Supersymmetry for Fermion Masses

It is proposed that supersymmetry （SUSY） may be used to understand fermion mass hierarchies. A family symmetry ZSL is introduced, which is the cyclic symmetry among the three generation SU（2） doublets. SUSY breaks at a high energy scale - 10^11 GeV. The electroweak energy scale- 100 GeV is unnaturally small No additional global symmetry, like the R-parlty, is imposed. The Yukawa couplings and R-parity violating couplings all take their natural values, which are О（10^0 -10^-2）. Under the family symmetry, only the third generation charged ferrnions get their masses. This family symmetry is broken in the soft SUSY breaking terms, which result in a hierarchical pattern of the fermion masses. It turns out that for the charged leptons, the r mass is from the Higgs vacuum expectation value （VEV） and the sneutrino VEVs, the muon mass is due to the sneutrino VEVs, and the electron gains its mass due to both ZZL and SUSY hreaking. The large neutrino mixing are produced with neutralinos playing the partial role of right-handed neutrinos. │Ve3│, which is for Ve-Vr mixing, is expected to be about 0.1. For the quarks, the third generation masses are from the Higgs VEVs, the second generation masses are from quantum corrections, and the down quark mass due to the sneutrino VEVs. It explains me/ms, ms/me, md 〉 mu and so on. Other aspects of the model are discussed.     

Four-Generation Condensate Scheme Without the Fourth Generation of Leptons

The renormalization group (RG) analyses show that in the four-generation fermion condensate scheme of electroweak symmetry breaking without the extra fourth generation of leptons thelimitation to the compositeness scale Λ could be greatly loosened and up to Λ<10¹⁰ GeV if the masses of the extra fourth generation of quarks are demanded to be bigger than the topquark mass m_t = 180 GeV. However, the mass constraints 2(m_Q)_minh⁰<2(m_Q)_max between the Higgs boson h⁰ and its constituent Q-fermions are no longer totally valid for Λ>10⁵ GeV. The ~redicted masses of the fourth generation of quarks and the Higgs boson will be larger than the corresponding ones in the four-generation quark-lepton scheme. The stability of the results for variation of the compositeness boundary conditions could be explained more clearly.     

Mass and CKM matrices of quarks and leptons, the leptonic CP-phase in neutrino oscillations

A general approach for construction of quark and lepton mass matrices is formulated. The hierarchy of quarks and charged leptons (“electrons”) is large, it leads using the experimental values of mixing angles to the hierarchical mass matrix slightly deviating from the ones suggested earlier by Stech and including naturally the CP-phase.

The same method based on the rotation of generation numbers in the diagonal mass matrix is used in the electron–neutrino sector of theory, where neutrino mass matrix is determined by the Majorano see-saw approach. The hierarchy of neutrino masses, much smaller than for quarks, was used including all existing (even preliminary) experimental data on neutrino mixing.

The leptonic mass matrix found in this way includes the unknown value of the leptonic CP-phase. It leads to large ν_μν_τ oscillations and suppresses the ν_eν_τ and also ν_eν_μ oscillations. The explicit expressions for the probabilities of neutrino oscillation were obtained in order to specify the role of leptonic CP-phase. The value of time reversal effect (proportional to sin δ′) was found to be small 1%. However, a dependence of the values of ν_eν_μ,ν_eν_τ transition probabilities, averaged over oscillations, on the leptonic CP-phase has found to be not small – of order of ten percent.     

Understanding neutrino masses and mixings

We discuss ways to understand large neutrino mixings using new symmetries of quarks and leptons beyond the standard model for the three allowed patterns of neutrino masses: normal, inverted hierarchy and degenerate masses.     

The lepton mixing matrix in a composite model

A generalized mixing matrix for leptons is presented based on a composite model of quarks and leptons. The mixing matrix is expressed in terms of one parameter, which is determined either by discussing that it is identical to that of the quark mixing matrix or by assuming that the observed solar neutrino flux results from neutrino oscillations.     

Explicit SO(10) supersymmetric grand unified model for the higgs and yukawa sectors

A complete set of fermion and Higgs superfields is introduced with well-defined SO(10) properties and U(1)xZ2xZ2 family charges from which the Higgs and Yukawa superpotentials are constructed. The structures derived for the four Dirac fermion and right-handed Majorana neutrino mass matrices coincide with those previously obtained from an effective operator approach. Ten mass matrix input parameters accurately yield the twenty masses and mixings of the quarks and leptons with the bimaximal atmospheric and solar neutrino vacuum solutions favored in this simplest version.     

Search for scalar fermions and long-lived scalar leptons at centre-of-mass energies of 130 GeV to 172 GeV

Data taken by DELPHI during the 1995 and 1996 LEP runs have been used to search for the supersymmetric partners of electron, muon and tau leptons and of top and bottom quarks. The observations are in agreement with standard model predictions. Limits are set on sfermion masses. Searches for long lived scalar leptons from low scale supersymmetry breaking models exclude stau masses below 55 GeV/c at the 95% confidence level, irrespective of the gravitino mass. Received: 13 July 1998 / Published online: 19 November 1998     

Search for composite and exotic fermions at LEP 2

A search for unstable heavy fermions with the DELPHI detector at LEP is reported. Sequential and non-canonical leptons, as well as excited leptons and quarks, are considered. The data analysed correspond to an integrated luminosity of about 48 pb at an centre-of-mass energy of 183 GeV and about 20 pb equally shared between the centre-of-mass energies of 172 GeV and 161 GeV. The search for pair-produced new leptons establishes 95% confidence level mass limits in the region between 70 GeV/ and 90 GeV/, depending on the channel. The search for singly produced excited leptons and quarks establishes upper limits on the ratio of the coupling of the excited fermion to its mass () as a function of the mass. Received: 30 October 1998 / Published online: 1 March 1999     

θ_(13) and the Higgs Mass from High Scale Supersymmetry

In the framework in which supersymmetry is used for understanding fermion masses rather than stabilizing the electroweak scale, we elaborate on the phenomenological analysis for the neutrino physics. A relatively large sinθ13 0.13 is naturally obtained. The model further predicts vanishingly small CP violation in neutrino oscillations. While the high scale supersymmetry generically results in a Higgs mass of about 141 GeV, our model reduces this mass to 126 GeV via introducing SU(2)L triplet fields which make the electroweak vacuum metastable (with a safe lifetime) and also contribute to neutrino masses.     

Bi-large Neutrino Mixing See-Saw Mass Matrix with Texture Zeros and Leptogenesis

We study constraints on neutrino properties for a class of bi-large mixing See-Saw mass matrices with texture zeros and with the related Dirac neutrino mass matrix to be proportional to a diagonal matrix of the form diag(ε,1,1). Texture zeros may occur in the light (class a) or in the heavy (class b) neutrino mass matrices. Each of these two classes has 5 different forms which can produce non-trivial three generation mixing with at least one texture zero. We find that two types of texture zero mass matrices in both class a and class b can be consistent with present data on neutrino masses and mixing. None of the neutrinos can have zero masses and the lightest of the light neutrinos has a mass larger than about 0.046 eV for class a and 0.0027 eV for class b. In these models although the CKM CP violating phase vanishes, the non-zero Majorana phases can exist and can play an important role in producing the observed baryon asymmetry in our universe through leptogenesis mechanism. The requirement of producing the observed baryon asymmetry can further distinguish different models and also restrict the See-Saw scale to be in the range of 10¹²～10¹⁵ GeV. We also discuss RG effects on V₁₃.     

Search for scalar top quark production in p&pmacr; collisions at sqrt

We have searched for direct production of scalar top quarks at the Collider Detector at Fermilab in 88 pb(-1) of p&pmacr; collisions at sqrt[s] = 1.8 TeV. We assume the scalar top quark decays into either a bottom quark and a chargino or a bottom quark, a lepton, and a scalar neutrino. The event signature for both decay scenarios is a lepton, missing transverse energy, and at least two b-quark jets. For a chargino mass of 90 GeV/c(2) and scalar neutrino masses of at least 40 GeV/c(2), we find no evidence for scalar top production and present upper limits on the production cross section in both decay scenarios.     

Geometrical basis for the Standard Model

The robust character of the Standard Model is confirmed. Examination of its geometrical basis in three equivalent internal symmetry spaces-the unitary planeC ², the quaternion spaceQ, and the real spaceR ⁴—as well as the real spaceR ³ uncovers mathematical properties that predict the physical properties of leptons and quarks. The finite rotational subgroups of the gauge groupSU(2) _L ×U(1) _Y generate exactly three lepton families and four quark families and reveal how quarks and leptons are related. Among the physical properties explained are the mass ratios of the six leptons and eight quarks, the origin of the left-handed preference by the weak interaction, the geometrical source of color symmetry, and the zero neutrino masses. The (u, d) and (c, s) quark families team together to satisfy the triangle anomaly cancellation with the electron family, while the other families pair one-to-one for cancellation. The spontaneously broken symmetry is discrete and needs no Higgs mechanism. Predictions include all massless neutrinos, the top quark at 160 GeV/c ², theb quark at 80 GeV/c ², and thet quark at 2600 GeV/c ².     

Neutrino

Neutrinos are the only fundamental fermions which have no electric charges. Because of that neutrinos have no direct electromagnetic interaction and at relatively small energies they can take part only in weak processes with virtual W ^± and Z ⁰ bosons. Neutrino masses are many orders of magnitude smaller than masses of charged leptons and quarks. These two circumstances make neutrinos unique, special particles. The history of the neutrino is very interesting, exciting and instructive. We try here to follow the main stages of the neutrino history starting from the famous Pauli letter and finishing with the discovery and study of neutrino oscillations. Outstanding contribution to the neutrino physics of Bruno Pontecorvo is discussed in some details.     

ANOMALOUS WEAK CHARGED CURRENTS OF LEPTONS AND QUARKS IN A SUBSTRUCTURE MODEL

We present a general approach to get the anomalous weak charged current of leptons and quarks in a substructure mode1,in which quarks, leptons and W-bosons are composed of preons (fermions and scalar bosons). We have shown that the (V+A) current can be determined by the structure of leptons and quarks and the anomalous weak current can be very small. In particular, it can approach zero, if the wave function of leptons (or quarks) has aspinor structure (I-P/m_f)F.     

Neutrino-lepton masses, Zee scalars, and muon g-2

Evidence for neutrino oscillations points to the existence of tiny but finite neutrino masses. Such masses may be naturally generated via radiative corrections in models, such as the Zee model, where a singlet Zee scalar plays a key role. We minimally extend the Zee model by including a right-handed singlet neutrino nu(R). The radiative Zee mechanism can be protected by a simple U(1)(X) symmetry involving only the nu(R) and a Zee scalar. We further construct a class of models with a single horizontal U(1)(FN) (à la Froggatt-Nielsen) such that the mass patterns of the neutrinos and leptons are naturally explained. We then analyze the muon anomalous magnetic moment (g(mu)-2) and the flavor changing mu-->egamma decay. The nu(R) interaction in our minimal extension is found to induce the BNL g(mu)-2 anomaly, with a light charged Zee scalar of mass 100-300 GeV.     

Mass spectral condition for leptons and quarks

Consideration is given to the mass spectral conditiona(a,_m)a =a _m, wherea is the annihilation operator forQ=–1 states in the Hilbert space of leptons and quarks anda _m is the commutator resolvent ofa with respect tom. It is observed that this spectral condition, which simply requires a to be a congruent automorph ofa _m , implies that the third-, fourth-, and fifth-generationQ=-1 leptons have the masses 1788.03 MeV, 42.1649 GeV, and 1.33422 TeV, respectively. With the assumption that the mass spectral condition also holds forQ=0 states in the Hilbert space, one obtains new theoretical upper and lower bounds on the neutrino masses.     

Consequences of flavor as a dynamical quantum number

Phenomenological consequences of composite leptons and quarks are studied in the class of models in which the fermions of the first generation (i.e. e, ν_e, u and d) are the ground states of (unspecified) composite systems and each new generation is a radial excitation level. We find that the standard QED results remain practically unaffected in such a scheme. The excited quarks/leptons having mass larger than 5 GeV could be produced in e⁺e^- experiments and would increase the value of R by several per cent as compared with the case of the pointlike quarks and leptons. An argument is given for the smallness of the anomalous magnetic moments of composite leptons.     

Formation and decay of scalar Leptoquarks/Squarks in ep collisions

The cross sections for the formation of scalar resonances, leptoquarks or squarks, in electron/positron-proton collisions at HERA are presented, including next-to-leading order QCD corrections. Depending mildly on the mass of the resonances, the K-factors increase the production cross sections by up to 30% if the target quarks are valence quarks. The QCD corrections to the partial decay widths of leptoquarks/ squarks to leptons and quarks are small. The electron spectrum in the decays is nevertheless softened by perturbative gluon radiation at a level of 2 GeV for a leptoquark/ squark mass of 200 GeV.     

Supersymmetry and weak,electromagnetic and strong interactions

We study a possible way to construct supersymmetric theories which could be considered as realistic, excepted that the problem of mass generation for electron, muon and quarks remains. There is a new class of leptons which includes charged ones, and a “photonic neutrino”. Spin $\text{1}\text{2}$-gluons and heavy spin 0- quarks are associated with ordinary vector gluons and quarks.