pNRQCD determination of E1 radiative transitions

Abstract: This contribution contains the first numerical computation of the complete set of relativistic corrections of relative order $v^{2}$ for electric dipole (E1) transitions in heavy quarkonium; in particular, for the processes $\chi_{bJ}(1P) \to \Upsilon(1S) + \gamma$ with $J=0,\,1,\,2$. We assume that the momentum transfer of the heavy mesons involved in the reactions lies in the weak-coupling regime of the low-energy effective field theory potential non-relativistic QCD (pNRQCD) and thus a full perturbative calculation can be performed.