Supersymmetry at ordinary energies. Masses and conservation laws

An assessment is made of the general problems encountered in formulating a realistic supersymmetric theory in which the spontaneous breakdown of supersymmetry occurs at ordinary energies accessible to accelerators. As a starting point, three problems are identified in SU(3)×SU(2)×U(1) supersymmetric models with only quark and lepton chiral superfields: the up quarks get no masses, baryon and lepton ($B$ and $L$) conservation are violated by renormalizable and hence unsuppressed interactions, and the scalar counterparts of the quarks and leptons are too light. An interesting SU(3)×SU(2)×U(1) model of Dimopoulos and Georgi that avoids these problems is considered; it is found that this model contains $B$- and $L$-nonconserving effective interactions of dimensionality 5 that lead to proton decay at too rapid a rate. To guarantee natural $B$ and $L$ conservation in effective interactions of dimensionality 4 and 5, it is suggested that the gauge group that describes physics at ordinary energies contains a factor, such as another U(1), in addition to SU(3)×SU(2)×U(1). Such theories do not contain dimension-5 $L$-nonconserving interactions which could produce an observable neutrino mass, but they do allow dimension-6 $B$- and $L$-nonconserving interactions that would lead to proton decay at an observable rate. Supersymmetry is found to constrain the matrix elements for proton decay in a phenomenologically interesting way. A general explanation is given of how such theories naturally avoid the problem of light scalars, as found by Fayet. The formalism is used to derive general approximate mass relations for the scalar superpartners of the quarks and leptons. The problem of anomalies in the new U(1) current is considered, and one attractive scheme for avoiding them is offered, in which the anomalies cancel for precisely three generations of quarks and leptons.