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Lifetime Difference and CP-Violating Phase in the B_s^0 System

From an analysis of the decay Bs ->J/psi phi we obtain the width difference between the light and heavy mass eigenstates, and the CP-violating phase.

(Dated: January 9, 2007) From an analysis of the decay B 0 s → J/ψφ we obtain the width difference between the light and heavy mass eigenstates, ∆Γ ≡ (ΓL − ΓH ) = 0.17 ± 0.09 (stat) ±0.02 (syst) ps −1 and the CPviolating phase φs = −0.79 ± 0.56 (stat) +0.14 −0.01 (syst). Under the hypothesis of no CP violation (φs ≡ 0), we obtain 1/Γ = τ (B 0 s ) =1.52 ±0.08 +0.01 −0.03 ps and ∆Γ = 0.12 +0.08 −0.10 ± 0.02 ps −1 . The data sample corresponds to an integrated luminosity of 1.1 fb −1 accumulated with the D0 detector at the Tevatron. PACS numbers: 13.25.Hw,11.30.Er In the standard model (SM), the light (L) and heavy (H) eigenstates of the mixed B 0 s system are expected to have a sizeable mass and decay width difference, ∆M ≡ M H − M L and ∆Γ ≡ Γ L − Γ H . The CP-violating phase, defined as the the relative phase of the off-diagonal elements of the mass and decay matrices in the B 0 s -B 0 s basis, is predicted to be small. Thus, to a good approximation the two mass eigenstates are expected to be CP eigenstates. New phenomena may alter the CP-violating mixing phase φ s , leading to a reduction of the observed ∆Γ compared to the SM prediction [1] ∆Γ SM : ∆Γ = ∆Γ SM × cos φ s . While the mass difference has recently been measured to high precision [2,3], the CP-violating phase remains unknown. The decay B 0 s → J/ψφ, proceeding through the quark process b → ccs, gives rise to both CP-even and CPodd final states. It is possible to separate the two CP components of the decay B 0 s → J/ψφ, and thus to measure the lifetime difference, through a study of the timedependent angular distribution of the decay products of the J/ψ and φ mesons. Moreover, with a sizeable lifetime difference, there is sensitivity to the mixing phase through the interference terms between the CP-even and CP-odd waves.
In Ref. [4] we presented an analysis of the decay chain B 0 s → J/ψφ, J/ψ → µ + µ − , φ → K + K − based on the first ≈450 pb −1 of pp data at a center-of-mas energy of 1.96 TeV collected with the D0 detector [5]. In that analysis, we extracted three parameters characterizing the B 0 s system and its decay B 0 s → J/ψφ: the average lifetime, τ = 1/Γ, where Γ ≡ (Γ H +Γ L )/2; ∆Γ/Γ; and the relative rate of the decay to the CP-odd states at time zero. Here we present new results, based on a two-fold increase in statistics. In addition to τ and ∆Γ, we extract for the first time the CP-violating phase φ s . We also measure the magnitudes of the decay amplitudes, and their relative phases.
The data, collected between June 2002 and January 2006, correspond to an integrated luminosity of 1.1 fb −1 . The selected events include two reconstructed muons of opposite charge, with a transverse momentum greater than 1.5 GeV and pseudorapidity |η| < 2. Each muon is required to be detected as a track segment in at least one of the three layers of the muon system, and to be matched to a central track. One muon is required to have segments both inside and outside the toroid magnet. We require the events to satisfy a muon trigger that does not include a cut on the impact parameter.
To select the B 0 s candidate sample, we set the minimum values of momenta in the transverse plane for B 0 s , φ, and K meson candidates at 6.0 GeV, 1.5 GeV, and 0.7 GeV, respectively. J/ψ candidates are accepted if Mass (GeV) 5 5. 1  the invariant mass of the muon pair is in the range 2.9 -3.3 GeV. For events in the central rapidity region (an event is considered to be central if the higher p T muon has |η µ1 | < 1), we require the transverse momentum of the J/ψ meson to exceed 4 GeV. Successful candidates are constrained to the world average mass of the J/ψ meson [6]. Decay products of the φ candidates are required to satisfy a fit to a common vertex and to have an invariant mass in the range 1.01 -1.03 GeV. We require the (J/ψ, φ) pair to be consistent with coming from a common vertex, and to have an invariant mass in the range 5.0 -5.8 GeV. In the case of multiple φ meson candidates, we select the one with the highest transverse momentum. Monte Carlo (MC) studies show that the p T spectrum of the φ mesons coming from B 0 s decay is harder than the spectrum of a pair of random tracks from hadronization. We define the signed decay length of a B 0 s meson L B xy as the vector pointing from the primary vertex to the decay vertex projected on the B 0 s transverse momentum. To reconstruct the primary vertex, we select tracks with p T > 0.3 GeV that are not used as decay products of the B 0 s candidate, and apply a constraint to the average beam spot position. The proper decay length, ct, is defined by the relation ct is the measured mass of the B 0 s candidate. The distribution of the proper decay length uncertainty σ(ct) of B 0 s mesons peaks around 25 µm. We accept events with σ(ct) < 60 µm. The invariant mass distribution of the accepted 23343 candidates is shown in Fig. 1. The curves are projections of the maximum likelihood fit, described below. The fit assigns 1039±45 (stat) events to the B 0 s decay.
We perform a simultaneous unbinned maximum likelihood fit to the proper decay length, three decay angles, and mass. The likelihood function L is given by: where N is the total number of events, and f sig is the fraction of signal in the sample. The function F i sig describes the distribution of the signal in mass, proper decay length, and the decay angles, and F i bck is the product of the background mass, proper decay length, and angular probability density functions. Background is di-vided into two categories. "Prompt" background is due to directly produced J/ψ mesons accompanied by random tracks arising from hadronization. This background is distinguished from "non-prompt" background, where the J/ψ meson is a product of a B hadron decay while the tracks forming the φ candidate emanate from a multibody decay of the same B hadron or from hadronization.
The time evolution of the angular distribution of the products of the decay of flavor untagged B 0 s mesons, i.e., summed over B 0 s and B 0 s , expressed in terms of the linear polarization amplitudes A x and their relative phases δ i is [1]: where T +/− = 1 2 (1 ± cos φ s )e −ΓLt + (1 ∓ cos φ s )e −ΓH t . In the coordinate system of the J/ψ rest frame (where the φ meson moves in the x direction, the z axis is perpendicular to the decay plane of φ → K + K − , and p y (K + ) ≥ 0), the transversity polar and azimuthal angles (θ, ϕ) describe the direction of the µ + , and ψ is the angle between p(K + ) and − p(J/ψ) in the φ rest frame.
We model the acceptance in the three angles by fits using polynomial functions, with parameters determined using Monte Carlo simulations. We have used the SVV HELAMP model in the EvtGen generator [7], interfaced to the Pythia program [8]. Simulated events were reweighted to match the kinematic distributions observed in the data.
The lifetime distribution shape of the background is described as a sum of a prompt component, simulated as a Gaussian function centered at zero, and a nonprompt component, simulated as a superposition of one exponential for the negative ct region and two exponentials for the positive ct region, with free slopes and normalization. The mass distributions of the backgrounds are parametrized by first-order polynomials. The distributions in the transversity polar and azimuthal an-gles are parametrized as 1 + X 2x cos 2 θ + X 4x cos 4 θ and 1+Y 1x cos(2ϕ)+Y 2x cos 2 (2ϕ), respectively. For the background dependence on the angle ψ, we use the function 1 + Z 2x cos 2 (ψ). We also allow for a background term analogous to the interference term of the CP-even waves, with one free coefficient. For each of the above background functions we use two separate sets of parameters for the prompt and non-prompt components.
Our results for the hypothesis of CP conservation and for the case of free φ s , are presented in Table I. For the CP-violating phase, which has a four-fold ambuguity discussed below, the fit value closest to the SM prediction of −0.03 [1] is φ s = −0.79 ± 0.56. Figures 2 -5 show the fit projections on the angular distributions and the proper decay length. Figure 6 shows the ∆ ln(L) = 0.5 error ellipse contour (corresponding to the confidence level of 39%) in the plane (∆Γ, φ s ). As seen from Eq. 2, the sign of sin φ s is reversed with the simultaneous reversal of the signs of cos δ 1 and cos δ 2 . For the case cos δ 1 < 0 and cos δ 2 > 0, our measurement correlates two possible solutions for φ s with the two signs of ∆Γ: φ s = −0.79±0.56, ∆Γ > 0, and φ s = 2.35±0.56, ∆Γ < 0. For the case cos δ 1 > 0 and cos δ 2 < 0 the two solutions are φ s = 0.79±0.56, ∆Γ > 0, and φ s = −2.35±0.56, ∆Γ < 0.  We perform a test using pseudo-experiments with similar statistical sensitivity, generated with the same parameters as obtained in this analysis under the condition of no CP violation. When fits allowing for CP violation are performed, ≈ 50% of the experiments have a fitted cos(φ s ) less than the measured value. About 80% of experiments have the statistical uncertainty of φ s greater than that for data.
We verify the procedure by performing fits on MC samples passed through the full chain of detector simulation, event reconstruction, and maximum likelihood fitting. We assign systematic uncertainties due to the statistical precision of this procedure test. We also repeat the fits to the data with the parameters describing the acceptance varied by ±1σ. Uncertainties from the data processing reflect the stability of the results with respect to different versions of the track and vertex reconstruction algorithms. The "interference" term in the background model accounts for the collective effect of various physics processes. However, its presence may be partially due to the detector acceptance effects. Therefore, we interpret the difference between fits with and without this term as a systematic uncertainty associated with the background model. Effects of the imperfect detector alignment are estimated using a modified geometry of the the silicon microstrip tracker, with silicon sensors moved within the known uncertainty. The effects of systematic uncertainties are listed in Table II.   The ∆ ln(L) = 0.5 contour (error elipse) in the plane (∆Γ, φs) for the fit to the B 0 s → J/ψφ data. Also shown is the band representing the relation ∆Γ = ∆ΓSM × |(cos(φs)|, with ∆ΓSM = 0.10 ± 0.03 ps −1 [10]. The 4-fold ambiguity is discussed in the text. lar distribution of the untagged decay B 0 s → J/ψφ, we obtain the average lifetime of the B 0 s system, τ (B 0 s ) = 1.52 ± 0.08 (stat) +0.01 −0.03 (syst) ps and the width difference between the two mass eigenstates, ∆Γ = 0.12 +0.08 −0.10 (stat) ±0.02 (syst) ps −1 .