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 non-perturbative 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 (HOPE) method. The resulting value for the second Mellin moment, determined in quenched QCD at a pion mass of $m_\pi=550$ MeV at a factorization scale of 2 GeV is $ \langle \xi^2 \rangle = 0.210 \pm 0.013\text{ (stat.)} \pm 0.034\text{ (sys.)}$. This result is compatible with those from previous determinations of this quantity.