Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the second moment of the pion distribution amplitude
William Detmold, Anthony V. Grebe, Issaku Kanamori, C.-J. David Lin, Santanu Mondal, Robert J. Perry, Yong Zhao
Abstract
The pion light-cone distribution amplitude (LCDA) is a central nonperturbative object of interest for high-energy exclusive processes in quantum chromodynamics. In this article, the second Mellin moment of the pion LCDA is determined as a proof-of-concept calculation for the first numerical implementation of the heavy-quark operator product expansion method. The resulting value for the second Mellin moment, determined in quenched QCD at a pion mass of ${m}_{\ensuremath{\pi}}=550\text{ }\text{ }\mathrm{MeV}$ at a factorization scale of 2 GeV is $⟨{\ensuremath{\xi}}^{2}⟩=0.210\ifmmode\pm\else\textpm\fi{}0.013(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.034(\mathrm{sys})$. This result is compatible with those from previous determinations of this quantity.