High order U-spin breaking: A precise amplitude relation in D0D0 decays

U-spin breaking corrections up to third order are studied in D0D0 decays 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−)||A(D0→K+π−)|/|A(D0→π+K−)| and |A(D0→K+K−)|/|A(D0→π+π−)||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.