Jet Mass Dependence of Fragmentation in Positron-Proton Collisions

We propose the characterization of fragmentation functions by the energy fraction x, a hadron takes away from the energy of the jet measured in the frame co-moving with the jet. Besides, we propose the usage of the jet mass as the fragmentation scale Q. We show that these two Lorentz-invariant variables emerge naturally in a microcanonical ensemble with conserved fourmomentum. Then, we construct a statistical hadronisation model, in which, two features of the hadronic final states in various high-energy reactions (power law spectra and negative-binomial multiplicity distributions) can be connected simply. Finally, we analyse the scale dependence of the parameters of the model (power of the spectrum and mean energy per hadron) in the phi^3 theory. Fitting fragmentation functions in diffractive positron-proton collisions, we obtain a prediction for the jet mass dependence of the hadron multiplicity distribution inside jets.