Insights on proton structure from lattice QCD: The twist-3 parton distribution function gT(x)

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 quantum chromodynamics (QCD). We use an ensemble of gauge configurations with two degenerate light, a strange, and a charm quarks (N-f = 2 + 1 + 1) of maximally twisted mass ferrnions with a clover improvement. The lattice has a spatial extent of 3 fm and lattice spacing of 0.093 fm and reproduces a pion mass of 260 MeV. We use the quasidistribution approach and employ three values of the proton momentum boost, 0.83, 1.25, and 1.67 GeV. We use a source-sink separation of 1.12 fm to suppress excited-states contamination. The lattice data are renonnalized nonperturbatively. 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 (MS) over bar 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.