# Medium Correction to Gravitational Form Factors

## TL;DR

This paper generalizes gravitational form factors for chiral fermions, calculates radiative corrections in QED plasma, and finds that these corrections enhance the axial chiral vortical effect, with implications for spin polarization in heavy ion collisions.

## Contribution

It introduces a generalized gravitational form factor for chiral fermions, including radiative corrections, and clarifies their role in the axial chiral vortical effect.

## Key findings

- Radiative corrections can suppress or enhance spin-vorticity coupling.
- Two structures in form factors contribute differently to the scattering amplitude.
- Radiative correction enhances the axial chiral vortical effect.

## Abstract

We generalize the gravitational form factor for chiral fermion in vacuum, which reproduces the well-known spin-vorticity coupling. We also calculate radiative correction to the gravitational form factors in quantum electrodynamics plasma. We find two structures in the form factors contributing to the scattering amplitude of fermion in vorticity field, one is from the fermion self-energy correction, pointing to suppression of spin-vorticity coupling in medium; the other structure comes from graviton-fermion vertex correction, which does not adopt potential interpretation, but corresponds to transition matrix element between initial and final states. Both structures contribute to axial chiral vortical effect. The net effect is that radiative correction enhances the axial chiral vortical effect. Our results clarify the relation and difference between spin-vorticity coupling and axial chiral vortical effect from the perspective of form factors. We also discuss the application of the results in quantum chromodynamic plasma, indicating radiative correction might have an appreciable effect in spin polarization effect in heavy ion collisions.