Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the second moment of the pion distribution amplitude

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 mπ=550 MeV at a factorization scale of 2 GeV is ⟨ζ2=0.210±0.013(stat)±0.034(sys). This result is compatible with those from previous determinations of this quantity.