Electric dipole transitions of 1P bottomonia

Abstract

We compute the electric dipole transitions χbJ(1P)→Î_s11Î¥(1S), with J=0,1,2, and hb(1P)→Î_s11ηb(1S) in a model-independent way. We use potential non-relativistic QCD (pNRQCD) at weak coupling with either the Coulomb potential or the complete static potential incorporated in the leading order Hamiltonian. In the last case, the perturbative series shows very mild scale dependence and a good convergence pattern, allowing predictions for all the transition widths. Assuming ΛQCD≪mv2, the precision that 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 relative velocity. Our results are: Γ(χb0(1P)→Î_s11Î¥(1S))=28_s162−2 keV, Γ(χb1(1P)→Î_s11Î¥(1S))=37_s162−2 keV, Γ(χb2(1P)→Î_s11Î¥(1S))=45_s163−3 keV and Γ(hb(1P)→Î_s11ηb(1S))=63_s166−6 keV.