Peter Kaus

A BCS QUARK MASS MATRIX

The quark mass gap and quark mass hierarchy is obtained by introducing a BCS interaction among ur-quarks. A 3×3 quark mass matrix with equal matrix elements, i.e., with all ur-flavors interacting with the same strength, has eigenvalues 0, 0 and 3; both the quark charge −1/3 and charge +2/3 systems with one heavy quark and two almost massless quarks resemble these eigenvalues. The physical mass splittings between the two lightest quarks come from higher-order corrections to the mass matrix which are obtained by fitting the Kobayashi-Maskawa matrix VKM.

ON NEUTRINO MASSES AND LEPTONIC MIXING

Using recent data on neutrino oscillations, we argue that a hierarchical solution for neutrino masses in a three-family context is possible, and that the masses of the and ? neutrinos are very nearly determined within that possibility. We also examine the predictions of a model that determines neutrino and charged lepton mass matrices as well as its consistency with data.

Neutrino mass matrix and hierarchy

We build a model to describe neutrinos based on strict hierarchy, incorporating as much as possible, the latest known data, for Δ_sol and Δ_atm and for the mixing angles determined from neutrino oscillation experiments, including that from KamLAND. Since the hierarchy assumption is a statement about mass ratios, it lets us obtain all three neutrino masses. We obtain a mass matrix, M_ν and a mixing matrix, U, where both M_ν and U are given in terms of powers of Λ, the analog of the Cabibbo angle λ in the Wolfenstein representation, and two parameters, ρ and k, each of order one. The expansion parameter, Λ, is defined by Λ^2 = m_2/m_3 = √(Δ_sol/Δ_atm) ≈ 0.16, and ρ expresses our ignorance of the lightest neutrino mass m_l, (m_1 = ρ(Λ^4)m_3), while k scales s_13 to the experimental upper limit, s_13 = k(Λ^2)≈ 0.16k. These matrices are similar in structure to those for the quark and lepton families, but with Λ about 1.6 times larger than the λ for the quarks and charged leptons. The upper limit for the effective neutrino mass in double β-decay experiments is 4 × 10^(–3)eV if s_13 = 0 and 6 × 10^(–3)eV if s_13 is maximal. The model, which is fairly unique, given the hierarchy assumption and the data, is compared to supersymmetric extension and texture zero models of mass generation.

Neutrino masses and mixing from hierarchy and symmetry

We construct a model that allows us to determine the three neutrino masses directly from the experimental mass squared differences,

Test of the α-expansion method for extracting the hadronic spectrum in QCD: The harmonic oscillator☆

\Delta_{\rm atm}

Possible adaptive values of the resonant slave in biological clocks.

and

On neutrinos and fermionic mass patterns

\Delta_{\rm sol}

BCS Mass Matricesa

, together with the assumption that

An approximation method for bound states in quantum chromodynamics

\Lambda = \surd (1/6) = \surd (m_2/m_3)

Experimental and theoretical high energy physics. Progress report 1 Oct 1979 to 30 Sep 1980

. The parameter,