# Relativistic corrections to light-cone distribution amplitudes of S-wave B c mesons and heavy quarkonia

Wang, Wei (0000 0004 0368 8293, INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China) ; Xu, Ji (0000 0004 0368 8293, INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China) ; Yang, Deshan (0000 0004 1797 8419, School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China) ; Zhao, Shuai (0000 0004 0368 8293, INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China)

02 December 2017

Abstract: In collinear factorization, light-cone distribution amplitudes (LCDAs) are key ingredients to calculate the production rate of a hadron in high energy exclusive processes. For a doubly-heavy meson system (such as B c , J / ψ , Y etc), the LCDAs contain perturbative scales that can be integrated out and then are re-factorized into products of perturbatively calculable distribution parts and non-relativistic QCD matrix elements. In this re-factorization scheme, the LCDAs are known at next-to-leading order in the strong coupling constant α s and at leading order in the velocity expansion. In this work, we calculate the O v 2 $\mathcal{O}\left({v}^2\right)$ corrections to twist-2 LCDAs of S-wave B c mesons. These results are applicable to heavy quarkonia like η c,b , J / ψ and Y by setting m b = m c . We apply these relativistically corrected LCDAs to study their inverse moments and a few Gegenbauer moments which are important for phenomenological study. We point out that the relativistic corrections are sizable, and comparable with the next-to-leading order radiative corrections. These results for LCDAs are useful in future theoretical analyses of the productions of heavy quarkonia and B c mesons.

Published in: JHEP 1712 (2017) 012