We present a lattice QCD determination of the distribution amplitude (DA) of the pion and the first few Mellin moments from an analysis of the quasi-DA matrix element within the leading-twist framework. We perform our study on a HISQ ensemble with $a=0.076\mathrm{fm}$ lattice spacing with the Wilson-clover valence quark mass tuned to the physical point. We analyze the ratios of pion quasi-DA matrix elements at short distances using the leading-twist Mellin operator product expansion (OPE) at the next-to-leading order and the conformal OPE at the leading-logarithmic order. We find a robust result for the first nonvanishing Mellin moment $⟨x^2⟩=0.287(6)(6)$ at a factorization scale $\mathrm{<ruby><rb>\mu </rb><rt>みゅー</rt></ruby>}=2\mathrm{GeV}$. We also present different Ansätze-based reconstructions of the $x$-dependent DA, from which we determine the perturbative leading-twist expectations for the pion electromagnetic and gravitational form-factors at large momentum transfers.

• Received 2 July 2022
• Accepted 3 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.074505

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Published by the American Physical Society