Extended Friedberg-Lee hidden symmetries, quark masses, and CP violation with four generations
- Physics Department, Technion-Institute of Technology, Haifa 32000 (Israel)
- Theory Group, Brookhaven National Laboratory, Upton, New York 11973 (United States)
Motivated in part by the several observed anomalies involving CP asymmetries of B and B{sub s} decays, we consider the standard model with a 4th sequential family (SM4) which seems to offer a rather simple resolution. We initially assume T-invariance by taking the up and down-quark 4x4 mass matrix to be real. Following Friedberg and Lee (FL), we then impose a hidden symmetry on the unobserved (hidden) up and down-quark SU(2) states. The hidden symmetry for four generations ensures the existence of two zero-mass eigenstates, which we take to be the (u,c) and (d,s) states in the up and down-quark sectors, respectively. Then, we simultaneously break T-invariance and the hidden symmetry by introducing two phase factors in each sector. This breaking mechanism generates the small quark masses m{sub u}, m{sub c} and m{sub d}, m{sub s}, which, along with the orientation of the hidden symmetry, determine the size of CP-violation in the SM4. For illustration we choose a specific physical picture for the hidden symmetry and the breaking mechanism that reproduces the observed quark masses, mixing angles and CP-violation, and at the same time allows us to further obtain very interesting relations/predictions for the mixing angles of t and t'. For example, with this choice we get V{sub td}{approx}(V{sub cb}/V{sub cd}-V{sub ts}/V{sub us})+O({lambda}{sup 2}) and V{sub t{sup '}}{sub b}{approx}V{sub t{sup '}}{sub d}{center_dot}(V{sub cb}/V{sub cd}), V{sub tb{sup '}}{approx}V{sub t{sup '}}{sub d}{center_dot}(V{sub ts}/V{sub us}), implying that V{sub t{sup '}}{sub d}>V{sub t{sup '}}{sub b}, V{sub tb{sup '}}. We furthermore find that the Cabibbo angle is related to the orientation of the hidden symmetry and that the key CP-violating quantity of our model at high energies, J{sub SM4}{identical_to}Im(V{sub tb}V{sub t{sup '}}{sub b}*V{sub t{sup '}}{sub b{sup '}}V{sub tb{sup '}}*), which is the high-energy analogue of the Jarlskog invariant of the SM, is proportional to the light-quark masses and the measured Cabibbo-Kobayashi-Maskawa quark-mixing matrix angles: |J{sub SM4}|{approx}A{sup 3}{lambda}{sup 5}x({radical}(m{sub u}/m{sub t})+{radical}(m{sub c}/m{sub t{sup '}})-{radical}(m{sub d}/m{sub b})+{radical}(m{sub s}/m{sub b{sup '}})){approx}10{sup -5}, where A{approx}0.81 and {lambda}=0.2257 are the Wolfenstein parameters. Other choices for the orientation of the hidden symmetry and/or the breaking mechanism may lead to different physical outcomes. A general solution, obtained numerically, will be presented in a forthcoming paper.
- OSTI ID:
- 21308548
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 1; Other Information: DOI: 10.1103/PhysRevD.80.015011; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Spontaneous CP violation in E{sub 6} supersymmetric grand unified theory with SU(2) flavor and anomalous U(1) symmetries
Relating the long B lifetime to a very heavy top quark