Quark mass matrices in left-right symmetric gauge theories

The most general left-right symmetry for SU(2)_L×SU(2)_R×U(1) gauge theories with any number of flavours and with at most two scalar multiplets transforming as $\text{q}\text{q}$ bilinears is analyzed. In order to get additional constraints on the structure of quark mass matrices, all possible horizontal groups (continuous or discrete) are investigated. We give a complete classification of physically inequivalent quark mass matrices for four and six flavours. It is argued that our methods and results are also applicable in the case of dynamical symmetry breaking. Parity invariance and horizontal symmetry are shown to imply CP conservation on the lagrangian level. For all non-trivial three-generation models there is spontaneous CP violation, which in most cases turns out to be naturally small. Several six-flavour models predict $\text{m}{}_{\mathrm{<mtext>t</mtext>}}\text{?m}{}_{\mathrm{<mtext>b</mtext>}}\text{(}\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{m}{}_{\mathrm{<mtext>c</mtext>}}\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and are, therefore, already ruled out experimentally. In the remaining few realistic models, predictions for the weak mixing angles are made.     

Low-energy behaviour of realistic locally-supersymmetric grand unified theories

The recently proposed cosmologically acceptable N=1 supergravity models based on the SU(5) unification group define unambigously the minimal particle content of the theory. This fact allows us to determine quite precisely their low-energy behaviour. The SU(2)×U(1) breaking to U(1)_e.m. is a consequence of radiative corrections of the supergravity induced soft breaking terms. The proposed mechanism (which is model independent) introduces naturally a hierarchy between the M_W and M_X scales. Calculating the low-energy effective potential we shot that a corrects SU(2)×U(1) breaking is obtained without any limit (except the experimental one) on the top-quark mass. The masses of the supersymmetric partners of mater and gauge fermions can be low and consequently accessible experimentally (sleptons, s quarks, gauginos $\text{? 20–50}\text{GeV}$). A neutral Higgs is also predicted wirth a mass $\text{m}{}_{\mathrm{H}}\text{?O(5)}\text{GeV}$. In addition, we show that if m_t?45 GeV, the gravitino and gluino masses are bounded from below by $\text{10}\text{GeV}\text{? m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{15}\text{GeV}\text{? m}{}_{\mathrm{<mtext>gluino</mtext>}}$. The values of sin²θ_W (in the two-loop approximation) and the $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$ ratio predicted are in very good agreement with the experimentally measured values.     

Irreducible gauge theory of a consolidated Salam-Weinberg model

We derive the Salam-Weinberg model by gauging an internal simple supergroup $\text{SU}\text{(}\text{2}\text{1}\text{)}$. The theory uniquely assigns the correct SU(2)_L ? U(1) eigenvalues for all leptons, fixes θ_W = 30°, generates the W^±_σ, Z⁰_σ and A_σ together with the Higgs-Goldstone $\text{I}{}_{\mathrm{<mtext>L</mtext>}}\text{=}\text{1}\text{2}$ scalar multiplets as gauge fields, and imposes the standard spontaneous breakdown of SU(2)_L ? U(1). The masses of intermediate bosons and fermions are directly generated by $\text{SU}\text{(}\text{2}\text{1}\text{)}$ universality, which also fixes the Higgs field coupling.     

Spontaneous CP violation in a Z4 horizontal symmetry model for flavor mixing

The implications of a Z₄ horizontal symmetry model of flavor mixing for CP violation are studied in the framework of minimal SU(2)_L × SU(2)_R × U(1)_{B – L} gauge theory. We show that CP violation in this model arises purely from right-handed currents. We also note that spontaneous breaking of CP symmetry requires a fine tuning of coupling parameters to the level of , which can be avoided by the inclusion of one additional singlet Higgs field, of the kind recently introduced for other purposes.     

Fermion and Higgs masses as probes of unified theories

The effects of Yukawa couplings of order of the gauge couplings in the SU(3) × SU(2) × U(1) renormalization group equations governing the evolution of observable parameters such as $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$ and the Higgs mass are studied systematically to one-loop order. These parameters are found to give useful constraints on the mass of the t quark, and of possible heavier fermion families, in theories with SU(5)-like boundary conditions at unification energies.     

Signatures of neutral heavy leptons in neutrino-induced dilepton events

The tentative indication in some experiments of μ^?e⁺ or π^?μ⁺ events with unusual characteristics revives the speculation that neutrino-induced dileptons may contain a weak signal of neutral heavy lepton (L⁰) production. We study the characteristics of dileptons expected from the production of an L⁰ through a current of the form $\text{L}{}^0\text{γ}{}_{\mathrm{\alpha }}\text{(1+γ}{}_5\text{)ν}{}_{\mathrm{\mu }}$. Both quasi-elastic and deep inelastic excitation are investigated and a comparison is made with dileptons of charm origin. As an illustration of a model with a ν_μ→L⁰ transition, we discuss the 2-2 version of the SU(2) × U(1) model and comment on the role of the Higgs particle in such transitions.     

A gauge theory of weak and electromagnetic interactions with spontaneous parity breaking

We present a unified gauge theory of weak and electromagnetic interactions in which parity is spontaneously broken together with gauge invariance, by the Higgs mechanism. The gauge group is SU(2) × U(1), and a heavy neutrino is associated with every charged lepton. After the breaking of the original parity-conserving theory, both a purely vector electromagnetic current and the usual V-A charged currents are obtained. Z is coupled to a vector electron current, and the model predicts equal $\text{ν}{}_{\mathrm{\mu }}\text{e}\text{and}\text{ν}{}_{\mathrm{\mu }}\text{e}$ cross sections. Extension to hadrons is made by introducing three charmed quarks p′, n′ and λ′ of the same charges as p, n and λ. All the experimental results $\text{(ν}{}_{\mathrm{\mu }}\text{e}\text{,}\text{ν}{}_{\mathrm{\mu }}\text{e}\text{,}\text{ν}{}_{\mathrm{<mtext>e</mtext>}}\text{e}$, ν_μ and $\text{ν}{}_{\mathrm{\mu }}$ hadron scatterings) are compatible with a value of sin²θ_W of order 0.4.     

Cosmological bounds on a left-right symmetric model

The right-handed neutrino cross sections of the processes ν_L + ? → ν_R + ? and ν_R + ? → ν_R + ?, where ? is a relativistic lepton, are calculated in the SU(2)_L × SU(2)_R × U(1) model. According to a cosmological criterion the parameters of the model are bounded. In particular we obtain the bound $\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}_{\mathrm{<mtext>R</mtext>}}\text{? 30 M}{}_{\mathrm{<mtext>W</mtext>}}{}_{\mathrm{<mtext>L</mtext>}}$, assuming the neutrinos are Dirac four-component particles.     

Light composite fermions in a dynamical subquark model of pregauge interactions

The masses of composite leptons and quarks are discussed in a “dynamical subquark model of pregauge interactions”. In this model, the leptons and quarks are made of a spinor and scalar subquark with equal mass, M, and the gauge bosons and Higgs scalar of the SU(3)_c×SU(2)_L×U(1)_Y model are made of a subquark-antisubquark pair. The SU(2)_L×U(1)_Y symmetry is spontaneously broken by the composite Higgs scalar and the (scalar) subquark mass parameter is in turn bounded as $\text{M > 5.4}\text{TeV}\text{(=2π(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{where}\text{G}{}_{\mathrm{<mtext>F</mtext>}}$ is the Fermi coupling constant). The spontaneously generated mass of a lepton or quark, m_i⁽ⁿ⁾ (i = 1, 2; n = 1 ～ N_g), is calculated to be: $\text{m}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{× (4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)α}{}_{\mathrm{<mtext>e.m.</mtext>}}\text{(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/3}\text{6}\text{(=0.35r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{(4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)}\text{GeV}\text{),}\text{where}\text{r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}$ are the parameters satisfying that 0 ? r_i⁽ⁿ⁾ ? 1 and Σ (r_i⁽ⁿ⁾)² = 1;N_g is the total number of generations of the leptons and quarks; α_e.m. is the fine structure constant. The appearance of light composite fermions is related to a specific mechanism of generating global chiral symmetries of the leptons and quarks. Global symmetries of scalar subquarks yield chiral symmetries of the leptons and quarks. Our model turns out to satisfy 't Hooft's anomaly conditions on massless composite fermions.     

More evidence for universality in the SU(2) lattice gauge theory

The O⁺ glueball mass in the fundamental-adjoint SU(2) la ttice gauge theory is extracted from the Monte Carlo data on the correlation functions at time distances t = 1 and t = 2 on a 8⁴ lattice. The ratio $\text{m}{}_{\mathrm{<mtext>g</mtext>}}\text{σ}$ is constant in the β_F ?β_A region explored giving more evidence in favour of the universality hypothesis.     

Phenomenological predictions of the SO(10) supersymmetric grand unified model

The phenomenological predictions of the SO(10) supersymmetric grand unified model (SO(10) SGUM) for the mass scales M₁, M₂, weak angle ifsin²θ_w, quark-leptons mass ratios $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, $\text{m}{}_{\mathrm{t}}\text{m}{}_{\mathrm{<mtext>b</mtext>}}$, $\text{m}{}_{\mathrm{\tau }}\text{m}{}_{\mathrm{\nu }}{}_{\mathrm{\tau }}$ and proton lifetime τ_p are estimated by using renormalization group analysis at one-loop level. In contrast with SU(5) SGUM, we find that the SO(10) SGUM still has problems with τ_p but not with sin²θ_w and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, which may suggest that supersymmetry would be bro at a mass scale $\text{?10}{}^7\text{GeV}$.     

Sakata-like electro/weak model

A left-handed SU (2)_L × U(1) × U′(1) electro/weak model (with $\text{Q = T}{}_3\text{+}\text{1}\text{2}\text{Y ?}\text{2}\text{3}\text{L}$) is proposed. For neutrino interactions, our predictions are à la WS only with sin²Θ_W → sin²Θ^eff_W < sin²_W for processes which involve quarks, and (b) sin²Θ^eff_W (purely leptonic processes) > sin²Θ^eff_W (νq-scattering). For the polarized process eD → eX, the asymmetry parameter agrees with the WS one up to a second-order term. The additional neutral gauge boson is expected to be only one order of magnitude heavier than W^±. We argue that the present neutral-current experimental results are not capable of distinguishing between the standard and the present models.     

From high energy supersymmetry breaking to low energy physics through decoupling

We reconsider a realistic model of electroweak and strong interactions with calculable mass spectrum at the tree level in which supersymmetry and an extra gauge group factor ?(1) beyond SU(3) × SU(2) × U(1) are both broken at very high energies: $\text{M}{}_{\mathrm{<mtext>SUSY</mtext>}}\text{?(M}{}_{\mathrm{<mtext>W</mtext>}}\text{M)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{M}{}_{\mathrm{<mtext>U</mtext><mtext>?</mtext><mtext>(1)</mtext>}}\text{?M}\text{with}\text{M?M}{}_{\mathrm{<mtext>W</mtext>}}$. In spite of these high-energy scales, especially the large scale of supersymmetry breaking, the low energy spectrum - including the relevant Higgs boson - is decoupled from the heavy degrees of freedom. Due to the “non-renormalization” theorems this decoupling persists to all orders in perturbation theory.     

Some properties of heavy lepton families

The simplest four-quark SU(2) ? U(1) models with an anomally-free heavy lepton sector can have two charged heavy leptons and one or two neutral leprons. Such models also explain the rise in R (the ratio of hadronic to muon pair production in e⁺e^? collisions). We study some consequences of different choices of leptonic numbers for L₁ and L₂. In particular, we derive, the leptonic decay width when several final-stae leptons are massive; the cross section for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_1\text{L}{}_2$ production; the branching ratio for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_2\text{L}{}_2\text{→}\text{e}\text{3μ+}\text{missing energy}$.     

Aspects of the grand unification of strong,weak and electromagnetic interactions

We study issues arising in attempts to unify strong and other elementary particle interactions. The proton lifetime is estimated in theories with second-order baryon number violation, and found to be O(10³–10⁴) longer than naive dimensional counting suggested. The renormalization of quark and lepton masses below the grand unification mass is considered in some detail. Application is made to the SU(5) model of Georgi and Glashow, and we find strange and bottom quark masses:

$\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 0.4–0.5}\text{GeV}\text{, m}{}_{\mathrm{<mtext>b</mtext>}}\text{≈ 4.8–5.6}\text{GeV}$

. Inputs are the values of the strong interactions coupling constant favoured by electroproduction and charmonium analyses, and the observed muon and heavy lepton (τ) masses. These estimates are substantially increased if there are more than six flavours of quark. Symmetry breaking in the SU(5) model is studied, including radiative corrections to the effective Higgs potential.     

Phenomenological consequences of N = 1 supergravity theories with non-minimal kinetic energy terms for vector superfields

It is shown that N=1 supergravity theories can have a GUT scale as large as the Planck scale if the kinetic energy terms for vector superfields are non-minimal. The canonical values for sin²θ_W (M_W), α₃ (M_W) and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}\text{(M}{}_{\mathrm{<mtext>W</mtext>}}\text{)}$ are respected. In those theories masses of SU(3), SU(2) and U(1) gauginos may be different at the unification scale. Consequences for the low-energy particle spectrum are discussed in the extreme case where one of the gaugino masses is large while the other two vanish.     

Obtaining Mw = Mz cos θ in technicolor theories

We show that the successful relation M_w = M_z cos θ is preserved in the technicolor formulation of the dynamical Higgs mechanism provided only that the creation operators for Goldstone bosons associated with broken generators belong to the $\text{I}{}_{\mathrm{<mtext>w</mtext>}}\text{=}\text{1}\text{2}$ representation of the weak isospin group. We present a plausibility argument that this is indeed the case. No additional isospin or isospin-like global SU(2) symmetries are then required allowing isospin to be spontaneously broken. This may be of help in producing a large $\text{m}{}_{\mathrm{<mtext>c</mtext>}}\text{m}{}_{\mathrm{<mtext>s</mtext>}}$ splitting. It is also shown how the weak hyperchange interaction can produce substantial vacuum isospin breaking in a theory which is only marginally asymptotically free. This mechanism predicts , providing a natural explanation for small neutrino masses.     

Higgs particle production by Z→Hγ

The rate for the decay of a Z-boson into a Higgs boson and monochromatic photon is computed to leading order in the standard SU(2) × U(1) gauge theory. The coupling has contributions from fermion and W-boson loops. The W-boson loop dominates unless the number of heavy fermion generations exceeds six. The branching ratio computed from the W-boson loop contribution, B(Z→Hγ), is approximately 2 × 10^?6$\text{(1?(}\text{M}{}_{\mathrm{<mtext>H</mtext>}}{}^2\text{M}{}_{\mathrm{<mtext>Z</mtext>}}{}^2\text{))}{}^3$.     

Parity violation in atoms in SO(3) gauge models

We have evaluated the parity-violation contribution in atoms in the framework of SO(3) gauge theory. Various hadronic models have been used: first, for simplicity, the unrealistic five-quark one, next, others involving three ordinary SU(3) triplets for which all unwanted strangeness-changing processes are suppressed, up to order $\text{Gα}\text{or}\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$. In the free quark approximation, we obtain quite similar parity-violation effects which are proportional to $\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$ (ΔM² is the difference of squared masses of leptons (M_X0² ? M_ν² = M_X0²), or of quarks (ΔM_q²)). Namely, in large atoms (Z ? 1) the electronic contribution which is proportional to

gives the largest effect ($\text{σ}{}_{\mathrm{?}}\text{,}\text{p}{}_{\mathrm{?}}\text{and}\text{m}{}_{\mathrm{?}}$are the spin, momentum operators and mass of the lepton). Parity-violating effects in SO(3) gauge models are ?10^?4 smaller than those evaluated in the Weinberg theory with a neutral parity-violating current and will remain undetectable in the near future.     

Coupling supersymmetric Yang-Mills theories to supergravity

We extend the technique of Cremmer et al. to couple arbitrary chiral multiplets with supersymmetric Yang-Mills interactions to N = 1 supergravity. We present the general form of the lagrangian and the detailed form of the scalar potential is spelled out. In the case of N chiral multiplets, “minimally” coupled to supergravity, we derive, in the absence of gauge interactions, a model-independent mass formula Supertrace $\text{M}{}^2\text{= Σ}{}_{\mathrm{J}}\text{(?)}{}^{\mathrm{2J}}\text{(2J + 1)m}{}_{\mathrm{J}}{}^2\text{= 2(N ? 1)m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^2$, where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the gravitino mass. A concrete example of the super Higgs effect involving N chiral multiplets is exhibited.