Reducing cutoff effects in maximally twisted lattice QCD close to the chiral limit

TL;DR

The paper analyzes infrared divergent cutoff artifacts in maximally twisted lattice QCD and shows that they can be substantially mitigated by either O(a) improvement with the SW clover term or by optimally tuning the critical mass. Using the Symanzik effective theory, it identifies the leading IR artifacts as arising from multiple pion poles and demonstrates that the remaining discretization errors can be constrained to a^2 (a^2/m_π^2)^{k-1}, enabling safe continuum extrapolations for m_q > a^2 Lambda_QCD^3. It derives a lattice GMOR relation and discusses hadron energies and f_π, showing that leading IR issues either cancel or shrink under the proposed cures, with the bending phenomenon disappearing when the critical mass is optimized. Practically, these results provide a pathway to reliable unquenched simulations at lighter quark masses and guide the monitoring of safe m_q regions via lattice observables like m_π^2 vs m_q.

Abstract

When analyzed in terms of the Symanzik expansion, lattice correlators of multi-local (gauge-invariant) operators with non-trivial continuum limit exhibit in maximally twisted lattice QCD ``infrared divergent'' cutoff effects of the type a^{2k}/(m_π^2)^{h}, 2k\geq h\geq 1 (k,h integers), which tend to become numerically large when the pion mass gets small. We prove that, if the action is O(a) improved a` la Symanzik or, alternatively, the critical mass counter-term is chosen in some ``optimal'' way, these lattice artifacts are reduced to terms that are at worst of the order a^{2}(a^2/m_π^2)^{k-1}, k\geq 1. This implies that the continuum extrapolation of lattice results is smooth at least down to values of the quark mass, m_q, satisfying the order of magnitude inequality m_q >a^2Λ^3_{\rm QCD}.