Chirally Extended Quantum Chromodynamics

TL;DR

This paper introduces an extended version of Quantum Chromodynamics (XQCD) with scalar fields coupled to fermions, aiming to improve lattice simulations by avoiding critical slowing down near the chiral limit, and explores its phase diagram and universality properties.

Contribution

It proposes a new lattice formulation of QCD with scalar couplings, studies its phase diagram, and provides large N solutions suggesting universality with conventional QCD.

Findings

XQCD may share the continuum limit with standard QCD.

Large N solutions show spurious resonances decouple at high cut-off.

XQCD could serve as a useful low-energy effective action for QCD.

Abstract

We propose an extended Quantum Chromodynamics (XQCD) Lagrangian in which the fermions are coupled to elementary scalar %$\sigma$ and $\pi$ fields through a Yukawa coupling which preserves chiral invariance. Our principle motivation is to find a new lattice formulation for QCD which avoids the source of critical slowing down usually encountered as the bare quark mass is tuned to the chiral limit. The phase diagram and the weak coupling limit for XQCD are studied. They suggest a conjecture that the continuum limit of XQCD is the same as the continuum limit of conventional lattice formulation of QCD. As examples of such universality, we present the large N solutions of two prototype models for XQCD, in which the mass of the spurious pion and sigma resonance go to infinity with the cut-off. Even if the universality conjecture turns out to be false, we believe that XQCD will still be useful as a low energy effective action for QCD phenomenology on the lattice. Numerical simulations are recommended to further investigate the possible benefits of XQCD in extracting QCD predictions. Postscript files for figures are attached. Search for strings "fig11.ps", "fig22.ps", "fig33.ps".