Structure functions of quarks, gluons and hadrons in quantum chromodynamics

Abstract

The Q 2 variation of hadronic structure functions and of fragmentation functions in QCD is formulated in terms of Q 2 dependent structure functions for the distribution of quarks and gluons in quark and gluon jets. This approach is completely equivalent to the standard moment analysis but is much more useful for obtaining qualitative results. Many old and new results for the behavior of quark and gluon jets and the implications for these results on the evolution of hadrons may be easily derived. It is easy to show, for example, that the ratio of gluon distributions in quark jets to that in gluon jets approaches a Q 2 independent constant ( 4 9 ) as x → 0, that guon distributions in gluon jets vanish 9 4 times as rapidly as quark distributions in a quark jet at large x, Q 2, and that at large x the leading hadrons in gluon jet fragmentation are produced via the sequential reaction gluon → quark → hadron, so that D h/g( x, Q 2) ∼ (1 − x) D h/q ( x, Q 2). I present simple analytic expressions for hadronic structure and fragmentation functions and derive counting rules for QCD-based large- p ⊥ inclusive jet and hadron cross sections.