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Baker, M. J., Bordes, J., Hong-Mo, C., & Tsun, T. S. (2012). Developing the Framed Standard Model. Int. J. Mod. Phys. A, 27(17), 1250087–45pp.
Abstract: The framed standard model (FSM) suggested earlier, which incorporates the Higgs field and three fermion generations as part of the framed gauge theory (FGT) structure, is here developed further to show that it gives both quarks and leptons hierarchical masses and mixing matrices akin to what is experimentally observed. Among its many distinguishing features which lead to the above results are (i) the vacuum is degenerate under a global su(3) symmetry which plays the role of fermion generations, (ii) the fermion mass matrix is “universal,” rank-one and rotates (changes its orientation in generation space) with changing scale mu, (iii) the metric in generation space is scale-dependent too, and in general nonflat, (iv) the theta-angle term in the quantum chromodynamics (QCD) action of topological origin gets transformed into the CP-violating phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix for quarks, thus offering at the same time a solution to the strong CP problem.
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Baker, M. J., Bordes, J., Hong-Mo, C., & Tsun, T. S. (2011). Mass Hierarchy, Mixing, CP-Violation And Higgs Decay – Or Why Rotation Is Good For Us. Int. J. Mod. Phys. A, 26(13), 2087–2124.
Abstract: The idea of a rank-one rotating mass matrix (R2M2) is reviewed detailing how it leads to ready explanations both for the fermion mass hierarchy and for the distinctive mixing patterns between up and down fermion states, which can be and have been tested against experiment and shown to be fully consistent with existing data. Further, R2M2 is seen to offer, as by-products: (i) a new solution to the strong CP problem in QCD by linking the theta-angle there to the Kobayashi-Maskawa CP-violating phase in the CKM matrix, and (ii) some novel predictions of possible anomalies in Higgs decay observable in principle at the LHC. A special effort is made to answer some questions raised.
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LHCb Collaboration(Aaij, R. et al), Martinez-Vidal, F., Oyanguren, A., Ruiz Valls, P., & Sanchez Mayordomo, C. (2014). Measurement of CP asymmetries in the decays B-0 -> K-*0 mu(+) mu(-) and B+ -> K+ mu(+) mu(-). J. High Energy Phys., 09(9), 177–18pp.
Abstract: The direct CP asymmetries of the decays B-0 -> K-*0 mu(+) mu(-) and B+ -> K+ mu(+) mu(-) are measured using pp collision data corresponding to an integrated luminosity of 3.0 fb(-1) collected with the LHCb detector. The respective control modes B-0 -> J/psi K+ and B+ -> J/psi K+ are used to account for detection and production asymmetries. The measurements are made in several intervals of mu(+)mu(-) invariant mass squared, with the phi(1020) and charmonium resonance regions excluded. Under the hypothesis of zero CP asymmetry in the control modes, the average values of the asymmetries are A(CP)(B-0 -> K-*0 mu(+) mu(-) and B+ -> K+ mu(+) mu(-)) = -0.035 +/- 0.024 +/- 0.003, A(CP)(B+ -> K+ mu(+) mu(-) = 0.012 +/- 0.017 +/- 0.001, where the first uncertainties are statistical and the second are due to systematic effects. Both measurements are consistent with the Standard Model prediction of small CP asymmetry in these decays.
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LHCb Collaboration(Aaij, R. et al), Martinez-Vidal, F., Oyanguren, A., Ruiz Valls, P., & Sanchez Mayordomo, C. (2015). First measurement of the differential branching fraction and CP asymmetry of the B-+/- -> pi(+/-)mu(+/-)mu(-) decay. J. High Energy Phys., 10(10), 034–21pp.
Abstract: The differential branching fraction with respect to the dimuon invariant mass squared, and the CP asymmetry of the B-+/- -> pi(+/-)mu(+/-)mu(-) decay are measured for the first time. The CKM matrix elements vertical bar V-td vertical bar, and vertical bar V-ts vertical bar, and the ratio vertical bar V-td/V-ts vertical bar are determined. The analysis is performed using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb(-1), collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The total branching fraction and CP asymmetry of B-+/- -> pi(+/-)mu(+/-)mu(-) decays are measured to be B(B-+/- -> pi(+/-)mu(+/-)mu(-)) = (1.83 +/- 0.24 +/- 0.05) x 10(-8) and A(cp)(B-+/- -> pi(+/-)mu(+/-)mu(-)) = -0.11 +/- 0.12 +/- 0.01, where the first uncertainties are statistical and the second are systematic. These are the most precise measurements of these observables to date, and they are compatible with the predictions of the Standard Model.
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Bordes, J., Chan, H. M., & Tsun, T. S. (2010). A solution to the strong CP problem transforming the theta angle to the KM CP-violating phase. Int. J. Mod. Phys. A, 25(32), 5897–5911.
Abstract: It is shown that in the scheme with a rotating fermion mass matrix (i.e. one with a scale-dependent orientation in generation space) suggested earlier for explaining fermion mixing and mass hierarchy, the theta angle term in the QCD action of topological origin can be eliminated by chiral transformations, while giving still nonzero masses to all quarks. Instead, the effects of such transformations get transmitted by the rotation to the CKM matrix as the KM phase giving, for theta of order unity, a Jarlskog invariant typically of order 10(-5), as experimentally observed. Strong and weak CP violations appear then as just two facets of the same phenomenon.
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