Speaker
Jaime Fabián Nieto Castellanos
(Nuclear Sciences Institute, UNAM)
Description
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
$N_f \geq 2$ 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 residual "pion" mass in the $\delta$-regime and the
Witten-Veneziano formula. With suitable assumptions, simulation
data inserted in these three QCD-inspired relations are all
compatible with $F_{\pi} \simeq 1/\sqrt{2\pi}$ at zero fermion
mass, and $N_{f}=2, \dots , 6$. Therefore this constant seems
to be meaningful in the Schwinger model.
| Topical area | Theoretical Developments |
|---|
Primary authors
Dr
Ivan Hip
(University of Zagreb)
Jaime Fabián Nieto Castellanos
(Nuclear Sciences Institute, UNAM)
Dr
Wolfgang Bietenholz
(Nuclear Sciences Institute, UNAM)