Twisting loops and global momentum non-conservation in Relative Locality

Recent work in Relative Locality has shown that the theory allows for a solution of an on-shell causal loop. We show that the theory contains a different type of a loop in which locally momenta are conserved, but there is no global momentum conservation. Thus a freely propagating particle can decay into two particles, which later recombine to give a particle with momentum and mass different than the original one.