Does anyone have any good introduction to theories of the quark and lepton mass matrices? Theories like textures and horizontal symmetry. My understanding of research into textures is that it often involves trying to make zero as many entries as possible in the mass matrices. Is that a fair statement?(adsbygoogle = window.adsbygoogle || []).push({});

Though the quarks have a rather strong mass hierarchy, their mixing matrix, the Cabibbo–Kobayashi–Maskawa matrix is close to the identity matrix.

The charged leptons also have a rather strong mass hierarchy, and likely also the neutrinos. However, the lepton mixing matrix, the Pontecorvo–Maki–Nakagawa–Sakata matrix, is rather far from the identity matrix.

Part of the reason for the difference may be that the neutrinos' masses may be due to a [http://en.wikipedia.org/wiki/Seesaw_mechanism seesaw mechanism]. In its simplest form, right-handed neutrinos have Majorana masses close to GUT energy scales, while left-handed and right-handed ones are coupled by Higgs-generated Dirac masses, like the charged leptons and the quarks.

So all the Dirac mass matrices could be nearly orthogonal, while the right-handed-neutrino mass matrix could be far from orthogonal to them.

GUT's? The Georgi-Glashow SU(5) GUT is the simplest, and its only mass-matrix constraint is for down-like quarks and charged leptons to have equal mass matrices. Strictly speaking, couplings to the Higgs particle.

SO(10)?Allthe Higgs couplings are equal, and right-handed neutrinos cannot have a Majorana mass. Thus,allthe mass matrices are orthogonal, making mass unification too successful. The non-orthogonality and the Majorana masses must come from symmetry breaking.

Its supersets, like E6, also have that problem.

Are there any halfway-simple symmetry-breaking scenarios that can start with SO(10) or E6 and get the Standard Model's masses and mixing? It may be asking too much to ask for something as simple as the Standard-Model Higgs mechanism, I will concede.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quark and Lepton Mass Matrices, Textures, Horizontal Symmetries

**Physics Forums | Science Articles, Homework Help, Discussion**