Using Dark Matter as a Guide to extend Standard Model: Dirac Similarity Principle and Minimum Higgs Hypothesis

Abstract

We introduce the "Dirac similarity principle" that states that only those point-like Dirac particles which can interact with the Dirac electron can be observed, such as in the Standard Model. We emphasize that the existing world of the Standard Model is a Dirac world satisfying the Dirac similarity principle and believe that the immediate extension of the Standard Model will remain to be so. On the other hand, we are looking for Higgs particles for the last forty years but something is yet to be found. This leads naturally to the "minimum Higgs hypotheses". Now we know firmly that neutrinos have tiny masses, but in the minimal Standard Model there is no natural sources for such tiny masses. If nothing else, this could be taken as the clue as the signature of the existence of the extra heavy $Z^{\prime 0}$ since it requires the extra Higgs field, that would help in generating the neutrino tiny masses. Alternatively, we may have missed the right-hand sector for some reason. A simplified version of the left-right symmetric electroweak model has the simplest Higgs sector (in which there is one standard left-hand Higgs doublet together with the image right-handed Higgs doublet), of which the Higgs sector also satisfies the "minimum Higgs hypothesis". Or, if we question the origin of the family symmetry, we may consider to enlarge it to the family gauge symmetry. It transpires very feeble family interactions. All the above possibilities satisfy both the so-called "Dirac similarity principle", the "minimum Higgs hypothesis", and renormalizability.