Role of the GPD-$E$ in exclusive dijet electroproduction at the Electron-Ion Collider

We calculate the contribution of the $E$-type generalized parton distributions (GPDs) to exclusive dijet electroproduction in $ep\to e'jjp$ in collinear QCD factorization, including both the proton helicity-flipping amplitude and the GPD-$E$ term in the helicity-conserving amplitude, using the double distribution approach for modeling. We include light sea and valence-quark exchanges as well as gluon exchanges and compare the proton helicity-conserving and helicity-flipping contributions for HERA-energy phase space and for Electron-Ion Collider (EIC) kinematics. We find that the helicity-flipping cross section is dominated by valence-quark exchange and has a markedly different dependence on $|t|$ and $x_{\mathbb P}$ from the helicity-conserving contribution. In the EIC kinematics considered here, the helicity-flip contribution becomes comparable to the helicity-conserving one at large $|t|$ and $x_{\mathbb P}$. The results show that exclusive dijet electroproduction can be sensitive to the $E$-type GPDs in the kinematic region accessible at the EIC.