# pNRQCD determination of E1 radiative transitions

## TL;DR

This paper presents the first numerical calculation of relativistic corrections up to order v^2 for E1 radiative transitions in heavy quarkonium within the pNRQCD framework, focusing on specific bottomonium decays.

## Contribution

It provides a comprehensive perturbative computation of relativistic effects in E1 transitions in heavy quarkonium using potential non-relativistic QCD.

## Key findings

- First numerical computation of relativistic corrections for E1 transitions.
- Application to bottomonium decay processes.
- Validation of pNRQCD in weak-coupling regime.

## Abstract

This contribution contains the first numerical computation of the complete set of relativistic corrections of relative order $v^{2}$ for electric dipole (E1) transitions in heavy quarkonium; in particular, for the processes $\chi_{bJ}(1P) \to \Upsilon(1S) + \gamma$ with $J=0,\,1,\,2$. We assume that the momentum transfer of the heavy mesons involved in the reactions lies in the weak-coupling regime of the low-energy effective field theory potential non-relativistic QCD (pNRQCD) and thus a full perturbative calculation can be performed.