421 research outputs found
Applicability of the -Analogue of Zeilberger's Algorithm
The applicability or terminating condition for the ordinary case of
Zeilberger's algorithm was recently obtained by Abramov. For the -analogue,
the question of whether a bivariate -hypergeometric term has a -pair
remains open. Le has found a solution to this problem when the given bivariate
-hypergeometric term is a rational function in certain powers of . We
solve the problem for the general case by giving a characterization of
bivariate -hypergeometric terms for which the -analogue of Zeilberger's
algorithm terminates. Moreover, we give an algorithm to determine whether a
bivariate -hypergeometric term has a -pair.Comment: 15 page
A Telescoping method for Double Summations
We present a method to prove hypergeometric double summation identities.
Given a hypergeometric term , we aim to find a difference operator and rational functions
such that .
Based on simple divisibility considerations, we show that the denominators of
and must possess certain factors which can be computed from . Using these factors as estimates, we may find the numerators of
and by guessing the upper bounds of the degrees and solving systems of
linear equations. Our method is valid for the Andrews-Paule identity, Carlitz's
identities, the Ap\'ery-Schmidt-Strehl identity, the Graham-Knuth-Patashnik
identity, and the Petkov\v{s}ek-Wilf-Zeilberger identity.Comment: 22 pages. to appear in J. Computational and Applied Mathematic
Spectroscopy of -States in Quark Model and Baryon-Antibaryon Enhancements
We study the mass spectrum of the mesons both from
the quark model with triquark correlations and from common quark model with
colormagnetic interactions and with relative S-waves between quarks. Two
cluster configurations and
are considered. In the spectrum
we find rather stable states which have the same quantum number with particle
resonances which are corresponding to the enhancement,
enhancement and enhancement with
spin- or . This imply these enhancements are NOT
experimental artifacts. The color-spin-flavor structures of ,
, and enhancements are revealed. The
existence of spin-
enhancements is predicted.Comment: 45 pages, 5 figure
Productions of X(1835) as baryonium with sizable gluon content
The X(1835) has been treated as a baryonium with sizable gluon content, and
to be almost flavor singlet. This picture allows us to rationally understand
X(1835) production in radiative decays, and its large couplings with
, . The processes and have been examined. It has been found
that , which is compatible with CLEO's recently
experimental result (Phys.Rev. (2006) 032001;hep-ex/0510015). The
branching fractions of , with and
have been estimated by the quark-pair
creation model. We show that they are heavily suppressed, so the signal of
X(1835) is very difficult, if not impossible, to be observed in these
processes. The experimental checks for these estimations are expected. The
existence of the baryonium nonet is conjectured, and a model independent
derivation of their production branching fractions is presented.Comment: 21 pages, 4 figure
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