  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 Feynman, Field and Fox, as shown by data from the CERN-ISR
experiments, that the $p_{T_a}$ distribution of away side hadrons from a single
particle trigger [with $p_{T_t}$], corrected for <z_t> of fragmentation would
be the same as that from a jet-trigger and follow the same fragmentation
function as observed in $e^+ e^-$ or DIS. PHENIX attempted to measure the
fragmentation function from the away side $x_E\sim p_{T_a}/p_{T_t}$
distribution of charged particles triggered by a $\pi^0$ in p-p collisions at
RHIC and showed by explicit calculation that the $x_E$ distribution is actually
quite insensitive to the fragmentation function. Illustrations of the original
arguments and ISR results will be presented. Then the lack of sensitivity to
the fragmentation function will be explained, and an analytic formula for the
$x_E$ distribution given, in terms of incomplete Gamma functions, for the case
where the fragmentation function is exponential. The away-side distribution in
this formulation has the nice property that it both exhibits $x_E$ scaling and
is directly sensitive to the ratio of the away jet $\hat{p}_{T_a}$ to that of
the trigger jet, $\hat{p}_{T_t}$, and thus can be used, for example, to measure
the relative energy loss of the two jets from a hard-scattering which escape
from the medium in A+A collisions. Comparisons of the analytical formula to
RHIC measurements will be presented, including data from STAR and PHENIX,
leading to some interesting conclusions.
