Determination of heavy meson light-cone distribution amplitudes: theoretical framework and lattice simulations

We present a first-principles determination of heavy meson light-cone distribution amplitudes (LCDAs) from lattice QCD in the continuum limit, improving substantially on our previous pioneering study. Within the heavy-quark large-momentum effective theory (HQLaMET) framework, supplemented by lattice QCD calculations of the OPE moments, we analyze six ensembles with lattice spacings ranging from $a=0.0519-0.1053$\,fm and pion masses from $m_\pi=135.5-317.2$\,MeV, thereby enabling controlled continuum, chiral, and infinite-momentum extrapolations to the physical point. Momentum-smeared sources, hypercubic-smeared Wilson lines, and optimized interpolating operators are adopted to significantly improved signals for the nonlocal correlators. Within a unified framework, we determine both QCD LCDAs and HQET LCDAs. Our resulting QCD LCDAs of $D$ meson peak at $y\approx 0.2-0.3$, with total uncertainties below $30\%$ for $0.1<y<0.9$. The leading-twist HQET LCDA is constructed using a peak-and-tail factorization, in which the nonperturbative peak region is obtained from lattice QCD and the perturbative tail is incorporated from HQET, with the two regions combined through a model-independent Laguerre-polynomial parametrization. At $\mu=1$\,GeV, we obtain the inverse moment of HQET LCDA $\lambda_B=0.340(20)$\,GeV and first inverse-logarithmic moment $\sigma_B^{(1)}=1.685(63)$, consistent with experimental constraints and phenomenological determinations. Direct lattice calculations based on operator product expansion provide a nontrivial cross-check of the LaMET results. Final results and phenomenological impact of these results are presented in a companion paper~\cite{HeavymesonDA_short_paper}. Our results remove the single-lattice-spacing limitation of the previous study, and provide a robust determinations of heavy meson LCDAs in both QCD and HQET for next-generation heavy flavor physics.