# Sum rules and 2-quark flux-tube structure

## TL;DR

This paper investigates sum rules connecting the static quark potential to flux-tube field distributions, using them to derive beta-functions, check flux-tube models, and estimate quark self-energies, with comparisons to string models.

## Contribution

It introduces new applications of sum rules for extracting beta-functions, validating flux-tube models, and estimating self-energies in the context of quark confinement.

## Key findings

- Derived generalized beta-functions from sum rules.
- Validated flux-tube profiles against hadronic string models.
- Provided estimates for quark self-energies.

## Abstract

Sum rules -- relating the static quark potential V(R) to the spatial distribution of the action and energy in the colour fields of flux-tubes -- are applied in three ways: 1) To extract generalised beta-functions: 2) As a consistency check for the use of excited gluon flux-tubes and as an estimate of the quark self-energies: 3) To extract approximate sum rules using a simplified form of V(R). Also the flux-tube profiles are compared with hadronic string and flux-tube models.