Hadronic contribution to the muong−2factor: A theoretical determination

Abstract

The leading-order hadronic contribution to the muon $g\ensuremath{-}2$, ${a}_{\ensuremath{\mu}}^{\mathrm{HAD}}$, is determined entirely from theory using an approach based on Cauchy's theorem in the complex squared energy $s$-plane. This is possible after fitting the integration kernel in ${a}_{\ensuremath{\mu}}^{\mathrm{HAD}}$ with a simpler function of $s$. The integral determining ${a}_{\ensuremath{\mu}}^{\mathrm{HAD}}$ in the light-quark region is then split into a low-energy and a high-energy part, the latter given by perturbative QCD (PQCD). The low energy integral involving the fit function to the integration kernel is determined by derivatives of the vector correlator at the origin, plus a contour integral around a circle calculable in PQCD. These derivatives are calculated using hadronic models in the light-quark sector. A similar procedure is used in the heavy-quark sector, except that now everything is calculable in PQCD, thus becoming the first entirely theoretical calculation of this contribution. Using the dual-resonance model realization of large ${N}_{c}$ QCD to compute the derivatives of the correlator leads to agreement with the experimental value of ${a}_{\ensuremath{\mu}}$. Accuracy, though, is currently limited by the model-dependent calculation of derivatives of the vector correlator at the origin. Future improvements should come from more accurate chiral perturbation theory and/or lattice QCD information on these derivatives, allowing for this method to be used to determine ${a}_{\ensuremath{\mu}}^{\mathrm{HAD}}$ accurately entirely from theory, independently of any hadronic model.