# Spin-dependent sum rules connecting real and virtual Compton scattering verified

## TL;DR

This paper derives and verifies sum rules linking spin polarizabilities in real and virtual Compton scattering, providing a theoretical framework and empirical checks relevant for understanding nucleon spin structure.

## Contribution

It presents a detailed derivation of sum rules connecting various spin polarizabilities across different scattering processes, verified within chiral perturbation theory.

## Key findings

- Sum rules relating real and virtual Compton scattering polarizabilities are derived.
- Verification of sum rules in chiral perturbation theory confirms their theoretical consistency.
- Empirical verification for the proton supports the applicability of these sum rules.

## Abstract

We present a detailed derivation of the two sum rules relating the spin polarizabilities measured in real, virtual, and doubly-virtual Compton scattering. For example, the polarizability $\delta_{LT}$, accessed in inclusive electron scattering, is related to the spin polarizability $\gamma_{E1E1}$ and the slope of generalized polarizabilities $P^{(M1,M1)1}-P^{(L1,L1)1}$, measured in, respectively, the real and the virtual Compton scattering. We verify these sum rules in different variants of chiral perturbation theory, discuss their empirical verification for the proton, and prospect their use in studies of the nucleon spin structure.