On Some Positivity Properties of the Interquark Potential in QCD

TL;DR

This paper proves that the Fourier transform of the exponential of the static interquark potential in QCD is positive, which has implications for mass relations among baryons with different quark flavors.

Contribution

It establishes a positivity property of the Fourier transform of the interquark potential, extending previous results and enabling new mass relation proofs in QCD.

Findings

Fourier transform of e^{- V(R)} is positive in QCD.

Positivity property aids in deriving baryon mass relations.

Builds on Lieb's earlier work to deepen understanding of interquark potentials.

Abstract

We prove that the Fourier transform of the exponential $e^{-\b V(R)}$ of the {\bf static} interquark potential in QCD is positive. It has been shown by Eliott Lieb some time ago that this property allows in the same limit of static spin independent potential proving certain mass relation between baryons with different quark flavors.