Charged Fermion Masses Research Articles

Flavor problem, proton decay and neutrino oscillations in SUSY models with anomalous [formula omitted

We discuss how realistic supersymmetric models can be constructed by employing an anomalous U(1) flavor symmetry which also mediates supersymmetry breaking. A judicious choice of U(1) charges enables the first two squark families to be sufficiently heavy (≳10 TeV), so that flavor changing neutral currents as well as dimension five nucleon decay are adequately suppressed. Using the SU(5) example, the charged fermion mass hierarchies, magnitudes of the CKM matrix elements, as well as the observed neutrino oscillations are simultaneously accommodated. We estimate the proton lifetime to be τ p∼10 3·τ p[ minimal SU(5)] , with the decay mode p→ Kμ being comparable to p→ Kν μ, τ .

An improved supersymmetric SU(5)

By supplementing minimal supersymmetric SU(5) (MSSU(5)) with a flavor U(1) symmetry and two pairs of 15+15 `matter' supermultiplets, we present an improved model which explains the charged fermion mass hierarchies and the magnitudes of the CKM matrix elements, while avoiding the undesirable asymptotic mass relations m s = m μ , m d m s = m e m μ . The strong coupling α s ( M Z ) is predicted to be approximately 0.115, and the proton lifetime is estimated to be about five times larger than the MSSU(5) value. The atmospheric and solar neutrino puzzles are respectively resolved via maximal ν μ − ν τ and small mixing angle ν e − ν s MSW oscillations, where ν s denotes a sterile neutrino. The U(1) symmetry ensures not only a light ν s but also automatic `matter' parity.

U(2)and maximal mixing ofνμ

A U(2) flavor symmetry can successfully describe the charged fermion masses and mixings, and supress SUSY FCNC processes, making it a viable candidate for a theory of flavor. We show that a direct application of this U(2) flavor symmetry automatically predicts a mixing of 45 degrees for nu_mu to nu_s, where nu_s is a light, right-handed state. The introduction of an additional flavor symmetry acting on the right-handed neutrinos makes the model phenomenologically viable, explaining the solar neutrino deficit as well as the atmospheric neutrino anomaly, while giving a potential hot dark matter candidate and retaining the theory's predictivity in the quark sector.

CHARGE QUANTIZATION IN THE LARGEST LEPTOQUARK–BILEPTON CHIRAL ELECTROWEAK SCHEME

The uniqueness of the hypercharge assignments in the three-fermion families leptoquark–bilepton SU (3)C× SU (4)L× U (1)N model is established. Although the gauge group contains an explicit U(1) factor, freedom from triangle anomalies combined with the requirement of nonvanishing charged fermion masses uniquely fix the electric charges of all fermions independently of the neutrinos being massless or not. The electric-charge quantization, flavor family replication, and the existence of three colors are interwoven.

Neutrino oscillations and other key issues in sypersymmetric SU(4) c × SU(2) L × SU(2) R

We try to gain an understanding of the recent Superkamiokande data on neutrino oscillations and several other important phenomenological issues within the framework of supersymmetric SU(4) c × SU(2) L × SU(2) R ( э G 422 ). By supplementing G 422 with a U(1)− R symmetry we can provide an explanation of the magnitude MG (∼ 10 16 GeV) of the G 422-symmetry breaking scale, resolve the MSSM μ problem, and understand why proton decay has not been seen ( τ p ⪢ 10 34 yr). The family dependent R -symmetry also helps provide an explanation of the charged fermion mass hierarchies as well as the magnitudes of the CKM matrix elements. Several additional heavy states in the mass range 10 4–10 7 GeV are predicted, and the MSSM parameter tan β turns out to be of order unity. The atmospheric neutrino problem is explained through ν μ − ν τ mixing with sin 22 θ μτ ≅ 1. The resolution of the solar neutrino puzzle is via the small angle MSW oscillations and necessarily requires a sterile neutrino ν s which, thanks to the R -symmetry, has a tiny mass.

Atmospheric and solar neutrino oscillations in νMSSM and beyond

We show how a unified description of the various two-flavor neutrino oscillation solutions, allowed by the atmospheric and solar neutrino experiments, are naturally realized within the framework of νMSSM (MSSM augmented with the seesaw mechanism) and beyond, especially grand unified theories. A general mechanism for achieving maximal mixing to resolve the atmospheric anomaly is discussed, and applied to the flipped SU(5) model. Except in the case of MSSM and SU(5), a light sterile neutrino is an inevitable consequence of our considerations. Neutrino hot dark matter is predicted in those models which exhibit bi-maximal neutrino mixings. A U(1) flavor symmetry, motivated by the charged fermion mass hierarchies and the magnitudes of the CKM matrix elements, plays a central role.

Maximal mixing neutrino models

We account for the solar and atmospheric neutrino problems by introducing maximal mixing between conventional neutrinos and sterile neutrino partners. We achieve this by invoking a seesaw-like mechanism which not only provides us with maximally mixed neutrino/sterile-neutrino mass eigenstates but also accounts for the relative suppression of the neutrino masses with the charged fermion masses. In obtaining such an extended seesaw mechanism we are required to introduce a new U(1) global symmetry together with an extended Higgs sector.

Hybrid MSW + VO solution of the solar neutrino problem in string-motivated unified theories

It is shown that the hybrid MSW + VO solution of the solar neutrino problem, according to which the solar ν e undergo matter-enhanced transitions into ν μ, τ in the Sun followed by long wave length ( ∼1.5×10 8 km) ν e ↔ ν μ, τ oscillations in vacuum between the Sun and the Earth, can occur naturally in string-motivated grand unified theories. We consider the supersymmetric version of a string-type SU(4)⊗ SU(2) L ⊗ SU(2) R theory with U(1) X family symmetry, which was shown to successfully describe the charged fermion masses and the quark mixing, and extend the earlier fermion mass analysis to the neutrino sector. We show that the four oscillation parameters Δm 31 2, Δm 21 2 and sin 22 θ 12, sin 22 θ 13, characterising the combined matter-enhanced transitions and vacuum oscillations of the solar ν e , naturally get values in the ranges of the hybrid MSW + VO solutions found recently.

Unified explanation of the solar and atmospheric neutrino puzzles in a supersymmetric SO(10) model

It was recently suggested that in a class of supersymmetric SO(10) models with Higgs multiplets in $10$, and a single $126+\overline{126}$ representation, if the $\overline{126}$ contributes both to the right handed neutrino masses as well as to the charged fermion masses, one can have a complete prediction of the neutrino masses and mixings. It turns out that if one chooses only one $10$, there are no regions in the parameter space where one can have a large ${\ensuremath{\nu}}_{\ensuremath{\mu}}$-${\ensuremath{\nu}}_{\ensuremath{\tau}}$ mixing angle necessary to solve the atmospheric neutrino deficit while at the same time solving the solar neutrino puzzle via the ${\ensuremath{\nu}}_{e}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ oscillation. We show that this problem can be solved in a particular class of SO(10) models with a pair of $10$ multiplets if we include the additional left-handed triplet contribution to the light neutrino mass matrix. This model cannot reproduce the mass and mixing parameters required to explain the Liquid Scintillation Neutrino Detector observations nor does it have neutrino hot dark matter.

Yukawa textures from family symmetry and unification

In this letter, we show how the combination of both a gauged U(1)_X family symmetry and an extended vertical gauge symmetry in a single model, allows for the presence of additional Clebsch texture zeroes in the fermion mass matrices. This leads to new structures for the textures, with increased predictivity, as compared to schemes with enhanced family symmetries only. We illustrate these ideas in the context of the Pati-Salam gauge group SU(4)xSU(2)_LxSU(2)_R$ supplemented by a U(1)_X gauged family symmetry. In the case of symmetric mass matrices, two of the solutions of Ramond, Roberts and Ross that may not be obtained by family symmetries only, are accurately reproduced. For non-symmetric textures, new structures arise in models of this type. To distinguish between the solutions in this latter case, we performed a numerical fit to the charged fermion mass and mixing data. The best solution we found allows a fit with a total chi^2 of 0.39, for three degrees of freedom.

Yukawa textures in string unified models withSU(4)⊗O(4)symmetry

We discuss the origin of Yukawa textures in the string-inspired and string derived models based on the gauge group SU(4)xSU(2)_LxSU(2)_R supplemented by a U(1)_X gauged family symmetry. The gauge symmetries are broken down to those of the minimal supersymmetric standard model which is the effective theory below 10^16 GeV. The combination of the U(1)_X family symmetry and the Pati-Salam gauge group leads to a successful and predictive set of Yukawa textures involving two kinds of texture zeroes: horizontal and vertical texture zeroes. We discuss both symmetric and non-symmetric textures in models of this kind, and in the second case perform a detailed numerical fit to the charged fermion mass and mixing data. Two of the Yukawa textures allow a low energy fit to the data with a total chi^2 of 0.39 and 1.02 respectively, for three degrees of freedom. We also make a first attempt at deriving the non - renormalisable operators required for the Yukawa textures from string theory.

Nucleon decay in non-minimal supersymmetric SO(10)

Evaluation of nucleon decay modes and branching ratios in a non-minimal supersymmetric SO(10) grand unified theory is presented. The non-minimal GUT considered is the supersymmetrised version of the ‘realistic’ SO(10) model originally proposed by Harvey, Reiss and Ramond, which is realistic in that it gives acceptable charged fermion and neutrino masses within the context of a phenomenological fit to the low-energy standard model inputs. Despite a complicated Higgs sector, the SO(10) 10 Higgs superfield mass insertion is found to be the sole contribution to the tree-level F-term governing nucleon decay. The resulting dimension-5 operators that mediate nucleon decay give branching ratio predictions parameterised by a single parameter, the ratio of the Yukawa couplings of the 10 to the fermion generations. For parameter values corresponding to a lack of dominance of the third family self-coupling, the dominant nucleon decay modes are p → K + + ν μ and n → K 0 + ν μ as expected. Further, the charged muon decay modes are enhanced by two orders of magnitude over the standard minimal SUSY SU(5) predictions, thus predicting a distinct spectrum of ‘visible’ modes. These charged muon decay modes, along with p → π + + ν μ and n → π 0 + ν μ , which are moderately enhanced over the SUSY SU(5) prediction, suggest a distinguishing fingerprint of this particular GUT model, and if nucleon decay is observed at Super-KAMIOKANDE the predicted branching ratio spectrum can be used to determine the validity of this ‘realistic’ SO(10) SUSY GUT model.

Neutrino masses and mixing angles in a supersymmetric SU (4) ⊗SU (2) L ⊗SU (2) R model

We consider the problem of neutrino masses and mixing angles in a supersymmetric model based on the gauge group SU(4) ⊗SU(2) L ⊗SU(2) R broken at the scale M X ≈ 10 16 GeV We extend a previous operator analysis of the charged lepton and quark masses and mixing angles in this model to include the neutrino sector, assuming a universal Majorana mass M for the right-handed neutrinos. The Dirac part of the neutrino matrix is then fixed by previous filtering of the ansatze of the charged fermion masses. The assumption of universal Majorana masses then leads to the physical neutrino masses and magnitudes of the elements of the leptonic mixing atrix all being predicted in terms of the single additional parameter M, whose value may be fixed by requiring that Δm eμ 2 be consistent with the small angle MSW solution. Having fixed M in this way the rest of the neutrino masses and mixing angles are then predicted in terms of the ansatze which reproduce the charged fermion masses and quark mixing angles, although we emphasise again that such predictions are based on the assumption that the neutrino Majorana mass matrix is proportional to a 3×3 unit matrix. With this assumption we find that some of the ansatze imply a tau neutrino mass in the relevant range for the dark matter problem and structure formation, muon-electron neutrino mixing angles consistent with the MSW solution to the solar neutrino problem, and tau-muon neutrino mixing at a level which should soon be observed by the CHORUS and NOMAD experiments.

Complete supersymmetric SO(10) model.

A complete supersymmetric SO(10) model is constructed, which is the most general consistent with certain $R$, discrete, and $U(1)$ flavor symmetries. The desired vacuum of the theory has vevs which lie in particular directions of group space. This leads to both doublet triplet splitting and to the generation of just four operators for charged fermion masses. The model illustrates how many features of superunification become related in the context of a complete theory. The features discussed here include: the weak mixing angle prediction, the doublet-triplet splitting problem, proton decay, the generation of the $\mu$ parameter, neutrino masses and the generation of the operators which lead to charged fermion mass predictions.

Natural doublet-triplet splitting in supersymmetric SO(10) models

We construct a supersymmetric SO(10) model, where the Dimopoulos-Wilczek mechanism for doublet-triplet splitting is stable under the addition of Higgs superfields belonging to 126 + 126 often used to implement the see-saw mechanism for neutrino masses and where the charged fermion and neutrino mass spectra arise from a single set of 10 and 126 Higgs representations.

Neutrino masses and mixing angles in a predictive theory of fermion masses.

A framework for predicting charged fermion masses in supersymmetric grand unified theories is extended to make predictions in the neutrino sector. Eight new predictions are made, and their relevance to neutrino oscillation experiments and the solar neutrino problem are discussed.

Reexamining the fermion mass relations in the supersymmetric SU (4) ⊗ O (4) GUT model

We study in detail the charged fermion masses in the context of the minimal GUT-version of the supersymmetric SU (4) ⊗ O (4) model. We show the presence of vacuum expectation values (VEVs) of the order of the GUT mass scale for the right-handed (RH) sneutrinos may modify the “naive” equality of the charged-lepton and the down-quark masses at M G =10 16 GeV. In particular, we indicate how one can successfully modify the problematic low-energy relation between m s and m μ , while preserving the good prediction m b/m τ = r ⋍ 2.7 ( r being the renormalization parameter). The fact that the VEVs of the RH sneutrinos are predicted to be of order ∼ M G , may also have interesting consequences in the mechanism of symmetry breaking of the model.

Heavy top quark, fermion mixings and all that

An attempt is made to incorporate the observed structure of the quark and lepton masses and mixings within the framework of SO(10) grand unification supplemented by a Peccei-Quinn U(1) symmetry that also distinguishes the three chiral families. All dimensionless couplings are assumed to be of order unity. The hierarchical structure among the charged fermion masses, including the t-b splitting, gets related to the ‘small’ (∼10 −2) ratio M c / M x (or its powers), where M c ( M x ) denote the SU(4) c ( SO(10)) breaking scales. An upper bound on the top quark mass is obtained which, for central values of the parameters, is more restrictive than other well known bounds. The mixing angles in the charged lepton sector are related via the SU(4) c symmetry to the quark mixing angles. One finds that asymptotically, θ μe ≅( m 8/ m μ ) θ 12, θ rμ ≅ θ 23, and θ re ≅ θ 13. In the neutral sector the tau neutrino may be cosmologically significant, whereas v e and v μ can play a role in the MSW effect.

Fermion masses and mixing in SO(10)

We attempt to incorporate the observed structure of quark and lepton masses and mixing within the framework of SO(10) grand unification supplemented by a Peccei-Quinn U(1) symmetry that also distinguishes the three chiral families. All dimensionless couplings are assumed to be of order unity. The hierarchical structure among the charged fermion masses, including the t- b mass splitting, becomes related to the “small” (∼ 10 −2) ratio M c/ M x (or its powers), where M c [ M x ] denote the SU(4) c [SO(10)] breaking scales. An upper bound on the top quark mass is obtained which for m s(1 GeV) = 175 MeV and 0.04⩽∥ V cb∥⩽0.055 yields 120 GeV≲ m t phys≲150 GeV. In the neutral sector the τ-neutrino may be cosmologically significant, whereas ν c and ν μ can play a role in the MSW effect. The mixing angles in the lepton sector are related via the SU(4) c symmetry to the quark mixing angles. One finds that asymptotically, θ μ c ⋍ (m s /m μ)θ 12, θ τμ ⋍ θ 23 and θ τ c ⋍ θ 13 .

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.