Evidence for D0-D0 mixing

Observation of the Mass Difference between Neutral Charm-Meson Eigenstates

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, corresponding to an integrated luminosity of 5.4  fb^{-1}. A total of 30.6 million D^{0}→K_{S}^{0}π^{+}π^{-} 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, the mass and decay-width differences are measured to be x_{CP}=[3.97±0.46(stat)±0.29(syst)]×10^{-3} and y_{CP}=[4.59±1.20(stat)±0.85(syst)]×10^{-3}, respectively. The CP-violating parameters are measured as Δx=[-0.27±0.18(stat)±0.01(syst)]×10^{-3} and Δy=[0.20±0.36(stat)±0.13(syst)]×10^{-3}. This is the first observation of a nonzero mass difference in the D^{0} meson system, with a significance exceeding seven standard deviations. The data are consistent with CP symmetry and improve existing constraints on the associated parameters.

Overview of recent LHCb results

A selection of the most recent and relevant measurements by the LHCb experiment is presented. It includes the determination of the CKM angle γ, obtained from a combination of a number of measurements of B meson decays, the measurement of the D0 - D0 mixing parameters and the results of several tests of the lepton-flavour universality of the electroweak couplings.

First Observation of D^{0}-D[over ¯]^{0} Oscillations in D^{0}→K^{+}π^{-}π^{+}π^{-} Decays and Measurement of the Associated Coherence Parameters

Charm meson oscillations are observed in a time-dependent analysis of the ratio of D^{0}→K^{+}π^{-}π^{+}π^{-} to D^{0}→K^{-}π^{+}π^{-}π^{+} decay rates, using data corresponding to an integrated luminosity of 3.0  fb^{-1} recorded by the LHCb experiment. The measurements presented are sensitive to the phase-space averaged ratio of doubly Cabibbo-suppressed to Cabibbo-favored amplitudes r_{D}^{K3π} and the product of the coherence factor R_{D}^{K3π} and a charm mixing parameter y_{K3π}^{'}. The constraints measured are r_{D}^{K3π}=(5.67±0.12)×10^{-2}, which is the most precise determination to date, and R_{D}^{K3π}y_{K3π}^{'}=(0.3±1.8)×10^{-3}, which provides useful input for determinations of the CP-violating phase γ in B^{±}→DK^{±}, D→K^{∓}π^{±}π^{∓}π^{±} decays. The analysis also gives the most precise measurement of the D^{0}→K^{+}π^{-}π^{+}π^{-} branching fraction, and the first observation of D^{0}-D[over ¯]^{0} oscillations in this decay mode, with a significance of 8.2 standard deviations.

Measurement of the Difference of Time-Integrated CP Asymmetries in D^{0}→K^{-}K^{+} and D^{0}→π^{-}π^{+} Decays

A search for CP violation in D^{0}→K^{-}K^{+} and D^{0}→π^{-}π^{+} decays is performed using pp collision data, corresponding to an integrated luminosity of 3  fb^{-1}, collected using the LHCb detector at center-of-mass energies of 7 and 8 TeV. The flavor of the charm meson is inferred from the charge of the pion in D^{*+}→D^{0}π^{+} and D^{*-}→D[over ¯]^{0}π^{-} decays. The difference between the CP asymmetries in D^{0}→K^{-}K^{+} and D^{0}→π^{-}π^{+} decays, ΔA_{CP}≡A_{CP}(K^{-}K^{+})-A_{CP}(π^{-}π^{+}), is measured to be [-0.10±0.08(stat)±0.03(syst)]%. This is the most precise measurement of a time-integrated CP asymmetry in the charm sector from a single experiment.

Observation of D0-D0 mixing in e+e- collisions

We observe D(0)-D(0) mixing in the decay D(0) → K+π- using a data sample of integrated luminosity 976 fb(-1) collected with the Belle detector at the KEKB e+e- asymmetric-energy collider. We measure the mixing parameters x'(2) = (0.09 ± 0.22) × 10(-3) and y'=(4.6 ± 3.4) × 10(-3) and the ratio of doubly Cabibbo-suppressed to Cabibbo-favored decay rates R(D) = (3.53 ± 0.13) × 10(-3), where the uncertainties are statistical and systematic combined. Our measurement excludes the no-mixing hypothesis at the 5.1 standard deviation level.

Measurement of D0-D0 mixing parameters and search for CP violation using D0 → K+ π- decays

Measurements of charm mixing parameters from the decay-time-dependent ratio of D0 → K+ π- to D0 → K- π+ 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)×10(-5), y'=(4.8±1.0)×10(-3), and RD=(3.568±0.066)×10(-3). Allowing for CP violation, the measurement is performed separately for D0 and D0 mesons yielding AD=(-0.7±1.9)%, for the direct CP-violating asymmetry, and 0.75<|q/p|<1.24 at the 68.3% confidence level, for the parameter describing CP violation in mixing. This is the most precise determination of these parameters from a single experiment and shows no evidence for CP violation.

Observation of D⁰-D¯⁰ mixing using the CDF II detector

We measure the time dependence of the ratio of decay rates for D0→K(+)π(-) to the Cabibbo-favored decay D(0)→K(-)π(+). The charge conjugate decays are included. A signal of 3.3×10(4) D(*+)→π(+)D(0), D(0)→K(+)π(-) decays is obtained with D0 proper decay times between 0.75 and 10 mean D0 lifetimes. The data were recorded with the CDF II detector at the Fermilab Tevatron and correspond to an integrated luminosity of 9.6  fb(-1) for pp¯ collisions at √s=1.96  TeV. Assuming CP conservation, we search for D0-D¯0 mixing and measure the mixing parameters to be R(D)=(3.51±0.35)×10(-3), y'=(4.3±4.3)×10(-3), and x'2=(0.08±0.18)×10(-3). We report Bayesian probability intervals in the x'2-y' plane and find that the significance of excluding the no-mixing hypothesis is equivalent to 6.1 Gaussian standard deviations, providing the second observation of D0-D¯0 mixing from a single experiment.

Observation of D0-D0 oscillations

We report a measurement of the time-dependent ratio of D(0) → K(+) π- to D(0) → K(-) π(+) decay rates in D(*+)-tagged events using 1.0 fb(-1) of integrated luminosity recorded by the LHCb experiment. We measure the mixing parameters x('2) = (-0.9 ± 1.3) × 10(-4), y' = (7.2 ± 2.4) × 10(-3), and the ratio of doubly-Cabibbo-suppressed to Cabibbo-favored decay rates R(D) = (3.52 ± 0.15) × 10^{-3}, where the uncertainties include statistical and systematic sources. The result excludes the no-mixing hypothesis with a probability corresponding to 9.1 standard deviations and represents the first observation of D0-D0 oscillations from a single measurement.

Experimental constraints from flavour changing processes and physics beyond the Standard Model

Flavour physics has a long tradition of paving the way for direct discoveries of new particles and interactions. Results over the last decade have placed stringent bounds on the parameter space of physics beyond the Standard Model. Early results from the LHC, and its dedicated flavour factory LHCb, have further tightened these constraints and reiterate the ongoing relevance of flavour studies. The experimental status of flavour observables in the charm and beauty sectors is reviewed in measurements of CP violation, neutral meson mixing, and measurements of rare decays.

Evidence for CP violation in time-integrated D0→h(-)h(+) decay rates

A search for time-integrated CP violation in D(0)→h(-)h(+) (h=K, π) decays is presented using 0.62 fb(-1) of data collected by LHCb in 2011. The flavor of the charm meson is determined by the charge of the slow pion in the D(*+)→D(0)π(+) and D(*-)→D[over ¯](0)π(-) decay chains. The difference in CP asymmetry between D(0)→K(-)K(+) and D(0)→π(-)π(+), ΔA(CP)≡A(CP)(K(-)K(+))-A(CP)(π(-)π(+)), is measured to be [-0.82±0.21(stat)±0.11(syst)]%. This differs from the hypothesis of CP conservation by 3.5 standard deviations.

Search for CP violation in the decays D(0)→K(S)(0)P(0)

We have searched for CP violation in the decays D(0)→K(S)(0)P(0) where P(0) denotes a neutral pseudoscalar meson that is either a π(0), η, or η' using KEKB asymmetric-energy e(+)e(-) collision data corresponding to an integrated luminosity of 791 fb(-1) collected with the Belle detector. No evidence of significant CP violation is observed. We report the most precise CP asymmetry measurement in the decay D(0)→K(S)(0)π(0) to date: A(CP)(D(0)→K(S)(0)π(0))=(-0.28±0.19±0.10)%. We also report the first measurements of CP asymmetries in the decays D(0)→K(S)(0)η and D(0)→K(S)(0)η': A(CP)(D(0)→K(S)(0)η)=(+0.54±0.51±0.16)% and A(CP)(D(0)→K(S)(0)η')=(+0.98±0.67±0.14)%, respectively.

Measurement of D0-D0 mixing parameters using D0 → K(S)(0)π+ π- and D0 → K(S)(0)K+ K- decays

We report a direct measurement of D0-D0 mixing parameters through a time-dependent amplitude analysis of the Dalitz plots of D(0) → K(S)(0) π+ π- and, for the first time, D0 → K(S)(0)K+ K- decays. The low-momentum pion π(s)(+) in the decay D*+ → D0 π(s)(+) identifies the flavor of the neutral D meson at its production. Using 468.5 fb(-1) of e+ e- colliding-beam data recorded near square root(s)=10.6 GeV by the BABAR detector at the PEP-II asymmetric-energy collider at SLAC, we measure the mixing parameters x = [1.6 ± 2.3(stat) ± 1.2(syst) ± 0.8(model)] × 10(-3), and y = [5.7 ± 2.0(stat) ± 1.3(syst) ± 0.7(model)] × 10(-3). These results provide the best measurement to date of x and y. The knowledge of the value of x, in particular, is crucial for understanding the origin of mixing.

Measurement of D{0}-D[-over]{0} mixing from a time-dependent amplitude analysis of D{0}-->K+pi{-}pi{0} decays

We present evidence of D{0}-D[-over ]{0} mixing using a time-dependent amplitude analysis of the decay D{0}-->K+pi{-}pi;{0} in a data sample of 384 fb{-1} collected with the BABAR detector at the PEP-II e+e{-} collider at the Stanford Linear Accelerator Center. Assuming CP conservation, we measure the mixing parameters x{Kpipi{0}}{'}=[2.61{-0.68}{+0.57}(stat)+/-0.39(syst)]%, y{Kpipi;{0}}{'}=[-0.06{-0.64}{+0.55}(stat)+/-0.34(syst)]%. This result is inconsistent with the no-mixing hypothesis with a significance of 3.2 standard deviations. We find no evidence of CP violation in mixing.

Determination of the strong phase in D0-->K+pi- using quantum-correlated measurements

We exploit the quantum coherence between pair-produced D0 and D[over]0 in psi(3770) decays to study charm mixing, which is characterized by the parameters x and y, and to make a first determination of the relative strong phase delta between D0-->K+pi- and D[over]0-->K+pi-. Using 281 pb(-1) of e+e- collision data collected with the CLEO-c detector at Ecm=3.77 GeV, as well as branching fraction input and time-integrated measurements of RM identical with (x2 + y2)/2 and RWS identical with Gamma(D0-->K+pi-)/Gamma(D[over]0-->K+pi-) from other experiments, we find cosdelta=1.03(-0.17)(+0.31)+/-0.06, where the uncertainties are statistical and systematic, respectively. By further including other mixing parameter measurements, we obtain an alternate measurement of cosdelta=1.10+/-0.35+/-0.07, as well as x sindelta=(4.4(-1.8)(+2.7)+/-2.9)x10(-3) and delta=(22(-12-11)(+11+9)) degrees .

Evidence for D0-D(0) mixing using the CDF II detector

We measure the time dependence of the ratio of decay rates for the rare decay D{0}-->K{+}pi{-} to the Cabibbo-favored decay D{0}-->K{-}pi;{+}. A signal of 12.7x10;{3} D{0}-->K{+}pi{-} decays was obtained using the Collider Detector at Fermilab II detector at the Fermilab Tevatron with an integrated luminosity of 1.5 fb;{-1}. We measure the D0-D[over ]{0} mixing parameters (R_{D},y{'},x{'2}), and find that the data are inconsistent with the no-mixing hypothesis with a probability equivalent to 3.8 Gaussian standard deviations.

Search for CP violation in the decays D0 --> K- K+ and D0 --> pi- pi+

We measure time-integrated CP-violating asymmetries of neutral charmed mesons in the modes D0 --> K(-) K(+) and D0 --> pi(-) pi(+) with the highest precision to date by using D0 --> K(-) pi(+) decays to correct detector asymmetries. An analysis of 385.8 fb(-1) of data collected with the BABAR detector yields values of a(CP)(KK)=(0.00+/-0.34(stat)+/-0.13(syst))% and a(CP)(pipi)=(-0.24+/-0.52(stat)+/-0.22(syst))%, which agree with standard model predictions.

Method for determining the D0-D0 mixing parameters

We propose a new method to determine the mass and width differences of the two D meson mass eigenstates as well as the CP violating parameters associated with D0-D[over ]0 mixing. We show that an accurate measurement of all the mixing parameters is possible for an arbitrary CP violating phase, by combining observables from a time dependent study of D decays to a doubly Cabibbo suppressed mode with information from a CP eigenstate. As an example we consider D0-->K*0pi0 decays where the K*0 is reconstructed in both K+pi- and K(S)pi0. We also show that decays to the CP eigenstate D-->K+K- together with D-->K+pi- decays can be used to extract all the mixing parameters. There is a fourfold ambiguity in the solutions for x and y in both the cases. A combined analysis using D0-->K*0pi0 and D-->K+K- can also be used to reduce the ambiguity in the determination of parameters.

Measurement of D0-D0 mixing parameters in D0 --> Ks pi+ pi- decays

We report a measurement of D0-D(0) mixing parameters in D(0) --> K(s)(0) pi(+) pi(-) decays using a time-dependent Dalitz-plot analysis. We first assume CP conservation and subsequently allow for CP violation. The results are based on 540 fb(-1) of data accumulated with the Belle detector at the KEKB e(+)e(-) collider. Assuming negligible CP violation, we measure the mixing parameters x = (0.80 +/- 0.29(-0.07-0.14)(+0.09+0.10))% and y = (0.33+/-0.24(-0.12-0.08)(+0.08+0.06))%, where the errors are statistical, experimental systematic, and systematic due to the Dalitz decay model, respectively. Allowing for CP violation, we obtain the CP-violating parameters |q / p| = 0.86(-0.29-0.03)(+0.30+0.06) +/- 0.08 and arg(q/p) = (-14(-18-3-4)(+16+5+2)) degrees .

Evidence for D0-D0 mixing

We observe evidence for D(0)-D(0) mixing by measuring the difference in the apparent lifetime when a D(0) meson decays to the CP eigenstates K(+)K(-) and pi(+)pi(-) and when it decays to the final state K(-)pi(+). We find the relative difference of the lifetimes y(CP) to be [1.31+/-0.32(stat)+/-0.25(syst)]%, 3.2 standard deviations from zero. We also search for a CP asymmetry between D(0) and D(0) decays; no evidence for CP violation is found. These results are based on 540 fb(-1) of data recorded by the Belle detector at the KEKB e(+)e(-) collider.