The leading twist light-cone distribution amplitudes for the S-wave and P-wave quarkonia and their applications in single quarkonium exclusive productions

Abstract

In this paper, we calculate twist-2 light-cone distribution amplitudes (LCDAs) of the S-wave and P-wave quarkonia (namely $^1S_0$ state $\eta_{Q}$, $^3S_1$ state $J/\psi(\Upsilon)$, $^1P_1$ state $h_{Q}$ and $^3P_J$ states $\chi_{QJ}$ with $J=0,1,2$ and $Q=c,b$) to the next-leading order of the strong coupling $\alpha_s$ and leading order of the velocity expansion $v$ in the non-relativistic QCD (NRQCD). We apply these LCDAs to some single quarkonium exclusive productions at large center-of-mass energy, such as $\gamma^*\to \eta_Q\gamma, \chi_{QJ}\gamma~(J=0,1,2)$, $Z\to \eta_Q\gamma, \chi_{QJ}\gamma~(J=0,1,2), J/\psi (\Upsilon)\gamma, h_Q\gamma$ and $h\to J/\psi \gamma$, by adopting the collinear factorization. The asymptotic behaviors of those processes obtained in NRQCD factorization are reproduced.