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

TL;DR

This paper calculates the hindered M1 radiative decay rate of Upsilon(2S) to eta_b(1S) using lattice NRQCD, including relativistic corrections and a full error analysis, and finds results consistent with experiments.

Contribution

It provides the first comprehensive lattice NRQCD calculation of the hindered Upsilon(2S) to eta_b(1S) decay, incorporating relativistic effects and a detailed error budget.

Findings

Branching fraction (5.4 b1 1.8) imes 10^{-4}

Results agree with experimental measurements

Includes relativistic corrections up to v^6 and full error analysis.

Abstract

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