Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

Abstract

We present a detailed study of the helicity-dependent and helicity-independent collinear parton distribution functions (PDFs) of the nucleon, using the quasi-PDF approach. The lattice QCD computation is performed employing twisted mass fermions with a physical value of the light quark mass. We give a systematic and in-depth account of the salient features entering in the evaluation of quasi-PDFs and their relation to the light-cone PDFs. In particular, we give details for the computation of the matrix elements, including the study of the various sources of systematic uncertainties, such as excited states contamination. In addition, we discuss the non-perturbative renormalization scheme used here and its systematics, effects of truncating the Fourier transform and different matching prescriptions. Finally, we show improved results for the PDFs and discuss future directions, challenges and prospects for evaluating precisely PDFs from lattice QCD with fully quantified uncertainties. arXiv:1902.00587v1 [hep-lat] 1 Feb 2019of the theoretical and numerical developments, see Ref.[33].On more general grounds, it is very important to realize that quasi-PDFs and light-cone PDFs have been shown to share the same infrared physics [34,35], which is the fundamental observation that allows one to relate both quantities using perturbation theory, provided that the hadron is moving with a large, although necessarily finite, momentum in a chosen spatial direction. It has also been proven that quasi-PDFs can be extracted from lattice QCD in Euclidean spacetime [35] and that they do not suffer from power-divergent mixings with lower-dimensional operators [36][37][38]. A factorization formula makes it possible to extract the PDFs from the quasi-PDFs, an operation called matching [19,20,29,31,34,[39][40][41][42][43]. In general, this procedure is based on a newly developed large-momentum effective theory (LaMET) [44], and it is renormalizable to all orders in perturbation theory [45][46][47][48]. Other approaches for a direct computation of the x-dependence of PDFs include the hadronic tensor [49][50][51], fictitious heavy quark [52], auxiliary light quark [53], good lattice cross sections [54,55] (closely related to the auxiliary light quark method), "OPE without OPE" [56] and pseudo-PDFs [57][58][59][60], where the latter can be seen as a generalization of PDFs off the light-cone. These alternative approaches have been explored in lattice QCD, and recent results can be found in Refs. [38,56,[61][62][63][64][65][66][67]. The new formulation and its successful implementation within lattice QCD has also led to a wider interest on phenomenological studies using models and toy theories of QCD [57,58,[68][69][70][71][72][73][74][75]. A detailed overview of the current status of lattice QCD calculation of PDFs and other partonic distributions can be found in the recent reviews of Refs. [33,76].The remainder of the paper is organized as follows: In Sec. II, we provide the general theoretical aspects, lattice QCD action and parameters. We di...

Parton distributions from lattice data: the nonsinglet case

“…Nevertheless, this modification is numerically very small, as also shown in Ref. [45]. An alternative modification of the MS scheme that guarantees vector current conservation was derived in an updated version of Ref.…”

“…The expression for the conversion of MS-renormalized matrix elements to the MMS scheme was worked out in Ref. [45] and we refer to it for the details of the procedure. Nevertheless, this modification is numerically very small, as also shown in Ref.…”

“…In this work, we exploit the factorization of quasi-PDFs in PDFs and perturbatively computable coefficients to extract nonsinglet distributions from the data of Refs. [30,45], setting a general strategy within the NNPDF framework, which allows to systematically extract parton distributions from the available lattice data. The discussion is focused on the quasi-PDFs case, but it can be extended to include data coming from different lattice approaches, like for example pseudo-PDFs [48][49][50], fictitious heavy/light quark [51,52] or current-current correlators [22,24,53], paving the way to a first global lattice QCD analysis [24].…”

Parton distribution functions from Ioffe time pseudo-distributions

“…The authors of [23] stressed the necessity of controlling the contamination from excited states which becomes an increasing concern as one approaches the limit of the physical pion mass. In this respect we discussed in detail how our method for the extraction of the matrix element possesses a number of advantages compared to the commonly utilized sequential source technique.…”

“…With a lattice regulator (unlike in dimensional regularization), the operator O WL (z) has a power divergence in z a . The handling of this power divergence in lattice QCD renormalization schemes, such as the popular RI-MOM scheme, and the associated matching relationships have generated a large amount of discussion, see [23] for a comparison of methods. In a lattice QCD calculation, renormalization constants require a separate calculation.…”