Mixing and CP Violation in the Bd and Bs Systems at ATLAS

This note includes a measurement of the Bos decay parameters in the Bs→J/ψϕ channel and a measurement of the B0 meson proper decay time and decay width using the statistics collected by the ATLAS experiment in Run I of the LHC. The first result presents the measurement of the CP -violating phase ϕs, the decay width Γs and the width difference between the mass eigenstates ΔΓs. The second result presents the measurement of the width difference ΔΓd, which is extracted from the measurement of the lifetime dependence of B0→J/ψKs and B0→J/ψK*° decays. The obtained results are ϕs = 0.098 ± 0.084(stat.) ± 0.040(syst.) rad. and ΔΓd/Γd = (-0.1 ± 1.1(stat.) ± 0.9(syst.)) × 10-2.


Introduction
ATLAS [1] is a general purpose detector that measures heavy flavour properties using its inner dectectors, muon spectrometers and electromagnetic calorimeters (for tagging). Measuring the properties of heavy-flavour particles has been part of the B physics program of the ATLAS experiment since the start of the proton-proton collisions at LHC in 2010. This note presents an overview of recent results obtained using data collected at √ s = 7 TeV during 2011 and √ s = 8 TeV during 2012. The analysis of CP violation and mixing can still access physics beyond the standard model; precise measurements may constrain new physics scenarios such as supersymmetry or advance b and c hadron spectroscopy and test QCD.
2. The B 0 q system The time evolution of the neutral B 0 q −B 0 q system is described by: The time dependence of the decay rate B 0 q → f is sensitive to f . The time-dependent decay rate is given by: Here t is the proper decay time of the B 0 q meson. The parameters A dir CP , A ∆Γ and A mix CP depend on the final state f . The abbreviations "dir" and "mix" stand for "direct" and "mixing". By definition: Assuming that the CP-violating phase φ 12 q is small, which is experimentally confirmed for both the B 0 and B s mesons [2]: The parameters A dir CP , A ∆Γ and A mix CP are theoretically well defined for flavour-specific final states and CP eigenstates [3]. For a flavour-specific final state f fs , such that only the decay B 0 q → f fs is allowed whileĀ f = f fs |B 0 q = 0, the parameters are: For a flavour-specific final statef fs , such that A f = f fs |B 0 q = 0, i.e. only the decayB 0 q →f fs is allowed, the parameters are: For the B 0 decay to the CP eigenstate J/ψK s the parameters are: If the initial flavour of the B 0 q meson is not tagged and the mixture of the states is equal and unbiased, the decay rates given by equations (2) and (4) are added together. In this case, the production asymmetry A P of the B 0 q meson in pp collisions should be taken into account. This asymmetry is defined as: The oscillation rates ∆m d and ∆m s have not been measured at ATLAS so the world averages [4] are used in our analyses. ∆m d = 0.510 ± 0.003 × 10 12 s −1 (10) ∆m s = 17.757 ± 0.021 × 10 12 s −1 (11)

CP Violation
ATLAS has performed a measurement of the CP-violating phase φ s using the 2012 protonproton dataset [5]. This is done using the exclusive decay B s → J/ψ(µ + µ − )φ(K + K − ), which is a mixture of CP-even and CP-odd eigenstates. CP violation arises from interference between the direct decay and the mixing. From existing measurements, the standard model constrains this to be φ s ≈ −0.04 rad.  The analysis measures the mass, lifetime, three transversity angles and tagging information. These are placed in an unbinned maximum likelihood fit function: w i is a per-candidate weight for trigger lifetime efficiency.
The fitted PDF has four components: The probability density function contains a number of symmetries. As the sign of the ∆Γ S is not resolved by the data, it is assumed to be > 0 and a measurement from LHCb confirms this [6]. A second ambiguity exists in φ s and the strong phases, this can be resolved by the flavour tagging information.

Tagging
The analysis uses opposite-side tagging which was calibrated from the B ± self-tagging channels. A combination of four tagging methods are used and they can be seen along with their efficiency , dilution D = (1 − ω) and power P = D 2 in the table 1.

Results
The results from the 2012 data set demonstrate compatability with the standard model and the 2011 dataset previously published [7]. The combined parameters are calculated using the Best Linear-Unbiased Estimate (BLUE) taking into account parameter correlations. The results can be seen in    installed for 2015 and the planned ITK detector that will be installed alongside the High-Luminosity LHC upgrade. Figure 4 shows the proper decay time uncertainty vs the p T of the decaying B s meson for the tested detector layouts. Table 3 includes information on the estimated signal yields and the estimated precision of the φ s measurements.
4. Measurement of the relative width difference of the B 0 -B 0 system with the ATLAS detector ∆Γ d is one of the least measured parameters in the B mass system. The standard model makes a precise prediction of a small value for ∆Γ d SM = 0.1 ± 1.0 × 10 −2 . The eigenstate information outlined in section 2 indicates we can measure this using a ratio of events from the decays B 0 d → J/ψK * and B 0 d → J/ψK 0 s . This is measured with the 2011 and 2012 datasets recorded by the ATLAS experiment [10]. A p is the particle/anti-particle production asymmetry. The observed asymmetry A obs is calculated in bins of proper decay length, the asymmetry A P is then obtained from a χ 2 The detector asymmetry A det and A p are fit to obtain values of A det = (+1.33 ± 0.24 ± 0.22) × 10 −2 and A p = (+0.25 ± 0.48 ± 0.05) × 10 −2 The A P is found to be consistent with LHCb, although since ATLAS is observing a different region it does not need to be equivalent.
The mass spectra are fitted in each proper decay length bin to extract the yields. Examples of the fits can be seen in figures 5 and 6. Each bin has an efficiency correction ratio applied; this ratio is determined using Monte Carlo data.
The final results are ∆Γ d /Γ d = (−2.8 ± 2.2(stat.) ± 1.5(MC stat.)) × 10 −2 for the 2011 dataset and ∆Γ d /Γ d = (+0.8 ± 1.3(stat.) ± 0.5(MC stat.)) × 10 −2 for the 2012 dataset. These results are combined using the χ 2 method. Correlations between sources of systematics common to the two datasets are taken into account. The systematic uncertainty due to the background description and the MC are considered to be uncorrelated. This combined result is ∆Γ d /Γ d = (−0.1 ± 1.1(stat.) ± 0.9(syst.)) × 10 −2 . This combined result is currently the most precise single measurement of this quantity; it agrees well with the standard model prediction and the indirect measurement by D0 [9]. The fact the asymmetry is a ratio cancels out most biases from the trigger, time resolution or B production properties. However, differences between the channels and simulation inaccuracies could remain. The systematics uncertainties are thus estimated and shown in table 4.   Figure 6. The J/ψK * 0 mass fit [10]