Transversity distributions in the nucleon in the large-N_c limit

TL;DR

The paper computes quark and antiquark transversity distributions at a low normalization point within the large-$N_c$ chiral quark-soliton model, revealing that isovector transversity dominates at leading order while isosinglet transversity is subleading. It develops master formulas based on the quark Green function in a rotating hedgehog background, analyzes ultraviolet regularization and an anomaly-like phenomenon, and provides detailed numerical results including tensor charges and antiquark behavior. The authors compare transversity to helicity distributions, show qualitative and quantitative differences—especially for antiquarks—and use the results to predict Drell–Yan spin asymmetries, finding sizable deviations from naive $δq(x)=Δq(x)$ assumptions. Overall, the work demonstrates the distinctive large-$N_c$ dynamics of transversity and its potential experimental implications, while ensuring consistency with large-$N_c inequalities and providing guidance for interpreting spin-physics measurements.

Abstract

We compute the quark and antiquark transversity distributions in the nucleon at a low normalization point of 600 MeV in the large-$N_c$ limit, where the nucleon can be described as a soliton of an effective chiral theory (chiral quark-soliton model). The flavor-nonsinglet distributions, $δu(x) - δd(x)$ and $δ\bar u(x) - δ\bar d(x)$, appear in leading order of the $1/N_c$-expansion, while the flavor-singlet distributions, $δu(x) + δd(x)$ and $δ\bar u(x) + δ\bar d(x)$, are non-zero only in next-to-leading order. The transversity quark and antiquark distributions are found to be significantly different from the longitudinally polarized distributions $Δu (x) \pm Δd (x)$ and $Δ\bar u (x) \pm Δ\bar d (x)$, respectively, in contrast to the prediction of the naive non-relativistic quark model. We show that this affects the predictions for the spin asymmetries in Drell-Yan pair production in transversely polarized pp and ppbar collisions.

Figures (7)

• Figure 1: The isovector (top) and isoscalar (bottom) transversity quark-- and antiquark distributions obtained from the chiral quark--soliton model. The functions shown here represent $[\delta u \mp \delta d](x)$ at $x > 0$ and $-[\delta \bar{u} \mp \delta \bar{d}] (-x)$ at $x < 0$. Dashed lines: Contributions of the bound--state level. Dotted lines: Contributions of the Dirac continuum. Solid lines: Total results (sums of bound--state level and Dirac continuum).
• Figure 2: The total isovector (top row) and isoscalar (bottom row) transversity and longitudinally polarized quark-- and antiquark distributions, multiplied by $x$. Shown are the total results (sum of level and continuum contributions), corresponding to the solid lines in Fig. \ref{['fig_delta']}.) Solid lines: Quark distributions. Dashed lines: Antiquark distributions.
• Figure 3: The transversity and longitudinally polarized antiquark distributions, see Fig. \ref{['fig_xdelta']}. Left: Isovector distributions, $x[\delta \bar{u} - \delta \bar{d}](x)$ and $x[\Delta \bar{u} - \Delta \bar{d}](x)$. Right: Isoscalar distributions, $x[\delta \bar{u} + \delta \bar{d}](x)$ and $x[\Delta \bar{u} + \Delta \bar{d}](x)$. Solid lines: Transversity antiquark distributions Dashed lines: longitudinally polarized antiquark distributions.
• Figure 4: The large--$N_c$ improved positivity bounds for quark distribution functions, Eqs.(\ref{['E0']}) and Eqs.(\ref{['E1']}), for the quark (left) and antiquark distributions (right). Solid lines:$x\, [u+d](x)/3$. Dashed lines:$|x\,[\delta u -\delta d](x)|$. Dotted lines:$x\,[\Delta u -\Delta d](x)$.
• Figure 5: The large--$N_c$ improved Soffer bound for the quark (left) and antiquark (right) distributions. Dashed lines:$|x\, [\delta u -\delta d](x)|$. Solid lines: The large $N_c$ Soffer bound $(x[u+d](x)/3+x\,[\Delta u -\Delta d](x))/2$. The small violation is due to the ultraviolet regularization; see the discussion in the main text.