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

In this paper, we studied the $\rho {\gamma }^{\ast }\to \pi$ and $\rho\gamma^\to \rho$transitionprocessesandmadethecalculationsforthe$\rho\pi$transitionformfactor$Q^4 F_{\rho\pi}(Q^2)$andthe$\rho$ meson electromagnetic form factors, $F_{\mathrm{L}\mathrm{L},\mathrm{L}\mathrm{T},\mathrm{T}\mathrm{T}}(Q^2)$ and $F_{1,2,3}(Q^2)$, by employing the perturbative QCD (PQCD) factorization approach. For the $\rho \gamma^ \to \pi$transition,wefoundthatthecontributiontoformfactor$Q^4 F_{\rho\pi}(Q)$ from the term proportional to the distribution amplitude combination ${\varphi }_{\rho }^T(x_1){\varphi }_{\pi }^P(x_2)$ 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 $\rho {\gamma }^{\ast }\to \rho$ transition and in the region of $Q^2\ge 3$ 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.