5,430 research outputs found
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
Effective Lagrangians for physical degrees of freedom in the Randall-Sundrum model
We derive the second variation Lagrangian of the Randall-Sundrum model with
two branes, study its gauge invariance and diagonalize it in the unitary gauge.
We also show that the effective four-dimensional theory looks different on
different branes and calculate the observable mass spectra and the couplings of
the physical degrees of freedom of 5-dimensional gravity to matter.Comment: 22 pages, LaTeX, typos correcte
Holonomy of the Ising model form factors
We study the Ising model two-point diagonal correlation function 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
, the -particle contributions, . The corresponding
extension of the two-point diagonal correlation function, , is shown, for arbitrary , 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 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 . Each is expressed polynomially in terms of the elliptic integrals and . The scaling limit of these differential operators breaks the
direct sum structure but not the ``Russian doll'' structure. The previous -extensions, are, for singled-out values ( 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
A geometrical angle on Feynman integrals
A direct link between a one-loop N-point Feynman diagram and a geometrical
representation based on the N-dimensional simplex is established by relating
the Feynman parametric representations to the integrals over contents of
(N-1)-dimensional simplices in non-Euclidean geometry of constant curvature. In
particular, the four-point function in four dimensions is proportional to the
volume of a three-dimensional spherical (or hyperbolic) tetrahedron which can
be calculated by splitting into birectangular ones. It is also shown that the
known formula of reduction of the N-point function in (N-1) dimensions
corresponds to splitting the related N-dimensional simplex into N rectangular
ones.Comment: 47 pages, including 42 pages of the text (in plain Latex) and 5 pages
with the figures (in a separate Latex file, requires axodraw.sty) a note and
three references added, minor problem with notation fixe
Three Numerical Puzzles and the Top Quark's Chiral Weak-Moment
Versus the standard model's t --> W b decay helicity amplitudes, three
numerical puzzles occur at the 0.1 % level when one considers the amplitudes in
the case of an additional (f_M + f_E) coupling of relative strength 53 GeV. The
puzzles are theoretical ones which involve the t --> W b decay helicity
amplitudes in the two cases, the relative strength of this additional coupling,
and the observed masses of these three particles. A deeper analytic realization
is obtained for two of them. Equivalent realizations are given for the
remaining one. An empirical consequence of these analytic realizations is that
it is important to search for effects of a large chiral weak-moment of the
top-quark, the effective mass-scale is about 53 GeV. A full theoretical
resolution would include relating the origin of such a chiral weak-moment and
the mass generation of the top-quark, the W-boson, and probably the b-quark.Comment: 18 pages, 1 postscript table (revised to better explain notation,
model #1, add a little material...
Two-loop corrections to the correlator of tensor currents in gluodynamics
Results of evaluating the leading order 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 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 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 colliders
We consider the possibility of detecting a heavy Higgs boson () in
proposed colliders through the semi-leptonic mode . 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 production
is expected to be negligible, we demonstrate the presence of and calculate
sizeable backgrounds from ,
with , respectively, and
.
This channel may be used to detect a Higgs of mass up to around 350~GeV
at a 0.5~TeV collider, assuming a nominal yearly luminosity of
10--20~fb.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..
- …