Hindered M1 Radiative Decay of ${\rm Y}(2S)$ from Lattice NRQCD

Abstract

We present a calculation of the hindered M$1$ ${\rm Y}(2S)\to {\eta }_b(1S)\gamma$ 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 $\mathcal{B}({\rm Y}(2S)\to {\eta }_b(1S)\gamma )=5.4(1.8)\times 10^{-4}$, which agrees with the current experimental value.

Comments: 26 pages, 11 figures. Updated to match version published in Phys.Rev.D