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The $ργ^* \to π(ρ)$ transition form factors in the Perturbative QCD factorization approach

In this paper, we studied the $ργ^* \to π$ and $ργ^*\to ρ$ transition processes and made the calculations for the $ρπ$ transition form factor $Q^4 F_{ρπ}(Q^2)$ and the $ρ$ 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 $ργ^* \to π$ transition, we found that the contribution to form factor $Q^4 F_{ρπ}(Q)$ from the term proportional to the distribution amplitude combination $ϕ^T_ρ(x_1)ϕ^P_π(x_2)$ is absolutely dominant, and the PQCD predictions for both the size and the $Q^2$-dependence of this form factor $Q^4 F_{ρπ}(Q^2)$ agree well with those from the extended ADS/QCD models or the light-cone QCD sum rule. For the $ργ^* \to ρ$ 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.