Invariant tensors inSU(3). II

InvariantSU(3) octet tensors are constructed in terms of matrices and applied to the problem of forming tensors from a single octet used repeatedly. Next a similar problem but with two octets is considered which demonstrates that different outer products of invariant tensors may be related. Finally, a theorem is proved which shows that the number of invariant tensors is essentially finite, and that relations of ranks greater than six exist on outer products of these tensors.     

Invariant tensors for simple groups

The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l, and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A_l algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) are su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given.     

Density ofZ(3) flux loops inSU(3) lattice gauge theory in four dimensions

A mixed actionSU(3)-SU(3)/Z(3) gauge theory is simulated by Monte Carlo methods on a 4⁴ lattice. The density ofZ(3) flux loops is measured.     

More on Higgs Bosons inSU(5)

In the framework of the minimalSU(5) model of Georgi and Glashow the explicit couplings between the various mass eigenstate Higgs bosons and the gauge fields as well as the Higgs boson self couplings are presented. As an application bounds for the parameters of the Higgs potential and for the Higgs boson masses are derived by applying partial wave unitarity to the tree graphs of Higgs-Higgs scattering.     

Higgs production inSU(2) c symmetric interactions

We study the sensitivity of Higgs production and decay processes to theSU(2) _c symmetric couplingsO _W andO _UW . Remarkable results are obtained in the case of γγ→H and for certain ratios of Higgs decay widths. We also discuss and complete previous results on unitarity constraints for such couplings.     

Rotating colored black hole inSU(5) GUT

Gravity coupled to theSU(5) GUT is considered. A family of stationary axisymmetric solutions is obtained, which represents a rotating black hole with a QCD color hair as well as electromagnetic hairs.     

Analytic solution inSU(N) lattice-gauge model of Migdal

Migdal's renormalization group transformation for theSU (N) pure lattice-gauge model is solved in the weak coupling regime by a perturbative expansion in the coupling constant. The heat-kernel model is shown to be a low-order perturbative solution of the Migdal recursion relation. The parameters of the -function are fixed within theSU (N) Migdal model. The critical coupling constant of the deconfining phase transition is approximately calculated and compared with constants obtained by the heat-kernel model and numerical calculations. The improved actions for theSU (2) andSU (3) are presented for realistic lattice-gauge methods such as the Monte Carlo simulation.     

The onset of deconfinement inSU(2) lattice gauge theory

InSU(2) lattice gauge theory, we study deviations from ideal gas behaviour near the deconfinement point. On lattices of sizeN _σ ³ ×4,N _σ=8, 12, 18 and 26, we calculate the quantityΔ≡(ε?3P)/T ⁴. It increases sharply just aboveT _c , peaks atT/T _c =1.15 ±0.05 and then drops quickly. This form of behaviour is shown to be the consequence of a second order phase transition. Dynamically it could arise because just aboveT _c , the low momentum states of the system are remnant massive modes rather than deconfined massless gluons.     

Proton decay induced by instantons inSU(5) grand unification

Instantons infinitesimally turned out of theSU _c (3) subspace of spontaneously brokenSU(5) gauge theory induce a baryon number violating interaction proportional 1/μ _X ² like heavy vector boson exchange, but with a different tensor structure.     

No domain wall problem inSU(N) Grand Unified Theory

It is shown that a wide class ofSU(n)×U(1)_P.Q. Grand Unified Theories can avoid the domain wall problem.     

A finite free energy density inSU(2) pure Yang-Mills thermodynamics

We show how monopoles, which are stabilized by quantum fluctuations and have a massM～T, contribute to yield an infrared finite expansion for the free energy density of Yang-Mills thermodynamics. The leading behaviour of this expansion is consistent with the perturbative one, but in higher orders it does involve both contributions, which are nonanalytic atg ²=0, and additional analytic terms, which are of nonperturbative origin.     

Dynamical electroweak symmetry breaking via fermion condensates inSU(5) model

TheSU(4) symmetry scheme, used in a previous paper for the study of the 2v double decay, is applied to the study of the 0v double decay. Differences and similarities between the 2 processes are emphasized. The sensitivity to short-range correlations is discussed.     

Polyakov loop distributions near deconfinement inSU(2) lattice gauge theory

The distribution function of the Polyakov loop is investigated on a 16³×3 lattice in the neighbourhood of the deconfinement transition ofSU(2) gauge theory. We find, that well above the transition the distribution is a Gaussian; when the coupling approaches the critical point it is modified due to phase flip attempts of the system. Corresponding distributions for the plaquettes remain, however, Gaussian. For one coupling close to the transition we study the distributions on 8³, 12³ and 18³×4 lattices and show that strong finite size effects are present. Using the maximum values of the Gaussian parts of the distributions we construct a more physical (and therefore scaling) order parameter whose critical exponent is in excellent agreement with the universality hypothesis.     

Scaling behaviour of Creutz ratios inSU(2) lattice gauge theory

An analysis of the scaling behaviour of Creutz ratios on large lattices is given forSU(2) gauge theory. The β-interval is 2.5≦β≦2.8. Under a factor 2 scaling test, after multiplicative corrections for lattice artifacts, the Monte Carlo data show deviations from scaling, which are similar for all values of β. The ratios can be fitted successfully by a sum of three perturbative terms and an exponentially decreasing nonperturbative term. For many ratios the latter turns out to be very small, and its size dependence at fixed β is consistent with that of an area term in the Wilson loops. The deviation of the corresponding exponents from the ones expected for an area term gives a coherent cxplanation of the observed departures from scaling. It is well possible that for fixed spatial extension (in lattice units) nonperturbative contributions vanish so fast that they cannot be interpreted as physical effects.     

Electric dipole moment and chromoelectric dipole moment of the top quark inSU(3)C×SU(3)L×U(1)X model

We show that inSU(3) _C ×SU(3) _L ×U(1) _X model, the leading contribution to the electric and chromolelectric dipole moment of the top quark is due to the one-loop diagrams which come from exchanging the charged and neutral Higgs bosons. The dipole moments are typically of the order of 10^?19 e-cm and 10^?19 g-cm respectively, for the values of relative phases of the vev's such that CP violation is maximal. From an experimental point of view, theq ² dependence of dipole moment form factors is given.     

Generalized permutation symmetry and the flavour problem inSU(2)L×U(1)

A generalized permutation group is introduced as a possible horizontal symmetry forSU(2)_L×U(1) gauge theories. It leads to the unique two generation quark mass matrices with a correct prediction for the Cabibbo angle. For three generations the model exhibits spontaneousCP violation, correlates the Kobayashi-Maskawa mixing parameterss ₁ ands ₃ and predicts an upper bound for the running top quark mass of approximately 45 GeV. The hierarchy of generations is due to a hierarchy of vacuum expectation values rather than of Yukawa coupling constants.