η → π0γγ and γγ → π0π0 in O( p6) chiral perturbation theory

Abstract

η → π 0 γγ and γγ → π 0 π 0 are considered in O( p 6) chiral perturbation theory. In addition to the usual ϱ, ω contributions, there are two O( p 6) operators ( L 6, m ) arising from explicit chiral symmetry breaking. Since only one of the two operators contributes to η → π 0 γγ, the coefficient of this operator (≡ d 3) can be determined in two ways: (i) from the measured decay rate of η → π 0 γγ, and (ii) by assuming the resonance saturations of the low energy coefficients in the O( p 6) chiral lagrangian. We find that two methods lead to vastly different values of d 3, which would indicate that either the measured decay rate for η → π 0 γγ is too large by a factor of 2∼3, or the resonance saturation assumptions do not work for d 3.