Chiral-odd generalized parton distributions, transversity decomposition of angular momentum, and tensor charges of the nucleon

TL;DR

This work investigates the forward limit of chiral-odd GPDs within the CQSM, focusing on Burkardt's transversity decomposition linking quark spin and orbital angular momentum. It shows G_T is predominantly isoscalar with 1/Nc-suppressed isovector corrections and reveals a strong Dirac-sea driven chiral enhancement at small x. The second moment of G_T encodes a spin–orbital correlation, while the first moment κ_T indicates isoscalar dominance in the anomalous tensor moment, implying similar signs for u and d Boer-Mulders functions. The paper also carefully discusses the scale dependence of tensor charges, advising caution when comparing model predictions to empirical extractions and highlighting the value of scale-invariant tensor-charge ratios for robust tests. Overall, the results provide insight into the nucleon's transverse spin structure and its experimental implications via Boer-Mulders and transversity observables.

Abstract

The forward limit of the chiral-odd generalized parton distributions (GPDs) and their lower moments are investigated within the framework of the chiral quark soliton model (CQSM), with particular emphasis upon the transversity decomposition of nucleon angular momentum proposed by Burkardt. A strong correlation between quark spin and orbital angular momentum inside the nucleon is manifest itself in the derived second moment sum rule within the CQSM, thereby providing with an additional support to the qualitative connection between chiral-odd GPDs and the Boer-Mulders effects. We further confirm isoscalar dominance of the corresponding first moment sum rule, which indicates that the Boer-Mulders functions for the $u$- and $d$-quarks have roughly equal magnitude with the same sign. Also made are some comments on the recent empirical extraction of the tensor charges of the nucleon by Anselmino et al. We demonstrate that a comparison of their result with any theoretical predictions must be done with great care, in consideration of fairly strong scale dependence of tensor charges, especially at lower renormalization scale.

Figures (9)

• Figure 1: The prediction of the CQSM for the forward limit of the isoscalar GPD $G_T^{(I=0)}(x,0,0) \equiv \lim_{\xi \rightarrow 0, t \rightarrow 0} \,[\,H_T^{(I=0)} (x,\xi,t) + 2 \, \tilde{H}_T^{(I=0)} (x,\xi,t) + E_T^{(I=0)} (x,\xi,t) \,]$. The dashed and dotted curves respectively stand for the contributions of $N_c \,(\,= 3)$ valence quarks and of deformed Dirac-sea quarks, while their sum is shown by the solid curve.
• Figure 2: The prediction of the CQSM for the forward limit of the isovector GPD $G_T^{(I=1)}(x,0,0) \equiv \lim_{\xi \rightarrow 0, t \rightarrow 0} \,[\,H_T^{(I=1)} (x,\xi,t) + 2 \, \tilde{H}_T^{(I=1)} (x,\xi,t) + E_T^{(I=1)} (x,\xi,t) \,]$. The meaning of the curves is the same as in Fig.\ref{['Fig:GTis0']}.
• Figure 3: The QCD running coupling constant $\alpha_S (Q^2)$ at the NLO in dependence of $Q^2$, obtained with the effective flavor number $n_f = 3$ and the QCD scale parameter $\Lambda_{\overline{MS}} = 0.248 \,\hbox{GeV}$. The energy scale $Q^2 = 0.16 \,\hbox{GeV}^2$ and $Q^2 = 0.40 \,\hbox{GeV}^2$ are marked by open squares as a guide.
• Figure 4: The scale dependence of the tensor charge, where the evolution is started at $\mu^2 = Q_{ini}^2 = 0.16 \,\hbox{GeV}^2$. The solid and dashed curves respectively correspond to the results obtained with the exact (Eq.(\ref{['Eq:exactRGE']})) and approximate (Eq.(\ref{['Eq:approximateRGE']}) solution of the NLO evolution equation.
• Figure 5: The scale dependence of the tensor charge, where the evolution is started at $\mu^2 = Q_{ini}^2 = 0.34 \,\hbox{GeV}^2$. The solid and dashed curves respectively correspond to the results obtained with the exact (Eq.(\ref{['Eq:exactRGE']})) and approximate (Eq.(\ref{['Eq:approximateRGE']})) solution of the NLO evolution equation.