Where Feynman, Field and Fox failed and how we fixed it at RHIC

Abstract

Hard-scattering of point-like constituents (or partons) in p-p collisions was discovered at the CERN-ISR in 1972 by measurements utilizing inclusive single or pairs of hadrons with large transverse momentum ($p_T$). It was generally assumed following a seminal paper by Feynman, Field and Fox (FFF) (and much discussed in a talk that I gave at the 1979 Rencontres de Moriond) that ``everything you wanted to know about hard-scattering and jets'' could be measured by these methods. Recently, we found in PHENIX that the $p_{T_a}$ distribution of away side hadrons from a single particle trigger [with $p_{T_t}$] which is a leading fragment of the trigger jet, could not be used to measure the fragmentation function of the away jet as originally claimed by FFF. A new formula was derived which both exhibits scaling in the variable $x_E\sim p_{T_a}/p_{T_t}$ (a hot topic in 1979) and relates $x_E$, $\sim$ the ratio of the transverse momenta of the measured particles, to $\hat{x}_h=\hat{p}_{T_a}/\hat{p}_{T_t}$, the ratio of the transverse momenta of the away-side to trigger-side jets. Tests of the validity of the formula and applications to Au+Au central collisions at RHIC (where jets can not be reconstructed) are discussed.