Flavor decomposition of the nucleon unpolarized, helicity, and transversity parton distribution functions from lattice QCD simulations

Abstract

We present results on the quark unpolarized, helicity and transversity parton distributions functions of the nucleon. We use the quasi-parton distribution approach within the lattice QCD framework and perform the computation using an ensemble of twisted mass fermions with the strange and charm quark masses tuned to approximately their physical values and light quark masses giving pion mass of 260 MeV. We use hierarchical probing to evaluate the disconnected quark loops. We discuss identification of ground state dominance, the Fourier transform procedure and convergence with the momentum boost. We find non-zero results for the disconnected isoscalar and strange quark distributions. The determination of the quark parton distribution and in particular the strange quark contributions that are poorly known provide valuable input to the structure of the nucleon.

First study of twist-3 PDFs for the proton from lattice QCD

“…The JAM20 data [5] show agreement with the lattice data in the region between 𝑥 = 0.15 and 𝑥 = 0.7. We emphasize again that the data presented in this section neglect contributions from the disconnected diagram, which are expected to be within the reported uncertainties for ℎ 𝐿 (𝑥) [33]. For the separate flavors, we show ℎ 𝐿 (𝑥) (red) with ℎ WW 𝐿 (𝑥) (orange) extracted from lattice QCD within this work.…”

“…According to the finding of Ref. [33], the disconnected contributions to ℎ 𝑢+𝑑 1 (𝑥) using the same ensemble as in this work are very small. We expect that the same applies for the operator entering ℎ 𝐿 (𝑥).…”

“…Another investigation is the exploration of the WW approximation, which also requires the twist-2 counterparts. For ℎ 𝐿 (𝑥), we perform a flavor decomposition, as the disconnected contributions for ℎ 1 (𝑥) have been found to be small [33]. We find that ℎ 𝑢 𝐿 (𝑥) is positive and ℎ 𝑑 𝐿 (𝑥) negative, like is the case for ℎ 𝑢 1 (𝑥) and ℎ 𝑑 1 (𝑥).…”

“…For 𝑔 𝑇 , we focus on the isovector flavor combination that receives contributions from the connected diagram only. For ℎ 𝐿 (𝑥), we perform a flavor decomposition, because the contribution from the disconnected diagram is expected to be small [33].…”

First moments of the nucleon transverse quark spin densities using lattice QCD

“…While significant progress has been made in recent years revealing the longitudinal spin structure of the nucleon [1][2][3], the transverse spin structure remains lesser known from phenomenology [4][5][6], a situation that will improve with results from planned experiments (SoLID [7,8], Electron-Ion Collider [9]). In lattice QCD, theoretical progress [10,11] has enabled the extraction of the x-dependence of parton distribution functions (PDFs) at the physical pion mass [12][13][14][15][16][17], as well as first results on generalized parton distributions (GPDs) [13]. For a summary of these approaches we refer the reader to [18][19][20][21][22].…”