New Limits on R–Parity Breakings in Supersymmetric Standard Models

New limits on couplings λjk , which break both the baryon number and the R–parity, are derived by using a new mechanism that contributes to the neutronanti-neutron oscillation. The constraints due to proton decay and its potential phenomenology are also reexamined. The minimal supersymmetric standard model (MSSM) [1] has been widely considered as a leading candidate for new physics beyond Standard Model. However, unlike the Standard Model, additional symmetry, called R–parity defined as (−1) , has to be imposed on the minimal supersymmetric extensions of Standard Model (MSSM) in order to avoid renormalizable interactions which violate the lepton and baryon numbers. It is in fact one of the main theoretical weakness of these models because the conservation of R-parity is an ad hoc imposition without fundamental theoretical basis. Therefore, it is interesting to ask how small these R-parity breaking couplings have to be by investigating the phenomenological constraints on them if they are indeed added to the MSSM [2]. The most general renormalizable R-violating superpotential using only the MSSM superfields is W = λkijLiLjĒk + λ ′ ijkLiQjD̄k + λ i jk ŪiD̄jD̄k . (1) Here, i, j, k are generation indices and we have rotated away a term of the form μijLiHj. The couplings λij must be antisymmetric in flavor, λ k ij = −λ k ji. Similarly, λ i jk ′′ = −λkj . There are 36 lepton number non-conserving couplings (9 of the λ type and 27 of the λ type) and 9 baryon number non-conserving couplings (all of the λ type) in Eq.(1). To avoid rapid proton decay, it is usually assumed in the literature that λ, λ type couplings do not coexist with λ type couplings. We make the same assumption here and consider constraints on λ couplings only. The constraints on λ and λ couplings [3] have been discussed quite extensively in the literature. We discuss a new set of constraints on λ due to their contributions to the neutron-anti-neutron oscillation (NANO) through a new mechanism. In addition, we wish to emphasize that couplings of λ type cannot give rise to the proton decay only when the proton is the lightest particle with (−) = + and (−) = −. If there are lighter fermions with (−) = +, such as lightest neutralino or gravitino, the proton can in principle decay into them. In that case strong constraint on λ can be derived and, if they indeed give the leading contributions to the proton decay, it will greatly affect the leading proton decay mode. There are many existing constraints on the 9 different λ couplings, λbs , λbd , λsd , λbs , λbd , λsd , λbs , λbd ′′ and λsd . First of all, one can show [4, 5] that the requirement of perturbative unification typically places a bound of order one on many of the couplings. A potential constraint on |λsd | due to neutron-anti-neutron oscillation was discussed in