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

In this work, we investigate production of Drell-Yan (DY) pairs in proton-nucleus collisions in kinematic regions where the corresponding coherence length does not exceed the nuclear radius, $R_A$, and the quantum coherence effects should be treated with a special care. The results for the nucleus-to-nucleon production ratio available in the literature so far are usually based on the assumption of a very long coherence length (LCL) $l_c\gg R_A$. Since the onset of coherence effects is controlled by the coherence length $l_c$, we estimated its magnitude in various kinematic regions of the DY process and found that the LCL approximation should not be used at small and medium c.m. collision energies ($\sqrt{s} \lesssim 200$ GeV) as well as at large dilepton invariant masses. In order to obtain realistic predictions, we computed for the first time the DY cross section using the generalised color dipole approach based on the rigorous Green function formalism, which naturally incorporates the color transparency and quantum coherence effects and hence allows to estimate the nuclear shadowing with no restrictions on the CL. In addition to the shadowing effect, we studied a complementary effect of initial state interactions (ISI) that causes an additional suppression at large values of the Feynman variable. Numerical results for the nuclear modification factor accounting for the ISI effect and the finite $l_c$ are compared to the data available from the fixed-target FNAL measurements and a good agreement has been found. Besides, we present new predictions for the nuclear suppression as a function of dilepton rapidity and invariant mass in the kinematic regions that can be probed by the RHIC collider as well as by the planned AFTER@LHC and LHCb fixed-target experiments.