Radiative Return at NLOPS Accuracy Advances Muon Moment Calculations for Pion Form Factors

Scientists are refining crucial calculations needed to unlock greater precision in measurements of the muon’s anomalous magnetic moment, a long-standing puzzle in particle physics. Ettore Budassi, Carlo M. Carloni Calame, and Marco Ghilardi, from the Universities of Pavia and INFN, alongside Andrea Gurgone et al, have calculated radiative corrections , the subtle effects of emitted photons , to an unprecedented level of accuracy, termed Next-to-Leading Order Parton Shower (NLOPS). This research focuses on the radiative return method used at flavour factories to measure the pion form factor, a vital input for determining the hadronic contribution to the muon’s magnetic moment, and represents a significant step towards resolving discrepancies between theoretical predictions and experimental observations , potentially hinting at new physics beyond the Standard Model. Their work, implemented within the BabaYaga@NLO Monte Carlo generator, provides a powerful tool for both simulating and analysing data from these precision experiments.

This innovative approach considers all radiative corrections stemming from both initial and final-state radiation, utilising QED for e+e−→μ+μ−γ and a combined QED and Factorised scalar QED (F×sQED) framework for e+e−→π+π−γ. Validation tests and comparisons with existing NLO predictions in the literature rigorously cross-checked the formulation’s various components, ensuring its reliability and precision. This detailed validation process confirms the accuracy of the newly developed theoretical framework and its ability to reproduce established results where applicable. This work addresses the need for accurate theoretical predictions for the muon anomalous magnetic moment, specifically refining the data-driven dispersive computation of the leading-order hadronic contribution. The study focused on the processes e+e−→X+X−γ, where X represents either π+π− or μ+μ−, meticulously calculating radiative corrections arising from both initial and final-state radiation and their interference, all governed by Quantum Electrodynamics (QED) and Factorised scalar QED (F×sQED) for different channels. Scientists harnessed this tool to generate numerical results at NLOPS accuracy, providing predictions for key observables used in the measurement of the pion form factor. The precision achieved, at the level of realistic event selection criteria, is vital for reducing uncertainties in the data-driven dispersive computation of the muon anomalous magnetic moment, potentially resolving discrepancies between lattice QCD calculations and experimental measurements. Furthermore, the study pioneered a detailed analysis of the size of leading order (LO) and NLO gauge-invariant subsets, providing valuable insights into the contributions of different orders of perturbation theory. By carefully examining these contributions, researchers could optimise the efficiency and accuracy of the NLOPS calculation. All sources of radiative corrections, including initial and final-state radiation and their interference, were considered using Quantum Electrodynamics (QED) for μ+μ−γ and a factorised scalar QED approach for π+π−γ. Results demonstrate the application of the radiative return technique, used at GeV-scale e+e−colliders, to measure hadronic cross sections by analysing events with a hard photon emission before the collision. This effectively reduces the centre of mass energy, allowing for cross section measurements across a continuous energy range at a fixed beam energy. The team’s calculations account for the suppression factor associated with photon emission, compensated by the high luminosity of flavour factories like φ, τ-charm, and B factories. The team meticulously accounted for all significant sources of radiation, both initial and final state, utilising both standard QED and a factorised scalar QED approach. The core achievement lies in the refined parton shower approach applied to fixed-order corrections, enhancing the accuracy of simulations for processes with a hard final-state photon.