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Parton physics from a heavy-quark operator product expansion: Dynamical lattice QCD calculation of moments of the pion and kaon light-cone distribution amplitudes

S. -P. Alex Chang, William Detmold, Anthony V. Grebe, Matías Gutiérrez-Escobari, Issaku Kanamori, C. -J. David Lin, Robert J. Perry, Yong Zhao

Abstract

The light-cone distribution amplitude (LCDA) is a fundamental non-perturbative quantity for understanding hadron structure and exclusive scattering processes. We report on our calculation of the pion and kaon LCDAs using the heavy-quark operator product expansion (HOPE) framework. This method employs an OPE analysis of hadronic amplitudes through the inclusion of a fictitious valence heavy quark. In these proceedings, we report progress on the determination of the first three nontrivial Mellin moments of the kaon LCDAs from dynamical lattice QCD calculations, and we summarize the recently published continuum-limit result for the pion fourth Mellin moment obtained in the quenched approximation, thereby demonstrating the feasibility of the HOPE method for accessing higher moments.

Parton physics from a heavy-quark operator product expansion: Dynamical lattice QCD calculation of moments of the pion and kaon light-cone distribution amplitudes

Abstract

The light-cone distribution amplitude (LCDA) is a fundamental non-perturbative quantity for understanding hadron structure and exclusive scattering processes. We report on our calculation of the pion and kaon LCDAs using the heavy-quark operator product expansion (HOPE) framework. This method employs an OPE analysis of hadronic amplitudes through the inclusion of a fictitious valence heavy quark. In these proceedings, we report progress on the determination of the first three nontrivial Mellin moments of the kaon LCDAs from dynamical lattice QCD calculations, and we summarize the recently published continuum-limit result for the pion fourth Mellin moment obtained in the quenched approximation, thereby demonstrating the feasibility of the HOPE method for accessing higher moments.
Paper Structure (9 sections, 19 equations, 5 figures, 1 table)

This paper contains 9 sections, 19 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. HOPE method
  3. Lattice calculation: correlators and analysis strategy
  4. Two- and three-point functions and the ratio construction
  5. Excited-state contamination and extrapolation
  6. Numerical details
  7. Preliminary results
  8. First continuum limit of fourth Mellin moment
  9. Conclusions and outlook

Figures (5)

  • Figure 1: Excited-state control for the kaon Euclidean-time ratio in the even channel. Shown are $a^{2}R_{\mathrm{even,Im}}$ as a function of the current separation $\tau/a$ with $\tau\equiv \tau_e-\tau_m$. For each $\tau/a$, the colored points correspond to different choices of the Euclidean time extent $\tau_e/a$ (equivalently $\tau_+$) used in the ratio construction, illustrating the approach to a plateau as $\tau_e$ increases. The inset highlights the $\tau/a=3$ case versus $\tau_e/a$, and the shaded band indicates the asymptotic value obtained from an exponential extrapolation to $\tau_e\to\infty$ (see Eq. \ref{['eq:R_excited_model']}).
  • Figure 2: Kaon one-loop HOPE fits to the excited-state--removed ratios, shown in the even/odd sectors and for the real and imaginary channels.
  • Figure 3: Preliminary kaon results for the first (left) and third (right) Mellin moments shown versus $a^2$ for different ensembles.and heavy-quark masses.
  • Figure 4: Preliminary kaon results for the bare decay constant $f_K^{B}=f_K/Z_A^{2}$ (left) and the second Mellin moment (right) shown versus $a^2$ for different ensembles and heavy-quark masses.
  • Figure 5: Comparison of results obtained in Ref. Detmold:2025lyb to other determinations Braun:2015axaBali:2018spjRQCD:2019oshZhang:2020gajDetmold:2021qlnGao:2022vyhCloet:2024vbv of the second and the fourth Mellin moments of the pion LCDA.