The subgroup structure of grand unified theories with application to the fermion mass matrix in O(10)

1982 ◽  
Vol 8 (3) ◽  
pp. 295-318 ◽  
Author(s):  
G Feldman ◽  
T Fulton ◽  
P T Matthews
Keyword(s):  
Mass Matrix ◽  
Fermion Mass ◽  
Grand Unified Theories ◽  
Subgroup Structure ◽  
Unified Theories ◽  
Fermion Mass Matrix ◽  
O 10

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 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 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.

PredictiveAnsatzfor fermion mass matrices in supersymmetric grand unified theories

1992 ◽  
Vol 45 (11) ◽  
pp. 4192-4200 ◽  
Author(s):  
Savas Dimopoulos ◽  
Lawrence J. Hall ◽  
Stuart Raby
Keyword(s):  
Fermion Mass ◽  
Grand Unified Theories ◽  
Mass Matrices ◽  
Unified Theories

scholarly journals CATEGORIFIED NONCOMMUTATIVE MANIFOLDS

2009 ◽  
Vol 24 (15) ◽  
pp. 2802-2819 ◽  
Author(s):  
R. A. DAWE MARTINS
Keyword(s):  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Tangent Bundle ◽  
Mass Matrix ◽  
Fermion Mass ◽  
Spectral Triples ◽  
Noncommutative Manifolds ◽  
Real Spectral Triples ◽  
Fermion Mass Matrix

We construct a noncommutative geometry with generalised 'tangent bundle' from Fell bundle C*-categories (E) beginning by replacing pair groupoid objects (points) with objects in E. This provides a categorification of a certain class of real spectral triples where the Dirac operator D is constructed from morphisms in a category. Applications for physics include quantization via the tangent groupoid and new constraints on D finite (the fermion mass matrix).

Permutation symmetries and the fermion mass matrix

1982 ◽  
Vol 25 (7) ◽  
pp. 1895-1903 ◽  
Author(s):  
Y. Yamanaka ◽  
H. Sugawara ◽  
S. Pakvasa
Keyword(s):  
Mass Matrix ◽  
Fermion Mass ◽  
Fermion Mass Matrix

STRING-MOTIVATED GRAND UNIFIED THEORIES WITH HORIZONTAL GAUGE SYMMETRY

1994 ◽  
Vol 09 (30) ◽  
pp. 5369-5385 ◽  
Author(s):  
A.A. MASLIKOV ◽  
S.M. SERGEEV ◽  
G.G. VOLKOV
Keyword(s):  
Gauge Symmetry ◽  
Fermion Mass ◽  
Family Symmetry ◽  
Grand Unified Theories ◽  
Higher Dimensional ◽  
Unified Theories ◽  
Low Dimensional ◽  
Diagonal Subgroup ◽  
Higgs Fields ◽  
Level 2

In the framework of four-dimensional heterotic superstring with free fermions, we investigate the rank 8 grand unified string theories (GUST’s) which contain the SU(3) H gauge family symmetry. GUST’s of this type accommodate naturally the three fermion families presently observed and, moreover, can describe the fermion mass spectrum without high-dimensional representations of conventional unification groups. We explicitly construct GUST’s with gauge symmetry G= SU(5) × U(1) ×[ SU(3) × U(1) ]H ⊂ SO (16) in free complex fermion formulation. As the GUST’s originating from Kac-Moody algebras (KMA’s) contain only low-dimensional representations, it is usually difficult to break the gauge symmetry. We solve this problem by taking for the observable gauge symmetry the diagonal subgroup G sym of the rank 16 group G×G ⊂ SO(16) × SO(16) ⊂ E(8)×E(8). Such a construction effectively corresponds to a level 2 KMA, and therefore some higher-dimensional representations of the diagonal subgroup appear. This (due to G×G tensor Higgs fields) allows one to break GUST symmetry down to SU (3c)× U(1) em . In this approach the observed electromagnetic charge Q em can be viewed as a sum of two Q I and Q II charges of each G group. In this case, below the scale where G×G breaks down to G sym the spectrum does not contain particles with exotic fractional charges.

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