Fundamental fermion masses from deformed SUq(2) triplets

Abstract

A spectrum-generating q-algebra, within the framework of SUq(2), as firstly suggested by Iachello, is studied in order to describe the mass spectrum of three generations of quarks and leptons. The SUq(2) quantum group is a q-deformed extension of SU(2), where q = ea (with α real) is the deformation parameter. In this work, the essential use of inequivalent representations of SUq(2) is introduced. The inequivalent representations are labelled by (j, v0), where j = 0, 1/2, 1, ... and v0 is a positive real number. A formula for the fermion masses Mm(j, v0), with -j ≤ m ≤ j is derived. As an example, a possible scheme which corresponds to two triplets (j = 1) associated to up and down quarks is presented here in some detail. They are associated to different values of the deformation parameter, indicating a dependence of the charge Q on the parameter α. The masses of the charged leptons are treated in a similar way. The current results show that some mass relations for quarks and leptons found in the literature can be considered as approximations of the equations obtained in the j = 1 representations. The breaking of SUq(2) necessary to describe the Cabibbo-Kobayashi-Maskawa (CKM) flavor mixing is briefly discussed.