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We revisit the calculation of the cross section for forward inclusive singlehadron production in $pA$ collisions within the hybrid approach. We show thatthe proper framework to perform this calculation beyond leading order is notthe collinear factorization, as has been assumed so far, but the TMD factorizedframework. Within the TMD factorized approach we show that all the largetransverse logarithms appearing in the fixed order calculation, are resummedinto the evolution of the TMD PDFs and TMD FFs with factorization scale. Theresulting expressions, when written in terms of TMDs evolved to theappropriate, physically well understood factorization scale, contain noadditional large logarithms. The absence of any large logarithms in theresummed result should ensure positivity of the cross section and eradicate thepersistent problem that have plagued the previous attempts at calculating thisobservable in the hybrid approach.

Single inclusive particle production at next-to-leading order in  proton-nucleus collisions at forward rapidities: hybrid approach meets TMD  factorization