Abstract
U-spin breaking corrections up to third order are studied in D0 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−)| 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.
Highlights
U-spin symmetry, an SU(2) subgroup of flavor SU(3) under which the quark pair (d, s) transforms like a doublet, has been shown to have powerful consequences in D meson decays and in D0-D 0 mixing
For final states |f = |K±π∓ we apply to the first two terms the Clebsch-Gordan identity (6) with n = 0 and n = 2. Since in this case the identity involves no sign change, contributions of these two terms to π+K− and K+π− are equal in magnitudes and have equal signs when leaving out the prefactors cos2 θC and − sin2 θC
We propose to consider another ratio involving products of amplitudes, R4 ≡
Summary
U-spin symmetry, an SU(2) subgroup of flavor SU(3) under which the quark pair (d, s) transforms like a doublet, has been shown to have powerful consequences in D meson decays and in D0-D 0 mixing. Measurements observed that while R1 ≡ |A(D0 → K+π−)|/ |A(D0 → π+K−)| tan θC = 1 holds within a reasonable approximation of order ten or twenty percent, the relation R2 ≡ |A(D0 → K+K−)|/|A(D0 → π+π−)| = 1 is badly broken by about 80% It has been recently suggested [3, 4] that the large discrepancy of this ratio with respect to the U-spin symmetry value may be due to constructive interference between symmetry breaking in ∆U = 1 “tree” and ∆U = 0 “penguin” operators contributing to SCS decays, in contrast to the ratio of DCS and CF amplitudes which involves purely ∆U = 1 transitions [5]. Three other well-known amplitude relations involving a neutral pion or kaon follow from isospin symmetry [14]
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