Jet calculus: A simple algorithm for resolving QCD jets

It is argued that, in the leading logarithm approximation (LLA) of asymptotically free quantum chromodynamics (QCD), a simple algorithm (jet calculus) can be justified for computing a large number of quantities related to the longitudinal and transverse structure of quark and gluon jets.We formulate the rules of jet calculus in two variables, x and y which are related to longitudinal (energy) and transverse momentum respectively. Throughout the paper, quark and gluon jets are contrasted. After reviewing what has been done on longitudinal spectra, we turn to the transverse structure of jets down to relative transverse momenta of the order of a few GeV (independently of the total energy). The relation of our work to that of Dokshitzer, D'Yakonov and Troyan is elucidated. We also study jets generated by (almost) real photons and compare both with standard “final” parton jets.We also discuss calorimeter measured quantities, compare our results with those of other authors and propose a new and easy way for measuring QCD-predictable anomalous dimensions.We finally give a Lagrangian formulation of jet calculus, as a non-local theory in 1 + 1 dimensions to be solved in the tree approximation.