Lattice QCD pseudo-distributions at m_π=358 MeV are inverted via multidimensional Gaussian process regression to reconstruct the full kinematic dependence of GPDs H^{u-d} and E^{u-d} while directly extracting double distributions.
Lattice QCD exploration of pseudo-PDFs
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abstract
We demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equal-time matrix element ${\cal M} (Pz_3, z_3^2)$ as a function of the Ioffe time $\nu = Pz_3$ and the distance $z_3$. The next step is to divide ${\cal M} (Pz_3, z_3^2)$ by the rest-frame density ${\cal M} (0, z_3^2)$. Our lattice calculation shows a linear exponential $z_3$-dependence in the rest-frame function, expected from the $Z(z_3^2)$ factor generated by the gauge link. Still, we observe that the ratio ${\cal M} (Pz_3 , z_3^2)/{\cal M} (0, z_3^2)$ has a Gaussian-type behavior with respect to $z_3$ for 6 values of $P$ used in the calculation. This means that $Z(z_3^2)$ factor was canceled in the ratio. When plotted as a function of $\nu$ and $z_3$, the data are very close to $z_3$-independent functions. This phenomenon corresponds to factorization of the $x$- and $k_\perp$-dependence for the TMD ${\cal F} (x, k_\perp^2)$. For small $z_3 \leq 4a$, the residual $z_3$-dependence is explained by perturbative evolution, with $\alpha_s/\pi =0.1$.
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In gauge-free quark models, quasi-PDFs converge to PDFs with proven sum rules, and the Covariant Parton Model supplies closed-form small-x results that match a Wandzura-Wilczek approximation for the quark energy-momentum tensor form factor.
Lattice QCD extracts the ratio of the third to first Mellin moment of the gluon PDF at 2 GeV from nonlocal operators on an Nf=2+1+1 ensemble.
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Analysis of non-perturbative lattice data shows that the inverse problem in LaMET introduces significant uncertainties in parton distributions, especially from harmonics around λ=5-15, and that exact asymptotic decay matters little in the currently applicable x range.
Reanalysis of lattice data produces proton u(x)-d(x) PDF consistent with global fits within 1 sigma, supporting large-momentum expansion for PDF predictions.
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Reconstructing the full kinematic dependence of GPDs from pseudo-distributions
Lattice QCD pseudo-distributions at m_π=358 MeV are inverted via multidimensional Gaussian process regression to reconstruct the full kinematic dependence of GPDs H^{u-d} and E^{u-d} while directly extracting double distributions.
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Quasi Parton Distribution Functions in Covariant Quark Models
In gauge-free quark models, quasi-PDFs converge to PDFs with proven sum rules, and the Covariant Parton Model supplies closed-form small-x results that match a Wandzura-Wilczek approximation for the quark energy-momentum tensor form factor.
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Mellin Moments of the Unpolarized Gluon PDF in the Proton from Nonlocal Operators in Lattice QCD
Lattice QCD extracts the ratio of the third to first Mellin moment of the gluon PDF at 2 GeV from nonlocal operators on an Nf=2+1+1 ensemble.
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Pion and Kaon PDFs from Lattice QCD via Large Momentum Effective Theory and Short-Distance Factorization
Lattice QCD calculation of pion and kaon unpolarized quark PDFs on a 32^3×64 ensemble with 260 MeV pion mass, using LaMET and SDF matching at boosts up to 2.07 GeV.
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Inverse problem in the LaMET framework
Analysis of non-perturbative lattice data shows that the inverse problem in LaMET introduces significant uncertainties in parton distributions, especially from harmonics around λ=5-15, and that exact asymptotic decay matters little in the currently applicable x range.
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Proton's isovector PDF with updated analysis of large-momentum lattice data
Reanalysis of lattice data produces proton u(x)-d(x) PDF consistent with global fits within 1 sigma, supporting large-momentum expansion for PDF predictions.
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Kinematic enhancement for nucleon interpolators
Kinematically enhanced nucleon interpolators improve precision of renormalized quark matrix elements by an order of magnitude at 2.5 GeV with no observed lattice spacing dependence on CLS ensembles.