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In this work, we investigate production of Drell-Yan (DY) pairs inproton-nucleus collisions in kinematic regions where the correspondingcoherence length does not exceed the nuclear radius, $R_A$, and the quantumcoherence effects should be treated with a special care. The results for thenucleus-to-nucleon production ratio available in the literature so far areusually based on the assumption of a very long coherence length (LCL) $l_c\ggR_A$. Since the onset of coherence effects is controlled by the coherencelength $l_c$, we estimated its magnitude in various kinematic regions of the DYprocess and found that the LCL approximation should not be used at small andmedium c.m. collision energies ($\sqrt{s} \lesssim 200$ GeV) as well as atlarge dilepton invariant masses. In order to obtain realistic predictions, wecomputed for the first time the DY cross section using the generalised colordipole approach based on the rigorous Green function formalism, which naturallyincorporates the color transparency and quantum coherence effects and henceallows to estimate the nuclear shadowing with no restrictions on the CL. Inaddition to the shadowing effect, we studied a complementary effect of initialstate interactions (ISI) that causes an additional suppression at large valuesof the Feynman variable. Numerical results for the nuclear modification factoraccounting for the ISI effect and the finite $l_c$ are compared to the dataavailable from the fixed-target FNAL measurements and a good agreement has beenfound. Besides, we present new predictions for the nuclear suppression as afunction of dilepton rapidity and invariant mass in the kinematic regions thatcan be probed by the RHIC collider as well as by the planned AFTER@LHC and LHCbfixed-target experiments.

Drell-Yan process in $pA$ collisions: the exact treatment of coherence effects