Nucleon Helicity and Transversity Parton Distributions from Lattice QCD

TL;DR

This work presents the first lattice-QCD extraction of the isovector polarized parton distributions, including helicity and transversity, using the LaMET framework to access direct Bjorken-$x$ dependence. It develops a comprehensive correction scheme—one-loop matching, exact mass corrections via $c=M^2/(4P_z^2)$, and twist-4/target-mass-like contributions—to relate Euclidean quasi-distributions $\tilde{q}(x,\Lambda,P_z)$ to lightcone PDFs $q(x,\mu)$, and demonstrates this for spin-polarized observables. Applying the methodology to an ensemble with $M_\pi \approx 310$ MeV, the authors show how finite-$P_z$ effects shift peaks, how mass corrections modify the distributions, and how an extrapolation to $P_z\to\infty$ yields physical, bounded $x$-distributions for density, helicity, and transversity. The results reveal insights into antiquark structure and sea-flavor asymmetries in polarized nucleon PDFs, offering quantitative predictions such as $\int_{0.08}^1 (\Delta\bar u - \Delta\bar d) dx = 0.14(9)$ and $\int_{-1}^1 (\delta\bar u - \delta\bar d) dx = 0.10(8)$, with implications for future experiments and global analyses. The work thus establishes a viable path for ab initio determination of polarized PDFs with direct $x$-dependence from lattice QCD.

Abstract

We present the first lattice-QCD calculation of the isovector polarized parton distribution functions (both helicity and transversity) using the large-momentum effective field theory (LaMET) approach for direct Bjorken-$x$ dependence. We first review the detailed steps of the procedure in the unpolarized case, then generalize to the helicity and transversity cases. We also derive a new mass-correction formulation for all three cases. We then compare the effects of each finite-momentum correction using lattice data calculated at $M_π\approx 310$ MeV. Finally, we discuss the implications of these results for the poorly known antiquark structure and predict the sea-flavor asymmetry in the transversely polarized nucleon.

Figures (6)

• Figure 1: Illustration of the stepwise procedure in Eq. \ref{['eq:steps']}.
• Figure 2:
• Figure 3: The nucleon isovector quasi-PDFs of Eq. \ref{['eq:49']} for the quark density (left), helicity (middle) and transversity (right) as functions of $x$. The different colors from $P_z$ (in units of $2\pi/L$) 1 (red), 2 (green), 3 (cyan). We see the data converging at large $P_z$.
• Figure 4: The nucleon isovector quasi-PDF (green), with one-loop correction (red), and with after one-loop and mass correction (i.e. $q_{II}$). (blue) for the quark density (left), helicity (middle) and transversity (right) as functions of $x$ for the higher two boosted momenta $P_z = 2$ (top row) and $3$ (bottom row) in units of $2\pi/L$.
• Figure 5: The momentum-dependence of the nucleon isovector distributions after one-loop and mass correction (i.e. $q_{II}$) for quark density (left), helicity (middle) and transversity (right) as functions of $x$. The orange band shows the momentum extrapolation using the higher two momenta.