Analog to the pion decay constant in the multiflavor Schwinger model
JF Nieto Castellanos, I Hip, W Bietenholz - Physical Review D, 2023 - APS
JF Nieto Castellanos, I Hip, W Bietenholz
Physical Review D, 2023•APSWe study the Schwinger model with N f≥ 2 degenerate fermion flavors, by means of lattice
simulations. We use dynamical Wilson fermions for N f= 2, and reweighted quenched
configurations for overlap-hypercube fermions with N f≤ 6. In this framework, we explore an
analogue of the QCD pion decay constant F π, which is dimensionless in d= 2, and which
has hardly been considered in the literature. We determine F π by three independent
methods, with numerical and analytical ingredients. First, we consider the 2-dimensional …
simulations. We use dynamical Wilson fermions for N f= 2, and reweighted quenched
configurations for overlap-hypercube fermions with N f≤ 6. In this framework, we explore an
analogue of the QCD pion decay constant F π, which is dimensionless in d= 2, and which
has hardly been considered in the literature. We determine F π by three independent
methods, with numerical and analytical ingredients. First, we consider the 2-dimensional …
We study the Schwinger model with degenerate fermion flavors, by means of lattice simulations. We use dynamical Wilson fermions for , and reweighted quenched configurations for overlap-hypercube fermions with . In this framework, we explore an analogue of the QCD pion decay constant , which is dimensionless in , and which has hardly been considered in the literature. We determine 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 -regime, i.e., a small spatial volume, where we assume formulas from chiral perturbation theory to apply even in the absence of Nambu-Goldstone bosons. We further postulate an effective relation between and the number of relevant, light bosons, which we denote as “pions”. Thus is obtained from the residual “pion” mass in the chiral limit, which is a finite-size effect. Finally, we address the 2-dimensional Witten–Veneziano formula: it yields a value for , which we identify with , as in large- QCD. All three approaches consistently lead to at fermion mass , which implies that this quantity is meaningful.
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