Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

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 $a\approx 0.084$ fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to $\overline{\rm MS}$ 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 $x\in[0.25,0.75]$ at the largest pion momentum $P_z\approx 1.85$~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 $2\sigma$ confidence level that the DA obtained from chiral fermions is flatter and lower near $x=0.5$.