High Energy Evolution: From JIMWLK/KLWMIJ to QCD Reggeon Field Theory

We study the high energy evolution of hadronic cross-sections and other physical observables. In Chapter 1 we start with the fundamental accomplishments on this long standing problem and give a brief review of DGLAP and BFKL evolution equations. We explain the concept of saturation and describe the general framework of JIMWLK/KLWMIJ evolution equations. In Chapter 2 we clarify the relation between JIMWLK/KLWMIJ language and the QCD Reggeon Field Theory. We show that the eigenvalues of the BFKL Hamiltonians are also exact eigenvalues of the KLWMIJ (and JIMWLK) Hamiltonian, albeit corresponding to possibly non normalizable eigenfunctions. The question whether a given eigenfunction of BFKL corresponds to a normalizable eigenfunction of KLWMIJ is rather complicated, except in sonic obvious cases, and requires independent investigation. As an example to illustrate this relation we concentrate on the color octet exchange in the framework of KLWMIJ Hamiltonian. We show that it corresponds to the reggeized gluon exchange of BFKL, and find first correction to the BFKL wave function, which has the meaning of the impact factor for shadowing correction to the reggeized gluon. We also show that the bootstrap condition in the KLWMIJ framework is satisfied automatically and does not carry any additional information to that contained in the second quantized structure of the KLWMIJ Hamiltonian. This is an example of how the bootstrap condition inherent in the t-channel unitarity, arises in the s-channel picture. In Chapter 3 we go beyond the two known limits (dilute target-JIMWLK limit, dilute projectile-KLWMIJ limit) of the high energy evolution. We derive a generalized evolution equation for the hadronic wave function whose kernel defines the second quantized Hamiltonian of the QCD Reggeon field theory. Our evolution equation takes into account both the nonlinear effects of the projectile wave function as well as the multiple scattering effects in the scattering amplitude. These multiple scattering effects are in eikonal approximation which means that individual partons in the hadronic wave function scatter eikonally. Thus, it includes the Pomeron loops. Finally, in Chapter 4 we derive expressions for a single inclusive gluon production amplitude and multigluon inclusive production amplitudes when the rapidities of all observed gluons are not very different. We also show that the evolution of these observables with total rapidity of the process is generated by the QCD Reggeon field theory Hamiltonian derived in Chapter 3.