Improved measurement of CP violation in neutral B decays to cc[over]s.

We present updated measurements of time-dependent CP asymmetries in fully-reconstructed neutral B decays to several CP eigenstates containing a charmonium meson. The measurements use a data sample of (cid:1) 383 (cid:2) 4 (cid:3) (cid:4) 10 6 (cid:1) (cid:1) 4 S (cid:3) ! BB decays collected with the BABAR detector at the PEP-II B factory. We determine sin2 (cid:2) (cid:5) 0 : 714 (cid:2) 0 : 032 (cid:1) stat (cid:3) (cid:2) 0 : 018 (cid:1) syst (cid:3) and j (cid:3) j (cid:5) 0 : 952 (cid:2) 0 : 022 (cid:1) stat (cid:3) (cid:2) 0 : 017 (cid:1) syst (cid:3) .

DOI: 10.1103/PhysRevLett.99.171803 PACS numbers: 13.25.Hw,11.30.Er,12.15.Hh The standard model (SM) of electroweak interactions describes CP violation as a consequence of an irreducible phase in the three-family Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1]. In the CKM framework, neutral B decays to CP eigenstates containing a charmonium and a K 0 meson through tree-diagram dominated processes provide a direct measurement of sin2 [2], where the angle is defined in terms of the CKM matrix elements V ij as argÿV cd V cb =V td V tb . We report updated measurements, based on a sample of 383 4 10 6 4S ! BB decays, of sin2 and of the parameter jj. Here q=p A=A [3], q and p are complex constants that relate the B-meson flavor eigenstates to the mass eigenstates, and A=A is the ratio of amplitudes of the decay of a B 0 or B 0 to the final state under study. We reconstruct B 0 decays to the final states J= K 0 S , J= K 0 L , 2SK 0 S , c1 K 0 S , c K 0 S , and J= K 0 [4]. Since our previously published result [5], we have added 157 10 6 BB decays and applied improved event reconstruction algorithms to the entire data set. We have also developed a new c K 0 S event selection based on the Dalitz plot structure of the c ! K 0 S K ÿ decay, and have performed a more detailed study of the CP properties of the background events, which results in reduced systematic errors. We now include the J= K 0 L and J= K 0 modes in the sample to measure jj, and we report individual measurements of sin2 and jj for each of the CP decay modes used in the analysis. Finally, we present separate results for the J= K 0 S ( ÿ 0 0 ) [6], and J= K 0 K 0 S K 0 L modes.
We identify (tag) the initial flavor of the reconstructed B candidate, B rec , using information from the other B meson, B tag , in the event. The decay rate g (g ÿ ) for a neutral B meson decaying to a CP eigenstate accompanied by a B 0 (B 0 ) tag can be expressed as where t t rec ÿ t tag is the difference between the proper decay times of the reconstructed and tag B mesons, B 0 is the neutral B lifetime and m d is the mass difference of the B meson mass eigenstates determined from B 0 -B 0 oscillations [7]. We assume that the corresponding decay-width difference ÿ d is zero. The average mistag probability w describes the effect of incorrect tags, and w is the difference between the mistag probabilities for B 0 and B 0 . The sine term in Eq. (1) results from the interference between direct decay and decay after B 0 ÿ B 0 oscillation. A nonzero cosine term arises from the interference between decay amplitudes with different weak and strong phases (direct CP violation) or from CP violation in B 0 ÿ B 0 mixing. In the SM, CP violation in mixing and direct CP violation in b ! c cs decays are both negligible [3]. Under these assumptions, f e ÿ2i , where f 1 is the CP eigenvalue of the final state f. Thus, the timedependent CP-violating asymmetry is The BABAR detector is described in detail elsewhere [8]. We select a sample of neutral B mesons (B CP ) decaying to the f ÿ1 final states J= K 0 S , 2SK 0 S , c1 K 0 S , and c K 0 S , and to the f 1 final state J= K 0 L . We reconstruct K 0 S ! ÿ , except in J= K 0 S , where we also include K 0 S ! 0 0 . The charmonium mesons are reconstructed in the decays J= ! e e ÿ , ÿ ; 2S ! e e ÿ , ÿ , J= ÿ ; c1 ! J= and c ! K 0 S K ÿ . We also reconstruct the J= K 0 K 0 ! K 0 S 0 final state, which can be CP even or CP odd due to the presence of even (L 0, 2) and odd (L 1) orbital angular momentum contributions. Ignoring the angular information in J= K 0 results in a dilution of the measured CP asymmetry by a factor j1 ÿ 2R ? j, where R ? is the fraction of the L 1 contribution. In Ref. [9] we have measured R ? 0:233 0:010stat 0:005syst, which gives an effective f 0:504 0:033 for f J= K 0 , after acceptance corrections.
In addition to the CP modes described above, we use a sample of B 0 mesons (B flav ) decaying to the flavor eigenstates D ÿ h (h , , a 1 ) and J= K 0 (K 0 ! K ÿ ) to calibrate the flavor-tagging performance and t resolution. We also perform studies to measure apparent CP violation arising from CP-conserving processes using a control sample of B mesons decaying to the final states J= K , 2SK , c1 K , and c K . The event selection and candidate reconstruction remain unchanged from those described in Refs. [5,10,11], with the exception of modes containing c mesons. In Ref. [5] we reconstructed the B 0 ! c K 0 S and B ! c K modes using the c ! K 0 S K ÿ decay, with the requirement 2:91 <m K 0 S K ÿ < 3:05 GeV=c 2 . We now exploit the fact that the c decays predominantly through a K resonance at around 1430 MeV=c 2 and a K 0 S K resonance close to threshold, and require that either m K 0 S ÿ or m K ÿ be in the mass-range 1:26; 1:63 GeV=c 2 , or that m K K 0 S 2 1:0;1:4 GeV=c 2 .
We calculate the time interval t between the two B decays from the measured separation z between the decay vertices of B rec and B tag along the collision (z) axis [10]. The z position of the B rec vertex is determined from the charged daughter tracks. The B tag decay vertex is determined by fitting tracks not belonging to the B rec candidate to a common vertex, while employing constraints from the beamspot location and the B rec momentum [10]. Events are accepted if the calculated t uncertainty is less than 2.5 ps and jtj is less than 20 ps. The fraction of all events satisfying these requirements is 95%.
The algorithm used to determine the flavor of the B tag at its decay to be either B 0 or B 0 is described in detail in Ref. [5]. In brief, we define six mutually exclusive tagging categories in order of decreasing tag purity: lepton, kaon I, kaon II, kaon-pion, pion, and other. The figure of merit for tagging is the effective tagging efficiency Q P i " i 1 ÿ 2w i 2 , where " i is the tagging efficiency of tagging category i. We measure Q 30:5 0:3%, consistent with the results in Ref. [5].
We determine the composition of our final sample using , where E beam and p B are the beam energy and B momentum in the e e ÿ center-of-mass (c.m.) frame. For the J= K 0 L mode we instead use the difference E between the candidate c.m. energy and E beam . The composition of our final sample is shown in Fig. 1. We use events with m ES > 5:2 GeV=c 2 (jEj < 80 MeV for J= K 0 L ) to determine the properties of the background contributions. We define a signal region 5:27 < m ES < 5:29 GeV=c 2 (jEj < 10 MeV for J= K 0 L ), which contains 12 677 CP candidate events that satisfy the tagging and vertexing requirements (see Table I). For all modes except c K 0 S and J= K 0 L , we use simulated events to estimate the fractions of events that peak in the m ES signal region due to cross-feed from other decay modes (peaking background). For the c K 0 S mode, the cross-feed fraction is determined from a fit to the m KK and m ES distributions in data. For the J= K 0 L decay mode, the sample composition, effective f , and E distribution of the individual background sources are determined either from simulation (for B ! J= X) or from the m ' ' ÿ sidebands in data (for non-J= background).
We determine sin2 and jj from a simultaneous maximum likelihood fit to the t distribution of the tagged B CP and B flav samples. The t distributions of the B CP sample are modeled by Eq. (1). Those of the B flav sample evolve according to Eq. (1) with 0. The observed amplitudes for the CP asymmetry in the B CP sample and for flavor oscillation in the B flav sample are reduced by the same factor, 1-2w, due to flavor mistags. The t distributions for the signal are convolved with a resolution function common to both the B flav and B CP samples, modeled by the sum of three Gaussian functions [10]. The combinatorial background is incorporated with an empirical description of its t spectra, containing prompt and nonprompt lifetime components convolved with a resolution function [10] distinct from that of the signal. The peaking background is assigned the same t distribution as the signal but with no CP violation, with the same t resolution function.
In addition to sin2 and jj, there are 68 free parameters in the CP fit. For the signal, these are the parameters of the t resolution (7), the average mistag fractions w and the differences w between B 0 and B 0 mistag fractions for each tagging category (12), and the difference between B 0 and B 0 reconstruction and tagging efficiencies (7). The background is described by mistag fractions (24), parameters of the t resolution (3) and B flav time dependence (3), and parameters for the CP background (8), including the apparent CP asymmetry of nonpeaking events in each tagging category. Finally, we allow for the possibility of direct CP violation in the c1 K 0 S background to J= K 0 (1), and in the main backgrounds to the J= K 0 L mode, coming from J= K 0 S , J= K 0 , and the remaining J= background (3 parameters). The effective jj of the non-J= background is fixed from a fit to the J= -candidate sidebands in J= K 0 L . We fix B 0 1:530 ps and m d 0:507 ps ÿ1 [7]. The determination of the mistag fractions and t resolution function parameters for the signal is dominated by the B flav sample, about 10 times more abundant than the CP sample.
The fit to the B CP and B flav samples yields sin2 0:714 0:032 and jj 0:952 0:022, where the errors are statistical only. The correlation between these two parameters is ÿ1:5%. We also perform a separate fit in which we allow different sin2 and jj values for each charmonium decay mode, a fit to the J= K 0 S ÿ 0 0 mode, and a fit to the J= K 0 K 0 S K 0 L sample. We split the data sample by run period and by tagging category. We perform the CP measurements on control samples with no expected CP asymmetry. The results of these fits are summarized in Table I. The difference in the c K 0 S sin2 value with respect to our previous publication [5] is partly due to the slightly different reconstruction algorithms and partly to the different selection; the two measurements are consistent when the systematic error is taken into account. Figure 2 shows the t distributions and asymmetries in yields between events with B 0 tags and B 0 tags for the f ÿ1 and f 1 samples as a function of t, overlaid with the projection of the likelihood fit result. We also performed the CP fit fixing jj 1, which yields sin2 0:713 0:032stat.
The dominant systematic errors on sin2 are due to limited knowledge of various background properties, including uncertainties in J= K 0 L -specific backgrounds and in the amounts of peaking backgrounds and their CP asymmetries (0.010), to possible differences between the B flav and B CP tagging performances (0.009), to the descrip-tion of the t resolution functions (0.008), to the knowledge of the event-by-event beam spot position (0.005). The only sizeable systematic uncertainties on jj are due to the possible interference between the suppressed b ! uc d amplitude with the favored b ! c ud amplitude for some tag side B decays [12] (0.015), and to the CP content of the peaking backgrounds (0.006). The total systematic error on sin2jj is 0.018 (0.017). We detail in [13] the main systematic uncertainties on both sin2 and jj for the full sample, for the seven individual modes, and for the fits to the J= K 0 and J= K 0 S samples. The large B CP sample allows a number of consistency checks, including separation of the data by decay mode and tagging category. The results of those checks, all consistent within the errors, are listed in Table I. We observe no statistically significant asymmetry from fits to the control samples of non-CP decay modes.
In summary, we report improved measurements of sin2 and jj that supersede our previous results [5]. We measure sin2 0:714 0:032stat 0:018syst and jj 0:952 0:022stat 0:017syst, providing an improved model-independent constraint on the position of the apex of the unitarity triangle [14]. Our measurements agree TABLE I. Number of events N tag and signal purity P in the signal region after tagging and vertexing requirements, and results of fitting for CP asymmetries in the B CP sample and various subsamples. In addition, fit results for the B flav and B control samples demonstrate that no artificial CP asymmetry is found where we expect no CP violation ( sin2 0, jj 1). Errors are statistical only. within errors with the published results [15,16] and with the theoretical estimates of the magnitudes of CKM matrix elements in the context of the SM [17]. The measured value of jj is consistent with no direct CP violation with a significance of 1.72 standard deviations. We report the first individual measurements of sin2 and jj for each of the decay modes within our CP sample, and of the J= K 0 K 0 S K 0 L sample. We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality.