First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints

H.-W Lin,W Melnitchouk,N Sato,H Shows,A Prokudin

doi:10.1103/physrevlett.120.152502

Abstract

We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new MonteCarlo method based on nested sampling and constraints on the isovector tensor charge g_{T} from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with g_{T} values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses, which found significantly smaller g_{T} values. The contributions to the nucleon tensor charge from u and d quarks are found to be δu=0.3(2) and δd=-0.7(2) at a scale Q^{2}=2 GeV^{2}.

Highlights

We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new Monte Carlo method based on nested sampling and constraints on the isovector tensor charge gT from lattice QCD
A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with gT values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses, which found significantly smaller gT values
Single-spin asymmetries in semi-inclusive deep-inelastic scattering (SIDIS), where h1 couples to the chiral-odd Collins fragmentation function (FF) H⊥1 [15], while two Collins FFs generate an azimuthal asymmetry in twohadron production in eþe− annihilation [16]

Summary

Published by the American Physical Society

With a number of simulations of gT having been performed [28,29,30,31,32,33,34] at physical pion masses and with multiple lattice spacings and volumes. We use the nested sampling algorithm [35,36,37], which maps the likelihood function into an MC-weighted parameter sample and allows a rigorous determination of PDF uncertainties This approach improves the fitting methodology of Refs. We instead combine the available dynamical simulation data, using only calculations with multiple lattice spacings, volumes and quark masses; we use several procedures to ensure that the final uncertainties are not underestimated. Each fit is weighted by the factor wi 1⁄4Pi=ð jPjÞ, where Pj 1⁄4exp1⁄2−ðAICj −minAICÞ=2, which yields glTatt 1⁄4 1.008ð56Þ Another approach is to average the lattice data using methods advocated by the Flavor Lattice Averaging Group (FLAG) [43]. For the experimental data used in our fit, we consider the sinðφh þ φsÞ modulation of the differential SIDIS cross section, or Collins asymmetry, AUsinTðφh þφs Þ

FUsinTðφhþφsÞ FUU

Findings

This gives four linear combinations of transversity TMD