High order U-spin breaking: A precise amplitude relation in D 0 decays

摘要

U-spin breaking corrections up to third order are studied inD0decays to pairs of a charged pion or kaon. We show that first and third order corrections vanish in|A(D0→K+K?)A(D0→π+π?)|/|A(D0→K+π?)A(D0→π+K?)|=1, while second order corrections cancel each other experimentally at a one percent level. We compare this ratio with three other ratios of amplitudes involving these same decays, for which expansions up to and including second order are obtained. A nonlinear relation between these four ratios is shown to hold excluding third order U-spin breaking at a fraction of a percent. Isospin breaking in this relation and in the above equality is suppressed by both isospin and U-spin breaking parameters. The ratios|A(D0→K+π?)|/|A(D0→π+K?)|and|A(D0→K+K?)|/|A(D0→π+π?)|determine values of 0.05 and 0.30 for real parts of two distinct first order U-spin breaking parameters of different origins.