The phenomenological predictions of Fritzsch-type quark mass matrices and the underlying structure of particle physics beyond the standard model

Abstract

The phenomenological predictions of Fritzsch-type quark mass matrices and their implications on the underlying structure of particle physics beyond the standard model are considered. Using a recent analysis on the K-M mixing matrix from the b-quark lifetime etc., R b ≡ Γ( b → ue ν)/Γ( b → ce ν) is predicted to be in the range 1.44 × 10 −3 ⩽ R b ⩽ 1.87 × 10 −2, while the present upper bound on R b is 5 × 10 −2. For B K=0.33, obtained by Donoghue et al. using current algebra and the measured ΔI = 3/2 contribution to k → ππ, the physical ( constituent) mass of the t-quark (for Λ MS = 100 MeV ) is predicted to be (73.5 ± 8.5) GeV and so the t-quark will not be found in PETRA and LEP experiments. For the same value of B K, our predictions on the value of R b, | V cb|, and the CP violating phase δ′ in the K-M mixing matrix are 0.79 × 10 −2 ⩽ R b ⩽ 1.01 × 10 −2, 0.066 ⩽ | V cb| 0.070, 85.6° ⩽ δ′ ⩽ 97.4°, and are subject to future experiments. Our predicted value of δ′ (which is independent of experimental input from CP violating phenomena) is in good agreement with the CP violation strength parameter Re ϵ and strongly supports the validity of the Fritszch form of quark mass matrices. It is conjectured that the underlying structure of particle physics is such that the two fundamental phases, σ and τ, that appear in the weak charged current mixing matrix, are equal to − π/2, corresponding to maximal CP violation in the weak interaction sector. This, together with the predicted value of the t-quark mass, can be used as a guide in future model building ( σ = τ = − π/2 can be achieved by the phases of the VEVs of complex Higgs fields). The dependence of our results on the quark mass ratios is considered and a large mass scale for light quarks (u, d, s) is shown to be inconsistent with the Fritzsch form of quark mass matrices. Measurement of the value of R b at CLEO and CUSB and improved determination of | V cb| will be the best tests of the validity of Fritzsch-type quark mass matrices in the near future.