The Hindered M1 Radiative Decay Υ(2S) → η_b(1S)γ from Lattice NRQCD

Abstract

We present a calculation of the hindered M1 Υ(2S) → η_b(1S)γ decay rate using lattice nonrelativistic QCD. The calculation includes spin-dependent relativistic corrections to the NRQCD action through O(v⁶ ) in the quark’s relative velocity, relativistic corrections to the leading order current which mediates the transition through the quark’s magnetic moment, radiative corrections to the leading spin-magnetic coupling and for the first time a full error budget. We also use gluon field ensembles at multiple lattice spacing values, all of which include u, d, s and c quark vacuum polarisation. Our result for the branching fraction is B(Υ(2S) → η_b(1S)γ) = 5.4(1.8) × 10‾⁴ , which agrees with the current experimental value.