An alternative evaluation of the leading-order hadronic contribution to the muon g-2 with MUonE

Abstract

We propose an alternative method to extract the leading-order hadronic contribution to the muon g-2, $a_{\mu }^{\text{HLO}}$, with the MUonE experiment. In contrast to the traditional method based on the integral of the hadronic contribution to the running of the effective fine-structure constant $\Delta {\alpha }_{had}$ in the space-like region, our approach relies on the computation of the derivatives of $\Delta {\alpha }_{had}(t)$ at zero squared momentum transfer $t$. We show that this approach allows to extract $\sim 99\%$ of the total value of $a_{\mu }^{\text{HLO}}$ from the MUonE data, while the remaining $\sim 1\%$ can be computed combining perturbative QCD and data on $e^{+}{e}^{-}$ annihilation to hadrons. This leads to a competitive evaluation of $a_{\mu }^{\text{HLO}}$ which is robust against the parameterization used to model $\Delta {\alpha }_{had}(t)$ in the MUonE kinematic region, thanks to the analyticity properties of $\Delta {\alpha }_{had}(t)$, which can be expanded as a polynomial at $t\sim 0$.

Comments: 12 pages, 8 figures, version accepted for publication in Phys. Lett. B