Extracting Nucleon Resonance Transition GPDs from $e^- N\to e^-γNπ$ Deeply Virtual Compton Scattering

TL;DR

This work investigates extracting $N\rightarrow N^*$ transition GPDs through resonance DVCS in the $N\to N\pi$ channel near the Roper resonance, while incorporating a background pion-emission process that can interfere with the resonance signal. Using a leading-twist handbag framework and a light-cone double-distribution GPD model with Regge-inspired $t$-dependence, the authors quantify how diagonal and transition amplitudes, along with final-state interactions, shape the $e^-N\to e^-\gamma N\pi$ cross section under CLAS12-like conditions. They find measurable interference effects and region-dependent sensitivity to transition GPDs, particularly at larger $-t$ and in charged-pion channels, suggesting resonance DVCS as a viable probe of nucleon-resonance structure. Limitations include the omission of the Bethe–Heitler contribution and a single-resonance analysis; future work aims to include Bethe–Heitler, additional resonances, and optimized observables to map transition GPDs and test the nature of the Roper resonance.

Abstract

We investigate the process in which Deeply Virtual Compton Scattering (DVCS) excites a baryon resonance. In particular, we assess, in DVCS leading to the Roper resonance, the relative importance of a "background'' process in which a pion is first emitted by the nucleon, which then undergoes a DVCS event. Our numerical results, using realistic DVCS kinematics, indicate that there can be measurable interference effects. They suggest that this process could substantially modify the experimentally observed cross sections at CLAS12-like kinematics, motivating their inclusion in precision analyses of DVCS experiments. We further find that in spite of this background, the transition to a Roper-like state through DVCS does contribute significantly to the $e^- N\to e^-γNπ$ cross section in some kinematic regions. This suggests that the creation of nucleon resonances via DVCS is a useful method for extracting information about the nucleon transition GPDs and the internal structure of the excited states.

Figures (4)

• Figure 1: A schematic for the kinematics of the DVCS to excited state process Semenov-Tian-Shansky:2023bsy.
• Figure 2: Handbag diagram of the DVCS process in the DGLAP region $x\in[\xi,1]$, corresponding to the scattering on a quark fig:handbag.
• Figure 3: Differential cross section for the DVCS process $p^+ e^- \to p^+ \pi^0 e^-\gamma$ evaluated at beam energy $E_e=10.6~\mathrm{GeV}$, photon virtuality $Q^2=2.3~\mathrm{GeV}^2$, Björken-$x$$x_B=0.2$, scattering plane angle $\Phi=\pi/2$, and various momentum transfers $-t$. Integrated over the pion decay solid angle $\Omega^*_\pi$ with the cut $M_{\pi\gamma}>1~\mathrm{GeV}$ applied.
• Figure 4: Differential cross section for the DVCS process $p^+ e^- \to n \pi^+ e^- \gamma$ evaluated at beam energy $E_e=10.6~\mathrm{GeV}$, photon virtuality $Q^2=2.3~\mathrm{GeV}^2$, Björken-$x$$x_B=0.2$, scattering plane angle $\Phi=\pi/2$, and various momentum transfers $-t$. Integrated over the pion decay solid angle $\Omega^*_\pi$ with the cut $M_{\pi\gamma}>1~\mathrm{GeV}$ applied.