Parton physics from a heavy-quark operator product expansion: Formalism and Wilson coefficients

Detmold, William; Grebe, Anthony V.; Kanamori, Issaku; Lin, C. -J. David; Perry, Robert J.; Zhao, Yong

doi:10.48550/arxiv.2103.09529

Cited by 3 publications

(3 citation statements)

References 91 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[52,53]). More recently, methods to extract higher moments have been proposed, using smeared operators [54], heavy-quark operator product expansion (HOPE) [55,56], and light-quark current-current correlators [57].…”

Section: Reconstruction Of Pdfsmentioning

confidence: 99%

The pion and kaon $\langle x^3 \rangle$ from lattice QCD and PDF reconstruction from Mellin moments

Alexandrou,

Bacchio,

Cloët

et al. 2021

Preprint

View full text Add to dashboard Cite

We present a calculation of the pion and kaon Mellin moment x 3 extracted directly in lattice QCD using a three-derivative local operator. We use one ensemble of gauge configurations with two degenerate light, a strange and a charm quark (N f = 2 + 1 + 1) of maximally twisted mass fermions with clover improvement. The ensemble reproduces a pion mass ∼ 260 MeV, and a kaon mass ∼ 530 MeV. Excited-states contamination is evaluated using four values of the source-sink time separation within the range of 1.12 − 1.67 fm. We use an operator that is free of mixing, and apply a multiplicative renormalization function calculated non-perturbatively. Our results are converted to the MS scheme and evolved at a scale of 2 GeV, using three-loop expressions in perturbation theory. The final values are x 3 u + π = 0.024( 18)stat(2)syst, x 3 u + K = 0.035( 6)stat(3)syst, and x 3 s + K = 0.075( 5)stat(1)syst, where the systematic error is the uncertainty due to excited state contamination.We combine x 3 with the two lower moments, namely x and x 2 , to obtain the ratios x 3 / x and x 3 / x 2 , as well as x 3 u + K / x 3 u + π and x 3 u + K / x 3 u + π . In addition, we reconstruct the xdependence of the pion and kaon PDFs via 2-and 3-parameter fits to our results. We find that the reconstruction is feasible and that our lattice data favor a large x-dependence that falls as (1 − x) 2 for both the pion and kaon PDFs. We integrate the reconstructed PDFs to extract the higher moments with 4 ≤ n ≤ 6. Finally, we compare the pion and kaon PDFs, as well as the ratios of their moments, to address the effect of SU(3) flavor symmetry breaking.

show abstract

Section: Reconstruction Of Pdfsmentioning

confidence: 99%

The pion and kaon $\langle x^3 \rangle$ from lattice QCD and PDF reconstruction from Mellin moments

Alexandrou,

Bacchio,

Cloët

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The perturbative matching frameworks that use equal-time matrix elements have proved particularly promising -the large momentum effective theory (LaMET) [22,23] and the perturbative QCD short-distance factorization based approaches, the pseudo-distribution approach [24,25], and the factorizable lattice cross-section approach [26,27] as applied to the current-current correlators [28][29][30]. We should, however, note that there are other methods to probe the x-dependent hadron structure, such as through the direct computation of the Mellin moments using leading-twist local operators [31], the analytic continuation of the hadronic tensor [32], operator product expansion (OPE) of the Compton amplitude [33], and the OPE of heavy-light current correlators (HOPE method) [34,35]. We refer the readers to the recent reviews [36][37][38][39][40] on these topics for technical discussions.…”

Section: Introductionmentioning

confidence: 99%

The transversity parton distribution function of the nucleon using the pseudo-distribution approach

Egerer,

Kallidonis,

Karpie

et al. 2021

Preprint

View full text Add to dashboard Cite

We present a determination of the non-singlet transversity parton distribution function (PDF) of the nucleon, normalized with respect to the tensor charge at µ 2 = 2 GeV 2 from lattice quantum chromodynamics. We apply the pseudo-distribution approach, using a gauge ensemble with a lattice spacing of 0.094 fm and the light quark mass tuned to a pion mass of 358 MeV. We extract the transversity PDF from the analysis of the short-distance behavior of the Ioffe-time pseudodistribution using the leading-twist next-to-leading order (NLO) matching coefficients calculated for transversity. We reconstruct the x-dependence of the transversity PDF through an expansion in a basis of Jacobi polynomials in order to reduce the PDF ansatz dependence. Within the limitations imposed by a heavier-than-physical pion mass and a fixed lattice spacing, we present a comparison of our estimate for the valence transversity PDF with the recent global fit results based on single transverse spin asymmetry. We find the intrinsic nucleon sea to be isospin symmetric with respect to transversity.

show abstract

“…The progress in determining the x-dependent hadron structures, such as the parton distribution functions (PDFs) and the generalized parton distribution functions (GPDs) [1][2][3] (for a review, see [4]), has been quite rapid in the recent years, particularly owing to the perturbative matching frameworks such as the quasi-PDF [5,6], pseudo-PDF [7,8], current-current correlators [9] and the good lattice cross-sections approach [10,11]. There are other ideas that are being used (for example, [12][13][14][15][16]), but we would restrict ourselves to the set of perturbative matching approaches for calculating PDFs in this paper. Roughly, the recurring idea in all the variants of the perturbative matching approaches is the factorization of certain equal-time boosted hadron matrix elements with a spatial operator separation z (or the Fourier transform thereof into x-space) into a matching kernel and the structure functions, such as the PDF as a specific case.…”

Section: Introductionmentioning

confidence: 99%

Bayesian-Wilson coefficients in lattice QCD computations of valence PDFs and GPDs

Karthik,

Sufian

2021

Preprint

View full text Add to dashboard Cite

We propose an analysis method for the leading-twist operator product expansion based lattice QCD determinations of the valence parton distribution function (PDF). In the first step, we determine the confidence-intervals of the leading-twist MS Wilson coefficients, Cn(µ 2 z 2 ), of the equal-time bilocal quark bilinear, given the lattice QCD matrix element of Ioffe-time distribution for a particular hadron H as well as the prior knowledge of the valence PDF, f (x, µ) of the hadron H determined via global fit from the experimental data. In the next step, we apply the numerically estimated Cn in the lattice QCD determinations of the valence PDFs of other hadrons, and for the zero-skewness generalized parton distribution (GPD) of the same hadron H at non-zero momentum transfers. Our proposal still assumes the dominance of leading-twist terms, but it offers a pragmatic alternative to the usage of perturbative Wilson coefficients and their associated higher-loop uncertainties such as the effect of all-order logarithms at larger sub-fermi quark-antiquark separations z.

show abstract

Parton physics from a heavy-quark operator product expansion: Formalism and Wilson coefficients

Cited by 3 publications

References 91 publications

The pion and kaon $\langle x^3 \rangle$ from lattice QCD and PDF reconstruction from Mellin moments

The pion and kaon $\langle x^3 \rangle$ from lattice QCD and PDF reconstruction from Mellin moments

The transversity parton distribution function of the nucleon using the pseudo-distribution approach

Bayesian-Wilson coefficients in lattice QCD computations of valence PDFs and GPDs

Contact Info

Product

Resources

About