Integrabilty of the BFKL dynamics and Pomeron trajectories in a thermostat

Abstract

We consider scattering amplitudes in QCD at high energies \(\sqrt s \) and fixed momentum transfers \(q = \sqrt { - t} \) with a non-zero temperature T in the t-channel. In the s-channel the temperature leads to a compactification of the impact parameter plane. We find that the thermal BFKL Hamiltonian in the leading logarithmic approximation proceeds to have the property of the holomorphic separability. Moreover, there exists an integral of motion allowing one to construct the Pomeron wave function for arbitrary T in the coordinate and momentum representations. The holomorphic Hamiltonian for n-reggeized gluons at T ≠ 0 in the multicolour limit Nc → ∞ turns out to be equal to the local Hamiltonian for an integrable Heisenberg spin model. Further, the two-gluon Baxter function coincides with the corresponding wave function in the momentum representation. We calculate the spectrum of the Pomeron Regge trajectories at a finite temperature with taking into account the QCD running coupling. The important effect of the t-channel temperature is the appearence of a confining potential between gluons.