Q2evolution of multihadron fragmentation functions

Abstract

In order to characterize jet structure more completely than is possible with the single-hadron fragmentation functions of partons, we deduce the evolution (in $Q^2$) equations for the fragmentation functions of a parton to fragment into an arbitrary number $N$ of hadrons. The solution to the evolution equations is explicitly displayed in terms of multiple moments for the $N$-hadron fragmentation functions. Our procedure is simpler than using the rules of the jet calculus. We also show how the $Q^2$ dependence of these fragmentation functions can be understood in a recursive cascade-model framework in which both the momentum and the amount by which a parton is off its energy shell (as measured by $Q^2$) are reduced at each branching step during jet formation. This reformulation suggests an alternative way for solving the evolution equations in which moment inversion is not required.