Fritzsch Mass Matrices Research Articles

REAL KM MATRIX AND CABIBBO MATRIX

Fritzsch type of real symmetric 3×3 matrices are chosen. From these matrices the mass matrices relevant to the four-quark cases are deduced. It is also shown that the orthogonal matrices that diagonalize the 3×3 Fritzsch mass matrices also yield the orthogonal matrices that diagonalize the mass matrices corresponding to the four-quark case. The Cabibbo mixing matrix is straightaway obtained from the KM real mixing matrix. An exact expression for the Cabibbo mixing angle is found here. The real KM matrix is reduced to a few parameters, which can be determined from the experiment. The results obtained here are the exact expressions for the KM real matrix.

SU(3) x SU(2) x U(1) model with Fritzsch mass matrices.

Discrete symmetries associated with the roots of unity are employed to construct Fritzsch-type mass matrices for the three generations of fermions in the standard model with SU(3)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1) gauge symmetry. The model requires four conventional Higgs doublets to account for the hierarchy of fermion masses and mixings.

Top quark mass bounds in the hierarchical chiral symmetry-breaking framework

By taking account of recent information on the B d-B̄ d mixing parameter, x d, and the B B ƒ B 2 , as well as uncertainties in the lighter quark masses, we are able to set search limits on the top quark mass of 84±8 GeV for the Fritzsch mass matrices with two Higgs doublets or 78±12 GeV for a modified set of Fritzsch mass matrices with minimal Higgs structure. We comment on the discovery complications involved when the top mass is very close to the W mass. If no top quark is eventually found with mass less than 100–110 GeV, the whole 3-family hierarchical chiral symmetry-breaking framework proposed by Fritzsch is ruled out.

Nearest-neighbor interactions and the physical content of Fritzsch mass matrices.

We show that in the standard model with fewer than five generations, starting with arbitrary Yukawa couplings, it is always possible to find a weak basis where the quark mass matrices have the nearest-neighbor interaction form. Therefore, for three or four generations, the zeros of the Fritzsch mass matrices are not a contrived feature of the Fritzsch /ital Ansatz/, but just a special choice of weak basis.

Nonlinear evolution of the three-family Fritzsch mass matrices

Renormalization of the Fritzsch mass matrices is studied to compare the predictions of the ansatz imposed at a high scale with low energy data. The evolution effects are expected to be moderate, but their impact can be compared with rather precise mixing data. The viability of the Fritzsch model is found to be little changed by renormalization: with standard Higgs structure it remains marginally acceptable, but with two Higgs doublets and a charged Higgs mass ⋍ 50 GeV, agreement with KM mixings and B- B mixings is retained with a slightly lowered top mass of ⋍90 GeV. Remarks concerning the four-family extension imply that the renormalization effects are very significant and can not be ignored.

Testing the Fritzsch quark mass matrices with the invariant function approach

The invariant function approach using projection operator techniques is applied to the Fritzsch mass matrices to calculate exactly the absolute squares of the Kobayashi-Maskawa matrix elements and the invariant J-value associated with CP violation. The overlap of the experimentally allowed annular KM region and the B d 0- B d 0 band in the Ø B' versus m t plane is small but consistent with a light strange quark and heavy top quark with mass, m t pphys ∼ 100 GeV. Mixing in the B s 0- B s 0 channel is predicted to be nearly complete, and the amplitude for the ( b → u) ( b → c transition is calculated to be about 0.06.

Implications of the E6SU

Besides the ordinary 27-multiplet fermions in the usual ${\mathrm{E}}_{6}$ grand unified theories, two superheavy 27-multiplet fermions are added to form the ${\mathrm{E}}_{6}$\ifmmode\times\else\texttimes\fi{}SU(3${)}_{\mathrm{H}}$ model. After both vertical and horizontal spontaneous symmetry breaking, the Fritzsch mass matrices of the ordinary fermions arise as a result of mixing of the ordinary fermions with the superheavy fermions. The charged-fermion masses and Kobayashi-Maskawa mixing follow as a consequence. The neutrino mass in this model is also discussed.

Fourth-generation quark masses and Fritzsch mass matrices from Abelian family symmetry.

We examine possible mass relations resulting from Fritzsch-type mass matrices for quarks in left-right-symmetric models with an Abelian family symmetry. While the three-generation model predicts no realistic mass relation, six possible schemes exist in the presence of a fourth generation of quarks (t',b'), with realistic constraints on the quark masses. The most attractive scheme predicts (${m}_{b\mathcal{'}}$-${m}_{b}$)(${m}_{t\mathcal{'}}$-${m}_{t}$)\ensuremath{\simeq}(${m}_{\mathrm{sb}}$${m}_{b}$${\mathcal{'}}_{\mathrm{ct}\mathcal{'}}^{13}$@B. When combined with the experimental constraints on the \ensuremath{\rho} parameter, this leads to ${m}_{t}$\ensuremath{\le}68 GeV, ${m}_{b\mathcal{'}}$\ensuremath{\le}46 GeV, and 145 GeV\ensuremath{\le}${m}_{t\mathcal{'}}$\ensuremath{\le}310 GeV.

SO(10)V x SU(3)H model.

The SO(10)/sub V/ x SU(3)/sub H/ model, in which the quark-mass hierarchy is induced through their mixing with horizontal superheavy fermions, is discussed. Fritzsch mass matrices are natural in our model, resulting from the mass matrices of horizontal superheavy up quarks and down quarks closely proportional to each other.

CP-violating Fritzsch mass matrices.

The phase-invariant measure J of CP violation defined by Jarlskog is applied to the Fritzsch mass matrices. Given the hierarchy of masses it is shown that the phases in the matrices do not maximize J. Two recent suggestions for maximal CP violation using the Fritzsch form are compared.

CP violation and Fritzsch mass matrices

We discuss a form for the quark mass matrices which produces maximal weak but no string CP violation. The quark mass matrices are of the Fritzsch type, with all phases equal to multiples of 1 2 π . We show that these matrices can be produced in an SO(10) model with CP violated spontaneously at the GUT scale. The model successfully predicts the entire K-M matrix. Radiative corrections to θ , however, are several orders of magnitude too large in the model, and θ is naturally of O(10 −5).