Hadronic contributions to light-by-light scattering and muon (g-2)

Abstract

Low-energy observables, such as the anomalous magnetic moment (AMM) of the muon and the energy spectra of light muonic atoms, provide a unique avenue for testing the Standard Model (SM) at the precision frontier of physics. However, the accuracy of SM predictions for these quantities is constrained by uncertainties in hadronic contributions. Understanding these contributions, particularly those related to light-by-light (LbL) scattering and Compton scattering processes, is therefore crucial for precise theoretical predictions. This thesis primarily focuses on these hadronic contributions while incidentally exploring exotic resonances, hadron polarizabilities, and briefly addressing parity and time-reversal violation effects in Compton scattering.

The hadronic corrections to the muonic AMM are analyzed from two perspectives. To refine the hadronic vacuum polarization (HVP) contribution using lattice QCD, a novel approach to compute electromagnetic corrections via a Cottingham-like formula is introduced. Verified within quantum electrodynamics (QED) and scalar QED, this approach demonstrates potential for lattice QCD calculations by circumventing the power-law finite-volume effects associated with photons on the lattice. Additionally, the Schwinger sum rule method--a dispersive, data-driven approach based on doubly-virtual Compton scattering--is investigated. This method offers alternative calculations for both the HVP and hadronic light-by-light (HLbL) contributions to the muon AMM. Tested within effective field theories and the SM, it is applied to the calculation of the leading-order HLbL contribution arising from neutral pion exchange.

Regarding exotic resonances, the recently observed fully charmed states in the di-$J/\psi$ spectrum are examined within the context of real LbL scattering to study their possible contribution in LbL cross sections at the Large Hadron Collider (LHC). To facilitate future LHC measurements, a phenomenological model based on LbL scattering sum rules is proposed to simulate the hadronic background at low energies or small scattering angles. An improved parametrization of scattering amplitudes for resonances in the elastic scattering of spinless particles is also proposed, developing a dispersive inverse amplitude method which will be helpful for analyzing lattice QCD data.

Within the Compton scattering framework, the Bernab\'eu-Tarrach sum rule for static electric dipole polarizability is investigated. This sum rule is perturbatively verified within covariant baryon chiral perturbation theory, yielding a dispersive formula for the subtraction contribution in the data-driven approach to the Lamb shift in hydrogen-like atoms. Additionally, the puzzling negative electric polarizability of the neutral pion, predicted by meson chiral perturbation theory ($\chi$PT), is revisited. For the first time, it is evaluated using a light-front quark model.

Forward Compton scattering analysis is also extended to cases involving parity and time-reversal violation. New sum rules for the anapole and electric dipole moments are derived and perturbatively verified.