1306.4113 (Bruno Machet)

Unlocking the Standard Model. IV. N=2 generations of quarks : spectrum
and mixing    [PDF]

Bruno Machet

The Glashow-Salam-Weinberg model for 2 generations of quarks is extended to 8 composite Higgs multiplets, with no adjunction of extra fermions. It is the minimal number of Higgs doublets required to suitably account, simultaneously, for the spectrum of pseudoscalar mesons that can be built with 4 quarks and for the mass of the W gauge bosons. These masses being used as input, together with elementary low energy considerations for the pions, we calculate all other parameters, masses and couplings. We focus in this work on the spectrum of the 8 Higgs bosons (which all potentially contribute to the W and quark masses), and on the mixing (Cabibbo) angle, leaving the study of couplings to a subsequent work. The Higgs bosons fall into one triplet, two doublets and one singlet. In the triplet stand three states with masses \sqrt{2} x that of heaviest pseudoscalar meson D_s, which, for 2 generations, pushes them up to 2.80 GeV. The 2 components of the first doublet have masses close to 1.25 GeV. The singlet has a mass of 19 MeV and the two members of the second doublet only get masses through quantum corrections. That the mass of (at least) one of the Higgs bosons grows like that of the heaviest \bar q \gamma_5 q bound state is a hint that calls for a third generation of quarks. Hierarchies between vacuum expectation values, which are large for 1 generation, become much smaller for 2 generations. Some orthogonality relations between neutral pseudoscalar mesons still fail to be satisfied; it looks however a reasonable bet that the situation will improve with 3 generations. Symmetries and their breaking are investigated in detail, in particular the chiral group SU(2)_L x SU(2)_R, and a second similar group, orthogonal to the first, the diagonal part of which flips the generations of quarks. At the level of composite quark operators, this last group moves inside the 8-dimensional space of Higgs multiplets and the generators of U(1)_L or U(1)_R are parity-switching operators. Mixing is fairly well described, both in terms of charged pseudoscalar masses and in terms of quark masses by the two formulas (1/m_{K^+}^2 -1/m_{D^+}^2) / (1/m_{\pi^+}^2 -1/m_{D_s^+}^2) = \tan^2\theta_c = (|m_d|+m_u) / (m_s-m_u), that we demonstrate. The mixing angle may however exhibit a dual behavior: while the formulas written above cast \theta_c quite close to the value of the Cabibbo angle measured with bosonic asymptotic states, this value turns out to also fall in the close neighborhood of a pole of the non-diagonal d-$ mass term that arises from the Yukawa Lagrangian, corresponding to a quasi-maximal "fermionic mixing angle".

View original: http://arxiv.org/abs/1306.4113