Saturation effects in SIDIS at very forward rapidities

Using the dipole picture for electron-nucleus deep inelastic scattering at small Bjorken x, we study the effects of gluon saturation in the nuclear target on the cross-section for SIDIS (single inclusive hadron, or jet, production). We argue that the sensitivity of this process to gluon saturation can be enhanced by tagging on a hadron (or jet) which carries a large fraction z ≃ 1 of the longitudinal momentum of the virtual photon. This opens the possibility to study gluon saturation in relatively hard processes, where the virtuality Q² is (much) larger than the target saturation momentum $$ {Q}_s^2 $$Q s 2 , but such that z(1 − z)Q² ≲ $$ {Q}_s^2 $$Q s 2 . Working in the limit z(1 − z)Q² ≪ $$ {Q}_s^2 $$Q s 2 , we predict new phenomena which would signal saturation in the SIDIS cross-section. For sufficiently low transverse momenta k_⊥ ≪ Q_s of the produced particle, the dominant contribution comes from elastic scattering in the black disk limit, which exposes the unintegrated quark distribution in the virtual photon. For larger momenta k_⊥ ≳ Q_s, inelastic collisions take the leading role. They explore gluon saturation via multiple scattering, leading to a Gaussian distribution in k_⊥ centred around Q_s. When z(1 − z)Q² ≪ Q², this results in a Cronin peak in the nuclear modification factor (the R_pA ratio) at moderate values of x. With decreasing x, this peak is washed out by the high-energy evolution and replaced by nuclear suppression (R_pA< 1) up to large momenta k_⊥ ≫ Q_s. Still for z(1 − z)Q² ≪ $$ {Q}_s^2 $$Q s 2 , we also compute SIDIS cross-sections integrated over k_⊥. We find that both elastic and inelastic scattering are controlled by the black disk limit, so they yield similar contributions, of zeroth order in the QCD coupling.