General issues connecting flavor symmetry and supersymmetry

We motivate and construct supersymmetric theories with continuous flavor symmetry, under which the electroweak Higgs doublets transform non-trivially. Flavor symmetry is spontaneously broken at a large mass scale in a sector of gauge-singlet fields; the light Higgs multiplets naturally emerge as special linear combinations that avoid acquiring the generic large mass. Couplings of the light Higgs doublets to light moduli fields from the singlet sector could lead to important effects in the phenomenology of the Higgs sector.     

A model for weak trimuon production

Neutrino-induced trimuon events have been interpreted by several authors as arising from cascade decay of a new lepton produced directly in neutrino reactions. We incorporate this idea in a gauge scheme based on the group Su(2) × SU(2) × U(1).     

Inequivalent embeddings of SU(2) and instanton interactions

The fact that SU(2) allows inequivalent embeddings inside larger groups is shown to have some consequences for the interaction of instantons.     

Diastereoselective Pictet-Spengler condensation of tryptophan with α-amino aldehydes as chiral carbonyl components

The Pictet-Spengler reaction of Trp with α-amino aldehydes derived from l and d-amino acids was studied in terms of double stereodifferentiation. The results observed for d-amino aldehydes represent ‘matched’ situation (one diastereoisomer was formed) whereas with l-amino aldehydes ‘mismatched’ (two diastereoisomers were formed). The conformation of newly formed six-membered ring was analyzed. It was found that stable conformers were different for cis and trans isomers.     

Non-uniqueness of gauge-field potentials

Two sets of phenomena peculiar to non-Abelian gauge theories are illustrated. The first concerns the existence of nonsingular potentials which generate the same field strength without being gauge-equivalent; a necessary condition for this ambiguity is obtained. The second exhibits the insufficiency of the cyclic identity in determining field strength-potential relations.     

Elementary examples of baryon number generation

Elementary examples are provided of reaction rate matrices satisfying the constraints of unitarity and CPT invariance, which can lead a system with baryon number initially zero to evolve toward non-zero baryon number. The importance of the unitarity constraint is emphasized.