Accessing the Pion 3D Structure at US and China Electron-Ion Colliders

We present the first systematic feasibility study of accessing generalized parton distributions of the pion at an electron-ion collider through deeply virtual Compton scattering. Relying on state-of-the-art models for pion GPDs, we show that quarks and gluons interfere destructively, modulating the expected event rate and maximizing it when parton content is generated via radiation from valence dressed quarks. Moreover, gluons are found to induce a sign inversion for the beam-spin asymmetry in every model studied, being a clear signal for pinning down the regime of gluon superiority.

Figure 1

DVCS off a virtual pion through the Sullivan process. Kinematic variables: $Q^2=-q^2$, $y=(p·q/p·l)$, $y_{\pi }=(p_{\pi }·q/p_{\pi }·l)$, and $x_B^{\pi }=(Q^2/2p_{\pi }·q)$.

Figure 2

Phase space considered in the present study: facilities and configurations (electron $\times$ proton beam energies in GeV) contributing the most to the statistics in the colored areas are specified.

Figure 3

Number of DVCS events (upper chart) and expected beam-spin asymmetries (lower chart) as functions of $Q^2$ for $x_B^{\pi }\in [{10}^{-3};{10}^{-2}]$. Black squares represent the full NLO calculation in the model of Ref. [43], while empty squares show the NLO evaluation without taking the gluon contribution into account. Red circles display NLO results from the GRS model, and blue crosses denote the BH event rate. The shaded gray area shows the evolution-induced uncertainty.

Figure 4

Expected beam-spin asymmetries as functions of $\varphi$ with ${\mathcal{H}}^{\mathrm{CSM}}$ (top) and ${\mathcal{H}}_{0g}^{\mathrm{CSM}}$ (bottom) from EicC for $x_B^{\pi }\in [0.1;0.5]$ and three different $Q^2$ bins: black circles for $Q^2$ between 1 and $2{\mathrm{GeV}}^2$, blue squares between 2 and $4{\mathrm{GeV}}^2$, and red triangles between 4 and $12{\mathrm{GeV}}^2$.