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

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.

13 pages, 3 figures. This version provides some corrections and clarifications to V2

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Cited by in corpus (4)

• Charged pion electric polarizability from four-point functions in lattice QCD
• Magnetic Polarisability of Octet Baryons via Lattice QCD
• Dipole polarizabilities of light pseudoscalar mesons within the Domain Model of QCD vacuum
• Measuring charged particle polarizabilities on the lattice without background fields