QCD with Bosonic Quarks at Nonzero Chemical Potential

TL;DR

This paper formulates the low-energy partition functions of QCD with bosonic quarks at nonzero chemical potential, revealing structural differences from fermionic cases and identifying phase transition behaviors unique to bosonic theories.

Contribution

It introduces a new formulation of QCD partition functions with bosonic quarks at nonzero chemical potential, highlighting their structural differences from fermionic theories and analyzing phase transition phenomena.

Findings

Partition functions with bosonic quarks differ structurally from fermionic ones.

A phase transition occurs in the bosonic theory at μ = m_π/2 for one bosonic flavor.

No phase transition is observed for conjugate bosonic flavors, unlike the fermionic case.

Abstract

We formulate the low energy limit of QCD like partition functions with bosonic quarks at nonzero chemical potential. The partition functions are evaluated in the parameter domain that is dominated by the zero momentum modes of the Goldstone fields. We find that partition functions with bosonic quarks differ structurally from partition functions with fermionic quarks. Contrary to the theory with one fermionic flavor, where the partition function in this domain does not depend on the chemical potential, a phase transition takes place in the theory with one bosonic flavor when the chemical potential is equal to $m_\pi/2$. For a pair of conjugate bosonic flavors the partition function shows no phase transition, whereas the fermionic counterpart has a phase transition at $\mu = m_\pi/2$. The difference between the bosonic theories and the fermionic ones originates from the convergence requirements of bosonic integrals resulting in a noncompact Goldstone manifold and a covariant derivative with the commutator replaced by an anti-commutator.