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Register a new userOn the Singular Behavior of the Chirality-Odd Twist-3 Parton Distribution e(x)
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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.
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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 nine functions has an important implication for studies of single transverse-spin asymmetries. We find that the evolutions of the three complex fragmentation functions defined by quark-gluon-quark operator are mixed with themselves. There is no mixing with the fragmentation functions defined only with bilinear quark field operators. In the large-$N_c$ limit the evolutions of the three complex fragmentation functions are simplified and reduced to six homogenous equations.
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 twist-2 distributions. In this work, we address, for the first time, the one-loop matching for the twist-3 parton distribution function $g_T(x)$. The results have been obtained using three different infrared regulators, while dimensional regularization has been adopted to deal with the ultraviolet divergences. We present the renormalized expressions of the matching coefficient for $g_{T}(x)$ in the $overline{rm MS}$ and modified $overline{rm MS}$ schemes. We also discuss the role played by a zero-mode contribution. Our results have already been used for the extraction of $g_T(x)$ from lattice QCD calculations.
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.
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 contributions from the twist-two and higher twist operators of the Wilson operator product expansion. Higher twist terms are evaluated using two different approaches, one motivated by BFKL and the other motivated by the renormalon formalism. The results of the latter approach are in very good agreement with deep inelastic scattering data from HERA.
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 motion and is given in terms of a leading-twist mass term, a pure interaction-dependent contribution, and singular terms. The leading-twist and pure twist-three terms are represented in terms of overlap of light-front wave functions (LFWFs), taking into account the Fock states with three valence quark ($3q$) and three-quark plus one gluon ($3q+g$). The $3q$ and $3q+g$ LFWFs with total orbital angular momentum zero are modeled using a parametrization derived from the conformal expansion of the proton distribution amplitudes, with parameters fitted to reproduce available phenomenological information on the unpolarized leading-twist quark and gluon collinear parton distributions. Numerical predictions for both the quark TMD $e^q(x,k_perp)$ and the collinear parton distribution $e^q(x)$ are presented, discussing the role of the quark-gluon correlations in the proton.
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