Restoration of kT factorization for low pT hadron hadroproduction

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.