$\gamma^{*}\rho^0\to\pi^0$ Transition Form Factor in Extended AdS/QCD Models

TL;DR

This paper investigates the $ ho^0 o ho^0 o ho^0$ transition form factor using extended AdS/QCD models, revealing power-law behavior consistent with perturbative QCD and Light-Cone Sum Rules, and explores implications for meson decays.

Contribution

It demonstrates the consistency of the extended AdS/QCD model with perturbative QCD and Light-Cone Sum Rules for the $ ho^0 o ho^0$ transition form factor, including duality relations and decay predictions.

Findings

Form factor exhibits $1/Q^4$ behavior at large momentum, matching QCD predictions.

Duality relation $z o ext{const} imes \sqrt{u(1-u)}$ supports Light-Front holography.

Numerical results support an asymptotic-like pion wave function and small finite quark mass corrections.

Abstract

The $\gamma^{*}\rho^0\to\pi^0$ transition form factor is extracted from recent result for the $\gamma^* \gamma^* \pi^0$ form factor obtained in the extended hard-wall AdS/QCD model with a Chern-Simons term. In the large momentum region, the form factor exhibits a $1/Q^4$ behavior, in accordance with the perturbative QCD analysis, and also with the Light-Cone Sum Rule (LCSR) result if the pion wave function exhibits the same endpoint behavior as the asymptotic one. The appearance of this power behavior from the AdS side and the LCSR approach seem to be rather similar: both of them come from the {"}soft" contributions. Comparing the expressions for the form factor in both sides, one can obtain the duality relation $z\propto \sqrt{u(1-u)}$, which is compatible with one of the most important relations of the Light-Front holography advocated by Brodsky and de Teramond. In the moderate $Q^2$ region, the comparison of the numerical results from both approaches also supports a asymptotic-like pion wave function, in accordance with previous studies for the $\gamma^* \gamma^* \pi^0$ form factor. The form factor at zero momentum transfer gives the $\gamma^{*}\rho^0\pi^0$ coupling constant, from which one can determine the partial width for the $\rho^0(\omega)\to \pi^0 \gamma$ decay. We also calculate the form factor in the time-like region, and study the corresponding Dalitz decays $\rho^0(\omega)\to \pi^0 e^+e^-, \pi^0\mu^+\mu^-$. Although all these results are obtained in the chiral limit, numerical calculations with finite quark masses show that the corrections are extremely small. Some of these calculations are repeated in the Hirn-Sanz model and similar results are obtained.