On the Experimental Effects of the Off-shell Structure in Anomalous Neutral Triple Gauge Vertices

We discuss differences between on-shell and off-shell treatments in the search for anomalous neutral triple gauge couplings in $\mathrm{e^+ e^-}$ collisions. We find that the usual on-shell framework represents an optimal starting point, covering all scenarios in which a reasonable experimental sensitivity is expected. We show that off-shell effects lead to negligible deviations at the experimental level, provided that $\mathrm{e^+ e^-}\to\mathrm{f}\bar{\mathrm{f}}\gamma$ and \mathrm{e^+ e^-}\to\mathr performed in regions where \mathrm{Z}^*\to\mathrm{f}\bar{\mathrm{f}},\mathrm{f^\prime}\math production is dominant. For consistency reasons, we advocate the use of a natural extension of the on-shell definitions, which takes into account the correct off-shell dependences. Contrary to what has been recently suggested in the literature, we find that no $SU(2)_L\times U(1)_Y$ constraints among neutral triple gauge couplings can be imposed in a general case.Comment: 15 pages, 6 figures. Final versio

Generalization of the matrix product ansatz for integrable chains

We present a general formulation of the matrix product ansatz for exactly integrable chains on periodic lattices. This new formulation extends the matrix product ansatz present on our previous articles (F. C. Alcaraz and M. J. Lazo J. Phys. A: Math. Gen. 37 (2004) L1-L7 and J. Phys. A: Math. Gen. 37 (2004) 4149-4182.)Comment: 5 pages. to appear in J. Phys. A: Math. Ge

Cerenkov angle and charge reconstruction with the RICH detector of the AMS experiment

The Alpha Magnetic Spectrometer (AMS) experiment to be installed on the International Space Station (ISS) will be equipped with a proximity focusing Ring Imaging Cerenkov (RICH) detector, for measurements of particle electric charge and velocity. In this note, two possible methods for reconstructing the Cerenkov angle and the electric charge with the RICH, are discussed. A Likelihood method for the Cerenkov angle reconstruction was applied leading to a velocity determination for protons with a resolution of around 0.1%. The existence of a large fraction of background photons which can vary from event to event, implied a charge reconstruction method based on an overall efficiency estimation on an event-by-event basis.Comment: Proceedings submitted to RICH 2002 (Pylos-Greece

Exactly solvable interacting vertex models

We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core interactions among pair of vertices at larger distances.The associated row-to-row transfer matrices are diagonalized by using the recently introduced matrix product {\it ansatz}. Similarly as the relation of the six-vertex model with the XXZ quantum chain, the row-to-row transfer matrices of these new models are also the generating functions of an infinite set of commuting conserved charges. Among these charges we identify the integrable generalization of the XXZ chain that contains hard-core exclusion interactions among the spins. These quantum chains already appeared in the literature. The present paper explains their integrability.Comment: 20 pages, 3 figure

The Exact Solution of the Asymmetric Exclusion Problem With Particles of Arbitrary Size: Matrix Product Ansatz

The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product {\it ansatz}. Due to the similarity of the master equation and the Schr\"odinger equation at imaginary times the solution of these problems reduces to the diagonalization of a one dimensional quantum Hamiltonian. We present initially the solution of the problem when an arbitrary mixture of molecules, each of then having an arbitrary size ($s=0,1,2, ...$) in units of lattice spacing, diffuses asymmetrically on the lattice. The solution of the more general problem where we have | the diffusion of particles belonging to $N$ distinct class of particles ($c=1, ..., N$), with hierarchical order, and arbitrary sizes is also solved. Our matrix product {\it ansatz} asserts that the amplitudes of an arbitrary eigenfunction of the associated quantum Hamiltonian can be expressed by a product of matrices. The algebraic properties of the matrices defining the {\it ansatz} depend on the particular associated Hamiltonian. The absence of contradictions in the algebraic relations defining the algebra ensures the exact integrability of the model. In the case of particles distributed in $N>2$ classes, the associativity of the above algebra implies the Yang-Baxter relations of the exact integrable model.Comment: 42 pages, 1 figur

Exact solutions of exactly integrable quantum chains by a matrix product ansatz

Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Bethe ansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonian are given by a sum of permutations of appropriate plane waves. In this paper, alternatively, we present a matrix product ansatz that asserts that those amplitudes are given in terms of a matrix product. The eigenvalue equation for the Hamiltonian define the algebraic properties of the matrices defining the amplitudes. The existence of a consistent algebra imply the exact integrability of the model. The matrix product ansatz we propose allow an unified and simple formulation of several exact integrable Hamiltonians. In order to introduce and illustrate this ansatz we present the exact solutions of several quantum chains with one and two global conservation laws and periodic boundaries such as the XXZ chain, spin-1 Fateev-Zamolodchikov model, Izergin-Korepin model, Sutherland model, t-J model, Hubbard model, etc. Formulation of the matrix product ansatz for quantum chains with open ends is also possible. As an illustration we present the exact solution of an extended XXZ chain with $z$-magnetic fields at the surface and arbitrary hard-core exclusion among the spins.Comment: 57 pages, no figure

Track fitting in slightly inhomogeneous magnetic fields

A fitting method to reconstruct the momentum and direction of charged particles in slightly inhomogeneous magnetic fields is presented in detail. For magnetic fields of the order of 1 T and inhomogeneity gradients as large as 1 T/m the typical momentum bias due to the proposed approximations is of the order of few MeV, to be compared with scattering components of the order of 20 MeV or even larger. This method is currently being employed in the reconstruction programs of the AMS experiment.Comment: 12 pages, Nulc. Instr. Meth. A accepte

Critical Behaviour of Mixed Heisenberg Chains

The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S') SU(2) operator interacting with a XXZ like interaction (anisotropy $\Delta$). Our results indicate universal properties for all these chains. The whole phase, $1>\Delta>-1$, where the models change from ferromagnetic $( \Delta=1 )$ to ferrimagnetic $(\Delta=-1)$ behaviour is critical. Along this phase the critical fluctuations are ruled by a c=1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions.Comment: 21 pages, standard LaTex, to appear in J.Phys.A:Math.Ge

Anomalous Gauge Boson Couplings in the e^+ e^- -> ZZ Process

We discuss experimental aspects related to the $\mathrm{e^+ e^-} \to \mathrm{Z}\mathrm{Z}$ process and to the search for anomalous ZZV couplings (V$= \mathrm{Z}, \gamma$) at LEP2 and future $\mathrm{e^+ e^-}$ colliders. We present two possible approaches for a realistic study of the reaction and discuss the differences between them. We find that the optimal method to study double Z resonant production and to quantify the presence of anomalous couplings requires the use of a complete four-fermion final-state calculation.Comment: 28 pages, 12 figures, final version for Phys. Rev.

Exactly Solvable Interacting Spin-Ice Vertex Model

A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest neighbor interactions, the vertices defining the model also interact alongone of the diagonals of the lattice. Such family of models includes in a special limit the standard six-vertex model. The exact solution of these models gives the first application of the matrix product ansatz introduced recently and applied successfully in the solution of quantum chains. The phase diagram and the free energy of the models are calculated in the thermodynamic limit. The models exhibit massless phases and our analyticaland numerical analysis indicate that such phases are governed by a conformal field theory with central charge $c=1$ and continuosly varying critical exponents.Comment: 14 pages, 11 figure