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Register a new userValence parton distribution of pion from lattice QCD: Approaching continuum
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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.
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We present a lattice QCD study of valence parton distribution inside the pion within the framework of Large Momentum Effective Theory. We use a mixed action approach with 1-HYP smeared valence Wilson clover quarks on 2+1 flavor HISQ sea with the valence quark mass tuned to 300 MeV pion mass. We use $48^3 times 64$ lattice at a fine lattice spacing $a=0.06$ fm for this computation. We renormalize the quasi-PDF matrix element in the non-perturbative RI-MOM scheme. As a byproduct, we test the validity of 1-loop matching procedure by comparing the RI-MOM renormalized quasi-PDF matrix element with off-shell quark external states as computed in the continuum 1-loop perturbation theory with the lattice results at $a=0.04$ and 0.06 fm. By applying the RI-MOM to ${bar{rm MS}}$ one-loop matching, implemented through a fit to phenomenologically motivated PDFs, we obtain the valence PDF of pion.
We extract the pion valence quark distribution $q^pi_{rm v}(x)$ from lattice QCD (LQCD) calculated matrix elements of spacelike correlations of one vector and one axial vector current analyzed in terms of QCD collinear factorization, using a new short-distance matching coefficient calculated to one-loop accuracy. We derive the Ioffe time distribution of the two-current correlations in the physical limit by investigating the finite lattice spacing, volume, quark mass, and higher-twist dependencies in a simultaneous fit of matrix elements computed on four gauge ensembles. We find remarkable consistency between our extracted $q^pi_{rm v}(x)$ and that obtained from experimental data across the entire $x$-range. Further, we demonstrate that the one-loop matching coefficient relating the LQCD matrix computed in position space to the $q_{rm v}^{pi}(x)$ in momentum space has well-controlled behavior with Ioffe time. This justifies that LQCD calculated current-current correlations are good observables for extracting partonic structures by using QCD factorization, which complements to the global effort to extract partonic structure from experimental data.
We present the first direct calculation of the transversity parton distribution function within the nucleon from lattice QCD. The calculation is performed using simulations with the light quark mass fixed to its physical value and at one value of the lattice spacing. Novel elements of the calculations are non-perturbative renormalization and extraction of a formula for the matching to light-cone PDFs. Final results are presented in the $overline{rm MS}$ scheme at a scale of $sqrt{2}$ GeV.
We present the first determination of the $x$-dependent pion gluon distribution from lattice QCD using the pseudo-PDF approach. We use lattice ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, at two lattice spacings $aapprox 0.12$ and 0.15~fm and three pion masses $M_piapprox 220$, 310 and 690 MeV. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.29 GeV. We find that the dependence of the pion gluon parton distribution on lattice spacing and pion mass is mild. We compare our results from the lightest pion mass ensemble with the determination by JAM and xFitter global fits.
We report on recent results for the pion matrix element of the twist-2 operator corresponding to the average momentum of non-singlet quark densities. For the first time finite volume effects of this matrix element are investigated and come out to be surprisingly large. We use standard Wilson and non-perturbatively improved clover actions in order to control better the extrapolation to the continuum limit. Moreover, we compute, fully non-perturbatively, the renormalization group invariant matrix element, which allows a comparison with experimental results in a broad range of energy scales. Finally, we discuss the remaining uncertainties, the extrapolation to the chiral limit and the quenched approximation.
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