Hindered M1 Radiative Decay of $Υ(2S)$ from Lattice NRQCD

Abstract

We present a calculation of the hindered M$1$ $Υ(2S) \to η_b(1S) γ$ decay rate using lattice non-relativistic QCD. The calculation includes spin-dependent relativistic corrections to the NRQCD action through $\mathcal{O}(v^6)$ 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 $\mathcal{B}(Υ(2S)\toη_b(1S)γ) = 5.4(1.8)\times 10^{-4} $, which agrees with the current experimental value.