KnE Energy | The 3rd International Conference on Particle Physics and Astrophysics (ICPPA) | pages: 399–405

1. Introduction

The CP -violating phase φs originates from the interference between the mixing and direct decay of Bs0 mesons to CP eigenstates. Ignoring subleading penguin contributions, the phase φs within the Standard Model (SM) is predicted to be -2βs where βs=arg(-VtsVtb*/VcsVcb*) [1]. An indirect determination of 2βs=0.0376-0.0007+0.0008 rad is obtained using a global fit to experimental data [2]. Any deviation from this prediction would be a clear sign, so-called New Physics effects, strongly motivating the need for precise experimental measurements of this quantity [3]. The measurement of CP -violating phase φs has been independently performed using Bs0J/ψK+K- , Bs0J/ψπ+π- and Bs0ψ(2S)φ decay modes. All measurements shown in the proceedings use 3 fb -1 of data collected by the LHCb experiment [4] in pp collisions during 2011 and 2012.

2. Measurements of the CP -violating phase φs

φs from Bs0J/ψφ

A tagged time-dependent angular fit to Bs0J/ψφ candidates is applied to extract the CP -violating phase φs [5]. The final state of the decay is an admixture of CP -even states, ηi=+1 for i{0,} and CP -odd states, ηi=-1 for i{,S} . It is decomposed into four amplitudes: three P-waves, A0 , A , A and one S-wave, AS accounting for the nonresonant K+K- configuration. The phase is determined by φs=-arg(λ) where λ=λi/ηi and λi=qpA¯iAi . In the absence of CP violation in decay, λ=1 . The complex parameters p and q describe the relation between flavour and mass eigenstates: |BL,H=p|Bs0±q|B¯s0 and p2+q2=1 .

Figure 1

Decay time and angle distributions for Bs0J/ψφ decays (black markers) with the one-dimensional projections of the PDF. The solid blue line shows the total signal contribution, which is composed of CP -even (long-dashed red), CP -odd (short-dashed green) and S-wave (dotted-dashed purple) contributions.

Figure 2

(left) Distribution of m(π+π-) invariant mass with contributing components. (right) Invariant mass of J/ψπ+π- combinations where the (red) solid curve shows the Bs0 signal, the (brown) dotted line shows the combinatorial background, other colour lines indicate different reconstructed background contributions.

fig-5    fig-6

The Bs0J/ψφ candidates are reconstructed as the decay J/ψμ+μ- combined with a pair of oppositely charged kaons. After applying a full offline and trigger selection, 95690±350 signal candidates of the Bs0J/ψφ are obtained [5]. The decay time and angular acceptances, decay time resolution as well as flavour tagging efficiency are taken into account in the fitting procedure. The decay time resolution is estimated using a large sample of prompt J/ψK+K- combinations produced directly in the pp interactions and is found to be 46 fs. Using a prescaled unbiased trigger sample and a tag and probe technique the decay time acceptance is determined from data. The angular acceptance is determined using simulated events that a subjected to the same trigger and selection criteria as the data. The flavour of the produced Bs0 candidate is identified using two independent tagging algorithms: same side and opposite side. The flavour tagging algorithms are optimised on simulations and calibrated on data using flavour specific control channels. The combined effective tagging power is (3.73±0.15)% [5].

A weighted unbinned maximum likelihood fit is performed using a signal-only Probability Density Function (PDF), as described in Ref. [6]. The signal weights are extracted using the sPlot technique [7]. The data set is divided into six independent invariant K+K- mass bins that allows the measurement of the small S-wave amplitude in each bin and minimizes correction factors in the interference terms of the PDF [8]. The projections of the decay time and angular distributions are shown in Fig. 1. The final results are φs=-0.058±0.049±0.006 rad, Γs=0.6603±0.0027±0.0015 ps -1 and ΔΓs=0.0805±0.0091±0.0032 ps -1 where the first uncertainty is statistical and the second is systematic [5]. The dominant contribution to the systematic uncertainty is contributed by the decay time and angular efficiency and background subtraction.

φs from Bs0J/ψπ+π-

Figure 3

Distribution of the m(ψ(2S)K+K-) invariant mass for the selected Bs0ψ(2S)φ candidates and decay time acceptance in arbitrary units.

fig-7    fig-8

The analysis of Bs0J/ψπ+π- decays has been also performed by the LHCb collaboration [9]. The decay is similar to the Bs0J/ψφ one with a noticeable simplification: the final state being CP -odd, there is no need for the angular analysis. Fig. 2 shows the five interfering π+π- states dominated by f0(980) component. After trigger and selection chain 27100±200 signal Bs0J/ψπ+π- candidates are reconstructed (Fig. 2). With the time-dependent amplitude analysis, the measured value of the phase φs is 0.070±0.068±0.08 rad. The dominant systematic uncertainty is coming from knowledge about π+π- resonance model. The combination of the Bs0J/ψφ and Bs0J/ψπ+π- fit results gives φs=-0.010±0.039 rad [5].

φs from Bs0ψ(2S)φ

Another Bs0 decay mode with b¯c¯cs¯ transition that has been exploited by the LHCb collaboration to measure φs is Bs0ψ(2S)(μ+μ-)φ(K+K-) [10]. The formalism used for this analysis is very close to that of Bs0J/ψφ decay [5] where the J/ψ meson is replaced with ψ(2S) . The number of signal candidates selected from a fit to the data sample is 4700 (Fig. 3). The decay time acceptance is determined using a control B0ψ(2S)K*0(K+π-) decay mode. Fig. 3 shows the decay time acceptance, which is defined as the product of the acceptance of the control channel and the ratio of acceptances of the simulated signal and control mode after full trigger and selection chain. The first measurement of the CP -violating parameters in a final state containing the ψ(2S) resonance is φs=-0.23-0.28+0.29±0.02 rad, Γs=0.668±0.011±0.006 ps -1 and ΔΓs=0.066-0.044+0.041±0.007 ps -1 . The fit result is consistent with Bs0J/ψφ measurement and the SM predictions. The systematic uncertainty is less than 20 % of the statistical uncertainty, except for Γs where it is close to 60 % .

φs from Bs0J/ψK+K- in high m(K+K-) range

The first measurement of the phase φs has been performed in the Bs0J/ψK+K- decay with K+K- invariant mass larger than 1050 MeV/c 2 [11] that is above the φ(1020) resonance region. This decay has been studied using an analysis method very similar to that used for the Bs0J/ψφ decay mode reported in Ref. [5]. The important difference between both decay analyses is that modelling of the m(K+K-) distribution is included to distinguish different resonant and nonresonant contributions. The decay time acceptance is determined with the same method as described in Ref. [10] by using a control channel B0J/ψK*0 . The K+K- mass spectrum is fitted by considering the different contributions found in the time-dependent amplitude analysis as shown in Fig. 4. The final fit has been performed allowing eight independent sets of CP -violating parameters: three corresponding to φ(1020) transversity states, K+K- S-wave, f2(1270) , f2'(1525) , φ(1680) and the combination of the two high-mass f2(1750) and f2(1950) states. The CP -violating parameters measurement of Bs0J/ψK+K- in high m(K+K-) region is φs=0.119±0.107±0.034 rad, Γs=0.650±0.006±0.004 ps -1 and ΔΓs=0.066±0.018±0.006 ps -1 . The largest contribution to systematic uncertainty results from the resonance fit model. The combination with the Bs0 decay fit results in the φ(1020) region gives φs=-0.025±0.045±0.008 rad, Γs=0.6588±0.0022±0.0015 ps -1 and ΔΓs=0.0813±0.0073±0.0036 ps -1 that improves a precision of the φs measurement by more than 9 % .

Figure 4

Distribution of the m(J/ψK+K-) invariant mass with contributing components.

Figure 5

68 % confidence level regions in ΔΓs and φs plane obtained from individual contours of CDF, D0, CMS, ATLAS and LHCb measurements and the combined contour (solid line and shaded area) [16]. The expectation within the SM [2] is shown as a black thin rectangle.


Global combination

The CP -violating phase and lifetime parameters have been measured by several experiments, namely four analysis using the Bs0J/ψφ final state from CDF [12], D0 [13], ATLAS [14] and CMS [15] collaborations and five analysis using different final states performed by the LHCb collaboration, four of which discussed here. The world average result of φs and ΔΓs measurements from the Heavy Flavour Averaging Group [16] is shown in Fig. 5. They find φs=-0.021±0.031 rad and ΔΓs=0.085±0.006 ps -1 that is dominated by the measurements from LHCb collaboration and is consistent with the SM predictions.

3. Summary

The most precise measurement of CP -violating phase φs and lifetime parameters in the Bs0 system has been performed using data collected by the LHCb experiment during Run I. So far all results are compatible with the Standard Model predictions. In order to reach an uncertainty of the measurement comparable or even better than the theoretical uncertainty of the SM prediction aside from improvements in available luminosity for the Bs0J/ψφ channels, inclusion of new decay modes have been investigated. For example, the Bs0J/ψ(e+e-)φ channel not only could bring about 10 % of the μ+μ- mode statistics, but it will be also an important verification of the Bs0J/ψ(μ+μ-)φ as kinematics for both channels are expected to be identical. The statistical sensitivity to φs measurement after the LHCb upgrade, with an integrated luminosity of 46 fb -1 , is expected 0.01 rad that will be close to the present theoretical uncertainty [17]. As the measurement precision improves, the penguin polluion contributions to the Bs0 meson decays have to been kept under control [18,19].


The work has been supported by the Polish National Science Centre (NCN) with Preludium grant UMO-2015/17/N/ST2/04056. I would like to thanks the organizers of the ICPPA'2017 conference for the invitation to present this work and my LHCb colleagues who helped in the preparation of this talk.



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