Diagrammatic representation of scalar QCD and sign problem at nonzero chemical potential

TL;DR

This paper introduces a diagrammatic approach to scalar QCD at strong coupling with chemical potential, aiming to eliminate the sign problem and analyze baryonic contributions across different flavor numbers.

Contribution

It presents a novel diagrammatic representation of scalar QCD that simplifies the path integral and addresses the sign problem, extending understanding of baryonic effects at nonzero chemical potential.

Findings

Sign problem is absent for three flavors with scalar baryons.

Baryon loops conserve baryon number explicitly.

Potential sign issues may arise for higher flavor numbers, but weights are conjectured to be positive.

Abstract

We consider QCD at strong coupling with scalar quarks coupled to a chemical potential. Performing the link integrals we present a diagrammatic representation of the path integral weight. It is based on mesonic and baryonic building blocks, in close analogy to fermionic QCD. Likewise, the baryon loops are subject to a manifest conservation of the baryon number. The sign problem is expected to disappear in this representation and we do confirm this for three flavors, where a scalar baryon can be built and thus a dependence on the chemical potential occurs. For higher flavor number we analyse examples for a potential sign problem in the baryon sector and conjecture that all weights are positive upon exploring the current conservation of each flavor.