We propose the approach for a lattice investigation of light cone distribution amplitudes (LCDA) of heavy-light mesons, such as the $B$ meson, using the formalism of parton pseudodistributions. A basic ingredient of the approach is the study of short-distance behavior of the $B$-meson Ioffe-time distribution amplitude (ITDA), which is a generalization of the $B$-meson LCDA in coordinate space. We construct a reduced ITDA for the $B$ meson, and derive the matching relation between the reduced ITDA and the LCDA. The reduced ITDA is ultraviolet finite, which guarantees that the continuum limit exists on the lattice.

• Received 17 November 2020
• Accepted 21 February 2021

DOI:https://doi.org/10.1103/PhysRevD.103.054022

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Published by the American Physical Society