Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2001-07-20
Phys.Rev. D64 (2001) 114019
Physics
High Energy Physics
High Energy Physics - Phenomenology
LaTex, 48 pages, 1 .ps figure, to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.64.114019
We investigate the Baxter equation for the Heisenberg spin model corresponding to a generalized BFKL equation describing composite states of n Reggeized gluons in the multi-color limit of QCD. The Sklyanin approach is used to find an unitary transformation from the impact parameter representation to the representation in which the wave function factorizes as a product of Baxter functions and a pseudo-vacuum state. We show that the solution of the Baxter equation is a meromorphic function with poles (lambda - i r)^{-(n-1)} (r= 0, 1,...) and that the intercept for the composite Reggeon states is expressed through the behavior of the Baxter function around the pole at lambda = i . The absence of pole singularities in the two complex dimensional lambda-plane for the bilinear combination of holomorphic and anti-holomorphic Baxter functions leads to the quantization of the integrals of motion because the holomorphic energy should be the same for all independent Baxter functions.
de Vega Hector J.
Lipatov Lev N.
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