Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe role of zero-mode contributions in the matching for the twist-3 PDFs $e(x)$ and $h_{L}(x)$
63
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The perturbative procedure of matching was proposed to connect parton quasi-distributions that are calculable in lattice QCD to the corresponding light-cone distributions which enter physical processes. Such a matching procedure has so far been limited to the twist-2 distributions. Recently, we addressed the matching for the twist-3 PDF $g_T(x)$. In this work, we extend our perturbative calculations to the remaining twist-3 PDFs, $e(x)$ and $h_{L}(x)$. In particular, we discuss the non-trivialities involved in the calculation of the singular zero-mode contributions for the quasi-PDFs.
rate research
Read More
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.
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.
The twist--2 heavy flavor contributions to the polarized structure function $g_2(x,Q^2)$ are calculated. We show that this part of $g_2(x,Q^2)$ is related to the heavy flavor contribution to $g_1(x,Q^2)$ by the Wandzura--Wilczek relation to all orders in the strong coupling constant. Numerical results are presented.
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.
We investigate the non-perturbative contribution of instantons to current matching kernels used in the context of the large momentum effective theory (LaMET). We derive explicitly these contributions using first principle semi-classical calculus for the unpolarized and polarized quark parton distributions and the matching kernel, and show that they are part of a trans-series expansion. These contributions are substantial at current lattice matching momenta.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
