Eur. Phys. J. C (2011) 71: 1687
https://doi.org/10.1140/epjc/s10052-011-1687-1

Regular Article - Theoretical Physics

Restoration of k _T factorization for low p _T hadron hadroproduction

¹ Institute of Physics, Academia Sinica, Taipei, Taiwan, 115, Republic of China
² Department of Physics, National Tsing-Hua University, Hsinchu, Taiwan, 300, Republic of China
³ Department of Physics, National Cheng-Kung University, Tainan, Taiwan, 701, Republic of China
⁴ Institute of Applied Physics, National Cheng-Chi University, Taipei, Taiwan, 116, Republic of China

^* e-mail: hnli@phys.sinica.edu.tw

Received: 27 February 2011
Revised: 10 May 2011
Published online: 28 June 2011

Abstract

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.