Electric dipole transitions in potential nonrelativistic QCD

Abstract

The electric dipole transitions χbJ(1P)→Î_s11Î¥(1S) with J=0,1,2 and hb(1P)→Î_s11ηb(1S) are computed using the weak-coupling version of a low-energy effective field theory named potential non-relativistic QCD (pNRQCD). In order to improve convergence and thus give firm predictions for the studied reactions, the full static potential is incorporated into the leading order Hamiltonian_s19 moreover, we must handle properly renormalon effects and re-summation of large logarithms. The precision we reach is k3Î_s11/(mv)2×O(v2), where kÎ_s11 is the photon energy, m is the mass of the heavy quark and v its velocity. Our analysis separates those relativistic contributions that account for the electromagnetic interaction terms in the pNRQCD Lagrangian which are v2 suppressed and those that account for wave function corrections of relative order v2. Among the last ones, corrections from 1/m and 1/m2 potentials are computed, but not those coming from higher Fock states since they demand non-perturbative input and are Λ2QCD/(mv)2 or Λ3QCD/(m3v4) suppressed, at least, in the strict weak coupling regime.