Perturbative QCD Analysis of Exclusive Processes $e^+e^-\rightarrow VP$ and $e^+e^-\rightarrow TP$

We study the $e^+e^-\to VP$ and $e^+e^-\to TP$ processes in the perturbative QCD approach based on $k_T$ factorization, where the $P,V$ and $T$ denotes a light pseudo-scalar, vector and tensor meson, respectively. We point out in the case of $e^+e^-\to TP$ transition due to charge conjugation invariance, only three channels are allowed: $e^+e^-\to a_2^{\pm} \pi^\mp$, $e^+e^-\to K_2^{*\pm} K^\mp$ and the V-spin suppressed $e^+e^-\to K_2^{*0} \bar K^0+\overline K_2^{*0} K^0$. Cross sections of $e^+e^-\to VP$ and $e^+e^-\to TP$ at $\sqrt{s}=3.67$ GeV and $\sqrt{s}=10.58$ GeV are calculated and the invariant mass dependence is found to favor the $1/s^4$ power law. Most of our theoretical results are consistent with the available experimental data and other predictions can be tested at the ongoing BESIII and forthcoming Belle-II experiments.