Order-v4corrections toS-wave quarkonium decay

Abstract

We compute corrections of relative order ${v}^{4}$ to the rates for the decays of ${}^{1}{S}_{0}$ heavy quarkonium into two photons and into light hadrons and for the decays of ${}^{3}{S}_{1}$ heavy quarkonium into a lepton pair and into light hadrons. In particular, we compute the coefficients of the decay operators that have the same quantum numbers as the heavy quarkonium. We also confirm previous calculations of the order-${v}^{2}$ corrections to these rates. We find that the $v$ expansion converges well for the decays of ${}^{1}{S}_{0}$ heavy quarkonium and for the decay of ${}^{3}{S}_{1}$ heavy quarkonium into a lepton pair. Large higher-order-in-$v$ corrections appear in the decay of ${}^{3}{S}_{1}$ heavy quarkonium into light hadrons. However, we find that the series of coefficients of operators with ${}^{3}{S}_{1}$ quantum numbers, which yields a large correction in order ${v}^{2},$ yields a smaller correction in order ${v}^{4}.$