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arXiv · 2311.14232

A pion decay constant in the multi-flavor Schwinger model

Jaime Fabián Nieto Castellanos·Ivan Hip·Wolfgang Bietenholz
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Abstract

The pion decay constant $F_{\pi}$ plays an important role in QCD and in Chiral Perturbation Theory. It is hardly known, however, that a corresponding constant exists in the Schwinger model with $N_{\rm f} \geq 2$ degenerate fermion flavors. In this case, the ``pion'' does not decay and $F_{\pi}$is dimensionless. Still, $F_{\pi}$ can be defined by 2d analogies to the Gell-Mann--Oakes--Renner relation, the Witten--Veneziano formula and the residual ``pion'' mass in the $\delta$-regime. With suitable assumptions, and by inserting simulation data, these QCD-inspired relations are all compatible with $F_{\pi} \simeq 1/\sqrt{2\pi}$ at zero fermion mass, as we observe for $N_{\rm f} = 2, \dots , 6$. We conclude that this is a meaningful constant in the multi-flavor Schwinger model.

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Jaime Fabián Nieto Castellanos, Ivan Hip, Wolfgang Bietenholz. 2023-11-24. A pion decay constant in the multi-flavor Schwinger model. https://arxiv.org/abs/2311.14232

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