Parton distributions and lattice QCD calculations: A community white paper

Abstract

In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and globalanalysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.The detailed understanding of the inner structure of nucleons is an active research field with phenomenological implications in high-energy, hadron, nuclear and astroparticle physics. Within quantum chromodynamics (QCD), information on this structure -specifically on how the nucleon's momentum and spin are divided among quarks and gluons -is encoded in parton distribution functions (PDFs).There exist two main methods to determine PDFs. 1 The first method is the global QCD analysis [3][4][5][6][7][8][9][10][11][12]. It is based on QCD factorization of physical observables, i.e. the fact that a class of hard-scattering cross-sections can be expressed as a convolution between short-distance, perturbative, matrix elements and long-distance, nonperturbative, PDFs. By combining a variety of available hard-scattering experimental data with state-of-the-art perturbative calculations, complete PDF sets, including the gluon and various combinations of quark flavors, are currently determined for protons, in both the unpolarized [13][14][15][16][17] and the polarized [18][19][20][21] case.Recent progress in global QCD analyses has been driven, on the one hand, by the increasing availability of a wealth of high-precision measurements from Jefferson Lab, HERA, RHIC, the Tevatron and the LHC and, on the other hand, by the advancement in perturbative calculations of QCD and electroweak (EW) higher-order corrections. Parton distributions are now determined with unprecedented precision, in many cases at the few-percent level. A paradigmatic illustration of this progress is provided by both the unpolarized and polarized gluon PDFs, which were affected by rather large uncertainties until recently, due to the limited experimental information available. In the unpolarized case, the gluon PDF is now constrained quite accurately from small to large x thanks to the inclusion of processes such a...

Parton distribution functions from Ioffe time pseudo-distributions

“…Our results, lie above the results of CJ 15 and MSTW, as expected, due to the relatively heavy masses of our pions but agree within errors with NNPDF due to the larger error bars of the latter. As was analyzed in detail in [39] the complementary synergies between the communities of global fits and Lattice QCD would be very fruitful in the forthcoming years. In the latter article different scenarios of lattice data included in the global fits analyses were presented.…”

“…Other Good Lattice Cross Sections have been calculated to extract the pion DA [36,37] and the pion PDF [38]. We refer the reader to [39][40][41][42] for detailed reviews of these topics. Possible difficulties with these approaches were raised in [43,44].…”

Pion valence structure from Ioffe-time parton pseudodistribution functions

“…Although significant achievements in the lattice QCD implementations of these approaches have been made in recent years [37][38][39][40][41][42][43][44][45][46][47][48], a proper understanding and control-ling various sources of systematics in these calculations still require further exploration and theoretical development. The status of current lattice QCD calculations of the x-dependent hadronic structure can be found in the following review articles [49][50][51]. Recently, an attempt to incorporate lattice QCD determination of PDFs together with experimental data to obtain the non-singlet quark distribution of the nucleon has been discussed in [52].…”

Orbital angular momentum of the proton and intrinsic five-quark Fock states

“…Lorcé and Pasquini studied the Wigner distributions in the light cone constituent quark model( LCCQM) [28], reaching to a comparable value, L q = 0.126. Lattice QCD calculations is an ongoing long endeavor; see, e.g., [29,30]. Recently, the intrinsic sea flavor content includingū,d,s andc in the nucleon were investigated employing our formalism, within which all the possible five-quark Fock components in the nucleon wave function were taken into account [32,33], coupling between the threeand five-quark components was assumed to be via 3 P 0 quark-antiquark pair creation mech-anism [27], and the coupling strength was fixed by fitting [32,33] the sea flavor asymmetry of the proton [1].…”