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Register a new userLinear programming analysis of the $R$-parity violation within EDM-constraints
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The constraint on the $R$-parity violating supersymmetric interactions is discussed in the light of current experimental data of the electric dipole moment of neutron, $^{129}$Xe , $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules. To investigate the constraints without relying upon the assumption of the dominance of a particular combination of couplings over all the rest, an extensive use is made of the linear programming method in the scan of the parameter space. We give maximally possible values for the EDMs of the proton, deuteron, $^3$He nucleus, $^{211}$Rn, $^{225}$Ra, $^{210}$Fr, and the $R$-correlation of the neutron beta decay within the constraints from the current experimental data of the EDMs of neutron, $^{129}$Xe, $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules using the linear programming method. It is found that the $R$-correlation of the neutron beta decay and hadronic EDMs are very useful observables to constrain definite regions of the parameter space of the $R$-parity violating supersymmetry.
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The nature of R-parity violating interactions in two classes of string inspired supersymmetric grand unified theories (SISUSY GUT), based on the gauge groups $SO(10)$ (and its subgroup $SU(2)_Ltimes SU(2)_Rtimes SU(4)_cequiv G_{224}$) as well as $[SU(3)]^3$, are discussed and their strengths are related to the ratio of symmetry breaking scales present in the model. We first argue that for the R-parity violating couplings $lambda_{R!!!/}$ to be suppressed to the desired level, the $B-L$ local symmetry must break at an intermediate scale $M_{B-L}$ since $lambda_{R!!!/} =M_{B-L}/M_{GUT}$. We then construct scenarios where such intermediate scales arise being consistent with gauge coupling unification in a two-loop renormalization group study. In the resulting $SO(10)$ models, higher-dimensional-operator-induced R-parity violating couplings are potentially large (except in one case), and are therefore inconsistent with limits on the proton life time unless the couplings associated with the higher dimensional terms are fine tuned to very small values. However, the $[SU(3)]^3$ and $G_{224}$ models can be consistent if a certain class of quark-lepton coupling in the superpotential is forbidden by a discrete summetry (unrelated to R-parity). An interesting prediction of these models is neutron-anti-neutron oscillation with observable strength.
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