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

TL;DR

This paper introduces a novel method to determine the leading-order hadronic contribution to the muon g-2 using derivatives of the hadronic vacuum polarization function at zero momentum transfer, offering a potentially more robust and precise evaluation.

Contribution

The paper presents an alternative approach based on derivatives at zero momentum transfer, reducing reliance on parameterization and improving robustness in evaluating the muon g-2 hadronic contribution.

Findings

Extracts ~99% of the hadronic contribution from MUonE data.

Remaining ~1% can be computed with perturbative QCD and e+e- data.

Method is robust against parameterization choices.

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 $t\sim 0$.