The chromomagnetic moment of a heavy quark with hyperasymptotic precision

TL;DR

This paper refines the calculation of the heavy quark chromomagnetic moment's infrared behavior, providing precise estimates and applying hyperasymptotic methods to compute meson hyperfine splittings.

Contribution

It introduces a hyperasymptotic approach to determine the chromomagnetic moment of heavy quarks with high precision, including the leading infrared renormalon effects.

Findings

Estimated the normalization of the leading infrared renormalon.

Computed the hyperfine splitting of B and D mesons with hyperasymptotic precision.

Fitted experimental data to extract the parameter b7b7

Abstract

We determine the normalization of the leading infrared renormalon of the chromomagnetic moment of a heavy quark. Estimates of higher order coefficients of the perturbative series are given. We compute the hyperfine splitting of the $B$ and $D$ mesons for the ground state with hyperasymptotic precision by including the leading terminant, associated with the first infrared renormalon. We fit the experimental data to the operator product expansion theoretical prediction with $\hat \mu^2_{G,\rm PV}$ as the free parameter. We obtain $\hat \mu^2_{G,\rm PV}=0.507(7)$ GeV$^2$ for the ground state.