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

Two-loop corrections to the correlator of tensor currents in gluodynamics

Results of evaluating the leading order $\alpha_s$ corrections to the correlator of tensor currents in pure gluodynamics are presented. These corrections to the parton result for the correlator are not large numerically that allows one to use perturbation theory for the analysis of the resonance spectrum within the sum rules method.Comment: 10 pages, latex, no figure

Asymptotics of Toeplitz Determinants and the Emptiness Formation Probability for the XY Spin Chain

We study an asymptotic behavior of a special correlator known as the Emptiness Formation Probability (EFP) for the one-dimensional anisotropic XY spin-1/2 chain in a transverse magnetic field. This correlator is essentially the probability of formation of a ferromagnetic string of length $n$ in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models. For the XY Spin Chain, the correlator can be expressed as the determinant of a Toeplitz matrix and its asymptotical behaviors for $n \to \infty$ throughout the phase diagram are obtained using known theorems and conjectures on Toeplitz determinants. We find that the decay is exponential everywhere in the phase diagram of the XY model except on the critical lines, i.e. where the spectrum is gapless. In these cases, a power-law prefactor with a universal exponent arises in addition to an exponential or Gaussian decay. The latter Gaussian behavior holds on the critical line corresponding to the isotropic XY model, while at the critical value of the magnetic field the EFP decays exponentially. At small anisotropy one has a crossover from the Gaussian to the exponential behavior. We study this crossover using the bosonization approach.Comment: 40 pages, 9 figures, 1 table. The poor quality of some figures is due to arxiv space limitations. If You would like to see the pdf with good quality figures, please contact Fabio Franchini at "[email protected]

Detection of the heavy Higgs boson at γγ\gamma\gamma colliders

We consider the possibility of detecting a heavy Higgs boson ($m_H>2m_Z$) in proposed $\gamma\gamma$ colliders through the semi-leptonic mode $\gamma\gamma \rightarrow H \rightarrow ZZ \rightarrow q\bar q \ell^+\ell^-$. We show that due to the non-monochromatic nature of the photon beams produced by the laser-backscattering method, the resultant cross section for Higgs production is much smaller than the on-resonance cross section and generally {\it decreases} with increasing collider energy. Although continuum $ZZ$ production is expected to be negligible, we demonstrate the presence of and calculate sizeable backgrounds from $\gamma\gamma\rightarrow \ell^+\ell^-Z,\,q\bar qZ$, with $Z\rightarrow q\bar q,\,\ell^+\ell^-$, respectively, and $\gamma\gamma\rightarrow t\bar t\rightarrow b\bar b\ell^+\ell^-\nu\bar\nu$. This channel may be used to detect a Higgs of mass $m_H$ up to around 350~GeV at a 0.5~TeV $e^+e^-$ collider, assuming a nominal yearly luminosity of 10--20~fb$^{-1}$.Comment: 18 pages (in RevTeX) plus Postscript figures (available by email or FAX), NUHEP-TH-92-29 and DOE-309-CPP-47. (Revised version: NO CHANGES to the manuscript, simply removed corrupted figure files

Investigation of correlation of generated nuclearactive particles in the protonantiproton annihilation at momenta 22.4 and 32 GeV / c

Separation of the individual events corresponding to antiproton-proton annihilation gives the possibility to carry out the analysis of multiparticle correlations for generated particles and to compare them with corresponding data for inelastic pp and non-annihilation p̃p interactions..

Investigation of correlation of generated nuclearactive particles in the protonantiproton annihilation at momenta 22.4 and 32 GeV / c

Separation of the individual events corresponding to antiproton-proton annihilation gives the possibility to carry out the analysis of multiparticle correlations for generated particles and to compare them with corresponding data for inelastic pp and non-annihilation p̃p interactions..

Form factors of integrable Heisenberg (higher) spin chains

We present determinant formulae for the form factors of spin operators of general integrable XXX Heisenberg spin chains for arbitrary (finite dimensional) spin representations. The results apply to any "mixed" spin chains, such as alternating spin chains, or to spin chains with magnetic impurities.Comment: 24 page

Chiral effective potential in N=1/2{\cal N}={1/2} non-commutative Wess-Zumino model

We study a structure of holomorphic quantum contributions to the effective action for ${\cal N}={1/2}$ noncommutative Wess-Zumino model. Using the symbol operator techniques we present the one-loop chiral effective potential in a form of integral over proper time of the appropriate heat kernel. We prove that this kernel can be exactly found. As a result we obtain the exact integral representation of the one-loop effective potential. Also we study the expansion of the effective potential in a series in powers of the chiral superfield $\Phi$ and derivative $D^2{\Phi}$ and construct a procedure for systematic calculation of the coefficients in the series. We show that all terms in the series without derivatives can be summed up in an explicit form.Comment: LaTeX, JHEP style, 32 pages, typos corrected, references adde