Abstract
We present a direct lattice QCD calculation of the x-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing a ≈ 0.084 fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to \( \overline{\textrm{MS}} \) with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction x ∈ [0.25, 0.75] at the largest pion momentum Pz ≈ 1.85 GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and a = 0.076 fm. By comparison we find with 2σ confidence level that the DA obtained from chiral fermions is flatter and lower near x = 0.5.
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Acknowledgments
Our calculations were performed using the Grid [95, 96] and GPT [97] software packages. We thank Christoph Lehner for his advice on using GPT. We thank Yushan Su for valuable discussions.
This material is based upon work supported by The U.S. Department of Energy, Office of Science, Office of Nuclear Physics through Contract No. DE-SC0012704, Contract No. DE-AC02-06CH11357, and within the frameworks of Scientific Discovery through Advanced Computing (SciDAC) award Fundamental Nuclear Physics at the Exascale and Beyond and the Topical Collaboration in Nuclear Theory 3D quark-gluon structure of hadrons: mass, spin, and tomography. This work was supported in part by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Science Undergraduate Laboratory Internships Program (SULI). YZ was partially supported by the 2023 Physical Sciences and Engineering (PSE) Early Investigator Named Award program at Argonne National Laboratory.
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Baker, E., Bollweg, D., Boyle, P. et al. Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass. J. High Energ. Phys. 2024, 211 (2024). https://doi.org/10.1007/JHEP07(2024)211
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DOI: https://doi.org/10.1007/JHEP07(2024)211