We report the first-ever calculation of the isovector flavor combination of the chiral-odd twist-3 parton distribution hL(x) for the proton from lattice QCD. We employ gauge configurations with two degenerate light, a strange and a charm quark (Nf=2+1+1) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3 fm and lattice spacing of 0.093 fm. The values of the quark masses lead to a pion mass of 260 MeV. We use a source-sink time separation of 1.12 fm to control contamination from excited states. Our calculation is based on the quasi-distribution approach, with three values for the proton momentum: 0.83 GeV, 1.25 GeV, and 1.67 GeV. The lattice data are renormalized non-perturbatively using the RI′ scheme, and the final result for hL(x) is presented in the MS scheme at the scale of 2 GeV. Furthermore, we compute in the same setup the transversity distribution, h1(x), which allows us, in particular, to compare hL(x) to its Wandzura-Wilczek approximation. We also combine results for the isovector and isoscalar flavor combinations to disentangle the individual quark contributions for h1(x) and hL(x), and address the Wandzura-Wilczek approximation in that case as well.
@article{arxiv.2107.02574,
title = {Parton distribution functions beyond leading twist from lattice QCD: The $h_L(x)$ case},
author = {Shohini Bhattacharya and Krzysztof Cichy and Martha Constantinou and Andreas Metz and Aurora Scapellato and Fernanda Steffens},
journal= {arXiv preprint arXiv:2107.02574},
year = {2022}
}