Natural Flavor Conservation Research Articles

SpontaneousCPviolation in SU(5) and proton decay

A minimal model of spontaneous CP violation and natural flavor conservation is presented in the context of the standard SU(5) grand unification. Some of its main features are analyzed, with special emphasis on implications for proton decay. A salient feature of the model is the fact that all vector-gauge-boson interactions are CP conserving. As a result of the gauge hierarchy, the interactions of the baryon-number-violating color triplets of Higgs bosons are also CP conserving, leading to no CP violation in proton decay.

Natural flavour conservation and generalized Cabibbo mixing in left-right symmetric models

Abstract Natural flavour conservation is ensured in left-right symmetric models based on SU(2) L ⊗ SU(2) R ⊗ U(1) with a proper choice of the Higgs content. By assuming spontaneous P and CP violation, this leads to specific, and reasonable, predictions for the generalized Cabibbo angles in the three-generation case.

Natural flavor conservation

It is shown that the fiats of natural flavor conservation for an arbitrary U(1)-unbroken gauge theory require that all quarks of a given charge and helicity transform identically under the gauge group.

SpontaneousCPnonconservation and natural flavor conservation: A minimal model

A minimal model based on the standard SU(2)\ifmmode\times\else\texttimes\fi{}U(1) gauge theory, with spontaneous $\mathrm{CP}$ violation and natural flavor conservation, is presented in some detail. In particular it is shown that one on the minima of the classical Higgs potential leads to spontaneous $\mathrm{CP}$ breaking. The generalized Cabibbo-type matrix is real and there is no $\mathrm{CP}$ violation in the manner of Kobayashi-Maskawa. The $\mathrm{CP}$ nonconservation is entirely due to Higgs-boson exchange, and can be characterized by a single phase for an arbitrary number of quark generations.

SpontaneousCPNonconservation in Theories with More Than Four Quarks

It is shown that the requirements of spontaneous CP breaking and natural flavor conservation lead to a class of theories where CP nonconservation is due solely to Higgs exchange, for an arbitrary number of fermion generations.

The concrete realization of the symmetries responsible for natural-flavour conservation laws

We propose and exploit a procedure which leads to the construction of the symmetries (K-symmetries) responsible for « natural » flavour conservation in Higgs-induced neutral processes in extended Weinberg-Salam models. We display a large class of examples of continuous and discreteK-symmetries concerning any number of fermion generations. A sufficient condition in order to avoid degenerate fermion masses is also proved.

Natural flavor conservation in Higgs induced neutral currents and the quark mixing angles

We present the complete characterization of horizontal symmetries ensuring natural flavor conservation in Higgs induced neutral currents in sequential SU(2) × U(1) models with n generations. The derivation necessitates developing some new mathematics of monomial representations and bi-diagonalization. The conclusion is that there exists a completely characterized set of horizontal symmetries, which would allow for SU(2) ⊗ U(1) models with natural flavor conservation. This result extends the well-known condition for natural flavor conservation in the case of a single Higgs, already given by Glashow and Weinberg. For the set of symmetries thus found we show that the corresponding quark mixing matrices (in the tree approximation) all have common features. In particular, the Cabibbo angle, whenever determined, in the tree approximation, by a horizontal symmetry ensuring natural flavor conservation, would be far off its experimental value (the trivial determination being furthermore unaffected by the radiative corrections).

The conflict between natural flavor conservation of Higgs couplings and cabibbo mixing in SU(2) L × U(1)

The general problem of conservation of strangeness and other quark flavors by the exchange of several neutral Higgs mesons is investigated in SU(2) L × U(1). We find that the horizontal symmetries necessary to enforce this conservation conflict with the known Cabibbo mixing. In particular, if the quarks form an irreducible representation of the horizontal symmetry, the mixing angles are all trivial (i.e., 0 or π 2 ); if they form a reducible representation, it is possible to have some nontrivial mixing angles, but only if there are several unmixed generations of quarks with exactly the same relative pattern of masses and mixings.

Natural flavour conservation and the fourth generation

In a sequential Weinberg-Salam model with eight quarks and two Higgs doublets we fix the Yukawa interaction by requiring S 4 invariance. The model yields naturally: (i) flavour conservation in the neutral currents; (ii) m u = m d = 0; (iii) m s: m b: m ℓ = m c: m t: m h;(iv) m ℓ = m s + m b, m h = m c + m t, where h and ℓ denote the new quarks. The model provides an explanation of why quark masses are so different. It follows from (iv) that the mass of ℓ ℓ is not much greater than m υ. Perhaps ℓ ℓ has already been seen.

Natural flavor conservation and the absence of radiatively induced cabibbo angles

Non-trivial flavor conservation of neutral Higgs couplings, enforced by discrete symmetries, is known to lead to the vanishing of generalized mixing angles. We prove that this result, valid in the tree approximation, is not altered by radiative corrections.

The mass of the t-quark from discrete symmetries

Natural flavour conservation in neutral currents could be ensured by discrete symmetries. Starting from some assumptions about these symmetries we find the zeroth order mass relation m c : m t : … = m s : m b : … in the sequential Weinberg-Salam model. Implications of this relation for the mass of the t-quark are discussed.

Symmetries leading to flavor conservation in Higgs-induced neutral currents and implications on the Cabibbo angle

We present a complete characterization of the discrete and/or continuous symmetry groups which ensure natural flavor conservation in Higgs-induced neutral currents, in the SU(2) × U(1) model. Explicit necessary and sufficient conditions are given for the quark and Higgs representations. In this framework natural (lowest order) determinations of the quark mixing angles do not lead to physically acceptable Cabibbo angles.

Discrete symmetries, natural flavor conservation and weak mixing angles

Through their physically relevant representations, I characterize the class of finite symmetry groups insuring natural conservation of all quark flavors in neutral current effects, in generalized Weinberg-Salam models. As pointed out by Gatto, Morchio and Strocchi, these situations lead to a natural determination of all the generalized Cabibbo angles. A necessary and sufficient condition for avoiding a trivial generalized Cabibbo matrix is also given.

Natural flavour conservation in the neutral currents and the determination of the Cabibbo angle

We point out a conflict between the requirement of natural flavour conservation in the neutral currents and the possibility of determining the generalized Cabibbo angles as a function of the quark masses in the SU(2) × U(1) and in the SU(2) L × SU (2) R × U (1) models. The general implications of natural flavour conservation in the neutral currents on the fermion mass matrices are also discussed.

SymmetricSU 2×U 1×U′ 1 model with natural-flavour conservation in neutral weak currents

SymmetricSU 2×U 1×U′ 1 model with natural-flavour conservation in neutral weak currents

The price of natural flavour conservation in neutral weak interactions

The natural conservation of flavours to O( G F 2) in neutral weak interactions severely constrains choices of gauge groups as well as their fermion representations. In the absence of exactly conserved quantum numbers other than charge, and of | ΔQ| ⩾ 2 charged currents, essentially the only weak and electromagnetic gauge groups whose neutral interactions naturally conserve all flavours are SU(2) L ⊗ U(1) and SU(2) L ⊗ [U(1)] 2. The plausible extensions of these gauge groups to grand unified models including the strong interactions are based on SU(5) and SO(10) respectively. Making the SU(5) model completely natural, including in the Higgs sector, gives the prediction m d /m e ⋍ m s /m μ ⋍ m b /m τ ⋍ 2605 where τ is the probable new heavy lepton and b is the conjectured third flavour of charge −1 3 quark . The SO(10) model contains a potential SU(2) L ⊗ SU(2) R ⊗ U(1) weak and electromagnetic gauge group, and has a complicated Higgs structure which does not naturally conserve quark flavours.

Flavor conservation in an SU(3) × U(1) × U(1) model

We discuss natural flavor conservation of the weak neutral current in a theory with non-Abelian neutral subgroups in the example of an SU(3) \ifmmode\times\else\texttimes\fi{} U(1) \ifmmode\times\else\texttimes\fi{} U(1) structure. It is only possible to suppress flavor-changing neutral currents in the manner of Glashow and Weinberg if stable heavy particles exist.