Decay constants of the pion and its excitations in holographic QCD

TL;DR

This paper uses a 5-dimensional holographic QCD model to study the decay constants of pions and their excitations, confirming that excited state decay constants vanish in the chiral limit, aligning with QCD predictions.

Contribution

It demonstrates, through numerical analysis, that the decay constants of pion excitations vanish in the chiral limit within a holographic QCD framework, extending current algebra relations.

Findings

Decay constants of excited pions vanish in the chiral limit.

The model confirms a generalized Gell-Mann-Oakes-Renner relation.

Extended axial-vector current relation includes excited states.

Abstract

We investigate the leptonic decay constants of the pion and its excitations with a 5-d holographic model for quantum chromodynamics. We prove numerically that the leptonic decay constants of the excited states of the pion vanish in the chiral limit when chiral symmetry is dynamically broken. This nontrivial result is in agreement with a solid prediction of quantum chromodynamics and is based on a generalized Gell-Mann-Oakes-Renner relationship involving the decay constants and masses of the excited states of the pion. We also obtain an extended partially conserved axial-vector current relation that includes the fields of the excited states of the pion, a relation that was proposed long ago in the context of current algebra.