The $\rho \gamma^* \to \pi (\rho)$ transition form factors in the Perturbative QCD factorization approach

TL;DR

This paper calculates the $ ho o ho$ and $ ho o ho o ho$ transition form factors using perturbative QCD, finding good agreement with other models for some form factors and discrepancies for others.

Contribution

It provides detailed PQCD calculations of $ ho o ho$ and $ ho o ho$ transition form factors, highlighting the dominant contributions and comparing with existing models.

Findings

The $ ho o ho o ho$ form factor $Q^4 F_{ ho o ho}$ agrees with light-cone QCD sum rules.

The form factors $F_1$ and $F_2$ match QCD sum rule predictions for $Q^2 extgreater 3$ GeV$^2$.

The $F_3$ form factor prediction exceeds QCD sum rule estimates.

Abstract

In this paper, we studied the $\rho \gamma^* \to \pi$ and $\rho\gamma^*\to \rho$ transition processes and made the calculations for the $\rho\pi$ transition form factor $Q^4 F_{\rho\pi}(Q^2)$ and the $\rho$ meson electromagnetic form factors, $F_{\rm LL, LT,TT}(Q^2)$ and $F_{1,2,3}(Q^2)$, by employing the perturbative QCD (PQCD) factorization approach. For the $\rho \gamma^* \to \pi$ transition, we found that the contribution to form factor $Q^4 F_{\rho\pi}(Q)$ from the term proportional to the distribution amplitude combination $\phi^T_{\rho}(x_1)\phi^P_{\pi}(x_2)$ is absolutely dominant, and the PQCD predictions for both the size and the $Q^2$-dependence of this form factor $Q^4 F_{\rho\pi}(Q^2)$ agree well with those from the extended ADS/QCD models or the light-cone QCD sum rule. For the $\rho \gamma^* \to \rho$ transition and in the region of $Q^2\geq 3$ GeV$^2$, further more, we found that the PQCD predictions for the magnitude and their $Q^2$-dependence of the $F_1(Q^2)$ and $F_2(Q^2)$ form factors agree well with those from the QCD sum rule, while the PQCD prediction for $F_3(Q^2)$ is much larger than the one from the QCD sum rule.