Transversity Generalized Parton Distributions of $Δ$ with the Diquark Spectator Model

TL;DR

This work provides the first numerical calculation of quark transversity GPDs for a spin-3/2 hadron, the Δ^+, using a diquark spectator model. It defines and computes the leading transversity GPDs $H^{qT}_{1,3,5,7}$, obtains the forward-limit transversity distribution $h_1(x)$, and analyzes helicity-flip amplitudes and tensor form factors through Mellin moments, yielding a tensor charge $g_T^{ riangle^+}=0.876$ for the $d$-quark with $ riangle^+$ symmetry giving $oldsymbol{δ}_u=2oldsymbol{δ}_d$. The results satisfy sum rules and are broadly consistent with lattice form factors for charge and axial channels, supporting the reliability of the leading spin-1/2 structure in the vertex. The study highlights experimental pathways to access Δ GPDs via DVCS, DVMP, GDAs, and two-photon processes, offering qualitative predictions for future measurements of higher-spin hadron structure.

Abstract

We show quark transversity generalized parton pistributions (GPDs) of $Δ^+$ isobar by using the diquark spectator model for the first time. First, this model is tested by electric charge, magnetic-dipole and axial charge form factors, and it is used for calculating the transversity GPDs $H^{qT}_{1,3,5,7}$ of $Δ^+$. The quark transversity distribution $h_1$ is then obtained from the transversity GPDs in the forward limit. Then, helicity-flip amplitudes are shown numerically by using relations between the helicity amplitudes and the GPDs. Finally, by taking first moments of the GPDs, tensor form factors are obtained and we predict the tensor charge. Experimentally, $N$-$Δ$ transition GPDs are investigated in deeply virtual Compton scattering and virtual meson-production processes, and generalized distribution amplitudes, which correspond to the $s$-channel GPDs, could be investigated by the two-photon processes $γ^* γ\to Δ\barΔ$ at the electron-positron colliders. Therefore, the spin-3/2 $Δ$ GPDs could become interesting quantities experimentally in future.

Figures (7)

• Figure 1: Diagram describing the quark GPDs.
• Figure 2: Feynman diagram for the $\Delta^+$ GPDs using the diquark spectator approach, and the single (double) line stands for the quark (diquark).
• Figure 3: The electric charge, magnetic moment and axial charge form factors of $\Delta^+$ with $c_2=c_3=0$, compared with Ref. Alexandrou:2008bnAlexandrou:2013opa.
• Figure 4: The 3D $d$ quark transversity GPDs of $\Delta^+$$H^{qT}_{1,3,5,7}$ at $\xi = 0, \, -0.2, \, -0.4$.
• Figure 5: (a): The GPDs $H^{qT}_{1}(x,\xi,-|t|_{\min})$ with different skewness $\xi$ and the corresponding minimal $|t|$. The red solid line, orange dashed line and blue dot dash line respectively represent the GPDs with $\left( \xi, -t \right) = \left( 0, 0 \,\text{GeV}^2 \right)$, $\left( -0.2, 0.2\,\text{GeV}^2 \right)$ and $\left( -0.4, 0.9\,\text{GeV}^2 \right)$. (b): The transversity PDF $h_1(x)$, where $h_1(x) = 2 H_1^{qT}(x,0,0)$.