Mass matrices for quarks and leptons in triangular form

TL;DR

This paper explores the structure of quark and lepton mass matrices assuming an upper triangular form, fitting experimental data to determine matrix elements and making predictions for neutrino masses under specific simplifying assumptions.

Contribution

It introduces a universal zero element assumption in all mass matrices and applies SU(5) motivated relations to reduce free parameters, providing new solutions consistent with experimental data.

Findings

Solutions with small off-diagonal mixing elements were found.

The lepton sector imposes more restrictive conditions than the quark sector.

Predictions for neutrino masses were derived from the fit.

Abstract

We assume that all quark and lepton mass matrices have upper triangular form. Using all available experimental data on quark and lepton masses and mixing angles we make a fit in which we determine mass matrices elements. There are too many free parameters and our solutions are not uniqe. We look for solutions with small non diagonal mixing matrix elements. In order to reduce the number of free parameters we assume that the matrix element $(M)_{13}$ vanishes in \underline{all} mass matrices. Such universal assumption was drown from considering different numerical solutions. The lepton sector, due to large mixing angles and very small errors for charged lepton masses, is more restrictive then quark sector. We present the solution in this case. The absolute values of neutrino masses are not fixed. The another possibility of reducing number of free parameters was considered by us before. With the additional assumption motivated by SU(5) symmetry which connects mixing in right handed down quarks with left handed charged leptons we get a solution in which observed Cabibbo-Kobayashi-Maskawa mixing for quarks comes mainly from non diagonal terms in up quark mass matrix. From the fit we get also predictions for neutrino masses.