Abstract
In this work, we present the first-ever calculation of the isovector flavor combination of the twist-3 parton distribution function $g_T(x)$ for the proton from lattice QCD. We use an ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3~fm, lattice spacing of 0.093~fm, and reproduces a pion mass of $260$ MeV. We use the quasi-distribution approach and employ three values of the proton momentum boost, 0.83 GeV, 1.25 GeV, and 1.67 GeV. We use a source-sink separation of 1.12~fm to suppress excited-states contamination. The lattice data are renormalized non-perturbatively. We calculate the matching equation within Large Momentum Effective Theory, which is applied to the lattice data in order to obtain $g_T$. The final distribution is presented in the $\overline{\rm MS}$ scheme at a scale of 2 GeV. We also calculate the helicity distribution $g_1$ to test the Wandzura-Wilczek approximation for $g_T$. We find that the approximation works well for a broad range of $x$. This work demonstrates the feasibility of accessing twist-3 parton distribution functions from novel methods within lattice QCD and can provide essential insights into the structure of hadrons.
Highlights
More than 99% of the mass of the visible world resides in atomic nuclei and, in nucleons, that is, protons and neutrons
We present the first-ever calculation of the isovector flavor combination of the twist-3 parton distribution function gTðxÞ for the proton from lattice quantum chromodynamics (QCD)
We presented a pioneering ab initio calculation of the proton twist-3 distribution gTðxÞ, using numerical simulations of lattice QCD, within the quasidistribution method
Summary
More than 99% of the mass of the visible world resides in atomic nuclei and, in nucleons, that is, protons and neutrons. The first experimental evidence of a partonic substructure of the proton emerged from measurements of deepinelastic electron-proton scattering (DIS), ep → eX, in the late 1960s [1,2]. These experiments were, instrumental for the discovery of QCD.
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