Traces on the Sklyanin algebra and correlation functions of the eight-vertex model

We propose a conjectural formula for correlation functions of the Z-invariant (inhomogeneous) eight-vertex model. We refer to this conjecture as Ansatz. It states that correlation functions are linear combinations of products of three transcendental functions, with theta functions and derivatives as coefficients. The transcendental functions are essentially logarithmic derivatives of the partition function per site. The coefficients are given in terms of a linear functional on the Sklyanin algebra, which interpolates the usual trace on finite dimensional representations. We establish the existence of the functional and discuss the connection to the geometry of the classical limit. We also conjecture that the Ansatz satisfies the reduced qKZ equation. As a non-trivial example of the Ansatz, we present a new formula for the next-nearest neighbor correlation functions.Comment: 35 pages, 2 figures, final versio

A Q-operator for the twisted XXX model

Taking the isotropic limit in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary conditions are needed to ensure convergence of the Q-operator construction and derive a quantum Wronskian relation which implies two different sets of Bethe ansatz equations, one above the other below the "equator" of total spin zero. We discuss the limit to periodic boundary conditions at the end and explain how this construction might be useful in the context of correlation functions on the infinite lattice. We also identify a special subclass of solutions to the quantum Wronskian for chains up to a length of 10 sites and possibly higher.Comment: 19 page

Search for the intermediate Mass Higgs Signal at TeV eγe\gamma colliders

The intermediate mass Higgs (IMH) can be abundantly produced through the process $e^-\gamma \rightarrow W^-H\nu$ at TeV $e^-\gamma$ colliders, which are realized by the laser back-scattering method. We search for the signature of $W^-H \rightarrow (jj)(b\bar b)$ plus missing transverse momentum, with and without considering the $b$-tagging. We also analyse all the potential backgrounds from $e^-\gamma \rightarrow W^-Z\nu,\,W^-W^+e^-,\,ZZe^-,\, \bar t b\nu$ and $t\bar t e^-$. With our selective acceptance cuts these backgrounds are reduced to a manageable level. We find that for the entire intermediate mass range 60 -- 150~GeV the Higgs discovery should be viable. We also present detail formulas for the helicity amplitudes of these processes.Comment: Latex(Revtex), 30 pages, 8 figures in postscript format (uuencoded), NUHEP-TH-93-

The Gaugephobic Higgs

We present a class of models that contains Randall-Sundrum and Higgsless models as limiting cases. Over a wide range of the parameter space WW scattering is mainly unitarized by Kaluza-Klein partners of the W and Z, and the Higgs particle has suppressed couplings to the gauge bosons. Such a gaugephobic Higgs can be significantly lighter than the 114 GeV LEP bound for a standard Higgs, or heavier than the theoretical upper bound. These models predict a suppressed single top production rate and unconventional Higgs phenomenology at the LHC: the Higgs production rates will be suppressed and the Higgs branching fractions modified. However, the more difficult the Higgs search at the LHC is, the easier the search for other light resonances (like Z', W', t', exotic fermions) will be.Comment: 20 pages, 3 figure

String correlation functions of the spin-1/2 Heisenberg XXZ chain

We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay. We also make contact with two-point spin-correlation functions in the asymptotic limit.Comment: 23 pages, 4 figures. An incomplete discussion on the limit to the spin-spin correlation function is corrected on page 1

Identifying the Higgs Boson in Electron--Photon Collisions

We analyze the production and detection of the Higgs boson in the next generation of linear $e^+e^-$ colliders operating in the $e\gamma$ mode. In particular, we study the production mechanism $e + \gamma \rightarrow e \gamma \gamma \rightarrow e + H$, where one photon is generated via the laser backscattering mechanism, while the other is radiated via the usual bremsstrahlung process. We show that this is the most important mechanism for Higgs boson production in a $500$ GeV $e\gamma$ collider for M_H\raisebox{-.4ex}{\rlap{\sim}} \raisebox{.4ex}{>}140 GeV. We also study the signals and backgrounds for detection of the Higgs in the different decay channels, $b \bar b$, $W^+W^-$, and $ZZ$, and suggest kinematical cuts to improve the signature of an intermediate mass Higgs boson.Comment: (REVTEX 2.0, 12 pages and 9 figures available upon request, Preprint MAD/PH/753

Holonomy of the Ising model form factors

We study the Ising model two-point diagonal correlation function $C(N,N)$ by presenting an exponential and form factor expansion in an integral representation which differs from the known expansion of Wu, McCoy, Tracy and Barouch. We extend this expansion, weighting, by powers of a variable $\lambda$, the $j$-particle contributions, $f^{(j)}_{N,N}$. The corresponding $\lambda$ extension of the two-point diagonal correlation function, $C(N,N; \lambda)$, is shown, for arbitrary $\lambda$, to be a solution of the sigma form of the Painlev{\'e} VI equation introduced by Jimbo and Miwa. Linear differential equations for the form factors $f^{(j)}_{N,N}$ are obtained and shown to have both a ``Russian doll'' nesting, and a decomposition of the differential operators as a direct sum of operators equivalent to symmetric powers of the differential operator of the elliptic integral $E$. Each $f^{(j)}_{N,N}$ is expressed polynomially in terms of the elliptic integrals $E$ and $K$. The scaling limit of these differential operators breaks the direct sum structure but not the ``Russian doll'' structure. The previous $\lambda$-extensions, $C(N,N; \lambda)$ are, for singled-out values $\lambda= \cos(\pi m/n)$ ($m, n$ integers), also solutions of linear differential equations. These solutions of Painlev\'e VI are actually algebraic functions, being associated with modular curves.Comment: 39 page

Searches for W' and Z' in models with large extra dimensions

Characteristic features of processes mediated by gauge bosons are discussed in the framework of theories with large extra dimensions. It is shown that if gauge bosons propagate in the bulk, then there arises a destructive interference not only between W and W' (or Z and Z'), but also between W' and Z' and the Kaluza-Klein towers of higher excitations of W and Z bosons respectively. Specific calculations are made and plotted for the LHC with the center of mass energy 14 TeV.Comment: 7 pages, 4 figures, added reference, corrected misprints. Talk given at 16th International Seminar on High Energy Physics "QUARKS-2010", Kolomna, Russia, 6-12 June, 2010. To appear in Theor. Math. Phy