On the $xi$-Distribution of Inclusively Produced Particles in $e^+e^-$ Annihilation.pdf

a r X i v : h e p - p h / 9 9 0 9 4 1 3 v 1 1 7 S e p 1 9 9 9 ADP-99-39/T376 IU/NTC 99-09 On the ξ-Distribution of Inclusively Produced Particles in e+e? Annihilation C. Boros, J.T. Londergan1 and A.W. Thomas Department of Physics and Mathematical Physics, and Special Research Center for the Subatomic Structure of Matter, University of Adelaide, Adelaide 5005, Australia 1 Department of Physics and Nuclear Theory Center, Indiana University, Bloomington, IN 47408, USA (February 1, 2008) Abstract We discuss the momentum distributions of inclusively produced particles in e+e? annihilation. We show that the dependence of the position of the maxima of the ξ = ln(1/z) spectra on the mass of the produced particles follows naturally from the general definition of fragmentation functions when energy-momentum conservation is correctly incorporated. 1 e+e? annihilation provides an excellent opportunity to study the fragmentation of quarks into hadrons. In particular, inclusive measurements of particle spectra allow us to extract fragmentation functions from such experiments and to test different theoretical models of fragmentation. Until now, fragmentation functions have not been calculated from first prin- ciples rather they have to be modeled in some way. Most of the current approaches use different algorithms, such as string and shower algorithms, and model fragmentation of a high energy quark in two phases, one of which is purely perturbative, describing the radiation and branching of the initial quarks and the other describing the subsequent non-perturbative hadronisation of the low energy quarks. Here, we follow a different approach. Starting from the general definition of the fragmentation functions, and explicitly guar- anteeing energy-momentum conservation we discuss the following interesting property of inclusive particle spectra in e+e? annihilation. When the number of inclusively produced particles is plotted as a function of ξ = ln(1/z), (where z is the moment