Lattice QCD Determination of the Bjorken-
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 Dependence of Parton Distribution Functions at Next-to-Next-to-Leading Order

Xiang, Gao; Hanlon, Andrew D.; Mukherjee, Swagato; Petreczky, Péter; Scior, Philipp; Syritsyn, Sergey; Zhao, Yong

doi:10.1103/physrevlett.128.142003

Cited by 36 publications

(25 citation statements)

References 73 publications

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“…with Z(a) coming from the fields and vertices renormalization, and e δm|z| coming from the self-energy divergence of the Wilson line. Nonperturbative renormalization (NPR) schemes such as RI-MOM [44,[50][51][52][53][54][55][56] and the Hybrid scheme [32,[57][58][59] are one possible way to remove the UV divergences. Alternatively, the renormalization factors, including the Wilson line renormalization, cancel out in the ratios of hadron matrix elements evaluated at different momenta, P z .…”

Section: Ratio-scheme Renormalization and Leading-twist Expansionmentioning

confidence: 99%

“…We also impose the constraint A > 0 during the extrapolation to ensure the extrapolated ITD is positive and decreasing in λ. Inspired by the asymptotic behavior of the Fourier transform of the two-parameter model N x α (1 − x) β , we also consider the form [32,57],…”

Section: Extrapolation Of the Qdnn(λ µ) And Ft To The Pdfsmentioning

confidence: 99%

“…Recently, next-to-next-to-leading order (NNLO) perturbative matching has been computed [30,31], which is supposed to be more reliable by reducing the perturbation theory uncertainty. Very recently the NNLO matching has been used to study the pion PDF using the socalled hydbrid renormalization scheme in x-space [32].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point

Gao¹,

Hanlon²,

Karthik³

et al. 2022

Preprint

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We present lattice QCD calculations of valence parton distribution function (PDF) of pion employing next-to-next-leading-order (NNLO) perturbative QCD matching. Our calculations are based on three gauge ensembles of 2+1 flavor highly improved staggered quarks and Wilson-Clover valance quarks, corresponding to pion mass mπ = 140 MeV at a lattice spacing a = 0.076 fm and mπ = 300 MeV at a = 0.04, 0.06 fm. This enables us to present, for the first time, continuumextrapolated lattice QCD results for NNLO valence PDF of the pion at the physical point. Applying leading-twist expansion for renormalization group invariant (RGI) ratios of bi-local pion matrix elements with NNLO Wilson coefficients we extract 2 nd , 4 th and 6 th Mellin moments of the PDF. We reconstruct the Bjorken-x dependence of the NNLO PDF from real-space RGI ratios using a deep neural network (DNN) as well as from momentum-space matrix elements renormalized using a hybrid-scheme. All our results are in broad agreement with the results of global fits to the experimental data carried out by the xFitter and JAM collaborations.

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Section: Ratio-scheme Renormalization and Leading-twist Expansionmentioning

confidence: 99%

Section: Extrapolation Of the Qdnn(λ µ) And Ft To The Pdfsmentioning

confidence: 99%

See 1 more Smart Citation

Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point

Gao¹,

Hanlon²,

Karthik³

et al. 2022

Preprint

Self Cite

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“…Since LaMET was proposed, a lot of progress has been made in the theoretical understanding of the formalism [5,. The method has been applied in lattice calculations of PDFs for the up and down quark content of the nucleon [20,26,27,29,[64][65][66][68][69][70][71][72][73][74][75][76][77][78], π [79][80][81][82][83] and K [81] mesons, and the ∆ + [84] baryon. Despite limited volumes [75,85] and relatively coarse lattice spacings, previous state-of-the-art nucleon isovector quark PDFs, determined from lattice data at the physical pion mass [71,72] and the physical-continuum limit (i.e.…”

Section: Introductionmentioning

confidence: 99%

One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions

Chou,

Chen

2022

Preprint

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Large momentum effective theory allows extraction of hadron parton distribution functions in lattice QCD by matching them to quark bilinear matrix elements of hadrons with large momenta. We calculate the matching kernels for the unpolarized, helicity, and transversity isovector parton distribution functions and skewless generalized parton distributions of all hadrons in the hybrid-RI/MOM scheme. This renormalization scheme uses RI/MOM when the Wilson line length is less then zs, otherwise a mass subtraction scheme is used. By design, the non-hybrid scheme is recovered as zs → ∞. In the opposite limit, z → 0, the self renormalization scheme is obtained. When the parameters p R z = 0 and µ R zs 1, the hybrid-RI/MOM scheme coincides with the hybrid-ratio scheme times the charge of the PDF. We also discuss the subtlety related to the commutativity of Fourier transform and expansion in the MS scheme.

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“…With the access to an infinite tower of completely stable large-N c mesons of different J P C , it is an ideal realization of QCD that is conducive to investigate the partonic origin of hadron physics. Development of such realistic models of mesons as hard-scatterers is especially important due to the reinvigorated experimental [11,24,25] and theoretical efforts towards the meson structures, especially of the pion, the Goldstone mode of Chiral symmetry-breaking (refer [26] for a review, and [27][28][29][30][31][32][33][34][35][36] for recent numerical works). Quite surprisingly, despite the continued effort to understand large-N c QCD over the years, the partonic nature of the large-N c mesons is to a large extent unknown.…”

Section: Introductionmentioning

confidence: 99%

Parton physics of the large-$N_c$ mesons

Karthik,

Narayanan

2022

Preprint

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We initiate the studies on the structural physics of the tower of stable large-N c mesons through a first computation of the collinear quark-structure of a large-N c pion using lattice Monte-Carlo methods.We adapt the large-N c continuum reduction for the determination of meson correlation functions involving the spatially-extended quasi-PDF operators as a perfect strategy to concentrate only on the short perturbative length scales. We find the internal structures of pion in the large-N c and N c = 3 theories to be quite similar. Interestingly, we find hints that even the observed differences could arise to a large extent via the different perturbative QCD evolution in the two theories from similar initial conditions at low factorization scales.

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Lattice QCD Determination of the Bjorken- x Dependence of Parton Distribution Functions at Next-to-Next-to-Leading Order

Cited by 36 publications

References 73 publications

Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point

Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point

One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions

Parton physics of the large-$N_c$ mesons

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