Different realizations of kappa-momentum space and relative-locality effect

We consider different realizations for the momentum sector of kappa-Poincare Hopf algebra, which is associated with a curved momentum space. We show that the notion of the particle mass as introduced recently by Amelino-Camelia et al. in the context of relative-locality is realization independent for a wide class of realizations, up to linear order in deformation parameter l. On the other hand, the time delay formula clearly shows a dependence on the choice of realization.
12 pages; extended version of the paper published in Phys. Rev. D 87, 125009 (2013)