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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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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Bodenstein, S., Bordes, J., Dominguez, C. A., Peñarrocha, J., & Schilcher, K. (2012). Bottom-quark mass from finite energy QCD sum rules. Phys. Rev. D, 85(3), 034003–5pp.
Abstract: Finite energy QCD sum rules involving both inverse-and positive-moment integration kernels are employed to determine the bottom-quark mass. The result obtained in the (MS) over bar scheme at a reference scale of 10 GeV is m (m) over bar (b)(10 GeV) = 3623(9) MeV. This value translates into a scale-invariant mass (m) over bar (b)((m) over bar (b)) = 4171(9) MeV. This result has the lowest total uncertainty of any method, and is less sensitive to a number of systematic uncertainties that affect other QCD sum rule determinations.
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Baker, M. J., Bordes, J., Hong-Mo, C., & Tsun, T. S. (2013). On the corner elements of the CKM and PMNS matrices. EPL, 102(4), 41001–6pp.
Abstract: Recent experiments show that the top-right corner element (U-e3) of the PMNS matrix is small but nonzero, and suggest further via unitarity that it is smaller than the bottom-left corner element (U-tau 1). Here, it is shown that if to the assumption of a universal rank-one mass matrix, long favoured by phenomenologists, one adds that this matrix rotates with scale, then it follows that A) by inputting the mass ratios m(c)/m(t), m(s)/m(b), m(mu)/m(tau), and m(2)/m(3), i) the corner elements are small but nonzero, ii) V-ub < V-td, U-e3 < U-tau 1, iii) estimates result for the ratios V-ub/V-td and U-e3/U-tau 1, and B) by inputting further the experimental values of V-us, V-tb and U-e2, U-mu 3, iv) estimates result for the values of the corner elements themselves. All the inequalities and estimates obtained are consistent with present data within expectation for the approximations made.
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Bodenstein, S., Bordes, J., Dominguez, C. A., Peñarrocha, J., & Schilcher, K. (2011). QCD sum rule determination of the charm-quark mass. Phys. Rev. D, 83(7), 074014–4pp.
Abstract: QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the (MS) over bar scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form p(s) = 1 -(s(0)/s)(2), where s(0) is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range s similar or equal to 20-25 GeV2. This feature leads to a substantial reduction in the sensitivity of the results to changes in s(0), as well as to a much reduced impact of the experimental uncertainties in the higher resonance region. The value obtained for the charm-quark mass in the (MS) over bar scheme at a scale of 3 GeV is (m) over bar (c)(3 GeV) = 987 +/- 9 MeV, where the error includes all sources of uncertainties added in quadrature.
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