scholarly journals DEVELOPING THE FRAMED STANDARD MODEL

2012 ◽  
Vol 27 (17) ◽  
pp. 1250087 ◽  
Author(s):  
MICHAEL J. BAKER ◽  
JOSÉ BORDES ◽  
HONG-MO CHAN ◽  
TSOU SHEUNG TSUN
Keyword(s):  
Standard Model ◽  
Mass Matrix ◽  
Higgs Field ◽  
Fermion Mass ◽  
Ckm Matrix ◽  
Changing Scale ◽  
Rank One ◽  
Distinguishing Features ◽  
Fermion Mass Matrix

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 μ, (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.

scholarly journals A first test of the framed standard model against experiment

2015 ◽  
Vol 30 (11) ◽  
pp. 1550051 ◽  
Author(s):  
José Bordes ◽  
Hong-Mo Chan ◽  
Sheung Tsun Tsou
Keyword(s):  
Standard Model ◽  
Mass Matrix ◽  
Internal Symmetry ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Order Unity ◽  
Changing Scale ◽  
The Standard Model ◽  
Symmetry Space ◽  
Fermion Mass Matrix

The framed standard model (FSM) is obtained from the standard model by incorporating, as field variables, the frame vectors (vielbeins) in internal symmetry space. It gives the standard Higgs boson and 3 generations of quarks and leptons as immediate consequences. It gives moreover a fermion mass matrix of the form: m = mTαα†, where α is a vector in generation space independent of the fermion species and rotating with changing scale, which has already been shown to lead, generically, to up–down mixing, neutrino oscillations and mass hierarchy. In this paper, pushing the FSM further, one first derives to 1-loop order the RGE for the rotation of α, and then applies it to fit mass and mixing data as a first test of the model. With 7 real adjustable parameters, 18 measured quantities are fitted, most (12) to within experimental error or to better than 0.5 percent, and the rest (6) not far off. (A summary of this fit can be found in Table 2 of this paper.) Two notable features, both generic to FSM, not just specific to the fit, are: (i) that a theta-angle of order unity in the instanton term in QCD would translate via rotation into a Kobayashi–Maskawa phase in the CKM matrix of about the observed magnitude (J ~ 10-5), (ii) that it would come out correctly that mu < md, despite the fact that mt ≫ mb, mc ≫ ms. Of the 18 quantities fitted, 12 are deemed independent in the usual formulation of the standard model. In fact, the fit gives a total of 17 independent parameters of the standard model, but 5 of these have not been measured by experiment.

scholarly journals A SOLUTION TO THE STRONG CP PROBLEM TRANSFORMING THE THETA ANGLE TO THE KM CP-VIOLATING PHASE

2010 ◽  
Vol 25 (32) ◽  
pp. 5897-5911 ◽  
Author(s):  
JOSÉ BORDES ◽  
HONG-MO CHAN ◽  
SHEUNG TSUN TSOU
Keyword(s):  
Mass Matrix ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Order Unity ◽  
Ckm Matrix ◽  
Cp Violations ◽  
Fermion Mass Matrix

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 θ 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.

scholarly journals A COMPREHENSIVE MECHANISM REPRODUCING THE MASS AND MIXING PARAMETERS OF QUARKS AND LEPTONS

2013 ◽  
Vol 28 (16) ◽  
pp. 1350070 ◽  
Author(s):  
MICHAEL J. BAKER ◽  
JOSÉ BORDES ◽  
HONG-MO CHAN ◽  
SHEUNG TSUN TSOU
Keyword(s):  
Mass Matrix ◽  
Ckm Matrix ◽  
Changing Scale ◽  
Mixing Parameters ◽  
Starting Point ◽  
Rank One ◽  
Experimental Errors ◽  
Experimental Values ◽  
The Right ◽  
The Masses

It is shown that if, from the starting point of a universal rank-one mass matrix long favored by phenomenologists, one adds the assumption that it rotates (changes its orientation in generation space) with changing scale, one can reproduce, in terms of only six real parameters, all the 16 mass ratios and mixing parameters of quarks and leptons. Of these 16 quantities so reproduced, 10 for which data exist for direct comparison (i.e. the CKM elements including the CP-violating phase, the angles θ12, θ13, θ23 in ν-oscillation, and the masses mc, mμ, me) agree well with experiment, mostly to within experimental errors; four others (ms, mu, md, mν2), the experimental values for which can only be inferred, agree reasonably well; while two others (mν1, δ CP for leptons), not yet measured experimentally, remain as predictions. In addition, one gets as bonuses, estimates for (i) the right-handed neutrino mass mνR and (ii) the strong CP angle θ inherent in QCD. One notes in particular that the output value for sin 2 2 θ13 from the fit agrees very well with recent experiments. By inputting the current experimental value with its error, one obtains further from the fit two new testable constraints: (i) that θ23 must depart from its "maximal" value: sin 2 2 θ23 ~ 0.935 ±0.021, (ii) that the CP-violating (Dirac) phase in the PMNS would be smaller than in the CKM matrix: of order only | sin δ CP | ≤ 0.31 if not vanishing altogether.

scholarly journals MASS HIERARCHY, MIXING, CP-VIOLATION AND HIGGS DECAY — OR WHY ROTATION IS GOOD FOR US

2011 ◽  
Vol 26 (13) ◽  
pp. 2087-2124 ◽  
Author(s):  
MICHAEL J. BAKER ◽  
JOSÉ BORDES ◽  
HONG-MO CHAN ◽  
SHEUNG TSUN TSOU
Keyword(s):  
Cp Violation ◽  
Mass Matrix ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Ckm Matrix ◽  
Higgs Decay ◽  
Rank One ◽  
Mixing Patterns ◽  
By Products ◽  
Existing Data

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.

scholarly journals THE DUALIZED STANDARD MODEL AND ITS APPLICATIONS — AN INTERIM REPORT

1999 ◽  
Vol 14 (14) ◽  
pp. 2173-2203 ◽  
Author(s):  
HONG-MO CHAN ◽  
SHEUNG TSUN TSOU
Keyword(s):  
Standard Model ◽  
High Energy ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Matrix Elements ◽  
Ckm Matrix ◽  
High Energy Cosmic Rays ◽  
Perturbative Method ◽  
Ckm Matrix Elements ◽  
Physical Consequences

Based on a non-Abelian generalization of electric–magnetic duality, the Dualized Standard Model (DSM) suggests a natural explanation for exactly three generations of fermions as the "dual colour" [Formula: see text] symmetry broken in a particular manner. The resulting scheme then offers on the one hand a fermion mass hierarchy and a perturbative method for calculating the mass and mixing parameters of the Standard Model fermions, and on the other hand testable predictions for new phenomena ranging from rare meson decays to ultra-high energy cosmic rays. Calculations to one-loop order gives, at the cost of adjusting only three real parameters, values for the following quantities all (except one) in very good agreement with experiment: the quark CKM matrix elements ‖Vrs‖, the lepton CKM matrix elements ‖Urs‖, and the second generation masses mc, ms, mμ. This means, in particular, that it gives near maximal mixing Uμ3 between νμ and ντ as observed by SuperKamiokande, Kamiokande and Soudan, while keeping small the corresponding quark angles Vcb, Vts. In addition, the scheme gives (i) rough order-of-magnitude estimates for the masses of the lowest generation, (ii) predictions for low energy FCNC effects such as KL→ eμ, and (iii) a possible explanation for the long-standing puzzle of air showers beyond the GZK cut-off. All these together, however, still represent but a portion of the possible physical consequences derivable from the DSM scheme, the majority of which are yet to be explored.

scholarly journals NEW ANGLE ON THE STRONG CP AND CHIRAL SYMMETRY PROBLEMS FROM A ROTATING MASS MATRIX

2009 ◽  
Vol 24 (01) ◽  
pp. 101-112 ◽  
Author(s):  
JOSÉ BORDES ◽  
HONG-MO CHAN ◽  
TSOU SHEUNG TSUN
Keyword(s):  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Mass Matrix ◽  
Energy Scale ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Quark Masses ◽  
Chiral Transformation ◽  
The Masses ◽  
Fermion Mass Matrix

It is shown that when the mass matrix changes in orientation (i.e. rotates) in generation space for a changing energy scale, the masses of the lower generations are not given just by its eigenvalues. In particular, these masses need not be zero even when the eigenvalues are zero. In that case, the strong CP problem can be avoided by removing the unwanted θ term by a chiral transformation not in contradiction with the nonvanishing quark masses experimentally observed. Similarly, a rotating mass matrix may shed new light on the problem of chiral symmetry breaking. That the fermion mass matrix may so rotate with the scale has been suggested before as a possible explanation for up–down fermion mixing and fermion mass hierarchy, giving results in good agreement with experiment.

scholarly journals The framed Standard Model (I) — A physics case for framing the Yang–Mills theory?

2015 ◽  
Vol 30 (30) ◽  
pp. 1530059
Author(s):  
Hong-Mo Chan ◽  
Sheung Tsun Tsou
Keyword(s):  
Standard Model ◽  
Mass Matrix ◽  
Renormalization Group Equation ◽  
Internal Space ◽  
Group Equation ◽  
Yang Mills ◽  
Changing Scale ◽  
Higgs Decay ◽  
Mass Matrices ◽  
Quantitative Results

Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: the standard Higgs scalar as the framon in the electroweak sector; a global [Formula: see text] symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale [Formula: see text]. From previous work, it is known already that a rotating mass matrix will lead automatically to: CKM mixing and neutrino oscillations, hierarchical masses for quarks and leptons, a solution to the strong-CP problem transforming the theta-angle into a Kobayashi–Maskawa phase. Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter.

scholarly journals Fermion mass hierarchies from modular symmetry

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Simon J.D. King ◽  
Stephen F. King
Keyword(s):  
Standard Model ◽  
Fermion Mass ◽  
Neutrino Masses ◽  
Fermion Fields ◽  
Level 3

Abstract We show how quark and lepton mass hierarchies can be reproduced in the framework of modular symmetry. The mechanism is analogous to the Froggatt-Nielsen (FN) mechanism, but without requiring any Abelian symmetry to be introduced, nor any Standard Model (SM) singlet flavon to break it. The modular weights of fermion fields play the role of FN charges, and SM singlet fields with non-zero modular weight called weightons play the role of flavons. We illustrate the mechanism by analysing A4 (modular level 3) models of quark and lepton (including neutrino) masses and mixing, with a single modulus field. We discuss two examples in some detail, both numerically and analytically, showing how both fermion mass and mixing hierarchies emerge from different aspects of the modular symmetry.

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