Novel patterns for vector mesons from the large-Nc limit

TL;DR

This paper derives a new relation between decay constants of vector mesons in the large-Nc limit, predicts a pattern for excited states, and confirms it with lattice data and spectral sum rules.

Contribution

It introduces a novel pattern for decay constants of vector mesons in the large-Nc limit, supported by lattice results and spectral sum rule analysis.

Findings

The ratio f_V^T/f_V approaches 1/√2 for highly excited states.

A sign alternation pattern in decay constants is observed.

Spectral sum rules support the proposed pattern.

Abstract

We report on a relation between the decay constants of \rho-like J^{PC}=1^{--} vector mesons, which arises solely from the perturbative analysis of the VV, TT and VT correlators at order \alpha_s^0 in the large-N_c limit. We find f_{V}^T/f_{V}=1/\sqrt{2} for highly excited states together with a pattern of alternation in sign. Quite remarkably, recent lattice determinations reported f_{\rho}^T/f_{\rho}=0.72(2), in excellent agreement with our large-N_c result. This seems to suggest a pattern like f_{Vn}^T/f_{Vn}=(-1)^n/\sqrt{2} for the whole (1^{--}) states. In order to test this conjecture in real QCD we construct a set of spectral sum rules, which turn out to comply nicely with this scenario.