Speaker
Description
The anomalous magnetic moment of the muon, $a_\mu = (g-2)_\mu/2$, provides one of the most stringent tests of the Standard Model and it is a sensitive probe of new physics.
The dominant theoretical uncertainty in the calculation of $a_\mu$ arises from the leading-order hadronic vacuum polarization effects. The latter are evaluated through ab initio lattice QCD calculations or through data-driven dispersive analyses based on $e^+e^- \to \mathrm{hadrons}$ cross section data. Presently, the predictions of the two approaches are in disagreement and clarifying this discrepancy, referred to as the ''new muon $g-2$ puzzle'', is essential for a satisfactory comparison between data and theory.
In dispersive evaluations, the $e^+e^- \to \pi^+\pi^-$ process gives the dominant contribution and is measured either via energy scans or through the radiative return method, where initial-state radiation allows to probe a continuous range of the hadronic invariant masses at fixed beam energy. A theoretical description of $e^+e^- \to X^+X^-\gamma$, with $X=\{\pi,\mu\}$, accurate at the 0.1\% level and including all relevant radiative effects, is crucial for radiative return measurements.
The contribution presented here focuses on a state-of-the-art theoretical description of radiative return processes at flavour factories, based on the matching of exact next-to-leading order (NLO) corrections with a Parton Shower (PS) algorithm. This NLOPS approach allows for the fully exclusive simulation of multiple photon emission while retaining NLO accuracy for observables involving a hard photon in the final state.
For pion pair production, the NLO corrections are evaluated in the ${\rm F}\times\mathrm{sQED}$ scheme, where the scalar QED amplitudes describing point-like pions are factorized and multiplied by the pion form factor at the appropriate virtualities. This approach provides a realistic and theoretically consistent description of photon radiation in the presence of hadronic structure effects, which is essential for precision studies of the $e^+e^- \to \pi^+\pi^-\gamma$ process.
These developments are implemented in an updated version of the Monte Carlo event generator BabaYaga@NLO, providing improved theoretical accuracy for the simulation and analysis of radiative return measurements. The resulting predictions are directly applicable to ongoing and future precision studies at flavour factories, where sub-percent control of radiative effects is required, and represent a concrete step toward reducing the theoretical uncertainties affecting the dispersive determination of the hadronic contribution to $a_\mu$.