1 research outputs found
On the origin of families of fermions and their mass matrices
We are proposing a new way of describing families of quarks and leptons,
using the approach unifying all the internal degrees of freedom, proposed by
one of us. Spinors, living in d(=1+13)-dimensional space, carry in this
approach only the spin and interact with only the gravity through vielbeins and
two kinds of the spin connection fields - the gauge fields of the Poincare
group and the second kind of the Clifford algebra objects. All the quarks and
the leptons of one family appear in one Weyl representation of a chosen
handedness of the Lorentz group, if analyzed with respect to the Standard model
gauge groups: the right handed (with respect to SO(1,3)) weak chargeless quarks
and leptons and the left handed weak charged quark and leptons. A part of the
starting Lagrange density of a Weyl spinor in d=1+13 transforms right handed
quarks and leptons into left handed quarks and leptons manifesting as the
Yukawa couplings of the Standard model. The second kind of Clifford algebra
objects generates families and contributes to diagonal and off diagonal Yukawa
couplings. The approach predicts an even number of families, treating leptons
and quarks equivalently. In this paper we investigate within this approach the
appearance of the Yukawa couplings within one family of quarks and leptons as
well as among the families (without assuming any Higgs fields). We present the
mass matrices for four families and investigate whether our way of generating
families might explain the origin of families of quarks and leptons as well as
their observed properties - the masses and the mixing matrices. Numerical
results are presented in the paper following this one.Comment: 34 pages, Revtex