Measurement of D0-D0bar mixing parameters and search for CP violation using D0->K+pi- decays

Measurements of charm mixing parameters from the decay-time-dependent ratio of D0->K+pi- to D0->K-pi+ rates and the charge-conjugate ratio are reported. The analysis uses data, corresponding to 3 fb^{-1} of integrated luminosity, from proton-proton collisions at 7 and 8 TeV center-of-mass energies recorded by the LHCb experiment. In the limit of charge-parity (CP) symmetry, the mixing parameters are determined to be x'^2=(5.5 +- 4.9)x10^{-5}, y'= (4.8 +- 1.0)x10^{-3}, and R_D=(3.568 +- 0.066)x10^{-3}. Allowing for CP violation, the mixing parameters are determined separately for D0 and D0bar mesons yielding A_D = (-0.7 +- 1.9)%, for the direct CP-violating asymmetry, and 0.75<|q/p|<1.24 at the 68.3% confidence level, where q and p are parameters that describe the mass eigenstates of the neutral charm mesons in terms of the flavor eigenstates. This is the most precise determination of these parameters from a single experiment and shows no evidence for CP violation.

Mass eigenstates of neutral charm mesons are linear combinations of flavor eigenstates |D 1,2 = p|D 0 ± q|D 0 , where p and q are complex parameters.This results in D 0 -D 0 oscillation.In the limit of charge-parity (CP ) symmetry, the oscillation is characterized by the difference in mass ∆m ≡ m 2 − m 1 and decay width ∆Γ ≡ Γ 2 − Γ 1 between the D mass eigenstates.These differences are usually expressed in terms of the dimensionless mixing parameters x ≡ ∆m/Γ and y ≡ ∆Γ/2Γ, where Γ is the average decay width of neutral D mesons.If CP symmetry is violated, the oscillation rates for mesons produced as D 0 and D 0 can differ, further enriching the phenomenology.Both short-and long-distance components of the amplitude contribute to the time evolution of neutral D mesons [1][2][3].Short-distance amplitudes could include contributions from non-standard-model particles or interactions, possibly enhancing the average oscillation rate or the difference between D 0 and D 0 meson rates.The study of CP violation in D 0 oscillation may lead to an improved understanding of possible dynamics beyond the standard model [4][5][6][7].
This Letter reports a search for CP violation in D 0 -D 0 mixing by comparing the decay-time-dependent ratio of D 0 → K + π − to D 0 → K − π + rates with the corresponding ratio for the charge-conjugate processes.An improved determination of the CP -averaged charm mixing parameters with respect to our previous measurement [18] is also reported.The analysis uses data corresponding to 1.0 fb −1 of integrated luminosity from √ s = 7 TeV pp collisions recorded by LHCb during 2011 and 2.0 fb −1 from √ s = 8 TeV collisions recorded during 2012.The neutral D flavor at production is determined from the charge of the low-momentum pion π + s in the flavor-conserving strong-interaction decay D * + → D 0 π + s .The inclusion of charge-conjugate processes is implicit unless stated otherwise.The D * + → D 0 (→ K − π + )π + s process is denoted as right sign (RS), and D * + → D 0 (→ K + π − )π + s is denoted as wrong sign (WS).The RS decay rate is dominated by a Cabibbo-favored amplitude.The WS rate arises from the interfering amplitudes of the doubly Cabibbosuppressed D 0 → K + π − decay and the Cabibbo-favored D 0 → K + π − decay following D 0 -D 0 oscillation, each of similar magnitude.In the limit of |x|, |y| 1, and assuming negligible CP violation, the time-dependent ratio R(t) of WS-to-RS decay rates is [1][2][3][4] where t is the decay time, τ is the average D 0 lifetime, and R D is the ratio of suppressed-tofavored decay rates.The parameters x and y depend linearly on the mixing parameters as x ≡ x cos δ+y sin δ and y ≡ y cos δ−x sin δ, where δ is the strong-phase difference between the suppressed and favored amplitudes A( Allowing for CP violation, the WS rates R + (t) and R − (t) of initially produced D 0 and D 0 mesons are functions of independent sets of mixing parameters (R ± D , x 2± , y ± ).A difference between R + D and R − D arises if the ratio between the magnitudes of suppressed and favored decay amplitudes is not CP symmetric (direct CP violation).Violation of CP symmetry either in mixing |q/p| = 1 or in the interference between mixing and decay amplitudes φ ≡ arg qA(D 0 → K + π − )/pA(D 0 → K + π − ) − δ = 0 are usually referred to as indirect CP violation and would result in differences between (x 2+ , y + ) and (x 2− , y − ).
The LHCb detector [20] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks.Detector components particularly relevant for this analysis are the silicon vertex detector, which provides reconstruction of displaced vertices of b-and c-hadron decays; the tracking system, which measures charged particle momenta with relative uncertainty that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c, corresponding to a typical mass resolution of approximately 8 MeV/c 2 for a two-body charm-meson decay; and the ring-imaging Cherenkov detectors, which provide kaon-pion discrimination [21].The magnet polarity is periodically inverted and approximately equal amounts of data are collected in each configuration to mitigate the effects of detection asymmetries.The online event-selection system (trigger) [22] consists of a first-level hardware stage based on information from the calorimeter and muon systems, followed by a software high-level trigger.
Events with D * + candidates consistent with being produced at the pp collision point (primary vertex) are selected following Ref.[18].In addition, a WS candidate is discarded if resulting from a D 0 candidate that, associated with another pion, also forms a RS candidate with M (D 0 π + s ) within 3 MeV/c 2 of the known D * + mass.This removes about 15% of the WS background with negligible signal loss.The two-body D 0 π + s mass M (D 0 π + s ) is computed using the known D 0 and π + masses [23] and their reconstructed momenta [18].In Ref. [18], we used events selected by the hardware trigger based on hadron calorimeter transverse-energy depositions that were geometrically matched with signal final-state tracks.In the present analysis, we distinguish two trigger categories.One category consists of events that meet the above trigger requirement (triggered-on-signal, TOS).The other comprises events with candidates failing the track-calorimeter matching and events selected based on muon hardware triggers decisions (TOS).The two subsamples contribute approximately equal signal yields with similar purities.However, they require separate treatment due to their differing kinematic distributions and trigger-induced biases.
The RS and WS signal yields are determined by fitting the M (D 0 π + s ) distribution of D 0 candidates with reconstructed mass within 24 MeV/c 2 of the known value.The time-integrated M (D 0 π + s ) distributions are shown in Fig. 1.The smooth background is dominated by favored D 0 → K + π − decays associated with random π + s candidates.The sample contains 1.15 × 10 5 (1.14 × 10 5 ) signal WS D 0 (D 0 ) decays and approximately 230 times more RS decays.Yield differences between D 0 and D 0 decays are dominated by differences in charm-anticharm production rates and reconstruction efficiencies.Each sample is divided into 13 subsamples according to the candidate's decay time, and signal yields are determined for each using shape parametrizations determined from simulation and tuned to data [18].We assume that for a given D * meson flavor, the signal shapes are common to WS and RS decays, while the descriptions of the background can differ.The decay-time-dependent WS-to-RS yield ratios R + and R − observed in the D 0 and D 0 samples, respectively, and their difference are shown in Fig. 2.These are corrected for the relative efficiencies for reconstructing K − π + and K + π − final states.
The mixing parameters are determined by minimizing a χ 2 variable that includes terms for the difference between the observed and predicted ratios and for systematic deviations of parameters The measured WS-to-RS yield ratio and its statistical uncertainty in the decay-time bin i are denoted by r ± i and σ ± i , respectively.The predicted value for the WS-to-RS yield ratio R ± i corresponds to the time integral over bin i of Eq. ( 1) including bin-specific corrections.These account for small biases due to the decay-time evolution of the approximately 3% fraction of signal candidates originating from b-hadron decays (∆ B ) and of the about 0.5% component of peaking background from RS decays in which both final-state particles are misidentified (∆ p ) [18].The relative efficiency ± r accounts for instrumental asymmetries in the Kπ reconstruction efficiencies, mainly caused by K − mesons having a larger interaction cross section with matter than K + mesons.These asymmetries are measured in data to be in the range 0.8-1.2% with 0.2% precision and to be independent of decay time.They are derived from the efficiency ratio yields divided by the product of the corresponding charge-conjugate decay yields.No CP violation is expected or experimentally observed [23] in these decays.Asymmetries due to CP violation in neutral kaons and their interaction cross-sections with matter are negligible.The 1% asymmetry between D + and D − production rates [24] cancels in this ratio, provided that the kinematic distributions are consistent across samples.We weight the D − → K + π − π − events so that their kinematic distributions match those in the D + → K 0 S π + sample.Similarly, these samples are weighted as functions of Kπ momentum to match the RS momentum spectra.The parameters associated with ∆ B , ∆ p , and r are determined separately for TOS and TOS subsets and vary independently in the fit within their Gaussian constraints χ 2 B , χ 2 p , and χ 2 [18].
To avoid experimenters' bias in the CP violation parameters, the measurement technique is finalized by adding arbitrary offsets to the WS-to-RS yield ratios for the D 0 and D 0 samples, designed to mimic the effect of different mixing parameters in the two samples.To rule out global systematic uncertainties not accounted for in Eq. ( 2), the data are first integrated over the whole decay-time spectrum and subsequently divided into statistically independent subsets according to criteria likely to reveal biases from specific instrumental effects.These include the number of primary vertices in the events, the K laboratory momentum, the π s impact parameter χ 2 with respect to the primary vertex, the D 0 impact parameter χ 2 with respect to the primary vertex, the magnetic field orientation, and the hardware trigger category.The variations of the time-integrated charge asymmetry in WS-to-RS yield ratios are consistent with statistical fluctuations.Then, we investigate decay-time-dependent biases by dividing the time-binned sample according to the magnet polarity and the number of primary vertices per event.In the TOS sample, differences of WS-to-RS yield ratios as functions of decay time for opposite magnet polarities yield , for events with one, two, and more than two primary vertices, respectively.The corresponding χ 2 values in the TOS sample, 9, 11, and 8, suggest a systematically better consistency.Hence, the statistical uncertainty of each of the WS-to-RS ratios in the TOS samples is increased by a factor of 17/12, following Ref.[23].These scaled uncertainties are used in all subsequent fits.Independent analyses of the 2011 and 2012 data yield consistent results.The ratio between RS D 0 to D 0 decay rates is independent of decay time with a 62% p value and a standard deviation of 0.16%, showing no evidence of correlations between particle identification or reconstruction efficiency and decay time.Three fits are performed to the data shown in Fig. 2. The first allows direct and indirect CP violation; the second allows only indirect CP violation by constraining R ± D to a common value; and the third is a CP -conserving fit that constrains all mixing parameters to be the same in the D 0 and D 0 samples.The fit results and their projections are shown in Table 1 and Fig. 2, respectively.Figure 3 shows the central values and confidence regions in the (x 2 , y ) plane.For each fit, 104 WS-to-RS ratio data points are used, corresponding to 13 ranges of decay time, distinguishing D * + from D * − decays, TOS from TOS decays, and 2011 data from 2012 data.The consistency with the hypothesis of CP symmetry is determined from the change in χ 2 between the fit without and with CP violation, taking into account the difference in number of degrees of freedom.The resulting p value, for the fit with direct and indirect (indirect only) CP violation allowed, is 91% (81%), showing that the data are compatible with CP symmetry.
The uncertainties incorporate both statistical and systematic contributions, since all relevant systematic effects depend on the true values of the mixing parameters, and are thus incorporated into the fit χ 2 .These include the uncertainty in the fraction of charm mesons from b-hadron decays, and their bias on the observed decay time; the uncertainty in the fraction of peaking background; and the uncertainty in the determination of the instrumental asymmetry.The statistical uncertainty is determined in a separate fit and used to calculate the systematic component by subtraction in quadrature.
Direct CP violation would produce a nonzero intercept at t = 0 in the efficiencycorrected difference of WS-to-RS yield ratios between D 0 and D 0 mesons shown in Fig. 2 (c).It is parametrized by the asymmetry measured in the first fit Indirect CP violation results in a time dependence of the efficiency-corrected difference of yield ratios.The slope observed in Fig. 2 (c) is about 5% of the individual slopes of Figs. 2 (a) and (b) and is consistent with zero.From the results of the fit allowing for direct and indirect CP violation, a likelihood for |q/p| is constructed using the relations x ± = |q/p| ±1 (x cos φ ± y sin φ) and y ± = |q/p| ±1 (y cos φ ∓ x sin φ).Confidence intervals are derived with a likelihood-ratio ordering and assuming that the correlations are independent of the true values of the mixing parameters.The magnitude of q/p is determined to be 0.75 < |q/p| < 1.24 and 0.67 < |q/p| < 1.52 at the 68.3% and 95.5% confidence levels, respectively.Significantly more stringent bounds on |q/p| and additional information on φ are available by combining the present results with other measurements [10], in particular when also using theoretical constraints, such as the relationship tan φ = x(1 − |q/p| 2 )/y(1 + |q/p| 2 ) [25,26], which applies in the limit that direct CP violation is negligible.
In summary, D 0 -D 0 oscillation is studied using D * + → D 0 (→ K + π − )π + decays reconstructed in the full sample of pp collisions, corresponding to 3 fb −1 of integrated luminosity collected by the LHCb experiment in 2011 and 2012.Assuming CP conservation, the mixing parameters are measured to be x 2 = (5.5 ± 4.9) × 10 −5 , y = (4.8± 1.0) × 10 −3 , and R D = (3.568± 0.066) × 10 −3 .The observed parameters are consistent with, 2.5 times more precise than, and supersede the results based on a subset of the present data [18].Studying D 0 and D 0 decays separately shows no evidence for CP violation and provides the most stringent bounds on the parameters A D and |q/p| from a single experiment.

Figure 3 :
Figure 3: Two-dimensional confidence regions in the (x 2 , y ) plane obtained (a) without any restriction on CP violation, (b) assuming no direct CP violation, and (c) assuming CP conservation.The dashed (solid) curves in (a) and (b) indicate the contours of the mixing parameters associated with D 0 (D 0 ) decays.The best-fit value for D 0 (D 0 ) decays is shown with an open (filled) point.The solid, dashed, and dotted curves in (c) indicate the contours of CP -averaged mixing parameters at 68.3%, 95.5%, and 99.7% confidence level (CL), respectively.The best-fit value is shown with a point.

Table 1 :
Results of fits to the data for different hypotheses on the CP symmetry.The reported uncertainties are statistical and systematic, respectively; ndf indicates the number of degrees of freedom.See App.A for fits results including correlation coefficients.

Table 2 :
Detailed fit results.Reported uncertainties and correlation coefficients include both statistical and systematic sources.