Remarks on A 2 Toda theory

We study the Toda field theory with finite Lie algebras using an extension of the Goulian-Li technique. In this way, we show that, after integrating over the zero mode in the correlation functions of the exponential fields, the resulting correlation function resembles that of a free theory. Furthermore, it is shown that for some ratios of the charges of the exponential fields the four-point correlation functions which contain a degenerate field satisfy the Riemann ordinary differential equation. Using this fact and the crossing symmetry, we derive a set of functional equations for the structure constants of the A ₂ Toda field theory.     

Bruhat Order in Full Symmetric Toda System

In this paper we discuss some geometrical and topological properties of the full symmetric Toda system. We show by a direct inspection that the phase transition diagram for the full symmetric Toda system in dimensions n = 3, 4 coincides with the Hasse diagram of the Bruhat order of symmetric groups S ₃ and S ₄. The method we use is based on the existence of a vast collection of invariant subvarieties of the Toda flow in orthogonal groups. We show how one can extend it to the case of general n. The resulting theorem identifies the set of singular points of dim = n Toda flow with the elements of the permutation group S _n , so that points will be connected by a trajectory, if and only if the corresponding elements are Bruhat comparable. We also show that the dimension of the submanifolds, spanned by the trajectories connecting two singular points, is equal to the length of the corresponding segment in the Hasse diagram. This is equivalent to the fact that the full symmetric Toda system is in fact a Morse–Smale system.     

Z′ mass limits,masses and coupling of higgs bosons,and Z′ decays in an E6 superstring based model

We demonstrate that current phenomenological constraints on Z-Z′ mixing for an E₆ grand unified group with low energy gauge group SU(2)_L×U(1)_Y×U(1)_Y, allow only a narrow range of Higgs vacuum expectation values consistent with possibilities favored by renormalization group expectations. Modest improvements in bounds on this mixing will lead to substantial bounds on the Z′ mass if alternative renormalization group solutions are not found. We then explore the constraints upon relations between Higgs masses in this model. In addition we explore the couplings of these Higgs to the gauge particles of the theory and emphasize the associated implications for Higgs detection in decays of the Z′.     

Characteristic Classes and Hitchin Systems. General Construction

We consider topologically non-trivial Higgs G-bundles over Riemann surfaces ?? _g with marked points and the corresponding Hitchin systems. We show that if G is not simply-connected, then there exists a finite number of different sectors of the Higgs bundles endowed with the Hitchin Hamiltonians. They correspond to different characteristic classes of the underlying bundles defined as elements of ${H^{2}(\Sigma_g, \mathcal{Z}(G))}$ , ( ${\mathcal{Z}(G)}$ is a center of G). We define the conformal version CG of G - an analog of GL(N) for SL(N), and relate the characteristic classes with degrees of CG-bundles. We describe explicitly bundles in the genus one (g =? 1) case. If ??₁ has one marked point and the bundles are trivial then the Hitchin systems coincide with Calogero-Moser (CM) systems. For the nontrivial bundles we call the corresponding systems the modified Calogero-Moser (MCM) systems. Their phase space has the same dimension as the phase space of the CM systems with spin variables, but less number of particles and greater number of spin variables. Starting with these bundles we construct Lax operators, quadratic Hamiltonians, and define the phase spaces and the Poisson structure using dynamical r-matrices. The latter are completion of the classification list of Etingof-Varchenko corresponding to the trivial bundles. To describe the systems we use a special basis in the Lie algebras that generalizes the basis of ??t Hooft matrices for sl(N). We find that the MCM systems contain the standard CM subsystems related to some (unbroken) subalgebras. The configuration space of the CM particles is the moduli space of the stable holomorphic bundles with non-trivial characteristic classes.     

Gauge theoretical realization of the superweak model of CP violation

It is pointed out that the presence in a gauge theory of vector bosons or left-over Higgs bosons with a weak interaction strength of the order of10^?11G_E and which have CPviolating couplings to the strangeness-changing neutral current, will lead to the superweak model of CP violation. An example of such a theory, based on the gauge group SU (2) ?U(1), is given.     

Higgs boson emission in very rare decays of an extra vector boson

We explore the phenomenological structure of E ₆-inspired grand unified group with the gauge group SU(3)_c×SU(2)_L×U(1)_Y×U(1), the emphasis being laid upon its implications for Higgs boson observation. In particular, we discuss the probability for the mass eigenstate Z ₂ to decay into a Higgs particle and a bound state composed of heavy quarks. Constraints on and relations between the Z ₂ and Higgs masses are presented.     

Degenerate Higgs andZ Boson at LEP200

We investigate the problem of detecting the Higgs boson ifM _H ≈M _z at LEP200, the main problem being the large background fromZZ production. Since this background should be accurately calculable, we estimate that the existence of the Higgs can be established with about 3 fb^?1 of integrated luminosity. We also discuss how the signal can be improved if efficient tagging ofb quarks is available.     

Electroweak baryon number violation at finite temperature

We consider baryon and lepton number violating processes in the electroweak theory induced by gauge and Higgs fields passing the sphaleron solution at finite temperature. We show that for temperatures larger than 19 GeV the anomalous baryon and lepton number violating processes are suppressed by the Boltzmann factor exp (?βE _sp), whereE _sp is the sphaleron energy, rather than by the instanton tunneling factor exp (?8π²/g ²). We caculate the rate of baryon and lepton number violating processes at finite temperature and determine the freezing temperature of the anomalous processes in the early universe as a function of the Higgs mass. We compare the freezing temperature with the critical temperature of the electroweak phase transition infered from the one-loop finite-temperature effective potential. We obtain a critical Higgs mass of the order of 100 GeV, slightly depending on the top mass and the magnitude of the pre-exponential factor in the rate of theB non-conservation, above which the anomalous processes are certainly in equilibrium after the electroweak phase transition. Assuming that the temperature-dependence of the sphaleron energy is given by that found from the one-loop finitetemperature effective potential, this critical Higgs mass is lowered to a value of the order of 50 GeV.     

Gaussian effective potential for the U(1) Higgs model

In order to investigate the Higgs mechanism nonperturbatively, we compute the Gaussian effective potential of the U(1) Higgs model (“scalar electrodynamics”). We show that the same simple result is obtained in three different formalisms. A general covariant gauge is used, with Landau gauge proving to be optimal. The renormalization generalizes the “autonomous” renormalization for λ?⁴ theory and requires a particular relationship between the bare gauge coupling e _B and the bare scalar self-coupling λ _B. When both couplings are small, then λ is proportional to e⁴ and the scalar/vector mass-squared ratio is of order e², as in the classic 1-loop analysis of Coleman and Weinberg. However, as λ increases, e reaches a maximum value and then decreases, and in this “nonperturbative” regime the Higgs scalar can be much heavier than the vector boson. We compare our results to the autonomously renormalized 1-loop effective potential, finding close agreement in the physical predictions. The main phenomenological implication is a Higgs mass of about 2 TeV.     

On a2(1) reflection matrices and affine Toda theories

We construct new non-diagonal solutions to the boundary Yang-Baxter equation corresponding to a two-dimensional field theory with U_q(a₂⁽¹⁾) quantum affine symmetry on a half-line. The requirements of boundary unitarity and boundary crossing symmetry are then used to find overall scalar factors which lead to consistent reflection matrices. Using the boundary bootstrap equations we also compute the reflection factors for scalar bound states (breathers). These breathers are expected to be identified with the fundamental quantum particles in a₂⁽¹⁾ affine Toda field theory and we therefore obtain a conjecture for the affine Toda reflection factors. We compare these factors with known classical results and discuss their duality properties and their connections with particular boundary conditions.     

Induced Higgs couplings to neutral bosons in e+e− collisions

We calculate induced couplings of the type HV_γ in the standard model, where H is a Higgs meson and V is a virtual or real neutral gauge boson (Z⁰ or photon). Numerous applications are given for e⁺e^? collisions and various Higgs meson decays. The calculated rates are in general somewhat too low to make these processed an attractive way to search for the Higgs boson. However, once it has been found, it is argued that these processes should be studied experimentally since the induced couplings probe the structure of the gauge theory in an interesting way. In particular, it may be possible to infer the existence of one or more heavy fermion generations (of mass ?m_Z) by observing their virtual effects in radiative decays into Higgs particles. We also briefly treat the related coupling HV_γ with V a heavy quarkonium vector state.     

A grand unified theory based onSU(n, 1)-minimal supergravity

We discuss a grand unified theory in the framework ofSU(n, 1) minimal supergravity with the Planck mass as the only input mass scale.M _W ≈m _3/2 is fixed by radiative corrections to be naturally ?M _P1. Due to the particular form of explicit soft supersymmetry breaking a light singlet can be used to obtain naturally light Higgs doublets and for a new mechanism for radiativeSU (2)×U(1) breaking. The low energy particle spectrum is very restricted withm _3/2≈10⁴ GeV.     

Constraints on extended neutral gauge structures

Indirect precision data are used to constrain the masses of possible extra Z^′ bosons and their mixings with the ordinary Z. We study a variety of Z^′ bosons as they appear in E₆ and left-right unification models, the sequential Z boson, and the example of an additional U(1) in a concrete model from heterotic string theory. In all cases the mixings are severely constrained (sinθ<0.01). The lower mass limits are generally of the order of several hundred GeV and competitive with collider bounds. The exception is the Z_ψ boson, whose vector couplings vanish and whose limits are weaker. The results change little when the ρ parameter is allowed, which corresponds to a completely arbitrary Higgs sector. On the other hand, in specific models with minimal Higgs structures the limits are generally pushed into the TeV region.     

Double Higgs production at the linear colliders and the probing of the Higgs self-coupling

We study double Higgs production in the e⁺e^? and γγ modes of the linear collider. It is also shown how one can probe the scalar potential in these reactions. We discuss the effective longitudinal W approximation in γγ processes and the W _LW_L luminosities in the two modes of a high-energy linear collider. A generalised non-linear gauge-fixing condition, which is particularly useful for tree-level calculations of electroweak processes for the laser induced collider, is presented. Its connection with the background-field approach to gauge fixing is given.     

Little heterotic strings

We discuss toroidal orbifolds of the E ₈×E ₈ heterotic string, in which the free-fermionic Higgs–matter splitting is implemented by a shift in the internal lattice coupled with the fermion numbers of the gauge degrees of freedom. We consider models in which some choices of the orbifold result in the projection of the graviton. In the models that we consider the projection also results in flipping the spin–statistics assignments in the massive string spectrum, whereas the massless spectrum retains the conventional spin–statistics assignments. We argue that the partition functions are mathematically consistent for one- and multi-loop amplitudes, owning to the existence of supersymmetry in the spectrum. A duality between different models at non-zero temperature is briefly discussed.     

Higgs–matter splitting in quasi-realistic orbifold string GUTs

E₆ grand unification combines the standard model matter and Higgs states in the single 27 representation. I discuss how the E₆ structure underlies the quasi-realistic free fermion heterotic-string models. E₆→SO(10)×U(1) breaking is obtained by a GSO phase in the N=1 partition function. The equivalence of this symmetry breaking phase with a particular choice of boundary condition basis vectors, which is used in the quasi-realistic models, is demonstrated in several cases. As a result, matter states in the spinorial 16 representation of SO(10) arise from the twisted sectors, whereas the Higgs states arise from the untwisted sector. Possible additional phenomenological implications of this E₆ symmetry breaking pattern are discussed.     

Vector boson scattering ate + e − colliders as a test ofW ±,Z 0, γ self-interactions

We investigate the potential of a high-energye ⁺ e ^? collider (e.g., CLIC,E _e ⁺=E _e ^?=1 TeV) for determining trilinear and quadrilinear vector boson self-interactions in various vector boson scattering processes which can be measured in reactions of the type \(e^ + e^ - \to (e^ + e^ - ,ve^ - ,\bar ve^ + ,v\bar v) + VV'\) . Our analysis is based upon a recently suggested single parameter Lagrangian model for vector boson self-interactions incorporating globalSU(2) weak isospin symmetry broken by electromagnetism and a minimal increase of vector boson scattering tree amplitudes as a function of the energy. The results are compared with theSU(2) _L ×U(1) _Y predictions for the cases of a light and a heavy Higgs boson. We find that the crosssection for the production of a vector boson pair,VV′, is very sensitively dependent on the magnitude of the single free parameter, κ, the anomalous magnetic dipole moment of theW ^±. The cross-section changes by approximately one order of magnitude, even near production threshold, if κ is varied by one unit around theSU(2) _L ×U(1) _Y value of κ=1.     

E6 symmetry breaking in the superstring theory

We derive two methods for determining the symmetry breaking of E₆ in the low energy superstring theory, and classify all breaking patterns. A method for calculating the effective Higgs vacuum expectation values is presented. We show that there are theories with naturally light SU₂^w Higgs doublets, and classify all theories in which this occurs. The phenomenology of spontaneously broken E₆ theories is discussed, emphasizing the issues of nucleon decay and neutrino masses.     

Quantum corrections to the classical reflection factor in a2(1) Toda field theory

The O(β²) quantum correction to the classical reflection factor is calculated for one of the integrable boundary conditions of a₂⁽¹⁾ affine Toda field theory. This is found to agree with the conjectured exact reflection factor of the quantum theory. We consider the existence of other exact reflection factors consistent with our perturbative answer and examine the question of how duality transformations might relate theories with different boundary conditions.     

String theory and the strong CP problem

The axion solution to the strong CP problem is reexamined. It is noted that in order for the axion to solve the problem, it is necessary that high-energy contributions to the axion potential be sufficiently small. Examples are constructed where this is not the case. It is noted that this problem arises in many interesting compactifications of string theory and in popular supergravity models, and that this provides a significant phenomenological constraint on model building. In string theory, these constraints are investigated both for compactifications with unification in E₆ and in O(10) and SU(5). We observe that the latter case is especially exciting, since one can have extra light Higgs doublets while satisfying renormalization group constraints.