[Paper Review] Testing universality and automatic O(a) improvement in massless lattice QCD with Wilson quarks

Björn Leder, Stefan Sint|arXiv (Cornell University)|Dec 12, 2010

Quantum Chromodynamics and Particle Interactions1 references4 citations

TL;DR

This paper demonstrates the successful implementation of chirally rotated Schrödinger functional boundary conditions in quenched massless lattice QCD with Wilson fermions. By tuning a dimension-3 boundary counterterm, the authors confirm automatic O(a) improvement and universality of renormalized correlation functions, validating the framework for precision continuum extrapolations and non-perturbative renormalization.

ABSTRACT

The chirally rotated Schroedinger functional provides a test bed for universality and automatic O(a) improvement. We here report on extensive quenched simulations of lattice QCD with Wilson quarks in the massless limit. We demonstrate that, after proper tuning of a dimension 3 boundary counterterm, the expected chirally rotated boundary conditions are indeed obtained. This implies automatic O(a) improvement which we then verify in a few examples. Universality of properly renormalized correlation functions is confirmed by comparing to the standard set-up of the Schroedinger functional. As a by-product of this study the non-singlet current renormalisation constants Z_A and Z_V are obtained from ratios of 2-point functions.

Motivation & Objective

• To test whether chirally rotated Schrödinger functional boundary conditions enable automatic O(a) improvement in massless lattice QCD with Wilson fermions.
• To verify universality of renormalized correlation functions between standard and chirally rotated SF setups.
• To determine finite renormalization constants Z_A and Z_V non-perturbatively via universality relations.
• To confirm that bulk O(a) effects vanish in γ5τ1-even correlation functions, as expected for automatic O(a) improvement.
• To establish a practical framework for O(a)-improved calculations with Wilson fermions using non-perturbative tuning.

Proposed method

• Implementation of chirally rotated boundary conditions using a dimension-3 boundary counterterm with tunable coefficient zf.
• Use of the Schrödinger functional with Wilson fermions and standard gauge action in the quenched approximation.
• Non-perturbative tuning of the boundary counterterm coefficient zf to realize the correct chiral boundary conditions.
• Comparison of correlation functions (e.g., g_A, g_P, f_A, f_P) between standard and chirally rotated SF setups to test universality.
• Analysis of γ5τ1-odd correlation functions to verify their O(a) suppression in the continuum limit.
• Determination of Z_A and Z_V via ratios of boundary-to-boundary and boundary-to-current correlators, leveraging universality.

Experimental results

Research questions

• RQ1 Can chirally rotated Schrödinger functional boundary conditions be successfully implemented in massless lattice QCD with Wilson fermions?
• RQ2 Does the implementation lead to automatic O(a) improvement, as predicted by theory?
• RQ3 Are universality relations between correlation functions in the standard and chirally rotated SF setups satisfied after proper renormalization?
• RQ4 Can finite renormalization constants like Z_A and Z_V be reliably extracted from correlation function ratios?
• RQ5 Do γ5τ1-odd correlation functions vanish as O(a) in the continuum limit, confirming automatic O(a) improvement?

Key findings

• The chirally rotated boundary conditions were successfully implemented after non-perturbative tuning of the boundary counterterm coefficient zf, with Δzf ∝ a, confirming the correct implementation.
• Universality of renormalized correlation functions was confirmed: ratios such as [g_A^{uu'}(T/2)/√g1] × [f_A(T/2)/√f1]^{-1} approach unity in the continuum limit.
• γ5τ1-odd correlation functions vanish as O(a) in the continuum limit, confirming automatic O(a) improvement.
• The axial current improvement coefficient c_A(a/L) vanishes in the chirally rotated SF but remains finite in the standard SF, confirming O(a^2) vs. O(a) behavior.
• Z_A and Z_V were determined via universality relations and show O(a^2) uncertainty, explaining discrepancies with previous Ward identity results.
• The framework provides a viable path for O(a)-improved calculations and non-perturbative renormalization in Wilson fermion lattice QCD.