Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

Ampcalculator (AMPC) is a Mathematica (c) based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O(p(4))) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G(27). Another illustrative set of amplitudes at tree level we provide is in the context of tau-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.

Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using phi-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a 6 function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of phi-mapping. In our solution, the flux of this soliton is naturally quantized.

Signatures of doubly charged Higgs in the SU(3)(L) circle times U(1)(N) model at the CERN LHC

The scalar sector of the simplest version of the 3-3-1 electroweak model is constructed with three Higgs triplets only. We show that a relation involving two of the constants of the model, two vacuum expectation values of the neutral scalars, and the mass of the doubly charged Higgs boson leads to important information concerning the signals of this scalar particle.

Neutral Higgs bosons in the SU(3)(L)circle times U(1)(N) model

The SU(3)(L)circle times U(1)(N) electroweak model predicts new Higgs bosons beyond the one of the standard model. In this work we investigate the signature and production of neutral SU(3)(L)circle times U(1)(N) Higgs bosons in the e(-)e(+) Next Linear Collider and in the CERN Linear Collider . We compute the branching ratios of two of the SU(3)(L)circle times U(1)(N) neutral Higgs bosons and study the possibility to detect them and the Z' extra neutral boson of the model.

A statistical law for multiplicities of SU(3) irreps (lambda, mu) in the plethysm {eta} circle times(3) {m} -> (lambda, mu)

A statistical law for the multiplicities of the SU(3) irreps (lambda, mu) in the reduction of totally symmetric irreducible representations {m} of U(N), N = (eta + 1) (eta + 2)/2 with eta being the three-dimensional oscillator major shell quantum number, is derived in terms of the quadratic and cubic invariants of SU(3), by determining the first three terms of an asymptotic expansion for the multiplicities. To this end, the bivariate Edgeworth expansion known in statistics is used. Simple formulae, in terms of m and eta, for all the parameters in the expansion are derived. Numerical tests with large m and eta = 4, 5 and 6 show good agreement with the statistical formula for the SU(3) multiplicities.

FLAVOR-CHANGING NEUTRAL CURRENTS IN SU(3)L-CIRCLE-TIMES-U(1)Y MODELS

We consider flavor changing neutral current effects coming from the Z' exchange in 3-3-1 models. We show that the mass of this extra neutral vector boson may be less than 2 TeV and discuss the problem of quark family discrimination.

HEAVY CHARGED LEPTONS IN AN SU(3)L-CIRCLE-TIMES-U(1)N MODEL

We consider an SU(3)L x U(1)N model for the electroweak interactions which includes extra charged leptons which do not mix with the known leptons. These new leptons couple to Z0 only through vector currents. We consider constraints on the mass of one of these leptons coming from the Z0 width and from the muon (g - 2) factor. The last one is less restrictive than the former.

Study of the ℤ3 symmetry in QCD at finite temperature and chemical potential using a worm algorithm

Traditional Monte Carlo simulations of QCD in the presence of a baryon chemical potential are plagued by the complex phase problem and new numerical approaches are necessary for studying the phase diagram of the theory. In this work we consider a ℤ3 Polyakov loop model for the deconfining phase transition in QCD and discuss how a flux representation of the model in terms of dimer and monomer variable solves the complex action problem. We present results of numerical simulations using a worm algorithm for the specific heat and two-point correlation function of Polyakov loops. Evidences of a first order deconfinement phase transition are discussed. © 2013 American Institute of Physics.

New fermions and a vectorlike third generation in SU(3)(C)circle times SU(3)(L)circle times U(1)(N) models

We study two 3-3-1 models with (i) five (four) charge 2/3 (-1/3) quarks and (ii) four (five) charge 2/3 (-1/3) quarks and a vectorlike third generation. Possibilities beyond these models are also briefly considered.

Aspectos teóricos de um modelo SU(3)C ' tensor product' SU(3)L ' tensor product' U(1)N

Pós-graduação em Física - IFT