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 $\Delta\alpha_{had}$ 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 $t\sim 0$.