SU(3)F sum rules for CP asymmetries of D(s) decays

Abstract

Charge-parity (CP) asymmetries in charm decays are extremely suppressed in the Standard Model and may well be dominated by new-physics contributions. The LHCb Collaboration reported the results of direct CP asymmetry measurements in D0→K+K− and D0→π+π− decays with unprecedented accuracy: aCP(K+K−)=(7.7±5.7)×10−4 and aCP(π+π−)=(23.2±6.1)×10−4, with the latter quantity inferred from the precise measurement of ΔaCP=aCP(K+K−)−aCP(π+π−)=(−15.7±2.9)×10−4. When interpreted within the Standard Model, these values indicate a breakdown of the approximate U-spin symmetry of QCD. If, however, this symmetry holds and the data stem from new physics, other CP asymmetries should be enhanced as well. We derive CP asymmetry sum rules based on SU(3) flavor symmetry for D meson decays into a pair of pseudoscalar mesons as well as a pair of a pseudoscalar and a vector meson for two generic scenarios, with ΔU=0 and |ΔU|=1 interactions, respectively. The correlations implied by the sum rules can be used to check the consistency between different measurements and to discriminate between these scenarios with future data. For instance, we find aCP(π+K*0)+aCP(K+K¯*0)=0 for ΔU=0 new physics and the opposite relative sign for the |ΔU|=1 case. One sum rule, connecting four decay modes, holds in both scenarios. We further extend our sum rules to certain differences of CP asymmetries from which the D production asymmetries drop out. Published by the American Physical Society 2025