PHYSICAL REVIEW LETTERS 127, 111801 (2021) Editors' Suggestion Featured in Physics Observation of the Mass Difference between Neutral Charm-Meson Eigenstates R. Aaij et al.* (LHCb Collaboration) (Received 8 June 2021; accepted 8 July 2021; published 7 September 2021) A measurement of mixing and CP violation in neutral charm mesons is performed using data reconstructed in proton-proton collisions collected by the LHCb experiment from 2016 to 2018, 5 4 −1 D0 → K0 πþπ− corresponding to an integrated luminosity of . fb . A total of 30.6 million S decays are analyzed using a method optimized for the measurement of the mass difference between neutral charm- meson eigenstates. Allowing for CP violation in mixing and in the interference between mixing and decay, −3 the mass and decay-width differences are measured to be xCP ¼½3.97 Æ 0.46ðstatÞ0.29ðsystÞ × 10 −3 and yCP ¼½4.59 Æ 1.20ðstatÞ0.85ðsystÞ × 10 , respectively. The CP-violating parameters are mea- sured as Δx¼½−0.27Æ0.18ðstatÞ0.01ðsystÞ×10−3 and Δy ¼½0.20 Æ 0.36ðstatÞ0.13ðsystÞ × 10−3. This is the first observation of a nonzero mass difference in the D0 meson system, with a significance exceeding seven standard deviations. The data are consistent with CP symmetry and improve existing constraints on the associated parameters. DOI: 10.1103/PhysRevLett.127.111801 Neutral charm mesons propagating freely can change as in the SM it is negligible for the doubly Cabibbo- (oscillate) into their own antiparticles, as the mass eigen- suppressed (DCS) and Cabibbo-favored (CF) amplitudes states are linear combinations of the flavor eigenstates. contributing to this process. With this assumption, the CP- These flavor-changing neutral currents do not occur at tree violating phase is independent of the final state, ϕf ≈ ϕ ≈ level in the standard model (SM) and allow for hypothetical argðq=pÞ [6,7]. particles of arbitrarily high mass to contribute significantly The current world average of the mixing and CP-violating to the process. This can affect the mixing of mesons and x¼ð3 7Æ1 2Þ 10−3 y¼ð6 8þ0.6Þ 10−3 parameters yields . × , . −0.7 × , antimesons such that measurements of these processes can jq=pj¼0.951þ0.053,andϕ¼−0.092þ0.085 [8]. Measurements – −0.042 −0.079 probe physics beyond the SM [1 4]. using decays such as D0 → Kþπ− have resulted in precise The mass eigenstates of charm mesons can be written as measurements of y and have allowed for the observation of jD i ≡ pjD0iqjD¯ 0i p q 1;2 , where and are complex mixing [9,10]. However, the data remain marginally com- CP parameters and, in the limit of charge-parity ( ) sym- patible with x ¼ 0 and are consistent with CP symmetry. jD i jD i CP metry, 1 ( 2 ) is defined as the even (odd) Theoretical predictions for the mixing parameters are of eigenstate. Mixing of flavor eigenstates is described by similar magnitude but less precise [11,12], while predic- x ≡ ðm − m Þc2=Γ the dimensionless parameters 1 2 and tions of the CP-violating phase are around 0.002 [13] and y ≡ ðΓ − Γ Þ=ð2ΓÞ m Γ 1 2 , where 1ð2Þ and 1ð2Þ are the mass are well below the current experimental precision. and decay width of the D1ð2Þ state, respectively, and Γ is the Sensitivity to the mixing and CP-violating parameters is D0 D¯ 0 D0 → K0πþπ− average decay width [5].In and decays to a common offered by the self-conjugate, multibody S final state, f, CP violation in mixing manifests itself if decay [14–18]. Inclusion of the charge-conjugate process is jq=pj ≠ 1 or in the interference between mixing and decay implied unless stated otherwise. This final state is acces- ¯ ¯ 0 ¯ 0 if ϕf ≡ argðqAf=pAfÞ ≠ 0. Here Af (Af) denotes the sible in both D and D decays and leads to interference amplitude of the decay process D0 → f (D¯ 0 → f). In between the mixing and decay amplitudes, as demonstrated D0 → K0πþπ− CP pictorially in Fig. 1. The dynamics of the decay are the S decay studied in this Letter, 2 ¯ 2 violation in the decay (jAfj ≠ jAfj ) is not considered, expressed as a function of two invariant masses following *Authors are listed at the end of this Letter. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, FIG. 1. Depiction of the interference of mixing and decay if a and DOI. Funded by SCOAP3. D0 and a D¯ 0 meson decay to a common final state f. 0031-9007=21=127(11)=111801(12) 111801-1 © 2021 CERN, for the LHCb Collaboration PHYSICAL REVIEW LETTERS 127, 111801 (2021) the Dalitz-plot formalism, in which a three-body decay is by the LHCb collaboration, yielding the single most precise parameterized by a pair of two-body invariant masses measurement of xCP and Δx [18]. m2ðK0πÆÞ [19,20]. The squared invariant mass S is denoted In the bin-flip method, data are partitioned into disjoint 2 0 2 ¯ 0 as mÆ for D decays and m∓ for D decays. A mixture of regions (bins) of the Dalitz plot, which are defined to DCS and CF decay amplitudes results in large variations of preserve nearly constant strong-phase differences 2 2 0 ¯ 0 the strong phase and, with mixing, causes a decay-time Δδðm−;mþÞ between the D and D amplitudes within evolution of the density of decays across the phase space. each bin [22]. Two sets of eight bins are formed symmet- 2 2 A joint analysis of the Dalitz-plot and decay-time distri- rically about the mþ ¼ m− bisector, as illustrated in Fig. 2. 2 2 butions may be used to determine the mixing parameters. The region satisfying mþ >m−, which includes regions Splitting the sample by flavor of the charm meson at dominated by the CF D0 → KÃð892Þ−πþ decay, is given a production probes for CP-violating effects. Usage of positive index þb, while the opposite region, where the multibody decay modes is typically challenging, as it relative contribution from decays following an oscillation is requires knowledge of the variation of the hadronic enhanced, is given a negative index −b. The data are further parameters and excellent control of efficiencies, resolu- split into 13 bins of decay time, chosen such that the bins tions, and background effects. are approximately equally populated. The squared-mass This Letter reports on a measurement of the mixing and and decay-time resolutions are typically 0.006 GeV2=c4 CP D0 → K0πþπ− violation parameters in S decays using and 60 fs, respectively, which are smaller than the bin sizes the “bin-flip” method [21], a model-independent approach used. Thus, they are neglected and accounted for in the that obviates the need for detailed models of the efficiency, systematic uncertainties. resolution, and contributing amplitudes. Mixing and CP For each decay-time interval (j), the ratio of the number violation are parametrized by zCP and Δz, which are of decays in each negative Dalitz-plot bin (−b) to its Æ1 defined by zCP Æ Δz ≡ −ðq=pÞ ðy þ ixÞ. The results positive counterpart (þb) is measured. The usage of ratios are expressed in terms of the CP-even mixing parameters minimizes the need for precise modeling of the efficiency xCP ≡ −ImðzCPÞ and yCP ≡ −ReðzCPÞ, and of the CP- variation across phase space and decay time. For small violating differences Δx ≡ −ImðΔzÞ and Δy ≡ −ReðΔzÞ. mixing parameters and CP-conserving decay amplitudes, 0 ¯ 0 Conservation of CP symmetry implies xCP ¼ x, yCP ¼ y, the expected ratios for initially produced D (D ) mesons, þ − and Δx ¼ Δy ¼ 0. The method has already been employed Rbj (Rbj), are [21] 2 2 ht ij 2 2 ht ij 2 pffiffiffiffiffi à rb þ rb Reðz − Δz Þþ jzCP Æ Δzj þ rbhti Re½X ðzCP Æ ΔzÞ RÆ ≈ 4 CP 4 j b : ð Þ bj 2 2 1 ht ij 2 2 ht ij 2 pffiffiffiffiffi 1 þ 4 ReðzCP − Δz Þþrb 4 jzCP Æ Δzj þ rbhtijRe½XbðzCP Æ ΔzÞ The parameter rb is the value of Rbj at t ¼ 0, while Xb is region where the mixed contribution is negligible, in units the amplitude-weighted strong-phase difference between of the D0 lifetime τ ¼ ℏ=Γ [5], calculated directly from 2 opposing bins. Finally, htij (ht ij) corresponds to the background-subtracted data. The other parameters are Æ average (squared) decay time in each positive Dalitz-plot determined from a simultaneous fit of the observed Rbj ratios, in which external information on cb ≡ ReðXbÞ and 3 8 sb ≡ −ImðXbÞ [22,23] is used as a constraint. Samples of D0 → K0πþπ− decays are reconstructed −b 7 S 2.5 from proton-proton (pp) collisions collected by the b ] 4 6 LHCb experiment from 2016 to 2018, corresponding to c / −1 2 2 +b 5 4 5 an integrated luminosity of . fb . The strong-interaction decay Dþ → D0πþ is used to identify the flavor of the 4 [GeV 1.5 neutral charm meson at production. Throughout this Letter, 2 − þ à þ m 3 D indicates the D ð2010Þ meson and soft pion indicates 1 the pion from its decay. The LHCb detector [24,25] is a 2 Absolute bin index single-arm forward spectrometer covering the pseudora- 0.5 1 pidity range 2 < η < 5, designed for the study of particles containing b or c quarks. 0.5 1 1.5 2 2.5 3 K0 → πþπ− 2 2 4 Decays of S are reconstructed in two different m+ [GeV /c ] 0 categories, the first involving KS mesons that decay early FIG.