Azimuthal spin asymmetries in light-cone constituent quark models

TL;DR

This work assesses all leading-twist azimuthal spin asymmetries in SIDIS arising from T-even TMDs within a light-cone constituent quark model, focusing on the valence region and the interplay of orbital angular momentum via Melosh-rotated LCWFs. It introduces a Gaussian transverse-momentum Ansatz to enable analytic handling of convolutions, tests scale evolution from a low model scale, and compares predictions with existing data. The Collins-induced single-spin asymmetry shows the strongest agreement with HERMES and COMPASS results, while other asymmetries are generally small or consistent with zero given current uncertainties. Collectively, the study provides a coherent framework linking TMDs, orbital motion, and experimental observables, with concrete predictions for upcoming measurements at CLAS, COMPASS, and JLab, and highlights the role of SU(6) symmetry and partial-wave content in shaping spin-asymmetry patterns.

Abstract

We present results for all leading-twist azimuthal spin asymmetries in semi-inclusive lepton-nucleon deep-inelastic scattering due to T-even transverse-momentum dependent parton distribution functions on the basis of a light-cone constituent quark model. Attention is paid to discuss the range of applicability of the model, especially with regard to the scale dependence of the observables and the transverse-momentum dependence of the distributions. We find good agreement with available experimental data and present predictions to be further tested by future CLAS, COMPASS and HERMES data.

Figures (12)

• Figure 1: Kinematics of the SIDIS process $lN\to l^\prime h X$ and the definitions of azimuthal angles in the lab frame.
• Figure 2: Parton distribution functions and transverse moments of TMDs as functions of $x$ from the light-cone CQM Pasquini:2008ax. In all panels the solid curves show the total results for the 'flavour-less' TMDs, i.e. the TMDs of definite flavour follow from multiplying by the spin-flavour factors $N^a$ or $P^a$, see Eqs. (\ref{['eq:f1']})-(\ref{['eq:h1T']}). The other curves show how much the different angular momentum components of the nucleon wave function contribute to the total results: In the case of $f_1(x)$, $g_1(x)$, $h_1(x)$ the dashed, and dotted curves correspond to the contribution from the squares of the S- and P-wave components of the nucleon wave function, respectively. The $D$-wave contribution is absent in $h_1$, while for $f_1$ and $g_1$ it is quite small and corresponds to the hardly-visible dashed-dotted curves. In the case of $g_{1T}^{\perp(1)}(x)$, $h_{1L}^{(1)\perp}(x)$ the dashed and dotted curves give the results from the S-P and P-D interference terms, respectively. In the case of $h_{1T}^{(1)\perp}(x)$, the dashed curve is the result from the P-wave interference, and the dotted curve is due to the interference of S and D waves.
• Figure 3: The inclusive (a) and semi-inclusive (b, c) double spin asymmetries, $A_1$ and $A_{LL}$, defined in Eqs. (\ref{['Eq:ALL']}, \ref{['Eq:A1']}), in DIS off proton as functions of $x$. The theoretical curves are obtained with $g_1^a(x)$ and $f_1^a(x)$ from the light-cone CQM Pasquini:2008ax as follows: both functions LO-evolved to the $\langle Q^2\rangle$ of the experiments (solid curves), and both at the low scale of the model (dashed curves). In (b, c) we use always the parametrization Kretzer:2000yf for $D_1^a$ at $Q^2=2.5$ GeV$^2$. The data in (a) are from Refs. Abe:1998wqAshman:1987hvAdeva:1999pa, in (b,c) are from SMC (open circles) Adeva:1997qz and HERMES (black squares) Airapetian:2004zf.
• Figure 4: $A_{LT}^{\cos(\phi_h-\phi_S)}$ in $\pi^+$ production off proton, as function of $x$. Solid curve: exact result obtained using $g_{1T}(x,p_T)$ from Pasquini:2008ax and $D_1(z,K_T)$ from Bacchetta:2007wc. Dashed curve: an approximation obtained using the integrated functions $g_{1T}^{(1)}(x)$, $D_1(z)$ from Pasquini:2008axBacchetta:2007wc and 'simulating' their $p_T$-dependence by means of the Gaussian Ansatz, as described in the text.
• Figure 5: The double-spin asymmetry $A_{LT}^{\cos(\phi_h-\phi_S)}$ in DIS production of pions, as function of $x$, obtained using $g_{1T}^{(1)a}(x)$ and $f_1^a(x)$ from the light-cone CQM Pasquini:2008ax in the following way: both functions are taken at the low scale of the model (dashed curves), and both are LO-evolved to $Q^2=2.5$ GeV$^2$ (solid curves). Hereby the scale dependence of $g_{1T}^{(1)a}(x)$ is 'simulated' using the $g_1^a(x)$ evolution pattern, see text. The data points are preliminary COMPASS data for charged hadron production off deuteron Kotzinian:2007uv.