meson. The transverse decay length, L xy , is the displacement in the transverse plane of the B 0 s meson decay vertex with respect to the primary vertex, projected onto the direction of the B 0 s transverse momentum. The position of the primary vertex used to calculate this quantity is refitted following the removal of the tracks used to reconstruct the B 0 s meson candidate.
For the selected events the average number of pileup interactions is 5.6, necessitating a choice of the best candidate for the primary vertex at which the B 0 s meson is produced. The variable used is the three-dimensional impact parameter d 0 , which is calculated as the distance between the line extrapolated from the reconstructed B 0 s meson vertex in the direction of the B 0 s momentum, and each primary vertex candidate. The chosen primary vertex is the one with the smallest d 0 . Using MC simulation it is shown that the fraction of B 0 s candidates which are assigned the wrong primary vertex is less than 1% and that the corresponding effect on the final results is negligible. No B 0 s meson decay time cut is applied in the analysis.

IV. FLAVOUR TAGGING
The determination of the initial flavour of neutral Bmesons can be inferred using information from the Bmeson that is typically produced from the other b-quark in the event [18]. This is referred to as the opposite-side tagging (OST).
To study and calibrate the OST methods, events containing the decays of B ± → J/ψK ± can be used, where flavour of the B-meson at production is provided by the kaon charge. Events from the entire 2011 run period satisfying the same data quality selections as described in section 2 are used.
To be selected for use in the calibration analysis, events must satisfy a trigger condition requiring two oppositely charged muons within an invariant mass range around the nominal J/ψ mass. Candidate B ± → J/ψK ± decays are identified using two oppositely charged combined muons forming a good vertex using information supplied by the inner detector. Each muon is required to have a transverse momentum of at least 4 GeV and pseudo-rapidity within |η| < 2.5. The invariant mass of the dimuon candidate is required to satisfy 2.8 < m(µ + µ − ) < 3.4 GeV. To form the B candidate an additional track with the charged kaon mass hypothesis, p T > 1 GeV and |η| < 2.5 is combined with the dimuon candidate and a vertex fit is performed with the mass of the di-muon pair constrained to the known value of the J/ψ mass. To reduce the prompt component of the combinatorial background, the requirement L xy > 0.1 mm is applied to the B candidate. The choice of primary vertex is determined using the same procedure as done for the B 0 s candidates. In order to study the distributions corresponding to the signal processes with the background component removed, a sideband subtraction method is defined. Events are separated into five equal regions of B candidate rapidity from 0 − 2.5 and three mass regions. The mass regions are defined as a signal region around the fitted peak signal mass position µ ± 2σ and the sidebands are [µ − 5σ, µ − 3σ] and [µ + 3σ, µ + 5σ], where µ and σ are the mean and width of the Gaussian function describing the B signal mass, for each rapidity region. Individual binned extended maximum likelihood fits to the invariant mass distribution are performed in each region of rapidity.
The background is modelled by an exponential to describe combinatorial background and a hyperbolic tangent function to parameterize the low-mass contribution from incorrectly or partially reconstructed B decays. A Gaussian function is used to model the B ± → J/ψπ ± contribution. The contributions of non-combinatorial backgrounds are found to have a negligible effect in the tagging procedure. Figure 1 shows the invariant mass FIG. 1. The invariant mass distribution for B ± → J/ψK ± candidates. Included in this plot are all events passing the selection criteria. The data are shown by points, and the overall result of the fit is given by the blue curve. The combinatorial background component is given by the red dotted line, partially reconstructed B decays by the green shaded area, and decays of B ± → J/ψπ ± , where the pion is mis-assigned a kaon mass by a purple dashed line.
distribution of B candidates for all rapidity regions overlaid with the fit result for the combined data.

B. Tagging methods
Several methods are available to infer the flavour of the opposite-side b-quark, with varying efficiencies and discriminating powers. The measured charge of a muon from the semileptonic decay of the B meson provides strong separation power; however, the b → µ transitions are diluted through neutral B meson oscillations, as well as by cascade decays b → c → µ which can alter the sign of the muon relative to the one from direct semileptonic decays b → µ. The separation power of tagging muons can be enhanced by considering a weighted sum of the charge of the tracks in a cone around the muon. If no muon is present, a weighted sum of the charge of tracks associated with the opposite-side B meson decay will provide some separation. The tagging methods are described in detail below.
For muon-based tagging, an additional muon is required in the event, with p T > 2.5 GeV, |η| < 2.5 and with |∆z| < 5 mm from the primary vertex. Muons are classified according to their reconstruction class, combined or segment tagged, and subsequently treated as distinct tagging methods. In the case of multiple muons, the muon with highest transverse momentum is selected.
A muon cone charge variable is constructed, defined as where q is the charge of the track, κ = 1.1 and the sum is performed over the reconstructed ID tracks within a cone size of ∆R = 0.5 [19] around the muon direction and the muon track is included as well. The reconstructed ID tracks must have a p T > 0.5 GeV and |η| < 2.5. The value of the parameter κ was determined while optimizing the tagging performance. Tracks associated with the signal decay are explicitly excluded from the sum. In figure 2 the opposite-side muon cone charge distributions are shown for candidates from B ± signal decays. In the absence of a muon, a b-tagged jet [20] is required in the event, which is seeded from calorimeter clusters, with minimum energy threshold of 10 GeV, and where a minimum b-tag weight requirement of at least −0.5 is applied. The jet tracks are required to be associated with the same primary vertex as the signal decay, excluding those from the signal candidate. Jets within a cone of ∆R < 0.5 of the signal momentum axis are excluded. The jet is reconstructed using the anti-k t algorithm with a cone size of 0.6. In the case of multiple jets, the jet with the highest value of the b-tag weight is used.
A jet charge is defined as where κ = 1.1, and the sum is over the tracks associated with the jet, using the method described in ref.
[21]. Figure 3 shows the distribution of charges for oppositeside jet charge from B ± signal candidate events.
The efficiency of an individual tagger is defined as the ratio of the number of tagged events to the total number of candidates. A probability that a specific event has a signal decay containing ab-quark given the value of the discriminating variable P (B|Q) is constructed from the calibration samples for each of the B + and B − samples, defining P (Q|B + ) and P (Q|B − ) respectively. The probability to tag a signal event as containing ab-quark is therefore P (B|Q) = P (Q|B + )/(P (Q|B + ) + P (Q|B − )) and P (B|Q) = 1−P (B|Q). The tagging power is defined as where the sum is over the bins of the probability distribution as a function of the charge variable and i is the number of tagged events in each bin divided by the total number of candidates. An effective dilution D is calculated from the tagging power and the efficiency.
The combination of the tagging methods is applied according to the hierarchy of performance, based on the dilution of the tagging method. The single best performing tagging measurement is taken, according to the order: combined muon cone charge, segment tagged muon cone charge, jet charge. If it is not possible to provide a tagging response for the event, then a probability of 0.5 is assigned. A summary of the tagging performance is given in table 1.

V. MAXIMUM LIKELIHOOD FIT
An unbinned maximum likelihood fit is performed on the selected events to extract the parameters of the The fit uses information about the reconstructed mass m and its uncertainty σ m , the measured proper decay time t and its uncertainty σ t , the tag probability, and the transversity angles Ω of each B 0 s → J/ψφ decay candidate. There are three transversity angles; Ω = (θ T , ψ T , φ T ) and these are defined in section V A.
The likelihood function is defined as a combination of the signal and background probability density functions as follows: where N is the number of selected candidates, w i is a weighting factor to account for the trigger efficiency, f s is the fraction of signal candidates, f B 0 is the fraction of B 0 (B 0 → J/ψK 0 * and B 0 → J/ψK ± π ∓ ) mesons mis-identified as B 0 s candidates calculated relative to the number of signal events; this parameter is fixed in the likelihood fit. The mass m i , the proper decay time t i and the decay angles Ω i are the values measured from the data for each event i. F s , F B 0 and F bkg are the probability density functions (PDF) modelling the signal, the specific B 0 background and the other background distributions, respectively. A detailed description of the signal PDF terms in equation (1) is given in section V A. The two background functions are, with the exception of new terms dependent on P (B|Q) which are explained in section V B, unchanged from the previous analysis [6]. They are each described by the product of eight terms which describe the distribution of each measured parameter. With the exception of the lifetime and its uncertainty the background parameters are assumed uncorrelated.

A. Signal PDF
The PDF describing the signal events, F s , has the form of a product of PDFs for each quantity measured from the data: The terms P s (m i , σ mi ), P s (Ω i , t i , P (B|Q), σ ti ) and A(Ω i , p Ti ) are explained in the current section. The tagging probability term P s (P (B|Q)) is described in section V B. The remaining probability terms P s (σ mi ), P s (σ ti ) and P s (p Ti ) are described by Gamma functions. They are unchanged from the previous analysis and explained in detail in ref. [6]. Ignoring detector effects, the joint distribution for the decay time t and the transversity angles Ω for the B 0 s → J/ψ(µ + µ − )φ(K + K − ) decay is given by the differential decay rate [22]: where O (k) (t) are the time-dependent amplitudes and g (k) (θ T , ψ T , φ T ) are the angular functions, given in table II. The formulae for the time-dependent amplitudes have the same structure for B 0 s and B 0 s but with a sign reversal in the terms containing ∆m s . The addition of flavour tagging to the analysis means that these terms no longer cancel, so there are more terms in the fit that contain φ s . In addition to this, the strong phase variable δ ⊥ becomes accessible and one of the symmetries in the untagged fit is removed. A ⊥ (t) describes a CP odd final-state configuration while both A 0 (t) and A (t) correspond to CP even final-state configurations. A S (t) describes the contribution of the CP odd non-resonant B 0 s → J/ψK + K − S-wave state as well as the B 0 s → J/ψf 0 decays. The corresponding amplitudes are given in the last four lines of table II (k = 7-10) and follow the convention used in the previous analysis [23]. The likelihood is independent of the K + K − mass distribution.
2 sin 2ψT sin 2θT cos φT ±e −Γst (sin δ ⊥ cos(∆mst) − cos δ ⊥ cos φs sin(∆mst))]  (t) and the functions of the transversity angles g (k) (θT , ψT , φT ). The amplitudes |A0(0)| 2 and |A (0)| 2 are for the CP even components of the B 0 s → J/ψφ decay, |A ⊥ (0)| 2 is the CP odd amplitude; they have corresponding strong phases δ0, δ and δ ⊥ , by convention δ0 is set to be zero. The S-wave amplitude |AS(0)| 2 gives the fraction of B 0 s → J/ψK + K − (f0) and has a related strong phase δS. The ± and ∓ terms denote two cases: the upper sign describes the decay of a meson that was initially a B 0 s , while the lower sign describes the decays of a meson that was initially B The equations are normalized, such that the squares of the amplitudes sum to unity; three of the four amplitudes are fit parameters and |A ⊥ (0)| 2 is determined according to this constraint.
The angles (θ T , ψ T , φ T ), are defined in the rest frames of the final-state particles. The x-axis is determined by the direction of the φ meson in the J/ψ rest frame, and the K + K − system defines the x-y plane, where p y (K + ) > 0. The three angles are defined as follows: • θ T , the angle between p(µ + ) and the normal to the x-y plane, in the J/ψ meson rest frame • φ T , the angle between the x-axis and p xy (µ + ), the projection of the µ + momentum in the x-y plane, in the J/ψ meson rest frame • ψ T , the angle between p(K + ) and − p(J/ψ) in the φ meson rest frame The signal PDF, P s (Ω, t, P (B|Q), σ t ), needs to take into account lifetime resolution, so each time element in table II is smeared with a Gaussian function. This smearing is done numerically on an event-by-event basis where the width of the Gaussian function is the proper decay time uncertainty, measured for each event, multiplied by a scale factor to account for any mis-measurements.
The angular sculpting of the detector and kinematic cuts on the angular distributions are included in the likelihood function through A(Ω i , p Ti ). This is calculated using a 4D binned acceptance method, applying an eventby-event efficiency according to the transversity angles (θ T , ψ T , φ T ) and the p T of the candidate. The p T binning is necessary, because the angular sculpting is influenced by the p T of the B 0 s . The acceptance was calculated from the B 0 s → J/ψφ MC events. In the likelihood function, the acceptance is treated as an angular sculpting PDF, which is multiplied with the time-and angular-dependent PDF describing the B 0 s → J/ψ(µ + µ − )φ(K + K − ) decays. As both the acceptance and time-angular decay PDFs depend on the transversity angles they must be normalized together. This normalization is done numerically during the likelihood fit.
The signal mass function, P s (m), is modelled using a single Gaussian function smeared with an event-by-event mass resolution. The PDF is normalized over the range 5.15 < m(B 0 s ) < 5.65 GeV.

B. Using tag information in the fit
The tag probability for each B 0 s candidate is determined from a weighted sum of charged-particle tracks in a cone, as described in section IV. The tag probability is obtained from this tag charge using the calibrations measured in the B ± → J/ψK ± data. For the case where there is only one track, the cone charge can only be ±1. This leads to a tag probability distribution with continuous and discrete parts (spikes), which are estimated separately. The distributions of tag probabilities for the signal and background are also different and since the background cannot be factorized out, extra PDF terms are included to account for this difference.
To describe the continuous parts, the sidebands are parameterized first. Sidebands are selected according to B 0 s mass, i.e. m(B 0 s ) < 5.317 GeV or m(B 0 s ) > 5.417 GeV. In the fit the same function as for the sidebands is used to describe events in the signal region: background parameters are fixed to the values obtained in sidebands while signal parameters are free in this step. The ratio of background to signal (obtained from simultaneous mass-lifetime fit) is fixed as well. The function describing tagging using combined muons has the form of a fourthorder Chebychev polynomial. A third-order polynomial is used for the segment tagged muons' tagging algorithm. A fourth-order Chebychev polynomial is also applied for the jet charge tagging algorithm. In all three cases unbinned maximum likelihood fits are used. Results of fits projected on histograms are shown in figure 4.
The spikes have their origin in tagging objects formed from a single track, providing a tag charge of exactly +1 or −1. When a background candidate is formed from a random combination of a J/ψ and a pair of tracks, the positive and negative charges are equally probable. However, some of the background events are formed of partially reconstructed B hadrons, and in these cases tag charges of +1 or −1 are not equally probable. For signal events the tag charges are obviously not symmetric. The fractions f +1 and f −1 of events tagged with charges of +1 and −1 are derived separately for signal and background. The remaining (1 − f +1 − f −1 ) is the fraction of events in the continuous region. The fractions f +1 and f −1 are determined using the same B 0 s mass sidebands and signal regions as in case of continuous parts. Table III summarizes the obtained relative probabilities between tag charges +1 and −1 for signal and background events and for all tag methods.
Similarly, the sideband subtraction method is also used to determine, for signal and background events, the relative fraction of each tagging method. The results are summarized in table IV.
If the tag-probability PDFs were ignored in the likelihood fit, equivalent to assuming identical signal and background behaviour, the impact on the fit result would be small, affecting the results by less than 10% of the statistical uncertainty.

VI. RESULTS
The full simultaneous maximum likelihood fit contains 25 free parameters. These include the nine physics parameters: ∆Γ s , φ s , Γ s , |A 0 (0)| 2 , |A (0)| 2 , δ || , δ ⊥ , |A S | 2 and δ S . The other parameters in the likelihood function are the B 0 s signal fraction f s , the parameters describing the J/ψφ mass distribution, the parameters describing the B 0 s meson decay time plus angular distributions of background events, the parameters used to describe the estimated decay time uncertainty distributions for signal and background events, and scale factors between the estimated decay time and mass uncertainties and their true uncertainties.
The number of signal B 0 s meson candidates extracted from the fits is 22670 ± 150. The results and correlations for the measured physics parameters of the simultaneous unbinned maximum likelihood fit are given in tables V and VI. Fit projections of the mass, proper decay time and angles are given in figures 5 and 6 respectively. For the parameters δ and δ ⊥ − δS a 68% confidence level interval is given. The reason for this is described in section 8.

VII. SYSTEMATIC UNCERTAINTIES
Systematic uncertainties are assigned by considering several effects that are not accounted for in the likelihood fit. These are described below.
• Inner detector alignment: Residual misalignments of the inner detector affects the impact parameter distribution with respect to the primary vertex. The effect of the residual mis-alignment is estimated using simulated events with and without distorted geometry. For this, the impact parameter distribution with respect to the primary vertex is measured with data as a function of η and φ with the maximum deviation from zero being less than 10 µm. The measurement is used to distort the geometry for simulated events in order to reproduce the impact parameter distribution measured as a function of η and φ. The difference between the measurement using simulated events with and without the distorted geometry is used as the systematic uncertainty.
• Trigger efficiency: It is observed that the muon trigger biases the transverse impact parameter of muons toward smaller values. To correct for this bias the events are re-weighted according to where τ sing is a single B 0 s lifetime measured before the correction, using an unbinned mass-lifetime maximum likelihood fit. The value of the parameter and its uncertainty are described in [6]. The systematic uncertainty is calculated by varying the value of by its uncertainty and rerunning the fit.
• B 0 contribution: Contaminations from B 0 → J/ψK 0 * and B 0 → J/ψKπ events misreconstructed as B 0 s → J/ψφ are accounted for in the default fit. The fractions of B 0 → J/ψK 0 * and B 0 → J/ψKπ events in the default fit are (6.5 + / − 2.4)% and (4.5 + / − 2.8)% respectively. They were determined in MC simulation and using branching fractions from ref. [17]. To estimate the systematic uncertainty arising from the precision of the fraction estimates, the data are fitted with these fractions increased and decreased by 1σ. The largest shifts in the fitted values from the default case are taken as the systematic uncertainty for each parameter of interest.
• Tagging: For the uncertainties in the fit parameters due to uncertainty in the tagging, the statistical and systematic components are separated. The statistical uncertainty is due to the sample size of B ± → J/ψK ± decays available and is included in the overall statistical error. The systematic uncertainty arises from the precision of the tagging calibration and is estimated by varying the model parameterizing the probability distribution, P (B|Q), as a function of tag charge. The default model is a linear function. For the combined-muon conecharge tag and the segment tagged muons the alternative fit function is a third-order polynomial. For the jet-charge tag with no muons, a third-and a fifth-order polynomial are used. The B 0 s fit was repeated using the alternative models and the largest difference was assigned as the systematic uncertainty.
• Angular acceptance method: The angular acceptance is calculated from a binned fit to Monte Carlo data. A separate set of Monte Carlo signal events were generated and fully simulated. Background was generated using pseudo-experiments as described below. There is sufficient data to perform 166 fits. The systematic uncertainty is calculated using the bias of the pull distribution multiplied by the statistical uncertainty of each parameter. In order to estimate the size of the systematic uncertainty introduced from the choice of binning, different acceptance functions are calculated using different bin widths and central values. These effects are found to be negligible.

VIII. DISCUSSION
The PDF describing the B 0 s → J/ψφ decay is invariant under the following simultaneous transformations: ∆Γ s has been determined to be positive [24]. Therefore there is a unique solution and only the case ∆Γ s > 0 is considered. Uncertainties on individual parameters were studied in detail in likelihood scans. Figure 7 shows the 1D likelihood scans for φ s and ∆Γ s . Figure 8 shows the likelihood contours in the φ s -∆Γ s plane.
The behaviour of the amplitudes around their fitted values is Gaussian, however the strong phases are more complicated. Figure 9 shows the 1D likelihood scans for the three measured strong phases.
The likelihood behaviour of δ ⊥ appears Gaussian and therefore it is reasonable to quote δ ⊥ = 3.89 ± 0.47(stat) rad. For δ ⊥ − δ S the scan shows a minimum close to π; however, it is insensitive over the rest of the scan at the level of 2.1σ. Therefore the measured value of the difference δ ⊥ − δ S is only given as 1σ confidence interval [3.02, 3.25] rad. For the strong phase δ || the central fit value is close to π (3.14±0.10) and the 1D likelihood scan shows normal Gaussian behaviour around this minimum. However, the systematic pull plot based on 2400 pseudoexperiments fits reveals a double-Gaussian shape with 68% of the results included in the interval [2.92, 3.35] rad and so we quote the result in the form of a 68% C.L. interval δ || ∈ [2.92, 3.35] rad (statistical only). [rad]

IX. CONCLUSION
A measurement of time-dependent CP asymmetry parameters in B 0 s → J/ψ(µ + µ − )φ(K + K − ) decays from a 4.9 fb −1 data sample of pp collisions collected with the ATLAS detector during the 2011 √ s = 7 TeV LHC run is presented. Several parameters describing the B 0 s meson system are measured. These include the mean B 0 s lifetime 1/Γ s , the decay width difference ∆Γ s between the heavy and light mass eigenstates, and the transversity amplitudes |A 0 (0)| and |A (0)|. Each of these is consistent with its respective world average. Likelihood contours in the φ s -∆Γ s plane are also provided. The fraction |A S (0)| 2 , the signal contribution from B 0 s → J/ψK + K − and B 0 s → J/ψf 0 decays, is measured to be consistent with zero, at 0.024 ± 0.014 (stat.) ± 0.028 (syst.). The values are consistent with those obtained in our untagged analysis [6] and significantly reduce the overall uncertainty on φ s . These results are consistent with the values predicted in the Standard Model.

ACKNOWLEDGMENTS
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.