The double radiative annihilation of the heavy-light fermion bound states

Abstract

We consider the double-radiative decays of heavy-light QED and QCD atoms, ${\mu }^{+}{e}^{-}\to \gamma \gamma$ and ${\bar{B}}_s^0\to \gamma \gamma$. Especially, we take under scrutiny contributions coming from operators that vanish on the free-quark mass shell. We show that by field redefinitions these operators are converted into contact terms attached to the bound state dynamics. A net off-shell contribution is suppressed with respect to the effect of the well known flavour-changing magnetic-moment operator by the bound-state binding factor. The negligible off-shellness of the weakly bound QED atoms becomes more relevant for strongly bound QCD atoms. We analyze this off-shellness in model-approaches to QCD, one of them enabling us to keep close contact to the related effect in QED. We also comment on the off-shell effect in the corresponding process ${\bar{B}}_d\to K^{\ast }\gamma$, and discuss possible hindering of the claimed beyond-standard-model discovery in this decay mode.

Comments: 24 pages, 5 figures; to be published in Fizika B