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 Q 2 is (much) larger than the target saturation momentum Q_s^2 , but such that z (1 − z ) Q 2 ≲ Q_s^2 . Working in the limit z (1 − z ) Q 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 ) Q 2 ≪ Q 2 , 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 ) Q 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.