2023/04/28 by Jaime Fabián Nieto Castellanos, Castellanos, Jaime Fabián Nieto, Ivan Hip +3
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High-Energy Particle Collisions Research #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2305.00128
openalex publication_date 2023/04/28 · openalex created_date 2023/05/03 · openalex updated_date 2026/07/28
We study the Schwinger model with N\rm f ≥ 2 degenerate fermion flavors, by means of lattice simulations. We use dynamical Wilson fermions for N\rm f = 2, and re-weighted quenched configurations for overlap-hypercube fermions with N\rm f ≤ 6. In this framework, we explore an analogue of the QCD pion decay constant Fπ, which is dimensionless in d=2, and which has hardly been considered in the literature. We determine Fπ by three independent methods, with numerical and analytical ingredients. First, we consider the 2-dimensional version of the Gell-Mann--Oakes--Renner relation, where we insert both theoretical and numerical values for the quantities involved. Next we refer to the δ-regime, \it i.e. a small spatial volume, where we assume formulae from Chiral Perturbation Theory to apply even in the absence of Nambu-Goldstone bosons. We further postulate an effective relation between N\rm f and the number of relevant, light bosons, which we denote as "pions". Thus Fπ is obtained from the residual "pion" mass in the chiral limit, which is a finite-size effect. Finally, we address to the 2-dimensional Witten--Veneziano formula: it yields a value for Fη, which we identify with Fπ, as in large-N\rm c QCD. All three approaches consistently lead to Fπ ≃ 1/√(2 π) at fermion mass m=0, which implies that this quantity is meaningful.