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.

arXiv comment25 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 $h\to J/\psi \gamma$

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