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We present a lattice-QCD calculation of the pion distribution amplitudes using large-momentum effective theory (LaMET). Our calculation is carried out using five ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC collaboration, at 310 MeV and 220 MeV pion mass with 0.06, 0.09, 0.12 and 0.15 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 compare different approaches to extract the x-dependence of the pion distribution amplitudes.
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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.
We present the current status of a non-perturbative lattice calculation of the moments of the pion and kaon distribution amplitudes by the RQCD collaboration. Our investigation is carried out using $N_f=2+1$ dynamical, non-perturbatively O(a)-improved Wilson fermions on the CLS ensembles with 5 different lattice spacings and pion masses down to the physical pion mass. A combined continuum and chiral extrapolation to the physical point is performed along two independent quark mass trajectories simultaneously. We employ momentum smearing in order to decrease the contamination by excited states and increase statistical precision.
We present the first lattice-QCD calculation of the nucleon isovector unpolarized parton distribution functions (PDFs) at the physical-continuum limit using Large-Momentum Effective Theory (LaMET). The lattice results are calculated using ensembles with multiple sea pion masses with the lightest one around 135~MeV, 3 lattice spacings $ain[0.06,0.12]$~fm, and multiple volumes with $M_pi L$ ranging 3.3 to 5.5. We perform a simultaneous chiral-continuum extrapolation to obtain RI/MOM renormalized nucleon matrix elements with various Wilson-link displacements in the continuum limit at physical pion mass. Then, we apply one-loop perturbative matching to the quasi-PDFs to obtain the lightcone PDFs. We find the lattice-spacing dependence to be much larger than the dependence on pion mass and lattice volume for these LaMET matrix elements. Our physical-continuum limit unpolarized isovector nucleon PDFs are found to be consistent with global-PDF results.
We present a high-statistics lattice QCD determination of the valence parton distribution function (PDF) of the pion, with a mass of 300 MeV, using two very fine lattice spacings of $a=0.06$ fm and 0.04 fm. We reconstruct the $x$-dependent PDF, as well as infer the first few even moments of the PDF using leading-twist 1-loop perturbative matching framework. Our analyses use both RI-MOM and ratio-based schemes to renormalize the equal-time bi-local quark-bilinear matrix elements of pions boosted up to 2.4 GeV momenta. We use various model-independent and model-dependent analyses to infer the large-$x$ behavior of the valence PDF. We also present technical studies on lattice spacing and higher-twist corrections present in the boosted pion matrix elements.
The pion distribution amplitude (DA) can be related to the fundamental QCD Greens functions as a function of the quark self-energy and the quark-pion vertex, which in turn are associated with the pion wave function through the Bethe-Salpeter equation. Considering the extreme hard asymptotic behavior in momentum space allowed for a pseudoscalar wave function, which is limited by its normalization condition, we compute the pion DA and its second moment. From the resulting amplitude, representing the field theoretical upper limit on the DA behavior, we calculate the photon-pion transition form factor $F_{pigammagamma^{ast}}(Q^{2})$. The resulting upper limit on the pion transition form factor is compared with existing data published by CLEO, BaBar and Belle collaborations.
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