Measurement of $y_{CP}$ in $D^0-\overline{D}^0$ oscillation using quantum correlations in $e^+e^-\to D^0\overline{D}^0$ at $\sqrt{s}$ = 3.773\,GeV

We report a measurement of the parameter $y_{CP}$ in $\ensuremath{D^0}\xspace-\ensuremath{\overline{D}^{0}}\xspace$ oscillations performed by taking advantage of quantum coherence between pairs of $\ensuremath{D^0}\xspace \ensuremath{\overline{D}^{0}}\xspace$ mesons produced in $e^+e^-$ annihilations near threshold. In this work, doubly-tagged $\ensuremath{D^0}\xspace \ensuremath{\overline{D}^{0}}\xspace$ events, where one $D$ decays to a $CP$ eigenstate and the other $D$ decays in a semileptonic mode, are reconstructed using a data sample of 2.92\,fb$^{-1}$ collected with the BESIII detector at the center-of-mass energy of $\sqrt{s}$ = 3.773\,GeV. We obtain $y_{CP} = (-2.0\pm1.3\pm0.7)\%$, where the first uncertainty is statistical and the second is systematic. This result is compatible with the current world average.

b Also at Ankara University, 06100 Tandogan, Ankara, Turkey c Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia and at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia d Currently at Istanbul Arel University, 34295 Istanbul, Turkey e Also at University of Texas at Dallas, Richardson, Texas 75083, USA f Also at the PNPI, Gatchina 188300, Russia g Also at Bogazici University, 34342 Istanbul, Turkey h Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia

Abstract
We report a measurement of the parameter y CP in D 0 − D 0 oscillations performed by taking advantage of quantum coherence between pairs of D 0 D 0 mesons produced in e + e − annihilations near threshold. In this work, doubly-tagged D 0 D 0 events, where one D decays to a CP eigenstate and the other D decays in a semileptonic mode, are reconstructed using a data sample of 2.92 fb −1 collected with the BESIII detector at the center-of-mass energy of √ s = 3.773 GeV. We obtain y CP = (−2.0 ± 1.3 ± 0.7)%, where the first uncertainty is statistical and the second is systematic. This result is compatible with the current world average.

Charm oscillation
It is well known that oscillations between meson and antimeson, also called mixing, can occur when the flavor eigenstates differ from the physical mass eigenstates. These effects provide a mechanism whereby interference in the transition amplitudes of mesons and antimesons may occur. They may also allow for manifestation of CP violation (CP V ) in the underlying dynamics [1,2]. Oscillations in the K 0 − K 0 [3], B 0 − B 0 [4] and B 0 s − B 0 s [5] systems are established; their oscillation rates are well-measured and consistent with predictions from the standard model (SM) [6]. After an accumulation of strong evidence from a variety of experiments [7,8,9], D 0 − D 0 oscillation were recently firmly established by LHCb [10]. The results were soon confirmed by CDF [11] and Belle [12].
The oscillations are conventionally characterized by two dimensionless parameters x = ∆m/Γ and y = ∆Γ/2Γ, where ∆m and ∆Γ are the mass and width differences between the two mass eigenstates and Γ is the average decay width of those eigenstates. The mass eigenstates can be written as |D 1,2 = p|D 0 ±q|D 0 , where p and q are complex parameters and φ = arg(q/p) is a CP -violating phase. Using the phase convention CP |D 0 = +|D 0 , the CP eigenstates of the D meson can be written as The difference in the effective lifetime between D decays to CP eigenstates and flavor eigenstates can be parameterized by y CP . In the absence of direct CP V , but allowing for small indirect CP V [6], we have

Type Mode
In the absence of CP V , one has |p/q| = 1 and φ = 0, leading to y CP = y.
Although D 0 − D 0 mixing from short-distance physics is suppressed by the CKM matrix [13,14] and the GIM mechanism [15], sizeable charm mixing can arise from long-distance processes and new physics [1,16]. Current experimental precision [17] is not sufficient to conclude whether physics beyond the SM is involved, and further constraints are needed. So far, the most precise determination of the size of the mixing has been obtained by measuring the time-dependent decay rate in the D → K ± π ∓ channel [10,11,12]. However, the resulting information on the mixing parameters x and y is highly correlated. It is important to access the mixing parameters x or y directly from time-integrated measurements to provide complementary constraints.
In this analysis, we use a time-integrated method to extract y CP , as proposed in the references [18,19,20,21], which uses threshold D 0 D 0 pair production in e + e − → γ * → D 0 D 0 . In this process, the D 0 D 0 pair is in a state of definite C = −1, such that the two D mesons necessarily have opposite CP eigenvalues. This provides a different way to probe the D 0 − D 0 oscillation.

Formalism
In the semileptonic decays of neutral D mesons (denoted as D → l) 1 , the partial decay width is only sensitive to flavor content and does not depend on the CP eigenvalue of the parent D meson. However, the total decay width of the D CP ± does depend on its CP eigenvalue: Γ CP ± = Γ(1 ± y CP ). Thus, the semileptonic branching fraction of the CP eigenstates D CP ± is B DCP ±→l ≈ B D→l (1 ∓ y CP ), and y CP can be obtained as At BESIII, quantum-correlated D 0 D 0 pairs produced at threshold allow us to measure B DCP ±→l . Specifically, we begin with a fully reconstructed D candidate decaying into a CP eigenstate, the so-called Single Tag (ST). We have thus tagged the CP eigenvalue of the partner D meson. For a subset of the ST events, the so-called Double Tag (DT) events, this tagged partner D meson is also observed via one of the semileptonic decay channels. CP violation in D decays is known to be very small [17], and can be safely neglected. Therefore, B DCP ∓→l can be obtained as where N CP ± (N CP ±;l ) and ε CP ± (ε CP ±;l ) denote the signal yields and detection efficiencies of ST decays D → CP ± (DT decays DD → CP ±; l), respectively. For CP eigenstates, as listed in Table 1, we choose modes with unambiguous CP content and copious yields. The CP violation in K 0 S decays is known to be very small, it is therefore neglected. The semileptonic modes used for the DT in this analysis are K ∓ e ± ν and K ∓ µ ± ν.

The BESIII detector and data sample
The analysis presented in this paper is based on a data sample with an integrated luminosity of 2.92 fb −1 [22] collected with the BESIII detector [23] at the center-of-mass energy of √ s = 3.773 GeV.
The BESIII detector is a general-purpose solenoidal detector at the BEPCII [24] double storage rings. The detector has a geometrical acceptance of 93% of the full solid angle. We briefly describe the components of BESIII from the interaction point (IP) outwards. A small-cell main drift chamber (MDC), using a heliumbased gas to measure momenta and specific ionizations of charged particles, is surrounded by a time-of-flight (TOF) system based on plastic scintillators which determines the flight times of charged particles. A CsI(Tl) electromagnetic calorimeter (EMC) detects electromagnetic showers. These components are all situated inside a superconducting solenoid magnet, which provides a 1.0 T magnetic field parallel to the beam direction. Finally, a multi-layer resistive plate counter system installed in the iron flux return yoke of the magnet is used to track muons. The momentum resolution for charged tracks in the MDC is 0.5% for a transverse momentum of 1 GeV. The energy resolution for showers in the EMC is 2.5% (5.0%) for 1 GeV photons in the barrel (end cap) region. More details on the features and capabilities of BESIII can be found elsewhere [23]. High-statistics Monte Carlo (MC) simulations are used to evaluate the detection efficiency and to understand backgrounds. The geant4-based [25] MC simulation program is designed to simulate interactions of particles in the spectrometer and the detector response. For the production of ψ(3770), the kkmc [26] package is used; the beam energy spread and the effects of initial-state radiation (ISR) are included. The MC samples consist of the DD pairs with consideration of quantum coherence for all modes relevant to this analysis, non-DD decays of ψ(3770), ISR production of low-mass ψ states, and QED and qq continuum processes. The effective luminosity of the MC samples is about 10 times that of the analyzed data. Known decays recorded by the Particle Data Group (PDG) [6] are generated with evtgen [27,28] using PDG branching fractions, and the remaining unknown decays are generated with lundcharm [29]. Final-state radiation (FSR) of charged tracks is taken into account with the photos package [30].

Event selection and data analysis
Each charged track is required to satisfy | cos θ| < 0.93, where θ is the polar angle with respect to the beam axis. Charged tracks other than K 0 S daughters are required to be within 1 cm of the IP transverse to the beam line and within 10 cm of the IP along the beam axis. Particle identification for charged hadrons h (h = π, K) is accomplished by combining the measured energy loss (dE/dx) in the MDC and the flight time obtained from the TOF to form a likelihood L(h) for each hadron hypothesis. The K ± (π ± ) candidates are required to satisfy L(K) > L(π) (L(π) > L(K)).
The K 0 S candidates are selected with a vertex-constrained fit from pairs of oppositely charged tracks, which are required to be within 20 cm of the IP along the beam direction; no constraint in the transverse plane is required. The two charged tracks are not subjected to the particle identification discussed above, and are assumed to be pions. We impose 0.487 GeV/c 2 < M π + π − < 0.511 GeV/c 2 and the two tracks are constrained to originate from a common decay vertex. The decay vertex is required to be separated from the IP with a significance greater than two standard deviations.
Reconstructed EMC showers that are separated from the extrapolated positions of any charged tracks by more than 10 standard deviations are taken as photon candidates. The energy deposited in nearby TOF counters is included to improve the reconstruction efficiency and energy resolution. Photon candidates must have a minimum energy of 25 MeV for barrel showers (| cos θ| < 0.80) and 50 MeV for end cap showers (0.84 < | cos θ| < 0.92). The showers in the gap between the barrel and the end cap regions are poorly reconstructed and thus excluded. The shower timing is required to be no later than 700 ns after the reconstructed event start time to suppress electronic noise and energy deposits unrelated to the event. The η and π 0 candidates are reconstructed from pairs of photons. Due to the poorer resolution in the EMC end cap regions, those candidates with both photons coming from EMC end caps are rejected. The invariant mass M γγ is required to be 0.115 GeV/c 2 < M γγ < 0.150 GeV/c 2 for π 0 and 0.505 GeV/c 2 < M γγ < 0.570 GeV/c 2 for η candidates. The photon pair is kinematically constrained to the nominal mass of the π 0 or η [6] to improve the meson four-vector calculation.
The ω candidates are reconstructed through the decay ω → π + π − π 0 . For all modes with ω candidates, sideband events in the M π + π − π 0 spectrum are used to estimate peaking backgrounds from non-ω D → K 0 S π + π − π 0 decays. We take the signal region as (0.7600, 0.8050) GeV/c 2 and the sideband regions as (0.6000, 0.7300) GeV/c 2 or (0.8300, 0.8525) GeV/c 2 . The upper edge of the right sideband is restricted because of the K * ρ background which alters the shape of M π + π − π 0 . The sidebands are scaled to the estimated peaking backgrounds in the signal region. The scaling factor is determined from a fit to the M π + π − π 0 distribution in data, as shown in Fig. 1, where the ω signal is determined with the MC shape convoluted with a Gaussian whose parameters are left free in the fit to better match data resolution, and the background is modeled by a polynomial function.

Single tags using CP modes
To identify the reconstructed D candidates, we use two variables, the beam-constrained mass M BC and the energy difference ∆E, which are defined as where p D and E D are the momentum and energy of the D candidate in the e + e − center-of-mass system, and E beam is the beam energy. The D signal peaks at the nominal D mass in M BC and at zero in ∆E. We accept only one candidate per mode per event; when multiple candidates are present, the one with the smallest |∆E| is chosen. We apply the mode-dependent ∆E requirements listed in Table 2.
For K + K − and π + π − ST modes, if candidate events contain only two charged tracks, the following requirements are applied to suppress backgrounds from cosmic rays and Bhabha events. First, we require at least one EMC shower separated from the tracks of the ST with energy larger than 50 MeV. Second, the two ST tracks must not be both identified as muons or electrons, and, if they have valid TOF times, the time difference must be less than 5 ns. Based on MC studies, no peaking background is present in M BC in our ST modes except for the K 0 S π 0 mode. In the K 0 S π 0 ST mode, there are few background events from D 0 → ρπ. From MC studies, the estimated fraction is less than 0.5%; this will be considered in the systematic uncertainties.
The M BC distributions for the six ST modes are shown in Fig. 2. Unbinned maximum likelihood fits are performed to obtain the numbers of ST yields except in the K 0 S ω mode, for which a binned least-square fit is applied to the M BC distribution after subtraction of the ω sidebands. In each fit, the signal shape is derived from simulated signal events convoluted with a bifurcated Gaussian with free parameters to account for imperfect modeling of the detector resolution and beam energy calibration. Backgrounds are described by the ARGUS [31] function. The measured ST yields in the signal region of 1.855 GeV/c 2 < M BC <1.875 GeV/c 2 and the corresponding efficiencies are given in Table 3.

Mode
Requirement (GeV)  Table 3: Yields and efficiencies of all ST and DT modes, where N CP ± (N CP ±;l ) and ε CP ± (ε CP ±;l ) denote signal yields and detection efficiencies of D → CP ± (DD → CP ±; l), respectively. The uncertainties are statistical only.

Double tags of semileptonic modes
In each ST event, we search among the unused tracks and showers for semileptonic D → Ke(µ)ν candidates. We require that there are exactly two oppositely-charged tracks which satisfy the fiducial requirements described above.
In searching for Kµν decays, kaon candidates are required to satisfy L(K) > L(π). If the two tracks can pass the criterion, the track with larger L(K) is taken as the K ± candidate, and the other track is assumed to be the µ candidate. The energy deposit in the EMC of the µ candidate is required to be less than 0.3 GeV. We further require the Kµ invariant mass M Kµ to be less than 1.65 GeV/c 2 to reject D → Kπ backgrounds. The total energy of remaining unmatched EMC showers, denoted as E extra , is required to be less than 0.2 GeV to suppress D → Kππ 0 backgrounds. To reduce backgrounds from the D → Keν process, the ratio R L ′ (e) ≡ L ′ (e)/[L ′ (e) + L ′ (µ) + L ′ (π) + L ′ (K)] is required to be less than 0.8, where the likelihood L ′ (i) for the hypothesis i = e, µ, π or K is formed by combining EMC information with the dE/dx and TOF information.
To select Keν events, electron candidates are required to satisfy L ′ (e) > 0.001 and R If both tracks satisfy these requirements, the one with larger R ′ L ′ (e) is taken as the electron. The remaining track is required to satisfy L(K) > L(π).
The variable U miss is used to distinguish semileptonic signal events from background: where, E K(l) ( p K(l) ) is the energy (three-momentum) of K ∓ (l ± ),p ST is the unit vector in the direction of the reconstructed CP -tagged D and m D is the nominal D mass. The use of the beam energy and the nominal D mass for the magnitude of the CP -tagged D improves the U miss resolution. Since E equals to | p|c for a neutrino, the signal peaks at zero in U miss . The U miss distributions are shown in Fig. 3, where the tagged-D is required to be in the region of 1.855 GeV/c 2 < M BC <1.875 GeV/c 2 . DT yields, obtained by fitting the U miss spectra, are listed in Table 3. Unbinned maximum likelihood fits are performed for all modes except for modes including ω. For modes including an ω, binned least-square fits are performed to the ω sideband-subtracted U miss distributions. In each fit, the Keν or Kµν signal is modeled by the MC-determined shape convoluted with a bifurcated Gaussian where all parameters are allowed to vary in the fit. Backgrounds for Keν are well described with a first-order polynomial. However, in the Kµν mode, backgrounds are more complex and consist of three parts. The primary background comes from D → Kππ 0 decay. To better control this background, we select a sample of D → Kππ 0 in data by requiring E extra >0.5 GeV, in which the U miss shape of Kππ 0 is proved to be basically the same than that in the region of E extra <0.2 GeV in MC simulation. The selected Kππ 0 sample is used to extract the resolution differences in the U miss shape of Kππ 0 in MC and data, and to obtain the D → Kππ 0 yields in E extra >0.5 GeV region. Then, in fits to U miss , the Kππ 0 is described by the resolution-corrected shape from MC simulations and its size is fixed according to the relative simulated efficiencies of the E extra >0.5 GeV and E extra <0.2 GeV selection criteria. The second background from Keν events is modeled by a MC-determined shape. Its ratio to the signal yields is about 3.5% based on MC studies and is fixed in the fits. Background in the third category includes all other background processes, which are well described with a first-order polynomial.

Systematic uncertainties
Most sources of uncertainties for the ST or DT efficiencies, such as tracking, PID, and π 0 , η, K 0 S reconstruction, cancel out in determining y CP . The main systematic uncertainties come from the background veto, modeling of the signals and backgrounds, fake tagged signals, and the CP -purity of ST events.
The cosmic and Bhabha veto is applied only for the KK and ππ ST events which have only two tracks. The effect of this veto is estimated based on MC simulation. We compare the cases with and without this requirement and the resultant relative changes in ST efficiencies are about 0.3% for both the KK and ππ modes. The resulting systematic uncertainty on y CP is 0.001.
Peaking backgrounds are studied for different ST modes, especially for ρπ backgrounds in the K 0 S π 0 tag mode and K 0 S π + π − π 0 backgrounds in the K 0 S ω tag mode. Based on a study of the inclusive MC samples, the fraction of peaking backgrounds in K 0 S π 0 is 0.3%. The uncertainties on y CP caused by this is about 0.001. Uncertainties from the sideband subtraction of peaking backgrounds for the K 0 S ω mode are studied by changing the sideband and signal regions; changes in the efficiency-corrected yields are negligible.
Fits to the M BC and U miss spectra could induce systematic errors by the modeling of the signal and background shape. The MC-determined signal shapes convoluted with a Gaussian are found to describe the data well, and systematic uncertainties from the modeling of the signal are assumed to be negligible. To estimate uncertainties from modeling of backgrounds, different methods are considered. For the CP ST yields, we include an additional background component to account for the ψ(3770) → DD process with a shape determined by MC simulation whose yield is determined in the fit. The uncertainties in the fits to M BC are uncorrelated among different tag modes, and the obtained change on y CP is 0.001. For the DT semileptonic yields, the polynomial functions which are used to describe backgrounds in our nominal fits are replaced by a shape derived from MC simulations. For the Kµν mode, the size of the main background Kππ 0 is fixed in our nominal fit, so the statistical uncertainties of the number of selected Kππ 0 events introduces a systematic error. To estimate the associated uncertainty, we vary its size by ±1 standard deviation based on the selected Kππ 0 samples. Systematic uncertainties due to the U miss fits are treated as positively correlated among different tag modes. We take the maximum change on the resultant y CP , which is 0.006, as systematic uncertainty.
The DT yields are obtained from the fit to the U miss spectra. However, one also has to consider events which peak at U miss but are backgrounds in the M BC spectra, the so-called fake tagged signals. This issue is   We study the CP -purities of ST modes by searching for same-CP DT signals in data. Assuming CP conservation in the charm sector, the same-CP process is prohibited, unless the studied CP modes are not pure or the initial C-odd D 0 D 0 system is diluted. The CP modes involving K 0 S are not pure due to the existence of small CP V in K 0 − K 0 mixing [6]. However, this small effect is negligible with our current sensitivity. Hence, K 0 S π 0 is assumed to be a clean CP mode, as its background level is very low. As a conservative treatment, we study DT yields of (K 0 S π 0 , K 0 S π 0 ) to verify its pure CP -odd eigenstate nature and the CP -odd environment of the D 0 D 0 pair. The observed numbers of this DT signals are quite small, and we estimate the dilution of the C-odd initial state to be less than 2% at 90% confidence level. This affects our measurement of y CP by less than 0.001. The purity of the K 0 S π 0 mode is found to be larger than 99%. Due to the complexity of the involved non-resonant and resonant processes in K 0 S π 0 π 0 and K 0 S ω, the CP -purities of these tag modes could be contaminated. We take the mode K + K − as a clean CP -even tag to test K 0 S π 0 π 0 , and take K 0 S π 0 to test K 0 S ω and K 0 S η. The CP -purities of K 0 S π 0 π 0 , K 0 S ω and K 0 S η are estimated to be larger than 89.4%, 93.3% and 93.9%, respectively. Based on the obtained CP purities, the corresponding maximum effect on the determined y CP is assigned as systematic uncertainty.
Systematic uncertainties from different sources are assumed to be independent and are combined in quadrature to obtain the overall y CP systematic uncertainties. The resultant total y CP systematic uncertainties is 0.007.

Results
The branching ratios of K ∓ e ± ν and K ∓ µ ± ν are summed to obtain B DCP ∓ →l = B DCP ∓ →Keν +B DCP ∓→K µν . To combine results from different CP modes, the standard weighted least-square method is utilized [6]. The weighted semileptonic branching fractionB DCP ±→l is determined by minimizing where α denotes different CP -tag modes and σ α CP ± is the statistical error of B α DCP ±→l for the given tag mode. The branching fractions of B DCP ±→l and the obtainedB DCP ± →l are listed in Table 5. Finally, y CP is calculated using Eq. (3), with B DCP ±→l replaced byB DCP ±→l . We obtain y CP = (−2.0 ± 1.3 ± 0.7)%, where the first uncertainty is statistical and the second is systematic.

Summary
Using quantum-correlated D 0 D 0 pairs produced at √ s = 3.773 GeV, we employ a CP -tagging technique to obtain the y CP parameter of D 0 − D 0 oscillations. Under the assumption of no direct CP V in the D sector, we obtain y CP = (−2.0 ± 1.3(stat.) ± 0.7(syst.))%. This result is compatible with the previous measurements [17,32,33] within about two standard deviations and is the most precise time-integrated measurement of y CP at charm threshold. However, the current precision is still statistically limited. Future efforts using a global fit [34] may better exploit the BESIII data, leading to a more precise result.

Acknowledgments
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National