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 ${}^1{S}_0$ state ${\eta }_Q$, ${}^3{S}_1$ state $J/\psi ({\rm Y})$, ${}^1{P}_1$ state $h_Q$ and ${}^3{P}_J$ 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 ${\gamma }^{\ast }\to {\eta }_Q\gamma ,{\chi }_{QJ}\gamma (J=0,1,2)$, $Z\to {\eta }_Q\gamma ,{\chi }_{QJ}\gamma (J=0,1,2),J/\psi ({\rm Y})\gamma ,h_Q\gamma$ and $h\to J/\psi \gamma$, by adopting the collinear factorization. The asymptotic behaviors of those processes obtained in NRQCD factorization are reproduced.

Comments: 25 pages, no figure. In this updated arXiv version, we add the explicit NLO expression for ${\varphi }_V^{\parallel }(x;\mu )$ which is missing in the published version in JHEP, and also correct the logarithmic term in NLO hard-kernel for $h\to J/\psi \gamma$