Role of(3*,3)operators in the chiral symmetry approach to nonleptonic decays andCPviolation

Abstract

We study the kaon-pole diagrams which involve the nonvanishing tadpole transition {l_angle}0{vert_bar}O{sub 6+i7}{vert_bar}{bar K}{sup 0}{r_angle} , where the operator O belongs to the (3{sup {asterisk}},3) representation of chiral SU(3){times}SU(3). As is well known, the pole contribution exactly cancels the direct contribution to K-2{pi} and s-wave nonleptonic hyperon decay in the SU(3) and chiral limits. It is shown that there are additional contributions which vanish in the SU(3) limit, these being of order (m{sub K}{sup 2}{minus}m{sub {pi}}{sup 2})/m{sub K}{sup 2} or (m{sub B{sup {prime}}}{minus}m{sub B})/m{sub K}{sup 2}. The contribution of such corrections to direct CP violation in K{r_arrow}2{pi} and hyperon decays is calculated, which could in some cases be a substantial fraction of the standard model predictions for direct CP violation in these transitions. {copyright} {ital 1997} {ital The American Physical Society}