R-Symmetry in the Minimal Supersymmetric Standard Model and Beyond with Several Consequences

The supersymmetric sector of minimal supersymmetric standard model (MSSM) possesses a U(1) R-symmetry which contains Z2 matter parity. Non-zero neutrino masses, consistent with a ‘redefined’ R-symmetry, are possible through the see-saw mechanism and/or a pair of superheavy (mass M) SU(2)L triplets with vev ∼ M 2 W /M . If this R-symmetry is respected by the higher order terms, then baryon number conservation follows as an immediate consequence. In the presence of right handed neutrinos, the observed baryon asymmetry of the universe arises via leptogenesis. An interplay of Rand Peccei-Quinn symmetry simultaneously resolves the strong CP and μ problems. [email protected] [email protected] Although quite compelling, the minimal supersymmetric standard model (MSSM) fails to address a number of important challenges. For instance, to explain the apparent stability of the proton, it must be assumed that the dimensionless coefficients accompanying dimension five operators are of order 10 or less. The strong CP and μ problems loom large in the background, and the observed baryon asymmetry, it appears, cannot be explained within the MSSM framework. Last, but by no means least, there is increasing evidence for non-zero neutrino masses from a variety of experiments. In a recent paper [1], we offered one approach for resolving many of the above problems. It relied on extending the gauge symmetry to SU(2)L×SU(2)R×U(1)B−L , with a global U(1) R-symmetry playing an essential role. The magnitude of the supersymmetric μ term of MSSM was directly related to the gravitino mass m3/2 (∼ 1 TeV) which, in turn, arises from the hidden sector a la supergravity. The left-right symmetry ensures the presence of right handed neutrino superfields and consequently non-zero neutrino masses, while the R-symmetry implies an accidental global U(1)B symmetry which explains why the proton is so stable. Note that the R-symmetry is spontaneously and perhaps even explicitly broken by the hidden sector. The soft (quadratic and trilinear) supersymmetry breaking terms in the visible sector are expected to explicitly break the R-symmetry. In this paper, we wish to provide a resolution of the problems listed above without departing from the SU(3)c×SU(2)L ×U(1)Y framework of MSSM. We observe that the MSSM superpotential W possesses a global U(1) R-symmetry [2] in which Z2 matter parity is embedded. We show how neutrino masses can be incorporated while preserving a (redefined) R-symmetry. When extended to higher orders, this symmetry ensures the appearance of global U(1)B, thereby guaranteeing proton stability. In the case where right handed neutrinos are included, the observed baryon asymmetry of the universe can arise, as we will see, via leptogenesis. The approach followed here also provides the framework for an elegant resolution of the strong CP and μ problems of MSSM, with the R-symmetry once again playing an essential role. The MSSM superpotential W contains the following renormalizable terms (we will not distinguish between the generations in this paper): HQU , HQD, HLE, HH . (1)