Abstract
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.
Highlights
QCD factorization implies that the cross-sections of hard inclusive hadronic processes can be written in terms of convolution of partonic cross section and parton distribution functions (PDF) [1]
We presented a lattice computation of the MS isovector u − d parton distribution function of 300 MeV pion and its moments using the recently proposed twist-2 perturbative matching framework (large momentum effective theory (LaMET) framework / shortdistance factorization framework)
In order to access the short distance physics required for the perturbative twist-2 framework, we used two lattices ensembles with very fine lattice spacings of a 1⁄4 0.06 fm and 0.04 fm for the first time in such pion PDF computations
Summary
QCD factorization implies that the cross-sections of hard inclusive hadronic processes can be written in terms of convolution of partonic cross section and parton distribution functions (PDF) [1]. Field theoretically [1,2], the quark PDF fðx; μÞ of a hadron H is defined in terms of quark fields ψ as Z fðx; μÞ 1⁄4. The above definition involves quark and antiquark displaced by z− along Wilson-line the W þliðgzh−t;c0oÞn1⁄4e The dimensionless light cone distance ν is referred to as the Ioffe-time and the matrix element. Is referred to as the Ioffe-time distribution (ITD). Notwithstanding such a straight-forward definition of PDF, the unequal Minkowski time separation in z− posed a challenge to the Euclidean lattice computation until recently
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