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.
Highlights
Electromagnetic polarizabilities are important properties that shed light on the internal structure of hadrons
The quarks respond to probing electromagnetic fields, revealing the charge and current distributions inside the hadron
There is an active community in nuclear physics partaking in this endeavor
Summary
Electromagnetic polarizabilities are important properties that shed light on the internal structure of hadrons. Since weak fields are needed, the energy shift involved is very small relative to the mass of the hadron (on the order of one part in a million depending on field strength). This challenge has been successfully overcome by relying on statistical correlations with or without the field. A charged hadron accelerates in an electric field and exhibits Landau levels in a magnetic field Such motions are unrelated to polarizability and must be isolated from the deformation due to quark and gluon dynamics inside the hadron.
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