Assessing the accuracy of the Brodsky-Lepage prediction

TL;DR

This paper derives high-energy constraints on meson form-factors within a resonance chiral Lagrangian framework, demonstrating that these constraints align with the Brodsky-Lepage prediction for the asymptotic behavior of form-factors.

Contribution

It introduces a set of short-distance conditions in the large-Nc limit that ensure consistency of resonance couplings and confirms their agreement with Brodsky-Lepage asymptotic predictions.

Findings

Constraints satisfy VVP Green function and form-factors

Results agree with Brodsky-Lepage prediction

Supports the resonance chiral Lagrangian approach

Abstract

We show that a consistent set of short-distance conditions on the odd-intrinsic parity resonance chiral Lagrangian couplings can be derived in the large-$N_C$ limit and the single resonance approximation. These constraints are satisfied both by the VVP Green function and all its associated form-factors. Moreover, they are in agreement with earlier results found in the normal parity sector, which further supports the overall consistency of the approach. Here we take a new perspective and examine the consequences of these high-energy relations on the precise coefficient of the $1/Q^2$-term of meson form-factors, which rules their asymptotic behavior. In particular, we show that the coefficient derived using our consistent set of short-distance constraints is in remarkable accordance with the Brodsky-Lepage prediction, being alternative results for these coefficients disfavored.