Determination of electric dipole transitions in heavy quarkonia using potential non-relativistic QCD

TL;DR

This paper calculates electric dipole transitions in heavy quarkonia using potential non-relativistic QCD, incorporating full static potential and resummation techniques for improved accuracy in theoretical predictions.

Contribution

It introduces a refined pNRQCD approach that includes the full static potential and handles renormalon effects, providing more precise predictions for heavy quarkonium transitions.

Findings

Computed transition rates with improved theoretical precision.

Separated relativistic electromagnetic and wave function corrections.

Analyzed the impact of potential and relativistic effects on transition amplitudes.

Abstract

The electric dipole transitions $\chi_{bJ}(1P)\to \gamma\Upsilon(1S)$ with $J=0,1,2$ and $h_{b}(1P)\to \gamma\eta_{b}(1S)$ are computed using the weak-coupling version of a low-energy effective field theory named potential non-relativistic QCD (pNRQCD). In order to improve convergence and thus give firm predictions for the studied reactions, the full static potential is incorporated into the leading order Hamiltonian; moreover, we must handle properly renormalon effects and re-summation of large logarithms. The precision we reach is $k_{\gamma}^{3}/(mv)^{2} \times \mathcal{O}(v^{2})$, where $k_{\gamma}$ is the photon energy, $m$ is the mass of the heavy quark and $v$ its velocity. Our analysis separates those relativistic contributions that account for the electromagnetic interaction terms in the pNRQCD Lagrangian which are $v^{2}$ suppressed and those that account for wave function corrections of relative order $v^{2}$. Among the last ones, corrections from $1/m$ and $1/m^2$ potentials are computed, but not those coming from higher Fock states since they demand non-perturbative input and are $\Lambda_{\text{QCD}}^{2}/(mv)^{2}$ or $\Lambda_{\text{QCD}}^{3}/(m^{3}v^{4})$ suppressed, at least, in the strict weak coupling regime. These proceedings are based on the forthcoming publication \cite{steinbeisser}