Incoherent diffractive production of jets in electron DIS off nuclei at high energy

We study incoherent diffractive production of two and three jets in electron-nucleus deep inelastic scattering (DIS) at small $x_{\scriptscriptstyle \rm Bj}$ using the color dipole picture and the effective theory of the Color Glass Condensate (CGC). We consider color fluctuations in the CGC weight-function as the source of the nuclear break-up and the associated momentum transfer $\sqrt{|t|}$. We focus on the regime in which the two jets are almost back-to-back in transverse space and have transverse momenta $P_{\perp}$ much larger than both the momentum transfer and the saturation scale $Q_s$. The cross section for producing such a hard dijet is parametrically dominated by large size fluctuations in the projectile wave-function that scatter strongly and for which a third, semi-hard, jet appears in the final state. The 2 + 1 jets cross section can be written in a factorized form in terms of incoherent quark and gluon diffractive transverse momentum distributions (DTMDs) when the third jet is explicit, or incoherent diffractive parton distribution functions (DPDFs) when the third jet is integrated over. We find that the DPDFs and the corresponding cross section saturate logarithmically when $|t| \ll Q_s^2$, while they fall like $1/|t|^2$ in the regime $Q_s^2 \ll |t| \ll P_{\perp}^2$. We further show that there is no angular correlation between the hard jet momentum and the momentum transfer. For typical EIC kinematics the 2 jets and 2 + 1 jets cross sections are of the same order.