Sum Rules of Charm CP Asymmetries beyond the SU(3)_{F} Limit

Enhanced Charm CP Asymmetries from Final State Interactions

We show that final state interactions (FSI) within a CPT invariant two-channel framework can enhance the charge-parity (CP) violation difference between D^{0}→π^{-}π^{+} and D^{0}→K^{-}K^{+} decays up to the current experimental value. This result relies upon (i) the dominant tree level diagram, (ii) the well-known experimental values for the D^{0}→π^{-}π^{+} and D^{0}→K^{-}K^{+} branching ratios, and (iii) the ππ→ππ and ππ→KK scattering data to extract the strong phase difference and inelasticity. Based on well-grounded theoretical properties, we find the sign and bulk value of the ΔA_{CP} and A_{CP}(D^{0}→π^{-}π^{+}) recently observed by the LHCb Collaboration.

A Review of CP Violation Measurements in Charm at LHCb

The LHCb experiment has been able to collect the largest sample ever produced of charm-hadron decays, performing a number of measurements of observables related to CP violation in the charm sector. In this document, the most recent results from LHCb on the search of direct CP violation in D0→Ks0Ks0, D(s)+→h+π0 and D(s)+→h+η decays are summarised, in addition to the most precise measurement of time-dependent CP asymmetry in D0→h+h− decays and the first observation of mass difference between neutral charm-meson eigenstates.

Observation of CP Violation in Charm Decays

A search for charge-parity (CP) violation in D^{0}→K^{-}K^{+} and D^{0}→π^{-}π^{+} decays is reported, using pp collision data corresponding to an integrated luminosity of 5.9  fb^{-1} collected at a center-of-mass energy of 13 TeV with the LHCb detector. The flavor of the charm meson is inferred from the charge of the pion in D^{*}(2010)^{+}→D^{0}π^{+} decays or from the charge of the muon in B[over ¯]→D^{0}μ^{-}ν[over ¯]_{μ}X decays. The difference between the CP asymmetries in D^{0}→K^{-}K^{+} and D^{0}→π^{-}π^{+} decays is measured to be ΔA_{CP}=[-18.2±3.2(stat)±0.9(syst)]×10^{-4} for π-tagged and ΔA_{CP}=[-9±8(stat)±5(syst)]×10^{-4} for μ-tagged D^{0} mesons. Combining these with previous LHCb results leads to ΔA_{CP}=(-15.4±2.9)×10^{-4}, where the uncertainty includes both statistical and systematic contributions. The measured value differs from zero by more than 5 standard deviations. This is the first observation of CP violation in the decay of charm hadrons.

Search for CP Violation in D_{s}^{+}→K_{S}^{0}π^{+}, D^{+}→K_{S}^{0}K^{+}, and D^{+}→ϕπ^{+} Decays

A search for charge-parity (CP) violation in Cabibbo-suppressed D_{s}^{+}→K_{S}^{0}π^{+}, D^{+}→K_{S}^{0}K^{+}, and D^{+}→ϕπ^{+} decays is reported using proton-proton collision data, corresponding to an integrated luminosity of 3.8  fb^{-1}, collected at a center-of-mass energy of 13 TeV with the LHCb detector. High-yield samples of kinematically and topologically similar Cabibbo-favored D_{(s)}^{+} decays are analyzed to subtract nuisance asymmetries due to production and detection effects, including those induced by CP violation in the neutral kaon system. The results areA_{CP}(D_{s}^{+}→K_{S}^{0}π^{+})=(1.3±1.9±0.5)×10^{-3},A_{CP}(D^{+}→K_{S}^{0}K^{+})=(-0.09±0.65±0.48)×10^{-3},A_{CP}(D^{+}→ϕπ^{+})=(0.05±0.42±0.29)×10^{-3},where the first uncertainties are statistical and the second systematic. They are the most precise measurements of these quantities to date, and are consistent with CP symmetry. A combination with previous LHCb measurements, based on data collected at 7 and 8 TeV, is also reported.

Neutral D→KK^{*} Decays as Discovery Channels for Charm CP Violation

We point out that the CP asymmetries in the decays D^{0}→K_{S}K^{*0} and D^{0}→K_{S}K[over ¯]^{*0} are potential discovery channels for charm CP violation in the standard model. We stress that no flavor tagging is necessary, the untagged CP asymmetry a_{CP}^{dir}(D[over (-)]→K_{S}K^{*0}) is essentially equal to the tagged one, so that the untagged measurement comes with a significant statistical gain. Depending on the relevant strong phase, |a_{CP}^{dir,untag}| can be as large as 0.003. The CP asymmetry is dominantly generated by exchange diagrams and does not require nonvanishing penguin amplitudes. While the CP asymmetry is smaller than in the case of D^{0}→K_{S}K_{S}, the experimental analysis is more efficient due to the prompt decay K^{*0}→K^{+}π^{-}. One may further search for favorable strong phases in the Dalitz plot in the vicinity of the K^{*0} peak.

CP Asymmetries in Charm Decays into Neutral Kaons

We find a new CP-violation effect in charm decays into neutral kaons, which results from the interference between two tree (Cabibbo-favored and doubly Cabibbo-suppressed) amplitudes with the mixing of final-state mesons. This effect, estimated to be of an order of 10^{-3}, is much larger than the direct CP asymmetries in these decays, but missed in the literature. It can be revealed by measuring the difference of the time-dependent CP asymmetries in the D^{+}→π^{+}K_{S}^{0} and D_{s}^{+}→K^{+}K_{S}^{0} modes, which are accessible at the LHCb and Belle II experiments. If confirmed, the new effect has to be taken into account, as the above direct CP asymmetries are used to search for new physics.

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.