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The first moment the chirality-odd twist-3 parton distribution $e(x)$ is related to the pion-nucleon $sigma$-term which is important for phenomenology. However, the possible existence of a singular contribution proportional to $delta(x)$ in the distribution prevents from the determination of the $sigma$-term with $e(x)$ from experiment. There are two approaches to show the existence. The first one is based on an operator identity. The second one is based on a perturbative calculation of a single quark state with finite quark mass. We show that all contributions proportional to $delta (x)$ in the first approach are in fact cancelled. To the second approach we find that $e(x)$ of a multi-parton state with a massless quark has no contribution with $delta (x)$. Considering that a proton is essentially a multi-parton state, the effect of the contribution with $delta(x)$ is expected to be suppressed by light quark masses with arguments from perturbation theory. A detailed discussion about the difference between cut- and uncut diagrams of $e(x)$ is provided.
We derive the complete set of evolutions of chirality-odd twist-3 fragmentation functions at one-loop level. There are totally nine real twist-3 fragmentation functions, among which seven are independent. The renormalization-scale dependence of the n
Perturbative matching relates the parton quasi-distributions, defined by Euclidean correlators at finite hadron momenta, to the light-cone distributions which are accessible in experiments. Previous matching calculations have exclusively focused on t
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 stra
Higher twist corrections to the structure function F_2 at small x are studied for the case of a flat initial condition for the twist-two QCD evolution in the next-to-leading order approximation. We present an analytical parameterization of the contri
We discuss the twist-three, unpolarized, chiral-odd, transverse momentum dependent parton distribution (TMD) $e^q(x,k_perp)$ within a light-front model. We review a model-independent decomposition of this TMD, which follows from the QCD equations of