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

TL;DR

This paper revisits the assumptions about measuring hard-scattering and jets in p-p collisions, identifies limitations in previous methods, and introduces a new formula that better relates observed particle distributions to jet properties, especially in heavy-ion collisions.

Contribution

The paper derives a new formula linking particle correlations to jet ratios, correcting previous misconceptions and enabling better analysis of jet behavior in RHIC collisions.

Findings

The old method could not accurately measure the away-side jet fragmentation.

The new formula exhibits scaling in the variable $x_E$ and relates it to jet momentum ratios.

Application to RHIC Au+Au collisions shows improved understanding of jet suppression.

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.