A local formulation of lattice QCD without unphysical fermion zero modes

TL;DR

The paper addresses unphysical fermion zero modes in lattice QCD with Wilson fermions by introducing a chirally twisted mass term $D_{ m twist}=D_{ m W}+i\mu_{ m q}\gamma_5\tau^3$, which protects against zero modes via ${\det D_{ m twist}=\det(D_{ m W}^
D_{ m W}+\mu_{ m q}^2)>0}$. It demonstrates that, at fixed lattice spacing and up to cutoff effects, twisted lattice QCD is equivalent to standard lattice QCD, with a chiral rotation mapping masses to $m' = \sqrt{m^2+\mu_{ m q}^2}$ and observables related accordingly; this equivalence extends to a GW-regulated lattice theory preserving flavor symmetry, yielding exact identities and a consistent renormalization framework. The authors develop an $O(a)$-improvement program using the SW term and define improved actions and operators with corresponding coefficients $b_i$, $c_i$, and renormalization constants, supported by perturbative checks showing the coefficients depend only on the bare coupling. The approach offers a clean, regulator-compatible solution to exceptional configurations, with potential benefits for near-chiral-limit QCD, extensions to ${N_f>2}$, and alternative choices of the twist angle $\alpha$, making twisted lattice QCD a practical and promising formulation for nonperturbative QCD studies.

Abstract

The problem of unphysical zero modes in lattice QCD with Wilson fermions can be solved in a clean way by including a mass term proportional to $i \psibar γ_5 τ^3 ψ$ in the standard lattice theory with Nf=2 mass degenerate Wilson quarks. We argue that up to cutoff effects, this lattice theory is equivalent to standard lattice QCD, for suitable choices of the mass parameters and with a natural re-interpretation of observables. On-shell O(a) improvement can be implemented in a straightforward way.