The chromomagnetic moment of a heavy quark with hyperasymptotic precision

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.