Z-boson decays to a vector quarkonium plus a photon

Abstract

We compute the decay rates for the processes Z -> V+gamma thorn., where Z is the Z-boson, gamma is the photon, and V is one of the vector quarkonia J/psi or gamma(nS) n = 1, 2, or 3. Our computations include corrections through relative orders alpha(s) and v(2) and resummations of logarithms of m(Z)(2)/m(Q)(2), to all orders in alpha(s), at next-to-leading-logarithmic accuracy. (v is the velocity of the heavy quark Q or the heavy antiquark (Q) over bar in the quarkonium rest frame, and m(Z) and m(Q) are the masses of Z and Q, respectively.) Our calculations are the first to include both the order-as correction to the light-cone distributions amplitude and the resummation of logarithms of m(Z)(2)/m(Q)(2) and are the first calculations for the.o2Sthorn and final states. The resummations of logarithms of m(Z)(2)/m(Q)(2) that are associated with the orderas and order-v(2) corrections are carried out by making use of the Abel-Pade method. We confirm the analytic result for the order-v(2) correction that was presented in a previous publication, and we correct the relative sign of the direct and indirect amplitudes and some choices of scales in that publication. Our branching fractions for Z -> J/psi + gamma and Z -> gamma(1S) + gamma. differ by 2.0 sigma and -4.0 sigma, respectively, from the branching fractions that are given in the most recent publication on this topic (in units of the uncertainties that are given in that publication). However, we argue that the uncertainties in the rates are underestimated in that publication.