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

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 $\mathrm{\Delta }{\alpha }_{had}$ in the space-like region, our approach relies on the computation of the derivatives of $\mathrm{\Delta }{\alpha }_{had}(t)$ at zero squared momentum transfer $t$. We show that this approach allows to extract $\sim 99\mathrm{\%}$ of the total value of $a_{\mu }^{\text{HLO}}$ from the MUonE data, while the remaining $\sim 1\mathrm{\%}$ 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 $\mathrm{\Delta }{\alpha }_{had}(t)$ in the MUonE kinematic region, thanks to the analyticity properties of $\mathrm{\Delta }{\alpha }_{had}(t)$, which can be expanded as a polynomial at $t\sim 0$.