Towards charged hadron polarizabilities from four-point functions in lattice QCD

TL;DR

This paper presents a method to compute electromagnetic polarizabilities of charged hadrons using four-point functions in lattice QCD, providing formulas and practical prescriptions for simulations.

Contribution

It introduces a new approach to determine hadron polarizabilities via four-point functions in lattice QCD, including explicit formulas and simulation strategies.

Findings

Formulas for electric and magnetic polarizabilities derived for pion and proton.

Connected diagrams are computationally feasible for current lattice projects.

Disconnection diagrams are challenging but attainable with dedicated resources.

Abstract

We show how to compute electromagnetic polarizabilities of charged hadrons using four-point functions in lattice QCD. The low-energy behavior of Compton scattering amplitude is matched to matrix elements of current-current correlation functions on the lattice. Working in momentum space, formulas for electric polarizability ($\alpha_E$) and magnetic polarizability ($\beta_M$) are derived for both charged pion and proton. Lattice four-point correlation functions are constructed from quark and gluon fields to be used in Monte-Carlo simulations. The content of the functions is assessed in detail and specific prescriptions are given to isolate the polarizabilities. The connected quark-line diagrams can be done today as a small lattice project. The disconnected diagrams are more challenging but are within reach of dedicated resources for medium to large lattice projects. We also draw attention to the potential of four-point functions as a multi-purpose tool for hadron structure.