Search for CP Violation in B0B0bar Mixing using Partial Reconstruction of B0-->D*-Xl+ nu and a Kaon Tag

We present results of a search for CP violation in B0B0bar mixing with the BABAR detector. We select a sample of B0-->D*-Xl+ nu decays with a partial reconstruction method and use kaon tagging to assess the flavor of the other B meson in the event. We determine the CP violating asymmetry ACP = (N(B0B0) - N(B0bar B0bar))/(N(B0B0) + N(B0bar B0bar))=(0.06+-0.17+0.38-0.32)%, corresponding to delta_CP =1 - |q/p| =(0.29+-0.84+1.88 -1.61)*10^-3.

We present results of a search for CP violation in B 0 B 0 mixing with the BABAR detector. We select a sample of B 0 → D * − X + ν decays with a partial reconstruction method and use kaon tagging to assess the flavor of the other B meson in the event. We determine the CP violating asymmetry ACP ≡ Experiments at B factories have observed CP violation in direct B 0 decays [1] and in the interference between B 0 mixing and decay [2]. CP violation in mixing has so far eluded observation.
Experiments measure A CP from the dilepton asymmetry, A = N ( + + )−N ( − − ) N ( + + )+N ( − − ) , where an + ( − ) tags a B 0 (B 0 ) meson, and refers either to an electron or a muon [4]. These measurements benefit from the large number of produced dilepton events. However, they rely on the use of control samples to subtract the charge-asymmetric background originating from hadrons wrongly identified as leptons or leptons from light hadron decays, and to compute the charge-dependent lepton identification asymmetry that may produce a false signal. The systematic uncertanties associated with the corrections for these effects constitute a severe limitation to the precision of the measurements.
Using a sample of dimuon events, the D∅ Collaboration measured a value of A CP for a mixture of B s and B 0 decays that deviates from the SM by 3.9 standard deviations [5]. Measurements of A CP for B s mesons performed by the D∅ Collaboration with B s → D s µX decays are consistent with the SM [7].
We present a measurement of A CP (B 0 ) with a new analysis technique. We reconstruct a sample of B 0 mesons (hereafter called B R ; charge conjugate states are implied unless otherwise stated) from the semileptonic transition B 0 → D * − X + ν, with a partial reconstruction of the D * − → π − D 0 decay (see Ref. [8] and references therein). The observed asymmetry between the number of events with an + compared to those with an − is then: where χ d = 0.1862 ± 0.0023 [9] is the integrated mixing probability for B 0 mesons and A r is the detector-induced charge asymmetry in the B R reconstruction. We identify ("tag") the flavor of the other B 0 meson (labeled B T ) using events with a charged kaon (K T ). An event with a K + (K − ) usually arises from a state that decays as a B 0 (B 0 ) meson. When mixing takes places, the and the K T then have the same electric charge. The observed asymmetry in the rate of mixed events is: where A K is the detector charge asymmetry in kaon reconstruction. A kaon with the same charge as the might also arise from the Cabibbo-Favored (CF) decays of the D 0 meson produced with the lepton from the partially reconstructed side (K R ). The asymmetry observed for these events is: Eqs. 1, 2, and 3 can be used to extract A CP and the detector induced asymmetries (A r and A K ).
A detailed description of the BABAR detector is provided elsewhere [10]. We use a sample with an integrated luminosity of 425.7 fb −1 [11] collected on the peak of the Υ (4S) resonance. A 45 fb −1 sample collected 40 MeV below the resonance ("off-peak") is used for background studies. We also use a simulated sample of BB events [12] with an integrated luminosity equivalent to approximately three times the data.
We preselect a sample of hadronic events requiring the number of charged particles to be at least four. We reduce non-BB (continuum) background by requiring the ratio of the second to the zeroth order Fox-Wolfram moments [13] to be less than 0.6.
We select the B R sample by searching for combinations of a charged lepton (in the momentum range 1.4 < p < 2.3 GeV/c) and a low momentum pion π − s (60 < p π − s < 190 MeV/c), which is taken to arise from D * − → D 0 π − s decay. Here and elsewhere momenta are calculated in the-center-of-mass frame. The + and the π − s must have opposite electric charge. Their tracks must be consistent with originating from a common vertex, which is constrained to the beam collision point in the plane transverse to the beam axis. Finally, we combine p , p π − s , and the probability of the vertex fit in a likelihood ratio variable (η) optimized to reject combinatorial BB events. If more than one candidate is found in the event, we choose the one with the largest value of η.
We determine the square of the unobserved neutrino mass as: where we neglect the momentum of the B 0 (p B ≈ 340 MeV/c) and identify the B 0 energy with the beam energy E beam in the e + e − center-of-mass frame; E and p are the energy and momentum of the lepton and p D * is the estimated momentum of the D * . As a consequence of the limited phase space available in the D * + decay, the soft pion is emitted nearly at rest in the D * + rest frame. The D * + four-momentum can therefore be computed by approximating its direction as that of the soft pion, and parametrizing its momentum as a linear function of the soft-pion momentum. All B 0 semileptonic decays with M 2 ν near zero are considered to be signal events, is erroneously identified as a lepton (in most cases, a muon). B 0 decays to flavor-insensitive CP eigenstates, B 0 → D * ± DX, D → ∓ X, and B + → D * − X + + ν decays accumulate around zero as the signal events ("peaking background"). The uncorrelated background consists of continuum and combinatorial BB events. The latter category includes events where a genuine D * − is combined with an + from the other B meson.
We identify charged kaons in the momentum range 0.2 < p K < 4 GeV/c with an average efficiency of about 85% and a ∼ 3% pion misidentification rate. We determine the K production point from the intersection of the K track and the beam spot, and then determine the distance ∆z between the + π − s and K vertices coordinates along the beam axis. Finally, we define the proper time difference ∆t between the B R and the B T in the so called "Lorentz boost approximation" [14], ∆t = ∆z βγ , where the product βγ = 0.56 is the average Lorentz boost of the Υ (4S) in the laboratory frame. Since the B mesons are not at rest in the Υ (4S) rest frame, and in addition the K is usually produced in the cascade process B T → DX, D → KY , ∆t is in fact only an approximation of the actual proper time difference between the B R and the B T . We reject events if the uncertainty σ(∆t) exceeds 3 ps. This selection reduces to a negligible level the contamination from protons produced in the scattering of primary particles with the beam pipe or the detector material and wrongly identified as kaons, which would otherwise constitute a large charge-asymmetric source of background.
We define an event as "mixed" if the K and the have the same electric charge and as "unmixed" otherwise. In about 20% of the cases, the K has the wrong charge correlation with respect to the B T , and the event is wrongly defined (mistags).
About 95% of the K R candidates have the same electric charge as the ; they constitute 75% of the mixed event sample. Due to the small lifetime of the D 0 meson, the separation in space between the K R and the π s production points is much smaller than for K T . Therefore, we use ∆t as a first discriminant variable. Kaons in the K R sample are usually emitted in the hemisphere opposite to the , while genuine K T are produced randomly, so we use in addition the cosine of the angle θ K between the and the K.
In about 20% of the cases, the events contain more than one K; most often we find both a K T and a K R candidate. As these two carry different information, we accept multiple-candidate events. Using ensembles of simulated samples of events, we find that this choice does not affect the statistical uncertainty.
The M 2 ν distribution of all signal candidates in shown in Fig. 1. We determine the signal fraction by fitting the M 2 ν distribution in the interval [−10, 2.5] GeV 2 /c 4 with the sum of continuum, BB combinatorial, and BB peaking events. We split peaking BB into direct (B 0 → D * − + ν), "D * * " (B → D * − X 0 + ν ), cascade, hadrons wrongly identified as leptons, and CP eigenstates. In the fit, we float the fraction of direct, D * * , and BB combinatorial background, while we fix the continuum contribution to the expectation from off-peak events, rescaled by the on-peak to off-peak luminosity ratio, and the rest (less than 2% of the total) to the level predicted by the Monte Carlo simulation. Based on the assumption of isospin conservation, we attribute 66% of the D * * events to B + decays and the rest to B 0 decays. We use the result of the fit to compute the fractions of continuum, combinatorial, and peaking B + background, CP eigenstates, and B 0 signal in the sample, as a function of M 2 ν . We find a total of (5.945 ± 0.007) × 10 6 peaking events (see Fig. 1).
We then repeat the fit after dividing events in the four lepton categories (e ± , µ ± ) and eight tagged samples (e ± K ± , µ ± K ± ).
We measure A CP with a binned four-dimensional fit to ∆t (100 bins), σ(∆t)(20), cos θ k (4), and p K (5). Following Ref. [15] and neglecting resolution effects, the ∆t distributions for signal events with a K T are represented by the following expressions: where the first index of F refers to the flavor of the B R and the second to the B T , Γ 0 = τ −1 B 0 is the average width of the two B 0 mass eigenstates, ∆m d and ∆Γ are respectively their mass and width difference, the parameter r results from the interference of CF and Doubly Cabibbo Suppressed (DCS) decays on the B T side [15] and has a very small value (O(1%)), and b and c are two parameters expressing the CP violation arising from that interference. In the SM, b = 2r sin(2β + γ) cos δ and c = −2r cos(2β + γ) sin δ , where β and γ are angles of the Unitary Triangle and δ is a strong phase. The quantities ∆m d , τ B 0 , b, c, and sin(2β + γ) are left free in the fit to reduce the systematic uncertainty. The value of ∆Γ is fixed to zero. Neglecting the tiny contribution from DCS decays, the main contribution to the asymmetry is time independent and due to the normalization factors of the two mixed terms.
The ∆t distribution for the decays of the B + mesons is parametrized by an exponential function, F B + = Γ + e −|Γ+∆t| , where the B + decay width is computed as the inverse of the lifetime Γ −1 + = τ B + = (1.641 ± 0.008) ps.
When the K T comes from the decay of the B 0 meson to a CP eigenstate (as, for example B 0 → D ( * ) D ( * ) [9]), a different expression applies: where the plus sign is used if the B R decays as a B 0 and the minus sign otherwise. The fraction of these events (about 1%) and the parameters S and C are fixed in the fits and are taken from simulation. We obtain the ∆t distributions for K T in BB events, G i (∆t), by convolving the theoretical ones with a resolution function, which consists of the superposition of several Gaussian functions, convolved with exponentials to take into account the finite lifetime of charmed mesons in the cascade decay b → c → K. Different sets of parameters are used for peaking and for combinatorial background events.
To describe the ∆t distributions for K R events, G K R (∆t), we select a subsample of data containing fewer than 5% K T decays, and use background-subtracted histograms in our likelihood functions. As an alternative, we apply the same selection to the simulation and correct the ∆t distribution predicted by the Monte Carlo by the ratio of the histograms extracted from data and simulated events. The cos θ K shapes are obtained from the histograms of the simulated distributions for BB events. The ∆t distribution of continuum events is represented by a decaying exponential convolved with Gaussians parametrized by fitting simultaneously the off-peak data.
The rate of events in each bin (j) and for each tagged sample are then expressed as the sum of the predicted contributions from peaking events, BB combinatorial, and continuum background. Accounting for mistags and K R events, the peaking B 0 contributions to the samesign samples are: where the reconstruction asymmetries have separate values for the e and µ samples. We allow for different mistag probabilities for K T (ω ± ) and K R (ω ± ). The parameters f ±± K R (p k ) describe the fractions of K R tags in each sample as a function of the kaon momentum.
A total of 168 parameters are determined in the fit. By analyzing simulated events as data, we observe that the fit reproduces the generated values of 1 − |q/p| (zero) and of the other most significant parameters (A r , A K , ∆m d , and τ B 0 ). We then produce samples of simulated events with ∆ CP = ±0.005, ±0.010, ±0.025 and A r or A K in the range of ±10%, by removing events. A total of 67 different simulated event samples are used to check for biases. In each case, the input values are correctly determined, and an unbiased value of |q/p| is always obtained.  The fit to the data yields ∆ CP = (0.29±0.84 +1.88 −1.61 )×10 −3 , where the first uncertainty is statistical and the second systematic. The values of the detector charge asymmetries are A r,e = (3.0 ± 0.4) × 10 −3 , A r,µ = (3.1 ± 0.5) × 10 −3 , and A K = (13.7±0.3)×10 −3 . The frequency of the oscillation ∆m d = 508.5±0.9 ns −1 is consistent with the world average, while τ B 0 = 1.553 ± 0.002 ps is somewhat larger than the world average, which we account for in the evaluation of the systematic uncertainties. Figures 2  and 3 show the fit projections for ∆t and cos θ K .
The systematic uncertainty is computed as the sum in quadrature of several contributions, described below and summarized in Table I: -Peaking Sample Composition: we vary the sample composition by the statistical uncertainty of the M 2 ν fit, the fraction of B 0 to B + in the D * * peaking sample in the range 50 ± 25% to account for possible violation of isospin symmetry, the fraction of the peaking contributions (taken from the simulation) by ±20%, and the fraction of CP eigenstates by ±50%.
-BB combinatorial sample composition: we vary the fraction of B + events in the BB combinatorial sample by ±4.5%, which corresponds to the uncertainty in the inclusive branching fraction for B 0 → D * − X.
-∆t resolution model: we quote the difference between the result when all resolution parameters are determined in the fit and those obtained when those that exhibit a weak correlation with |q/p| are fixed.
-K R fraction: we vary the ratio of B + → K R X to B 0 → K R X by ±6.8%, which corresponds to the uncertainty of the fraction BR(D * 0 →K − X) BR(D * + →K − X) . -K R ∆t distribution: we use half the difference between the results obtained using the two different strategies to describe the K R ∆t distribution.
-Fit bias: parametrized simulations are used to check the estimate of the result and its statistical uncertainty. We add the statistical uncertainty on the validation test using the detailed simulation and the difference between the nominal result and the central result determined from the ensemble of parametrized simulations.
-CP eigenstates description : we vary the S and C parameters describing the CP eigenstates by their statistical uncertainties as obtained from simulation.
-Physical parameters: we repeat the fit setting the value of ∆Γ to 0.02 ps −1 . The lifetimes of the B 0 and B + mesons and ∆m d are floated in the fit. Alternatively, we check the effect of fixing each parameter in turn to the world average.
We are grateful for the excellent luminosity and ma-chine 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. This work is supported by DOE