2,702 research outputs found

### Dynamical differential equations compatible with rational qKZ equations

For the Lie algebra $gl_N$ we introduce a system of differential operators
called the dynamical operators. We prove that the dynamical differential
operators commute with the $gl_N$ rational quantized Knizhnik-Zamolodchikov
difference operators. We describe the transformations of the dynamical
operators under the natural action of the $gl_N$ Weyl group.Comment: 7 pages, AmsLaTe

### Difference Equations Compatible with Trigonometric KZ Differential Equations

The trigonometric KZ equations associated with a Lie algebra \g depend on a
parameter \lambda\in\h where \h\subset\g is the Cartan subalgebra. We
suggest a system of dynamical difference equations with respect to $\lambda$
compatible with the KZ equations. The dynamical equations are constructed in
terms of intertwining operators of \g-modules.Comment: 23 pages, AmsTeX, third version, some misprints were correcte

### Selberg Type Integrals Associated with $sl_3$

We present several formulae for the Selberg type integrals associated with
the Lie algebra $sl_3$.Comment: Errata added; 13 pages, amstex.tex 2.2 and amssym.tex require

### Quark loop contribution to \pi^0 \to 4\gamma

We find the contribution of constituent quark loop mechanism to the branching
ratio B_{4\gamma} = \Gamma_{4\gamma}/\Gamma_{4\gamma} \sim 5.45 \cdot 10^{-16}
for the reasonable choice of constituent quark mass m \sim 280 MeV. This result
is in agreement with vector-dominance approach result obtained years ago. Thus
the main contribution arises from QED mechanism \pi^0 \to \gamma (\gamma^*) \to
\gamma (3\gamma) including light-light scattering block with electron loop.
This contribution was investigated in paper of one of us and gave B_{4\gamma}
\sim 2.6 \cdot 10^{-11}.Comment: 7 pages, 2 figure

### Gluon Shadowing and Heavy Flavor Production off Nuclei

Gluon shadowing which is the main source of nuclear effects for production of
heavy flavored hadrons, remains unknown. We develop a light-cone dipole
approach aiming at simplifying the calculations of nuclear shadowing for heavy
flavor production, as well as the cross section which does not need
next-to-leading and higher order corrections. A substantial process dependence
of gluon shadowing is found at the scale of charm mass manifesting a deviation
from QCD factorization. The magnitude of the shadowing effect correlates with
the symmetry properties and color state of the produced c-cbar pair. It is
about twice as large as in DIS, but smaller than for charmonium production. The
higher twist shadowing correction related to a nonzero size of the c-cbar pair
is not negligible and steeply rises with energy. We predict an appreciable
suppression by shadowing for charm production in heavy ion collisions at RHIC
and a stronger effect at LHC. At the same time, we expect no visible difference
between nuclear effects for minimal bias and central collisions, as is
suggested by recent data from the PHENIX experiment at RHIC. We also
demonstrate that at medium high energies when no shadowing is possible, final
state interaction may cause a rather strong absorption of heavy flavored
hadrons produced at large x_F.Comment: Preprint NSF-ITP-02-40, ITP, UCSB, Santa Barbara; Latex 52 pages and
8 figure

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