Pion and Kaon Distribution Amplitudes in the Continuum Limit

We present a lattice-QCD calculation of the pion, kaon and $\eta_s$
distribution amplitudes using large-momentum effective theory (LaMET). Our
calculation is carried out using three ensembles with 2+1+1 flavors of highly
improved staggered quarks (HISQ), generated by MILC collaboration, at 310 MeV
pion mass with 0.06, 0.09 and 0.12 fm lattice spacings. We use clover fermion
action for the valence quarks and tune the quark mass to match the lightest
light and strange masses in the sea. The resulting lattice matrix elements are
nonperturbatively renormalized in regularization-independent
momentum-subtraction (RI/MOM) scheme and extrapolated to the continuum. We use
two approaches to extract the $x$-dependence of the meson distribution
amplitudes: 1) we fit the renormalized matrix elements in coordinate space to
an assumed distribution form through a one-loop matching kernel; 2) we use a
machine-learning algorithm trained on pseudo lattice-QCD data to make
predictions on the lattice data. We found the results are consistent between
these methods with the latter method giving a less smooth shape. Both
approaches suggest that as the quark mass increases, the distribution amplitude
becomes narrower. Our pion distribution amplitude has broader distribution than
predicted by light-front constituent-quark model, and the moments of our pion
distributions agree with previous lattice-QCD results using the operator
production expansion.