Phenomenological SU(1, 1) supergravity

We investigate the structure of phenomenological supergravity models which permit the hierarchy problem to be “solved” in the sense that $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and m_W are determined dynamically to be exp [-O(1)/α] × m_P. Such models must have a flat hidden sector potential, which is only possible if the theory has an underlying SU(1, 1) invariance. Flat SU(1, 1) theories necessarily have a zero cosmological constant and the hidden sector is an Einstein space with . The SU(1, 1) invariance is necessarily broken down to U(1) by the gravitino mass. If $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the only source of SU(1, 1) breaking then the tree-level gaugino masses are small and $\text{A =}\text{3}\text{2}$, while values of A up to 3 and non-zero gaugino masses are possible if other sources of SU(1, 1) breaking are tolerated. Yukawa couplings may scale as some power of $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}$ in these models where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is generated dynamically, which may explain the hierarchy of Higgs-fermion Yukawa couplings: $\text{m}{}_{\mathrm{<mtext>f</mtext>}}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{=}\text{O}\text{(}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}\text{)}{}^{\mathrm{\lambda >0}}$? These models also permit the spontaneous violation of CP in the Yukawa coupling matrix. Numerical studies yield 20 GeV < m_t < 100 GeV in these phenomenological SU(1, 1) supergravity models. Speculations are presented about their relation to a fundamental theory based on extended supergravity.     

Primordial two-component maximally symmetric inflation

We propose a two-component inflation model, based on maximally symmetric supergravity, where the scales of reheating and the inflation potential at the origin are decoupled. This is possible because of the second-order phase transition from SU(5) to SU(3)×SU(2)×U(1) that takes place when φ?φ_c<φ₀, when φ₀?O(M) is the value of the inflation at the global minimum, and leads to a reheating temperature T_R?(10¹⁵–10¹⁶) GeV. This makes it possible to generate baryon asymmetry in the conventional way without any conflict with experimental data on proton lifetime. The mass of the gravitinos is $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{?10}{}^{12}\text{GeV}$, thus avoiding the gravitino problem. Monopoles are diluted by residual inflation in the broken phase below the cosmological bounds if φ_c?0.3M.     

γ-W0 mixing as an alternative to unified weak-electromagnetic gauge theories

A very simple model based on γ-W⁰ mixing (but not on spontaneously broken gauge symmetry) is shown to reproduce all the quantitative predictions of the standard (Weinberg-Salam) model as far as low-energy phenomenology is concerned. The model predicts intermediate-boson mass relations weaker than Weinberg's. Weinberg's mass formulae, however, can be accommodated in our model provided the γ-W⁰ mixing parameter and the coupling constants (e and g) satisfy a special relation. This relation also guarantees asymptotic SU(2) × U(1), decent high-energy behavior in processes like $\text{v +}\text{v}\text{→}\text{W}{}^{\mathrm{+}}\text{+}\text{W}{}^{\mathrm{?}}$ and the SU(2) × U(1) value for the W^± boson gyromagnetic ratio. Speculative attempts are made to understand the sign and magnitude of “sin² θ_W”.     

Oscillator-like unitary representations of non-compact groups with a jordan structure and the non-compact groups of supergravity

We give a general bosonic construction of oscillator-like unitary irreducible representations (UIR) of non-compact groups whose coset spaces with respect to their maximal compact subgroups are Hermitian symmetric. With the exception of E₇₍₇₎, they include all the non-compact invariance groups of extended supergravity theories in four dimensions. These representations have the remarkable property that each UIR is uniquely determined by an irreducible representation of the maximal compact subgroup. We study the connection between our construction, the Hermitian symmetric spaces and the Tits-Koecher construction of the Lie algebras of corresponding groups. We then give the bosonic construction of the Lie algebra ofE ₇₍₇₎ in SU(8), SO(8) and U(7) bases and study its properties. Application of our method toE ₇₍₇₎ leads to reducible unitary representations.Dedicated to Feza Gürsey on the occasion of his 60th birthdayAlexander von Humboldt Fellow, on leave from Physics Dept., Bogaziçi University, Istanbul/Turkey: work supported in part by TBTAK, The National Science and Technology Council of Turkey     

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 $\text{?10}{}^7\text{GeV}$.     

Parity violating effects in dilepton production using polarized targets

Parity violating effects in PP → μ⁺μ^?X and $\text{P}\text{P}\text{→ μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{X}$ with the polarized targets have been calculated in the parton picture. The weak neutral currents used are based on an SU(2)_L × SU(2)_R × U(1) model. The result for the Weinbergy-Salam model occurs as a special case.     

SU(3) ⊗ SU(2) ⊗ U(1) from D = 11 supergravity

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ? SU(2) ? U(1) as a symmetry of the internal space M₇. These solutions lead, in dimensional reduction, to SU(3) ? SU(2) ? U(1) gauge fields.In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ? U(1) ? U(1) of M₇ in SU(3) ? SU(2) ? U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl $\text{F}{}_{\mathrm{\alpha \beta \gamma \delta }}\text{≠ 0}$. It breaks all sypersymmetries.     

Spatial theory for algebras of unbounded operators

In this paper, the spatial theory of ¹-automorphisms is investigated in the context of algebras of unbounded operators. In particular, it is shown that ¹-automorphisms, satisfying some order relation, of the Op¹-algebra generated by the position and momentum operators q_j, p_j(j=1,...., n) on the Schwartz space $\text{I}\text{(}\text{R}{}^{\mathrm{n}}\text{)}$ are unitarily implemented.     

Production of very massive Higgs bosons

We compare Higgs boson production mechanisms at multi-TeV hadronic colliders. In addition to the previously investigated processes gluon + gluon → H and $\text{q}\text{q}\text{→ V}{}^1\text{→}\text{VH}\text{(}\text{V}\text{=}\text{W, Z}\text{)}$, we consider Higgs boson formation by pairs of virtual W's or Z's, a process analogous to two-photon collisions in e⁺e^? scattering. The Higgs production process $\text{W}{}^1\text{W}{}^1\text{→}\text{H}$ is dominated by longitudinal W's and is the most important mechanism for M_H > 6 M_W, if the top quark mass is about 30 GeV.     

Fluid-dynamical description of nuclear collective excitations

The role of antisymmetric tensor fields in the gauging of groups is related to theorems on cohomology theory, and Cartan integrable systems are discussed. Examples are given. Various possibilities to gauge d = 11 supergravity by decontracting its underlying group are considered. In particular the simple supergroups Osp (1 | 64) and SU(32 | 1) yield a negative result, but a certain non-semisimple supergroup containing Osp (1 | 32) is proposed as a viable candidate. The corresponding action would no longer contain the 3-index photon A_μν?, but instead a second spin $\text{3}\text{2}$ field η_μ and boson fields $\text{B}{}_{\mathrm{\mu }}{}^{\mathrm{a1a2}}$ and $\text{B}{}_{\mathrm{\mu }}{}^{\mathrm{a1\dots a5}}$. A first order formalism for d = 11 is presented. It is to be used for an improved form of dimensional reduction.     

1616 supergravity coupled to matter: The low energy limit of the superstring

We analyze irreducible, N = 1 supergravity theories with 16 fermionic degrees of freedom. The lagrangians for pure $\text{16}\text{16}$ supergravity, and for $\text{16}\text{16}$ supergravity coupled to arbitrary chiral superfields are constructed. These theories are shown to have natural SU(1,1) non-compact symmetry. The low energy field theory limit of the superstring is conjectured to be of this type.     

Magnetic moments at backbending and spectroscopy of 134Ce

Employing the static hyperfine fields at cerium nuclei in magnetized Fe and Gd hosts, the g-factor of the ¹³⁴Ce(10⁺) state at backbending (E_{x = 3719.3 keV}) has been determined as g = ? 0.30 (25). The coexistence of this neutron-dominated state with the ($\text{v}\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{n}}\text{10}{}^{\mathrm{+}}$ isomer (E_x = 3208.5 keV, g = ?0.19(1)) is unexpected. A comprehensive spectroscopic study following the ¹²²Sn(¹⁶O, 4n) reaction, including γ-angular distributions, prompt and delayed γ coincidence and recoil-distance measurements has yielded new information on quasi-collective bands of both parities. The properties of the low-lying positive-parity states are well described by the interacting boson model.     

Classical integrable finite-dimensional systems related to Lie algebras

During the last few years many dynamical systems have been identified, that are completely integrable or even such to allow an explicit solution of the equations of motion. Some of these systems have the form of classical one-dimensional many-body problems with pair interactions; others are more general. All of them are related to Lie algebras, and in all known cases the property of integrability results from the presence of higher (hidden) symmetries. This review presents from a general and universal viewpoint the results obtained in this field during the last few years. Besides it contains some new results both of physical and mathematical interest.The main focus is on the one-dimensional models of n particles interacting pairwise via potentials V(q) = g²ν(q) of the following 5 types: $\text{ν}{}_{\mathrm{<mtext>I</mtext>}}\text{(q)=q}{}^{\mathrm{?2}}\text{, ν}{}_{\mathrm{<mtext>II</mtext>}}\text{(q)=a}{}^{\mathrm{?2}}\text{sinh}{}^2\text{(aq), ν}{}_{\mathrm{<mtext>III</mtext>}}\text{(q)=a}{}^2\text{/}\text{sin}\text{2(aq), ν}{}_{\mathrm{<mtext>IV</mtext>}}\text{=a}{}^2\text{P}\text{(aq), , ν}{}_{\mathrm{<mtext>V</mtext>}}\text{(q)=q}{}^{\mathrm{?2}}\text{+ω}{}^2\text{q}{}^2$. Here $\text{P}$(q) is the Weierstrass function, so that the first 3 cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbor potential, g_j²exp[-a(q_j?q_j+1)], is moreover considered. Various generalizations of these models, naturally suggested by their association with Lie algebras, are also treated.     

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$\text{(1?(}\text{M}{}_{\mathrm{<mtext>H</mtext>}}{}^2\text{M}{}_{\mathrm{<mtext>Z</mtext>}}{}^2\text{))}{}^3$.     

Theory of cyclotron resonance lineshape for an electron-impurity system in two dimensions

Using the proper connected diagram expansion which incorporates the quasi-particle effect in a natural manner, we calculated the cyclotron resonance width Γ and frequency shift Δ in the extreme quantum limit, (a) Δ = 0 for any form of interaction potential, (b) Γ ∝ n_I^{$\text{1}\text{2}$}B^{$\text{1}\text{2}$} for a short range interaction, and (c) $\text{Γ = π}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{ze}{}^2\text{k}{}^{\mathrm{?1}}\text{n}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{I}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ for the unscreened Coulomb interaction, are obtained in the weak coupling approximation. The result (a) and the field (B)- and concentration (n_I)-dependence in case (b) are in satisfactory agreement with experimental data on the Si space-charge layers at the surface carrier densities higher than 1 × 10¹²cm^-2 and at liquid helium temperatures, where the main source of relaxation is thought to arise from a short-range interaction.     

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.     

Preliminary evidence for UA(1) breaking in QCD from lattice calculations

We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d⁴x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g^?12 and g⁶, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{≌(0.11±0.02)K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, K being the SU(2) quarkless string tension. Although a larger value for $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ would be preferable, we are led to conclude (at least tentatively) that the U_A(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.     

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.