Abstract
We report the first-ever calculation of the isovector flavor combination of the chiral-odd twist-3 parton distribution $h_L(x)$ for the proton from lattice QCD. We employ 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 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 $h_L(x)$ is presented in the $\overline{\rm MS}$ scheme at the scale of 2 GeV. Furthermore, we compute in the same setup the transversity distribution, $h_1(x)$, which allows us, in particular, to compare $h_L(x)$ to its Wandzura-Wilczek approximation. We also combine results for the isovector and isoscalar flavor combinations to disentangle the individual quark contributions for $h_1(x)$ and $h_L(x)$, and address the Wandzura-Wilczek approximation in that case as well.
Highlights
Parton distribution functions (PDFs) are the most important quantities characterizing the structure of strongly interacting systems such as the nucleon in terms of quarks and gluons, the elementary degrees of freedom of quantum chromodynamics (QCD) [1,2]
Twist-2 PDFs have been studied for decades, and in the meantime the community has gathered a wealth of information about those quantities
We summarize the findings of our work in Sec
Summary
Parton distribution functions (PDFs) are the most important quantities characterizing the structure of strongly interacting systems such as the nucleon in terms of quarks and gluons, the elementary degrees of freedom of quantum chromodynamics (QCD) [1,2]. We present the first-ever lattice-QCD calculation of the isovector flavor combination huL−dðxÞ for the proton, which represents an extension of our previous study of guT−dðxÞ [20] To this end, we employ the so-called quasiPDF approach suggested by X. This includes a discussion of the numerical impact of the zero-mode term in the matching kernel and, in particular, a study of the so-called WandzuraWilczek approximation for hLðxÞ [13,90]. In this approximation, hLðxÞ is entirely determined through the twist-2 transversity PDF h1ðxÞ [91], which we have computed as well in the same lattice setup.
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