Baryon Light-Cone Distribution Amplitudes from Lattice QCD: Formalism, Renormalization, Extrapolation, and Matching

Baryon light-cone distribution amplitudes (LCDAs) are inherently multidimensional objects parametrized by two independent longitudinal momentum fractions, making their first-principles determination substantially more challenging than that of meson LCDAs. We present a systematic large-momentum effective theory (LaMET) framework for determining baryon leading-twist LCDAs from lattice QCD. The framework covers the complete path from equal-time three-quark quasi-distribution amplitudes to physical baryon LCDAs. We formulate the leading-twist $V$, $A$, and $T$ quasi-DAs and analyze their spin-flavor and coordinate-space symmetries, including antisymmetric amplitudes with vanishing local limits. We develop a hybrid renormalization prescription on the $(z_1,z_2)$ plane, introduce a newly developed large-$\lambda$ extrapolation strategy based on the asymptotic large-distance behavior of Euclidean correlators, and derive the corresponding one-loop LaMET matching relation in the hybrid renormalization scheme. As a demonstration, we apply the complete analysis pipeline to the $\Lambda$-baryon $A$-structure quasi-DAs using seven $2+1$--flavor lattice ensembles, and use this amplitude to examine the impact of large-distance extrapolation, perturbative matching, and extrapolation to the continuum, physical-pion-mass, and infinite-momentum limits, together with the associated systematic uncertainties. This work provides the formalism, renormalization, extrapolation, and matching infrastructure for first-principles determinations of $x$-dependent baryon LCDAs.