The decay constant of the first excited pion from lattice QCD

TL;DR

This paper computes the decay constant of the first excited pion using lattice QCD, confirming theoretical predictions of suppression relative to the pion decay constant in the chiral limit.

Contribution

It provides a lattice QCD calculation of the excited pion decay constant with unquenched quarks at low masses, highlighting sensitivity to improvement conditions.

Findings

The ratio of decay constants $f_{ ext{pi}'} / f_{ ext{pi}}$ is approximately 0.078.

The result shows significant uncertainty due to improvement conditions.

Supports the theory that excited pseudoscalar meson decay constants are suppressed in the chiral limit.

Abstract

We review the theory that predicts that the decay constant of the excited light pseudo-scalar mesons are suppressed in the chiral limit relative to the pion decay constant. We compute the decay constant of the first excited pion ($\pi^\prime$) using unquenched QCD at a fixed lattice spacing with sea quarks of mass as low as a third the mass of the strange quark. The final result is very sensitive to the improvement conditions. We obtain $f_{\pi^\prime} / f_{\pi}$ = 0.078(93) in the chiral limit.