The C-odd four-gluon state in the color glass condensate

The study of the perturbative Odderon at high gluon densities in the color glass condensate requires to take into account states with more than three gluons. We formulate evolution equations for these states in which the number of gluons is not fixed during the evolution. We further determine the coupling of these Odderon states to the γ→ηc impact factor for arbitrary numbers of gluons. We find an exact solution of the evolution equation for the four-gluon Odderon state in terms of the three-gluon Odderon state. It is shown that a similar solution exists also for a different class of Odderon solutions which does not couple to the γ→ηc impact factor. We discuss the implications of our result from the perspective of constructing an effective field theory of reggeized gluons for the color glass condensate.