Double parton scattering in pA collisions at the LHC revisited

We consider the production of $W$-boson plus dijet, $W$-boson plus b-jets and same sign $WW$ via double parton scattering (DPS) in $pA$ collisions at the LHC and evaluate the corresponding cross sections. The impact of a novel DPS contribution pertinent to $pA$ collisions is quantified. Exploiting the experimental capability of performing measurements differential in the impact parameter in $pA$ collisions, we discuss a method to single out this novel DPS contribution. The method allows the subtraction of the leading twist (LT) single parton scattering background and it gives access in a very clean way to double parton distribution functions in the proton. We calculate leading twist and DPS cross sections and study the dependence of the observables on the cuts in the jets phase space. In the $Wjj$ channel the observation of DPS is possible with data already accumulated in $pA$ runs and the situation will greatly improve for the next high luminosity runs. For the $Wb\bar{b}$ final state, the statistics within the current data is too low, but there is possibility to observe DPS in this channel in future runs, albeit with much reduced sensitivity than in $Wjj$ final state. Finally the DPS observation in the same sign $WW$ channel will require either significant increase of integrated luminosity beyond that foreseen in next $pA$ runs or improved methods for $W$ reconstruction, along with its charge, in hadronic decay channels.