A Microscopic View of Parton $k_T$ Effects In High $p_T$ Processes

A microscopic mechanism is proposed for understanding the rather large $k_T$ effects ($<k_T>$ = $1-1.5 GeV/c$, as yet unaccounted for by hard QCD), found by the Fermilab E706 Collaboration for 530 and 800 GeV/c protons incident on light nuclear targets (mass $A$) like Be. The essential idea is that such high incident projectile momenta tend to break up the confinement barriers for the quark-partons residing in the individual nucleonic constituents of the target nucleus that fall in a tube-like zone around the projectile's path, so that these particles tend to behave as a collection of quark-partons confronting the beam. Using simple combinatorial principles, the resultant $<k_T>^2$ value works out as $(3A_{eff}-1) \beta^2$, where $A_{eff}$ is the number of affected nucleons in the tube-like zone, and $\beta$ is a scale parameter derived from the basic quark-pair interaction. Using the previously found results of a Bethe-Salpeter model (attuned to $q{\bar q}$ and $qqq$ spectroscopy), one in which a key ingredient is the infrared part of the gluon propagator, giving $\beta^2= 0.068 GeV^2$, the desired $<k_T>$ range is reproduced, suggesting the persistence of $soft$ QCD effects even at high $p_T$. Keywords: Direct photon; high-$p_T$ reaction; parton $k_T$ distribution; soft-QCD effect.