Traveling waves and the renormalization group improved Balitsky–Kovchegov equation

I study the incorporation of renormalization group (RG) improved BFKL kernels in the Balitsky–Kovchegov (BK) equation which describes parton saturation. The RG improvement takes into account important parts of the next-to-leading and higher order logarithmic corrections to the kernel. The traveling wave front method for analyzing the BK equation is generalized to deal with RG-resummed kernels, restricting to the interesting case of fixed QCD coupling. The results show that the higher order corrections suppress the rapid increase of the saturation scale with increasing rapidity. I also perform a “diffusive” differential equation approximation, which illustrates that some important qualitative properties of the kernel change when including RG corrections.