On the Singular Behavior of the Chirality-Odd Twist-3 Parton Distribution e(x)

Abstract

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.

arXiv commentPublished version

References in corpus (22)

• Parton Physics on Euclidean Lattice
• Measurement of Beam-Spin Asymmetries for Deep Inelastic ${\pi }^{+}$ Electroproduction
• Fine structure of spectrum of twist-three operators in QCD
• Nucleon charges with dynamical overlap fermions
• Polarized Structure Functions in QCD
• Azimuthal asymmetries at CLAS: Extraction of e^a(x) and prediction of A_{UL}
• Scale dependence of the chiral-odd twist-3 distributions $h_L(x)$ and $e(x)$
• Q^2 Evolution of Chiral-Odd Twist-3 Distributions h_L(x, Q^2) and e(x, Q^2) in Large-N_c QCD
• The chirally-odd twist-3 distribution e(x)
• The chirally-odd twist-3 distribution function e(x) in the chiral quark-soliton model
• Violation of Sum Rules for Twist-3 Parton Distributions in QCD
• The twist-three distribution $e^q(x,k_{\perp })$ in a light-front model
• Fundamental Properties of the Proton in Light-Front Zero Modes
• $Q^2$ evolution of chiral-odd twist-3 distribution $e(x,Q^2)$
• The nonperturbative origin of delta-function singularity in the chirally-odd twist-3 distribution function e(x)
• Holomorphic maps and the complete 1/N expansion of 2D SU(N) Yang-Mills
• Scale Dependence of Twist-3 Quark-Gluon Operators for Single Spin Asymmetries
• Soft-Gluon-Pole Contribution in Single Transverse-Spin Asymmetries of Drell-Yan Processes
• Single Transverse Spin Asymmetries at Parton Level
• Insights into the higher-twist distribution $e(x)$ at CLAS
• Collinear Factorization for Single Transverse-Spin Asymmetry in Drell-Yan Processes
• QCD Evolutions of Twist-3 Chirality-Odd Operators

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• Structure of the nucleon at leading and subleading twist in the covariant parton model
• CP violating effects in ${}^{210}$Fr and prospects for new physics beyond the Standard Model
• Transverse structure of the proton beyond leading twist: A light-front Hamiltonian approach
• Extraordinary nature of the nucleon scalar charge and its densities as a signal of nontrivial vacuum structure of QCD
• Parton Interpretation and Twist-4 Parton Distributions