Non-abelian flavour symmetry and R-parity

If R-parity violation turns out to be a true aspect of Nature, a speculation about its possible origin could add a new dimension to the supersymmetric flavour problem. It has been shown in the past by Barbieri, Hall and their collaborators that the small breaking parameters of an approximate non-abelian flavour symmetry could govern the light quark and lepton masses and at the same time could account for the near degeneracies of squarks and sleptons. A possible connection of the above feature to the natural suppressions of R-parity-violating couplings has been investigated here. With some modifications of the approximate flavour symmetry, a supersymmetric theory without R-parity has been motivated that has testable experimental signatures. 1. Is it possible to reconcile the conventional notion of flavour physics in supersymmetry concerning masses and mixings and the scenario of R-parity violation? In this Letter, we seek for a phenomenologically viable solution to this question within the framework of a non-abelian flavour symmetry. R-parity is a discrete symmetry, defined as (−1)3B+L+2S , where B and L are the baryonand leptonnumbers and S is the intrinsic spin of a particle [1]. It is +1 for all Standard Model particles and −1 for their superpartners. But neither L nor B is a fundamental symmetry of Nature. But their uncontrolled violation leads to rapid proton decay and speeds up many other physical processes at unwanted rates: these prompted to impose R-parity in canonical supersymmetric theories. However, violating R-parity [2, 3] in a controlled way has rich phenomenological consequences that in recent times have received considerable attention. An attempt to link R-parity violation to the origin of masses and mixings was made in the past by invoking a horizontal U(1)-symmetry where charges dictated by fermion masses and mixings are shown to produce sufficient suppression in R-parity-violating (6 R) couplings [4]. Here we are concerned with a non-abelian flavour symmetry, conjectured first [5] to realise the conventional supersymmetric theory of flavour, generalized now to admit 6 R interactions as well. In addition to maintaining the existing consistencies and predictions [6, 7], our generalization predicts 6 R couplings that are within the level of phenomenological tolerence and lead to detectable signatures. In the present analysis we consider only the L-violating interactions and leave aside the B-violating ones. 2. In a nutshell, flavour-problem in a supersymmetric theory addresses the question as how to relate the flavour structure of the fermions and scalars to each other by the same symmetry principle. An E-mail: [email protected]