Restoration of

We discuss the applicability of the k T factorization theorem to low-p T hadron production in hadron–hadron collision in a simple toy model, which involves only scalar particles and gluons. It has been shown that the k T factorization for high-p T hadron hadroproduction is broken by soft gluons in the Glauber region, which are exchanged among a transverse-momentum-dependent (TMD) parton density and other subprocesses of the collision. We explain that the contour of a loop momentum can be deformed away from the Glauber region at low p T , so the above residual infrared divergence is factorized by means of the standard eikonal approximation. The k T factorization is then restored in the sense that a TMD parton density maintains its universality. Because the resultant Glauber factor is independent of hadron flavors, experimental constraints on its behavior are possible. The k T factorization can also be restored for the transverse single-spin asymmetry in hadron–hadron collision at low p T in a similar way, with the residual infrared divergence being factorized into the same Glauber factor