Modeling pion physics in the $\epsilon$-regime of two-flavor QCD using strong coupling lattice QED

Abstract

In order to model pions of two-flavor QCD we consider a lattice field theory involving two flavors of staggered quarks interacting strongly with U(1) gauge fields. For massless quarks, this theory has an $S{U}_L(2)\times S{U}_R(2)\times U_A(1)$ symmetry. By adding a four-fermion term we can break the U_A(1) symmetry and thus incorporate the physics of the QCD anomaly. We can also tune the pion decay constant F, to be small compared to the lattice cutoff by starting with an extra fictitious dimension, thus allowing us to model low energy pion physics in a setting similar to lattice QCD from first principles. However, unlike lattice QCD, a major advantage of our model is that we can easily design efficient algorithms to compute a variety of quantities in the chiral limit. Here we show that the model reproduces the predictions of chiral perturbation theory in the $\epsilon$-regime.

24 pages, 7 figures

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Cited by in corpus (11)

• Approaches to the sign problem in lattice field theory
• Selected Topics in the Large Quantum Number Expansion
• Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field
• A qubit regularization of the $O(3)$ sigma model
• Conformal dimensions in the large charge sectors at the O(4) Wilson-Fisher fixed point
• Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions
• Strong Coupling Lattice QCD in the Continuous Time Limit
• Sub-leading conformal dimensions at the O(4) Wilson-Fisher fixed point
• Space-time symmetric qubit regularization of the asymptotically free two-dimensional O(4) model
• Anomaly and a QCD-like phase diagram with massive bosonic baryons
• Role of the $\sigma$-resonance in determining the convergence of chiral perturbation theory