Low Energy Tests of Minimal N = 1 Supergravity.

The possibility of obtaining an indirect confirmation of Spontaneously Broken N = 1 Minimal Supergravity Models is considered. On completely general grounds, it is shown that radiative decays, mediated through penguin-like diagrams are expected to exhibit a significant enhancement from the exchange of supersymmetric particles. An interesting example is the decay b to Sgamma which has been studied here in the Standard Model (SM) and Supersymmetry (SUSY). In the SM it is shown that the QCD corrections enhance by more than one order of magnitude the prediction for the BR(b to sgamma ) for m_{rm t} < m_{rm w} . In Supersymmetry it is shown that an upper bound BR(b to sgamma) < 2cdot10 ^{-3}<=ads, for m_ {rm t} ~ 45-80 Gev, to bounds on squarks and gluino masses comparable to the ones coming from the analysis of the missing energy events at the CERN pp collider. Viceversa for supersymmetric masses of about 60 Gev and m_{rm t} ~ 45-80 Gev, an enhancement of one order of magnitude for the SUSY predictions with respect to the SM ones is found even when the SM is QCD corrected. The decay b to s gluon, contributing to the non-charmed strange decays of the B meson, is also studied. For gluino and squark masses of about 60-80 Gev amd m_{rm t} between 50 and 80 Gev a branching ratio as high as 10-30% can be reached. The SUSY contribution to the B_ {rm d}^0 - B_{rm d}^0 mixing is also studied. For squark and gluino masses which respect the bounds coming from the CERN pp collider, the SUSY contribution turns out to be substantially smaller than the corresponding SM predictions. Muon and electron lepton - number nonconservation is also studied in an extension of the supersymmetric SM where light Majorana neutrinos are obtained involving the "seesaw" mechanism. The rates for mu to egamma, mu to eee, and mu + nucleus to e + nucleus are much larger than in the SM and even the present experimental upper bounds impose non trivial constraints on these supersymmetric models: for supersymmetric masses between 80 and 150 Gev, one gets a value for m _sp{nu}{rm D}, the Dirac entry in the neutrino mass matrix, between 10 and 20 Gev.