The Lambda-Measure and the Generalised Dipoles in the Lund Model

We demonstrate that the multiple gluon emission phase space in the dipole cascade model has a strong linear correlation with the number of gluons emitted. The number of gluons per unit available phase space at a certain resolution scale is found to be remarkably independent of the cms energy and global event properties like thrust, and even changes in the ordering variable or resolution scale. We show that the distribution of sizes of gluon-gluon dipoles in a parton cascade has stability properties which are sufficient to account for those of the phase space variable. We observe that certain more abstract entities, defined in the context of hadronisation and related to the gluon emission phase space, share those properties of colour dipoles and name them Generalised Dipoles. We also present an analytical model to qualitatively describe our findings.