A measurement of the Bs0→J/ψϕ\documentclass[12pt]{minimal}
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\begin{document}$$ B_{s}^{0} \rightarrow J/\psi \phi $$\end{document} decay parameters using 80.5fb-1\documentclass[12pt]{minimal}
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\begin{document}$$ 80.5\, \mathrm {fb^{-1}} $$\end{document} of integrated luminosity collected with the ATLAS detector from 13 Te\documentclass[12pt]{minimal}
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\begin{document}$$\text {Te}\text {V}$$\end{document} proton–proton collisions at the LHC is presented. The measured parameters include the CP-violating phase ϕs\documentclass[12pt]{minimal}
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\begin{document}$$ \Gamma _{s}$$\end{document}. The values measured for the physical parameters are combined with those from 19.2fb-1\documentclass[12pt]{minimal}
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\begin{document}$$\text {Te}\text {V}$$\end{document} data, leading to the following: ϕs=-0.087±0.036(stat.)±0.021(syst.)radΔΓs=0.0657±0.0043(stat.)±0.0037(syst.)ps-1Γs=0.6703±0.0014(stat.)±0.0018(syst.)ps-1\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \phi _{s}= & {} -0.087 \pm 0.036 ~\mathrm {(stat.)} \pm 0.021 ~\mathrm {(syst.)~rad} \\ \Delta \Gamma _{s}= & {} 0.0657 \pm 0.0043 ~\mathrm {(stat.)}\pm 0.0037 ~\mathrm {(syst.)~ps}^{-1} \\ \Gamma _{s}= & {} 0.6703 \pm 0.0014 ~\mathrm {(stat.)}\pm 0.0018 ~\mathrm {(syst.)~ps}^{-1} \end{aligned}$$\end{document}Results for ϕs\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta \Gamma _{s}$$\end{document} are also presented as 68% confidence level contours in the ϕs\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta \Gamma _{s}$$\end{document} plane. Furthermore the transversity amplitudes and corresponding strong phases are measured. ϕs\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta \Gamma _{s}$$\end{document} measurements are in agreement with the Standard Model predictions.
publisher-imprint-nameSpringervolume-issue-count12issue-article-count72issue-toc-levels0issue-pricelist-year2021issue-copyright-holderThe Author(s)issue-copyright-year2021article-contains-esmNoarticle-numbering-styleContentOnlyarticle-registration-date-year2021article-registration-date-month3article-registration-date-day1article-toc-levels0toc-levels0volume-typeRegularjournal-productNonStandardArchiveJournalnumbering-styleContentOnlyarticle-grants-typeOpenChoicemetadata-grantOpenAccessabstract-grantOpenAccessbodypdf-grantOpenAccessbodyhtml-grantOpenAccessbibliography-grantOpenAccessesm-grantOpenAccessonline-firstfalsepdf-file-referenceBodyRef/PDF/10052_2021_Article_9011.pdfpdf-typeTypesettarget-typeOnlinePDFissue-typeRegulararticle-typeOriginalPaperjournal-subject-primaryPhysicsjournal-subject-secondaryElementary Particles, Quantum Field Theoryjournal-subject-secondaryNuclear Physics, Heavy Ions, Hadronsjournal-subject-secondaryQuantum Field Theories, String Theoryjournal-subject-secondaryMeasurement Science and Instrumentationjournal-subject-secondaryAstronomy, Astrophysics and Cosmologyjournal-subject-secondaryNuclear Energyjournal-subject-collectionPhysics and Astronomyopen-accesstrueIntroduction
In the presence of new physics (NP) phenomena, sources of CP violation in b-hadron decays can arise in addition to those predicted by the Standard Model (SM) [1]. In the Bs0→J/ψϕ\documentclass[12pt]{minimal}
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\begin{document}$$ B_{s}^{0} \rightarrow J/\psi \phi $$\end{document} decay, CP violation occurs due to interference between a direct decay and a decay with Bs0\documentclass[12pt]{minimal}
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\begin{document}$$\bar{B}^{0}_{s}$$\end{document} mixing. The oscillation frequency of Bs0\documentclass[12pt]{minimal}
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\begin{document}$$B_{s}^{0}$$\end{document} meson mixing is characterised by the mass difference, Δms\documentclass[12pt]{minimal}
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\begin{document}$$\Delta m_{s} $$\end{document}, of the heavy (BH\documentclass[12pt]{minimal}
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\begin{document}$$B_{\mathrm H} $$\end{document}) and light (BL\documentclass[12pt]{minimal}
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\begin{document}$$B_{\mathrm L} $$\end{document}) mass eigenstates. The CP-violating phase ϕs\documentclass[12pt]{minimal}
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\begin{document}$$\phi _{s} $$\end{document} is defined as the weak phase difference between the Bs0\documentclass[12pt]{minimal}
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\begin{document}$$b \rightarrow c \overline{c} s$$\end{document} decay amplitude. In the SM the phase ϕs\documentclass[12pt]{minimal}
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\begin{document}$$\phi _{s} $$\end{document} is small and is related to the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing matrix elements via the relation ϕs≃-2βs\documentclass[12pt]{minimal}
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\begin{document}$$\phi _{s} \simeq -2 \beta _{s}$$\end{document}, with βs=arg[-(VtsVtb∗)/(VcsVcb∗)]\documentclass[12pt]{minimal}
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\begin{document}$$\beta _{s} = \mathrm {arg} [- (V_{ts} V^{*}_{tb})/(V_{cs} V_{cb}^{*}) ]$$\end{document}. By combining beauty and kaon physics observables, and assuming no NP contributions to Bs0\documentclass[12pt]{minimal}
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\begin{document}$$B_{s}^{0}$$\end{document} mixing and decays, a value of -2βs=-0.03696-0.00082+0.00072\documentclass[12pt]{minimal}
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\begin{document}$$-2 \beta _{s} = -0.03696^{+0.00072}_{-0.00082}$$\end{document} rad was predicted by the CKMFitter group [2] and -2βs=-0.03700±0.00104\documentclass[12pt]{minimal}
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\begin{document}$$-2 \beta _{s} = -0.03700 \pm 0.00104$$\end{document} rad according to the UTfit Collaboration [3]. While large NP enhancements of the mixing amplitude have been excluded by the precise measurement of the oscillation frequency [4], the NP couplings involved in the mixing may still increase the size of the observed CP violation by enhancing the mixing phase ϕs\documentclass[12pt]{minimal}
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\begin{document}$$\phi _{s} $$\end{document} with respect to the SM value.
Other physical quantities involved in Bs0\documentclass[12pt]{minimal}
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\begin{document}$$\bar{B}^{0}_{s}$$\end{document} mixing are the decay width Γs=(ΓL+ΓH)/2\documentclass[12pt]{minimal}
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\begin{document}$$ \Gamma _{s}=(\Gamma _{\mathrm L} + \Gamma _{\mathrm H} )/2$$\end{document} and the width difference ΔΓs=ΓL-ΓH\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta \Gamma _{s}= \Gamma _{\mathrm L} - \Gamma _{\mathrm H} $$\end{document}, where ΓL\documentclass[12pt]{minimal}
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\begin{document}$$\Gamma _{\mathrm H} $$\end{document} are the decay widths of the light and heavy mass eigenstates, respectively. The latest predictions for the width difference in the SM are ΔΓs=0.091±0.013\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta \Gamma _{s}= 0.091 \pm 0.013$$\end{document} ps-1\documentclass[12pt]{minimal}
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\begin{document}$$^{-1}$$\end{document} [5] and ΔΓs=0.092±0.014\documentclass[12pt]{minimal}
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\begin{document}$$^{-1}$$\end{document} [6]. A potential NP enhancement of ϕs\documentclass[12pt]{minimal}
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\begin{document}$$\phi _{s} $$\end{document} would also decrease the size of ΔΓs\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta \Gamma _{s}$$\end{document}, but it is not expected to be affected as significantly as ϕs\documentclass[12pt]{minimal}
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\begin{document}$$\phi _{s} $$\end{document} [7]. Nevertheless, extracting ΔΓs\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta \Gamma _{s}$$\end{document} from the data is an important test of theoretical predictions [7].
Theory predictions have been made for the lifetime ratios τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau (B^+)$$\end{document}, with the latest update Ref. [8]. The lifetime τ\documentclass[12pt]{minimal}
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\begin{document}$$B_{s}^{0}$$\end{document}) has not been calculated in theory yet at a precision comparable with those obtained by experiments. The current world combined value of the decay width, Γs\documentclass[12pt]{minimal}
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\begin{document}$$ \Gamma _{s}$$\end{document}, obtained from experimental results is Γs=0.6600±0.0016\documentclass[12pt]{minimal}
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\begin{document}$$ \Gamma _{s}= 0.6600\pm 0.0016$$\end{document} ps-1\documentclass[12pt]{minimal}
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\begin{document}$$^{-1}$$\end{document} [9].
The analysis of the time evolution of the Bs0→J/ψϕ\documentclass[12pt]{minimal}
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\begin{document}$$ B_{s}^{0} \rightarrow J/\psi \phi $$\end{document} decay provides the most precise determination of ϕs\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta \Gamma _{s}$$\end{document}. Previous measurements of these quantities have been reported by the D0, CDF, LHCb, ATLAS and CMS Collaborations [10–17]. Additional improvements in measuring ϕs\documentclass[12pt]{minimal}
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\begin{document}$$B_{s}^{0} \rightarrow J/\psi \pi ^+\pi ^-$$\end{document} decays have been achieved by the LHCb Collaboration [18–21].
The analysis presented here introduces a measurement of the Bs0→J/ψϕ\documentclass[12pt]{minimal}
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\begin{document}$$ B_{s}^{0} \rightarrow J/\psi \phi $$\end{document} decay parameters using 80.5fb-1\documentclass[12pt]{minimal}
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\begin{document}$$ 80.5\, \mathrm {fb^{-1}} $$\end{document} of the LHC proton–proton (pp) data collected by the ATLAS detector during 2015–2017, at a centre-of-mass energy, s\documentclass[12pt]{minimal}
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\begin{document}$$\text {Te}\text {V}$$\end{document}. The analysis closely follows a previous ATLAS measurement [13] that was performed using 19.2 fb-1\documentclass[12pt]{minimal}
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\begin{document}$$\text {Te}\text {V}$$\end{document}, and introduces more precise signal and background models.
ATLAS detector and Monte Carlo simulation
The ATLAS detector1 consists of three main components: an inner detector (ID) tracking system immersed in a 2 T axial magnetic field, electromagnetic and hadronic calorimeters, and a muon spectrometer (MS). The inner tracking detector covers the pseudorapidity range |η|<2.5\documentclass[12pt]{minimal}
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\begin{document}$$|\eta | < 2.5$$\end{document}, and consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors. The ID is surrounded by a high-granularity liquid-argon (LAr) sampling electromagnetic calorimeter. A steel/scintillator tile calorimeter provides hadronic coverage in the central rapidity range. The endcap and forward regions are equipped with LAr calorimeters for electromagnetic and hadronic measurements. The MS surrounds the calorimeters and provides a system of tracking chambers and detectors for triggering. A full description can be found in Refs. [22–24].
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\begin{document}$$ 80.5\, \mathrm {fb^{-1}} $$\end{document} of pp collision data. The uncertainty in the combined 2015–2017 integrated luminosity is 2.0% [25], obtained using the LUCID-2 detector [26] for the primary luminosity measurements.
To study the detector response, estimate backgrounds, and model systematic effects, 100M Monte Carlo (MC) simulated Bs0→J/ψϕ\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}, as determined from the re-fitted track parameters of the vertex, are retained for further analysis. To form the B±\documentclass[12pt]{minimal}
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\begin{document}$$B^{\pm }$$\end{document} candidate, an additional track is required, which is not identified as an electron or muon. The track is assigned the charged-kaon mass hypothesis and combined with the dimuon candidate using a vertex fit, performed with the mass of the dimuon pair constrained to the J/ψ\documentclass[12pt]{minimal}
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\begin{document}$$t > 0.2$$\end{document} ps.
The tagging probabilities are determined from B+\documentclass[12pt]{minimal}
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\begin{document}$$B^{\pm }\rightarrow J/\psi K^{\pm }$$\end{document} signal, two Gaussian functions with a common mean are used. An exponential function is used to describe the combinatorial background and a hyperbolic tangent function to parameterise the low-mass contribution from incorrectly or partially reconstructed b-hadron decays. A Gaussian function is used to describe the B±→J/ψπ±\documentclass[12pt]{minimal}
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\begin{document}$$B^{\pm }\rightarrow J/\psi \pi ^{\pm }$$\end{document} contribution, with fixed parameters taken from simulation except for the normalisation, which is a free parameter. A fit to the overall mass distribution is used to define the shapes of signal and backgrounds. Subsequent fits are performed in the intervals of the tagging discriminating variables, separately for B+\documentclass[12pt]{minimal}
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\begin{document}$$B^{-}$$\end{document} signal yields are extracted from these fits. Figure 1 shows the invariant mass distribution of B±\documentclass[12pt]{minimal}
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\begin{document}$$B^{\pm }$$\end{document} candidates overlaid with a fit to all selected candidates, and including the individual fit components for the signal and backgrounds.
The invariant mass distribution for selected B±→J/ψK±\documentclass[12pt]{minimal}
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\begin{document}$$B^{\pm }\rightarrow J/\psi K^{\pm }$$\end{document} candidates. Data are shown as points, and the overall result of the fit is given by the blue curve. The contributions from the combinatorial background component are indicated by the red dotted line, partially reconstructed b-hadron decays by the purple shaded area, and decays of B±→J/ψπ±\documentclass[12pt]{minimal}
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\begin{document}$$B^{\pm }\rightarrow J/\psi \pi ^{\pm }$$\end{document}, where the pion is misassigned as a kaon, by the green dashed line
Flavour tagging methods
The flavour of the signal B meson at the point of production is inferred using several methods, which differ in their efficiency and discrimination power. The measured charge of a lepton (electron or muon) from the semileptonic decay of a B meson provides strong discrimination; however, the ATLAS sensitivity to b→ℓ\documentclass[12pt]{minimal}
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\begin{document}$$b\rightarrow c\rightarrow \ell $$\end{document}. The separation power of lepton tagging is enhanced by considering a weighted sum of the charge of the tracks in a cone around the lepton. If no lepton is present, a weighted sum of the charge of the tracks in a jet associated with the opposite-side b-hadron decay is used to provide discrimination. This weighted sum, or cone charge, is defined as:Qx=∑iNtracksqi·(pTi)κ∑iNtracks(pTi)κ,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} Q_{x} = \frac{ \sum ^{N\;\mathrm {tracks}}_{i} q_{i} \cdot (p_{\mathrm {T} i })^{\kappa }}{ \sum ^{N\;\mathrm {tracks}}_{i}(p_{\mathrm {T} i })^{\kappa }}, \end{aligned}$$\end{document}where x={μ,e,jet}\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T} i }$$\end{document}, over a selected set of tracks, including the lepton, in a cone of size ΔR=(Δϕ)2+(Δη)2\documentclass[12pt]{minimal}
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\begin{document}$$\Delta R = \sqrt{(\Delta \phi )^2+(\Delta \eta )^2}$$\end{document}, around the lepton or jet direction. The value of the parameter κ\documentclass[12pt]{minimal}
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\begin{document}$$\Delta R$$\end{document} are described below, dependent on the OST method.
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\begin{document}$$-1<Q_{x}<1$$\end{document} for each OST algorithm.
A probability P(B|Qx)\documentclass[12pt]{minimal}
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\begin{document}$$P(B|Q_{x}) = P(Q_{x}|B^{+}) / (P(Q_{x}|B^{+}) + P(Q_{x}|B^{-}))$$\end{document}, and correspondingly P(B¯|Qx)=1-P(B|Qx)\documentclass[12pt]{minimal}
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Muon tagging
For muon-based tagging, at least one additional muon is required in the event, with pT>2.5\documentclass[12pt]{minimal}
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Electron tagging
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Jet tagging
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Flavour tagging performance
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\begin{document}$$P_{\text {s}}(P(B|Q_{x}))$$\end{document} is used to model the probability distributions for these contributions (described further in Sect. 5.2). The PDFs consist of the fraction of events that are tagged with a particular method (or are untagged), the fractions of those events categorised as discrete or continuous, and for those that are continuous, a PDF of the corresponding probability distribution.
Continuous PDF
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\begin{document}$$D_{x}$$\end{document}) is obtained from the measured efficiency and tagging power. For the efficiency, effective dilution, and tagging power, the corresponding uncertainty is determined by combining the appropriate uncertainties in the individual bins of each charge distribution
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\begin{document}$$-1$$\end{document}, respectively, for signal and background events and for the different tagging methods. Only statistical uncertainties are given
The fractions of signal and background events tagged using the different OST methods are found using a similar sideband-subtraction method, and are summarised in Table 3.
To account for possible deviations of the data from the selected fit models, variations of the procedure described here are used to determine systematic uncertainties, as described in Sect. 6.
Maximum likelihood fit
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\begin{document}$$\Omega = (\theta _T,\psi _T,\phi _T)$$\end{document} are defined in Sect. 5.1. The likelihood function is defined as a combination of the signal and background PDFs as follows:lnL=∑i=1Nwi·ln[fs·Fs(mi,ti,σmi,σti,Ωi,Pi(B|Qx),pTi)+fs·fB0·FB0(mi,ti,σmi,σti,Ωi,Pi(B|Qx),pTi)+fs·fΛb·FΛb(mi,ti,σmi,σti,Ωi,Pi(B|Qx),pTi)+(1-fs·(1+fB0+fΛb))Fbkg(mi,ti,σmi,σti,Ωi,Pi(B|Qx),pTi)],\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \ln ~\mathcal{L}&= \sum _{i=1}^N w_i \cdot \mathrm {ln} [ f_{\text {s}} \cdot \mathcal{F}_{\text {s}}( m_{i}, t_{i}, \sigma _{m_{i}}, \sigma _{t_{i}}, \Omega _i , P_{i}(B|Q_{x}), { p _{\mathrm {T}_{i}}} )\nonumber \\&\quad + f_{\text {s}} \cdot f_{B^0} \cdot \mathcal{F}_{B^0} ( m_{i}, t_{i}, \sigma _{m_{i}}, \sigma _{t_{i}}, \Omega _i , P_{i}(B|Q_{x}), {{ p }_{\mathrm {T}_{i}}} ) \nonumber \\&\quad + f_{\text {s}} \cdot f_{\Lambda _b} \cdot \mathcal{F}_{\Lambda _b} ( m_{i}, t_{i}, \sigma _{m_{i}}, \sigma _{t_{i}}, \Omega _i , P_{i}(B|Q_{x}), {{ p }_{\mathrm {T}_{i}}} ) \nonumber \\&\quad + ( 1 - f_{\text {s}} \cdot (1 + f_{B^0} + f_{\Lambda _b}) ) \mathcal{F}_{\text {bkg}} ( m_{i}, t_{i}, \sigma _{m_{i}}, \sigma _{t_{i}}, \nonumber \\&\qquad \Omega _i, P_{i}(B|Q_{x}), { p _{\mathrm {T}_{i}}} ) ], \end{aligned}$$\end{document}where N is the number of selected candidates, wi\documentclass[12pt]{minimal}
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\begin{document}$$w_i$$\end{document} is a weighting factor to account for the trigger efficiency (described in Sect. 5.3). The terms Fs\documentclass[12pt]{minimal}
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\begin{document}$$B_{s}^{0}$$\end{document} candidates, calculated relative to the number of signal events. These background fractions are fixed to their expectation from the MC simulation, and variations are applied as part of the evaluation of the effects of systematic uncertainties. The mass mi\documentclass[12pt]{minimal}
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\begin{document}$$\Omega _i $$\end{document} are the values measured from the data for each event i. A detailed description of the signal PDF terms in Eq. (2) is given in Sect. 5.1. The three background functions are described in Sect. 5.2.
Fractions of signal and background events tagged using the different methods. The efficiencies include both the continuous and discrete contributions. Only statistical uncertainties are quoted
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\begin{document}$$\begin{aligned}&\mathcal{F}_{\text {s}}( { m _{i}, t_{i},} \sigma _{m_{i}}, \sigma _{t_{i}}, \Omega _i, P_{i}(B|Q_{x}), { p _{\mathrm {T}_{i}}} ) \\&\quad = P_{\text {s}}(m_{i}|\sigma _{m_{i}}) \cdot P_{\text {s}}(\sigma _{m_{i}}|{{ p }_{\mathrm {T}_{i}}}) \cdot P_{\text {s}}(t_{i},\Omega _i|\sigma _{t_{i}},P_{i}(B|Q_{x})) \\&\qquad \cdot P_{\text {s}}(\sigma _{t_{i}}|{{ p }_{\mathrm {T}_{i}}}) \cdot P_{\text {s}}(P_{i}(B|Q_{x})) \cdot A(\Omega _i,{ p _{\mathrm {T}_{i}}}) \cdot P_{\text {s}}({ p _{\mathrm {T}_{i}}}). \end{aligned}$$\end{document}The mass term Ps(mi|σmi)\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} { P}_{\mathrm {s}} ( m _{i}|\sigma _{m_{i}} ) \equiv \frac{1}{ \sqrt{2\pi } S_m \sigma _{m_{i}} } \cdot \mathrm {e}^{ \frac{ -(m_i -m_{B_s})^{2} }{2( S_m \sigma _{m_{i}} )^{2} } }. \end{aligned}$$\end{document}The term Ps(mi|σmi)\documentclass[12pt]{minimal}
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\begin{document}$$P_{\text {s}}(t_{i}, \Omega _i|\sigma _{t_{i}}, P_{i}(B|Q_{x}))$$\end{document} takes into account the lifetime resolution, so each time element in Table 4 is convolved with a Gaussian function defined as:R(t′-ti,σti)≡12πStσti·e-(ti′-ti)22(Stσti)2.\documentclass[12pt]{minimal}
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The proper decay time uncertainty distribution for data (black), and the fits to the background (blue) and the signal (purple) contributions. The total fit is shown as a red curve
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\begin{document}$$\begin{aligned} \frac{\mathrm {d}^4 \Gamma }{\mathrm {d}t\ \mathrm {d}\Omega }= \sum _{k=1}^{10}\mathcal{O}^{(k)}(t) g^{(k)}(\theta _T,\psi _T,\phi _T), \end{aligned}$$\end{document}where O(k)(t)\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}.
Background PDF
The background PDF has the following composition:Fbkg(mi,ti,σti,Ωi,Pi(B|Qx),pTi)=Pb(mi)·Pb(ti|σti)·Pb(Pi(B|Qx))·Pb(Ωi)·Pb(σmi|pTi)·Pb(σti|pTi)·Pb(pTi).\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned}&\mathcal{F}_{\text {bkg}}( { m _{i}, t_{i}}, \sigma _{t_{i}}, \Omega _i, P_{i}(B|Q_{x}), { { p }_{\mathrm {T}_{i}}} ) \\&\quad = P_{\text {b}}(m_{i})\cdot P_{\text {b}}(t_{i}|\sigma _{t_{i}}) \cdot P_{\text {b}}(P_{i}(B|Q_{x})) \\&\qquad \cdot P_{\text {b}}(\Omega _i)\cdot P_{\text {b}}(\sigma _{m_{i}}|{{ p }_{\mathrm {T}_{i}}}) \cdot P_{\text {b}}(\sigma _{t_{i}}|{{ p }_{\mathrm {T}_{i}}}) \cdot P_{\text {b}}({{ p }_{\mathrm {T}_{i}}}). \end{aligned}$$\end{document}The proper decay time function Pb(ti|σti)\documentclass[12pt]{minimal}
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\begin{document}$$P_{\text {b}}(\Omega _i)$$\end{document} arises primarily from detector and kinematic acceptance effects. The best description is achieved by Legendre polynomial functions:Ylm(θT)=(2l+1)/(4π)(l-m)!/(l+m)!Pl|m|(cosθT),Pk(x)=12kk!dkdxk(x2-1)k,Pl|m|(x)=(-1)|m|(1-x2)|m|/2d|m|dx|m|(Pl(x)),\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned}&P_{\mathrm {b}}(\theta _T,\psi _T,\phi _T) \\&\quad = \sum _{k=0}^{k_{max}}\sum _{l=0}^{l_{max}}\sum _{m=-l}^{l} {\left\{ \begin{array}{ll} a_{k,l,m}\sqrt{2} Y^m_l(\theta _T) \cos (m\phi _T) P_k(\cos \psi _T) &{} \text {where } m > 0 \\ a_{k,l,m}\sqrt{2} Y^{-m}_l(\theta _T) \sin (m\phi _T) P_k(\cos \psi _T) &{} \text {where } m < 0 \\ a_{k,l,m}\sqrt{2} Y^{0}_l(\theta _T) P_k(\cos \psi _T) &{} \text {where } m = 0 \\ \end{array}\right. } \end{aligned}$$\end{document}where lmax=14\documentclass[12pt]{minimal}
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\begin{document}$$B_d \rightarrow J/\psi K^{0*}$$\end{document} decays are included in the PDF of the fit, using the parameters measured in Ref. [47].
Proper decay time dependence of muon trigger efficiency
In the triggers used in this analysis, there is no minimum cut applied on the transverse impact parameter d0\documentclass[12pt]{minimal}
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\begin{document}$$B_{s}^{0}$$\end{document} proper decay time distribution obtained before and after applying the trigger selection. To account for this inefficiency in the fit, the events are reweighted by a factor w, inversely proportional to the trigger efficiency:1/w=p0·[1-p1·(Erf((t-p3)/p2)+1)],\documentclass[12pt]{minimal}
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\begin{document}$$B_{s}^{0}$$\end{document} candidates the inefficiency is below 2%. For the most affected candidates the inefficiency reaches up to 50% at high decay time. No significant bias or inefficiency due to offline track reconstruction, vertex reconstruction, or track quality selection criteria is observed.
Summary of the fit parameters
The joint PDF of proper decay time and decay angles includes the main physics parameters of interest:
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The likelihood function also includes other parameters referred to as “nuisance parameters” such as: the Bs0\documentclass[12pt]{minimal}
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Systematic uncertainties
Systematic uncertainties are evaluated for effects that are described below.
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ID alignment: The changes of the fit parameters due to residual misalignments of the ID were studied and the observed deviations are included in the systematic uncertainties.
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Fit bias: Due to its complexity, the fit model can be sensitive to some nuisance parameters. This limited sensitivity could potentially lead to a bias in the measured physics parameters, even when the model describes the fitted data well. To test the stability of the results obtained from the chosen default fit model, a set of pseudo-experiments is conducted using the default model in both the generation and fit. The systematic uncertainties are determined from the mean of the pull distributions of the pseudo-experiments scaled according to the statistical uncertainty of that parameter in the fit to data. The observed deviations are included in the systematic uncertainties.
The systematic uncertainties are listed in Table 5. For each parameter, the total systematic uncertainty is obtained by adding all of the contributions in quadrature.
ResultsFit results
The results of the likelihood fit are shown in Table 6. The total number of Bs0\documentclass[12pt]{minimal}
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\begin{document}$$B_{s}^{0}$$\end{document} mass agrees well with the world average value [33]. Fit projections, including ratio plots, are shown in Fig. 7 for the mass and proper decay time and in Fig. 8 for the angles. The ratio plots show the difference between each data point and the total fit line divided by the statistical and systematic uncertainties summed in quadrature (σ\documentclass[12pt]{minimal}
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\begin{document}$$2\sigma $$\end{document}, which shows that the total uncertainties cover any discrepancy between data and fit model.
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\begin{document}$$\Delta $$\end{document}ln(L) between solutions (b) and (a) is 0.03. For the rest of the variables the values for the two minima are consistent. The same is true for the statistical and systematic uncertainties of all the variables
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\begin{document}$$ B_{s}^{0} \rightarrow J/\psi \phi $$\end{document} signal component is shown by the magenta dashed line and the blue dotted line shows the contribution of all background components. Below each figure is a ratio plot that shows the difference between each data point and the total fit line divided by the statistical and systematic uncertainties summed in quadrature (σ\documentclass[12pt]{minimal}
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\begin{document}$$ \Gamma _{s}$$\end{document}, the fit determines a single solution with Gaussian behaviour of the projection of the log-likelihood (see Fig. 10 in Sect. 7.2), for the strong-phases δ‖\documentclass[12pt]{minimal}
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\begin{document}$$\delta _\perp $$\end{document} two well separated local maxima of the likelihood are found, and shown as solution (a) and (b) in Table 6. The difference in -2Δ\documentclass[12pt]{minimal}
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\begin{document}$$-2\Delta $$\end{document}ln(L) between the two solutions is 0.03. As discussed in Sect. 7.2, the two-fold behaviour of the likelihood in the strong phases is the result of an approximate symmetry of the signal PDF. The effect is completely negligible for all other variables, for which the fit values and uncertainty ranges overlap accurately.
The correlation between statistical uncertainties of the parameters are also shown in Table 7 for solution (a) and in Table 8 for solution (b). The correlations do not change significantly between the physics variables which remain stable between the solutions (a) and (b). The correlations with the two strong phases: δ‖\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \{ \delta _{\parallel }, \delta _{\perp }, \delta _{S} \} \rightarrow \{ 2 \pi -\delta _{\parallel }, \delta _{\perp } + 2 (\pi -\delta _{\parallel }), \delta _{S} + 2 (\pi - \delta _{\parallel }) \}. \end{aligned}$$\end{document}This transformation is proportional to π-δ‖\documentclass[12pt]{minimal}
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\begin{document}$$-~2 \Delta { \ln (L)}$$\end{document}, between the two solutions is equal to 0.03, favouring (a) but without ruling out (b).
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Summary
This paper presents a measurement of the time-dependent CP asymmetry parameters in Bs0→J/ψϕ\documentclass[12pt]{minimal}
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Acknowledgements
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. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRT, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; JINR; MES of Russia and NRC KI, Russian Federation; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada, CRC and IVADO, Canada; Beijing Municipal Science & Technology Commission, China; COST, ERC, ERDF, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [53].
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All ATLAS scientific output is published in journals, and preliminary results are made available in Conference Notes. All are openly available, without restriction on use by external parties beyond copyright law and the standard conditions agreed by CERN. Data associated with journal publications are also made available: tables and data from plots (e.g. cross section values, likelihood profiles, selection efficiencies, cross section limits, ...) are stored in appropriate repositories such as HEPDATA (http://hepdata.cedar.ac.uk/). ATLAS also strives to make additional material related to the paper available that allows a reinterpretation of the data in the context of new theoretical models. For example, an extended encapsulation of the analysis is often provided for measurements in the framework of RIVET (http://rivet.hepforge.org/). This information is taken from the ATLAS Data Access Policy, which is a public document that can be downloaded from http://opendata.cern.ch/record/413[opendata.cern.ch].]
ReferencesBotellaFJBrancoGCNebotMCP violation and limits on New Physics including recent Bs measurementsNucl. Phys. B200776812007NuPhB.768....1B10.1016/j.nuclphysb.2006.12.022arXiv:hep-ph/0608100CKMfitter Group, J. Charles et al., Current status of the Standard Model CKM fit and constraints on ΔF=2\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\Delta F = 2$$\end{document} New Physics. Phys. Rev. D 91, 073007 (2015). Numbers updated using the results from the 2019 values in https://ckmfitter.in2p3.fr/www/results/plots_summer19/ckm_res_summer19.html. arXiv:1501.05013 [hep-ph]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 Δms\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\Delta m_s$$\end{document} and BR(B→τντ)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$BR(B \rightarrow \tau \nu _\tau )$$\end{document}. JHEP 10, 081 (2006). Numbers updated to the 2018 results from https://www.utfit.org/UTfit/ResultsSummer2018SM. arXiv:hep-ph/0606167LHCb Collaboration, Precision measurement of the Bs0-B¯s0\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$B^{0}_{s} - \bar{B}^0_s$$\end{document} oscillation frequency with the decay Bs0→Ds-π+\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$B^0_s \rightarrow D^-_s \pi ^+$$\end{document}. New J. Phys. 15, 053021 (2013). arXiv:1304.4741 [hep-ex]LenzATetlalmatzi-XolocotziGModel-independent bounds on new physics effects in non-leptonic tree-level decays of B-mesonsJHEP2020071772020JHEP...07..177L10.1007/JHEP07(2020)177arXiv:1912.07621 [hep-ph]DaviesCTLattice QCD matrix elements for the Bs0-B¯s0\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$B^{0}_{s} - \bar{B}^0_s$$\end{document} width difference beyond leading orderPhys. Rev. Lett.20201240820012020PhRvL.124h2001D10.1103/PhysRevLett.124.082001arXiv:1910.00970 [hep-lat]LenzANiersteUTheoretical update of Bs-B¯s\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$B_{s} - \bar{B}_s$$\end{document} mixingJHEP2007060722007JHEP...06..072L10.1088/1126-6708/2007/06/072arXiv:hep-ph/0612167A. Lenz, M.L. Piscopo, A.V. Rusov, Contribution of the Darwin operator to non-leptonic decays of heavy quarks. J. High Energ. Phys. 2020, 199 (2020). https://doi.org/10.1007/JHEP12(2020)199ZylaPReview of particle physicsPTEP20202020083C01D0 Collaboration, Measurement of the CP-violating phase ϕsJ/ψϕ\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\phi ^{J/\psi \phi }_{s}$$\end{document} using the flavor-tagged decay Bs0→J/ψϕ\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
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\begin{document}$$B^0_s \rightarrow {J/\psi \phi }$$\end{document} in 8 fb-1\documentclass[12pt]{minimal}
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\begin{document}$$p\bar{p}$$\end{document} collisions. Phys. Rev. D 85, 032006 (2012). arXiv:1109.3166 [hep-ex]CDF Collaboration, Measurement of the bottom-strange meson mixing phase in the full CDF data set. Phys. Rev. Lett. 109, 171802 (2012). arXiv:1208.2967 [hep-ex]LHCb Collaboration, Precision measurement of CP violation in Bs0→J/ψK+K-\documentclass[12pt]{minimal}
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\begin{document}$$B^0_s \rightarrow {J/\psi }\ K^{+}K^-$$\end{document} decays. Phys. Rev. Lett. 114, 041801 (2015). arXiv:1411.3104 [hep-ex]ATLAS Collaboration, Measurement of the CP-violating phase ϕs\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
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\begin{document}$$B^0_s \rightarrow {J/\psi }\phi $$\end{document} difference with decays in ATLAS. JHEP 08, 147 (2016). arXiv:1601.03297 [hep-ex]CMS Collaboration, Measurement of the CP-violating weak phase ϕs\documentclass[12pt]{minimal}
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\usepackage{wasysym}
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\begin{document}$$B^0_s \rightarrow {J/\psi }\phi $$\end{document}(1020) decay channel in pp collisions at s=8TeV\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s} = 8 TeV$$\end{document}. Phys. Lett. B 757, 97 (2016). arXiv:1507.07527 [hep-ex]LHCb Collaboration, Resonances and CP violation in Bs0\documentclass[12pt]{minimal}
\usepackage{amsmath}
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\begin{document}$$\phi $$\end{document}(1020). JHEP 08, 037 (2017). arXiv:1704.08217 [hep-ex]LHCb Collaboration, Updated measurement of time-dependent CP-violating observables in Bs0→J/ψK+K-\documentclass[12pt]{minimal}
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\begin{document}$${B}^0_s \rightarrow {J/\psi }\ K^{+}K^-$$\end{document} decays. Eur. Phys. J. C 79, 706 (2019). arXiv:1906.08356 [hep-ex] [Erratum: Eur. Phys. J. C 80, 601 (2020)]CMS Collaboration, Measurement of the CP-violating phase ϕs\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s} = 13~TeV$$\end{document}. Phys. Lett. B 816, 136188 (2021). https://doi.org/10.1016/j.physletb.2021.136188LHCb Collaboration, First study of the CP-violating phase and decay-width difference in Bs0→ψ(2S)ϕ\documentclass[12pt]{minimal}
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\begin{document}$${B}^0_s \rightarrow \psi (2S)\phi $$\end{document} decays. Phys. Lett. B 762, 253 (2016). arXiv:1608.04855 [hep-ex]LHCb Collaboration, Measurement of the CP-violating phase ϕs\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
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\begin{document}$$\phi _s$$\end{document} in B¯s0→Ds+Ds-\documentclass[12pt]{minimal}
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\begin{document}$$\bar{B}^0_s \rightarrow D^{+}_{s} D^-_s$$\end{document} decays. Phys. Rev. Lett. 113, 211801 (2014). arXiv:1409.4619 [hep-ex]LHCb Collaboration, Measurement of the CP-violating phase ϕs\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
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\begin{document}$$\phi _s$$\end{document} in B¯s0→J/ψπ+π-\documentclass[12pt]{minimal}
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\begin{document}$$\bar{B}^0_s \rightarrow {J/\psi }\ \pi ^{+}\pi ^-$$\end{document} decays. Phys. Lett. B 736, 186 (2014). arXiv:1405.4140 [hep-ex]LHCb Collaboration, Measurement of the CP-violating phase ϕs\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
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\begin{document}$$\phi _s$$\end{document} from Bs0→J/ψπ+π-\documentclass[12pt]{minimal}
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\begin{document}$${B}^0_s \rightarrow {J/\psi }\ \pi ^{+}\pi ^-$$\end{document} decays in 13 TeV pp collisions. Phys. Lett. B 797, 134789 (2019). arXiv:1903.05530 [hep-ex]ATLAS Collaboration, The ATLAS experiment at the CERN large hadron collider. JINST 3, S08003 (2008)ATLAS Collaboration, ATLAS insertable B-layer technical design report. ATLAS-TDR-19; CERN-LHCC-2010-013 (2010). https://cds.cern.ch/record/1291633AbbottBProduction and integration of the ATLAS insertable B-layerJINST201813T050082018JInst..13.5008A10.1088/1748-0221/13/05/T05008arXiv:1803.00844 [physics.ins-det]ATLAS Collaboration, Luminosity determination in pp collisions at s=13TeV\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
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\begin{document}$$\sqrt{s} = 13~TeV$$\end{document} using the ATLAS detector at the LHC. ATLAS-CONF-2019-021 (2019). https://cds.cern.ch/record/2677054AvoniGThe new LUCID-2 detector for luminosity measurement and monitoring in ATLASJINST201813P0701710.1088/1748-0221/13/07/P07017SjöstrandTAn introduction to PYTHIA 8.2Comput. Phys. Commun.20151911592015CoPhC.191..159S10.1016/j.cpc.2015.01.024arXiv:1410.3012 [hep-ph]ATLAS Collaboration, ATLAS Pythia 8 tunes to 7 TeV data. ATL-PHYS-PUB-2014-021 (2014). https://cds.cern.ch/record/1966419PumplinJNew generation of parton distributions with uncertainties from global QCD analysisJHEP2002070122002JHEP...07..012P10.1088/1126-6708/2002/07/012arXiv:hep-ph/0201195ATLAS Collaboration, The ATLAS simulation infrastructure. Eur. Phys. J. C 70, 823 (2010). arXiv:1005.4568 [physics.ins-det]AgostinelliSGEANT4-a simulation toolkitNucl. Instrum. Methods A20035062502003NIMPA.506..250A10.1016/S0168-9002(03)01368-8ATLAS Collaboration, Muon reconstruction performance of the ATLAS detector in proton–proton collision data at s=13TeV\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s} = 13~TeV$$\end{document}. Eur. Phys. J. C 76, 292 (2016). arXiv:1603.05598 [hep-ex]TanabashiMReview of particle physicsPhys. Rev. D2018980300012018PhRvD..98c0001T10.1103/PhysRevD.98.030001ATLAS Collaboration, Electron and photon performance measurements with the ATLAS detector using the 2015–2017 LHC proton–proton collision data. JINST 14, P12006 (2019). arXiv:1908.00005 [hep-ex]ATLAS Collaboration, Topological cell clustering in the ATLAS calorimeters and its performance in LHC Run 1. Eur. Phys. J. C 77, 490 (2017). arXiv:1603.02934 [hep-ex]CacciariMSalamGPSoyezGThe anti-kt\documentclass[12pt]{minimal}
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\begin{document}$$anti-k_t$$\end{document} jet clustering algorithmJHEP2008040632008JHEP...04..063C10.1088/1126-6708/2008/04/063arXiv:0802.1189 [hep-ph]CacciariMSalamGPSoyezGFastJet user manualEur. Phys. J. C20127218962012EPJC...72.1896C10.1140/epjc/s10052-012-1896-2arXiv:1111.6097 [hep-ph]ATLAS Collaboration, ATLAS b-jet identification performance and efficiency measurement with tt¯\documentclass[12pt]{minimal}
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\begin{document}$$t\bar{t}$$\end{document} events in pp collisions at s=13TeV\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s} = 13~TeV$$\end{document}. Eur. Phys. J. C 79, 970 (2019). arXiv:1907.05120 [hep-ex]DigheASDunietzIFleischerRExtracting CKM phases and Bs-B¯s\documentclass[12pt]{minimal}
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\begin{document}$$B_s - \bar{B}_s$$\end{document} mixing parameters from angular distributions of non-leptonic B decaysEur. Phys. J. C199966471999EPJC....6..647D10.1007/s100529800954arXiv:hep-ph/9804253StoneSZhangLS-waves and the measurement of CP violating phases in Bs\documentclass[12pt]{minimal}
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\begin{document}$$B_s$$\end{document} decaysPhys. Rev. D2009790740242009PhRvD..79g4024S10.1103/PhysRevD.79.074024arXiv:0812.2832 [hep-ph]ATLAS Collaboration, Time-dependent angular analysis of the decay Bs0→J/ψϕ\documentclass[12pt]{minimal}
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\begin{document}$$B^0_s \rightarrow {J/\psi }\phi $$\end{document} and extraction of ΔΓs\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \Gamma _s$$\end{document} and the CP-violating weak phase ϕs\documentclass[12pt]{minimal}
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\begin{document}$$\phi _s$$\end{document} by ATLAS. JHEP 12, 072 (2012). arXiv:1208.0572 [hep-ex]LHCb Collaboration, Updated average fs\documentclass[12pt]{minimal}
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\begin{document}$$f_d$$\end{document} b-hadron production fraction ratio for 7 TeV pp collisions. LHCb-CONF-2013-011 (2013). https://cds.cern.ch/record/1559262CollaborationBaBarSearch for the Z(4430)-\documentclass[12pt]{minimal}
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\begin{document}$$-$$\end{document} at BABARPhys. Rev. D20097911200110.1103/PhysRevD.79.112001arXiv:0811.0564 [hep-ex]LHCb Collaboration, Study of the kinematic dependences of Λb0\documentclass[12pt]{minimal}
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\begin{document}$$\Lambda ^0_b$$\end{document} production in pp collisions and a measurement of the Λb0→Λc+π-\documentclass[12pt]{minimal}
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\begin{document}$$\Lambda ^0_b \rightarrow \Lambda _c^+ \pi ^-$$\end{document} branching fraction. JHEP 08, 143 (2014). arXiv:1405.6842 [hep-ex]LHCb Collaboration, Study of the production of Λb0\documentclass[12pt]{minimal}
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\usepackage{wasysym}
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\begin{document}$$\Lambda ^0_b$$\end{document} and B¯0\documentclass[12pt]{minimal}
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\begin{document}$$\bar{B}^0$$\end{document} hadrons in pp collisions and first measurement of the Λb0→J/ψpK-\documentclass[12pt]{minimal}
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\begin{document}$$\Lambda ^0_b \rightarrow J/\psi pK^-$$\end{document} branching fraction. Chin. Phys. C 40, 011001 (2016). arXiv:1509.00292 [hep-ex]LHCb Collaboration, Observation of J/ψp\documentclass[12pt]{minimal}
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\usepackage{wasysym}
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\begin{document}$$J/\psi p$$\end{document} resonances consistent with pentaquark states in Λb0→J/ψK-p\documentclass[12pt]{minimal}
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\begin{document}$$\Lambda ^0_b \rightarrow J/\psi K^-p$$\end{document} decays. Phys. Rev. Lett. 115, 072001 (2015). arXiv:1507.03414 [hep-ex]LHCb Collaboration, Measurement of the polarization amplitudes in B0→J/ψK∗(892)0\documentclass[12pt]{minimal}
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\usepackage{wasysym}
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\begin{document}$$B^0 \rightarrow J/\psi K^* (892)^0$$\end{document} decays. Phys. Rev. D 88, 052002 (2013). arXiv:1307.2782 [hep-ex]FlattéSMCoupled-channel analysis of the πη\documentclass[12pt]{minimal}
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\begin{document}$$K\bar{K}$$\end{document} thresholdPhys. Lett. B1976632241976PhLB...63..224F10.1016/0370-2693(76)90654-7LHCb Collaboration, Measurement of resonant and CP components in B¯s0→J/ψπ+π-\documentclass[12pt]{minimal}
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\begin{document}$$\bar{B}^0_s \rightarrow J/\psi \pi ^+\pi ^-$$\end{document} decays. Phys.Rev. D 89, 092006 (2014). arXiv:1402.6248 [hep-ex]LyonsLGibautDCliffordPHow to combine correlated estimates of a single physical quantityNucl. Instrum. Methods1988A2701101988NIMPA.270..110L10.1016/0168-9002(88)90018-6ValassiACombining correlated measurements of several different physical quantitiesNucl. Instrum. Methods2003A5003912003NIMPA.500..391V10.1016/S0168-9002(03)00329-2CharlesJCurrent status of the Standard Model CKM fit and constraints on ΔF=2\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \text{F} = 2$$\end{document} New PhysicsPhys. Rev. D2015910730072015PhRvD..91g3007C10.1103/PhysRevD.91.073007arXiv:1501.05013 [hep-ph]ATLAS Collaboration, ATLAS computing acknowledgements, ATL-SOFT-PUB-2020-001. https://cds.cern.ch/record/2717821
ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point. The z-axis is along the beam pipe, the x-axis points to the centre of the LHC ring and the y-axis points upward. Cylindrical coordinates (r,ϕ)\documentclass[12pt]{minimal}
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Tight muon reconstruction is optimised to maximise the purity of muons at the cost of some efficiency, requiring combined muons with hits in at least two stations of the MS and additional criteria, described in Ref. [32].
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