Kinematical Lepton Transmutation in $e^+ e^-$ Collision and Vector Boson Decay

Abstract

The change in orientation in generation space (rotation) of the fermion mass matrix with changing scales can lead to flavour-violations through just the kinematics of a non-diagonal mass matrix. Such effects for the reactions: $e^+ e^- \longrightarrow e^\pm μ^\mp, e^\pm τ^\mp, μ^\pm τ^\mp$, and for the decays of vector bosons into the same channels, are calculated following a method suggested earlier which gives the differential cross section for each reaction and the branching ratio for each decay mode in terms of an overall normalization depending only on the speed at which the mass matrix rotates. A rotation speed estimated earlier, under certain assumptions from the fermion mixing angles and mass ratios, is found to give the above effects at a level readily detectable in modern high sensitivity experiments such as Bepc, Cleo, BaBar and Belle, at least in principle. The observation of these effects would not only confirm the concept of a rotating mass matrix with a significance on par with the running coupling constant, but also offer some valuable insight into the origin of fermion generations. However, a negative result cannot unfortunately rule out the rotating mass matrix since the effects deduced here from this mechanism alone could in principle be cancelled by other rotation effects.