# Complex Probability Distributions: A Solution for the Long-Standing Problem of QCD at Finite Density

## TL;DR

This paper proposes a novel approach using complex probability distributions to address the long-standing problem of simulating QCD at finite density, effectively reproducing correct thermodynamics and reducing finite size effects.

## Contribution

It introduces a method of using the absolute value of the fermion determinant to correctly simulate QCD at finite density, applicable to other gauge theories with non-positive measures.

## Key findings

- Reproduces the correct thermodynamical limit in finite density QCD
- Reduces finite size effects caused by small mean values of the phase cosine
- Explains the pathological behavior of quenched QCD at finite density

## Abstract

We show how the prescription of taking the absolute value of the fermion determinant in the integration measure of QCD at finite density, forgetting its phase, reproduces the correct thermodynamical limit. This prescription, which applies also to other gauge theories with non-positive-definite integration measure, also has the advantage of killing finite size effects due to extremely small mean values of the cosine of the phase of the fermion determinant. We also give an explanation for the pathological behaviour of quenched QCD at finite density.