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 sl3sl_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