From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy

TL;DR

This paper derives a unified evolution equation for hadronic wave functions at high energy, valid across different density regimes, by employing a Bogoliubov transformation that diagonalizes the light-cone Hamiltonian.

Contribution

It provides a comprehensive derivation that unifies the JIMWLK and KLWMIJ evolution equations through a Bogoliubov operator approach.

Findings

Unified evolution framework valid at all densities

Explicit form of the Bogoliubov operator for soft and valence sectors

Diagonalization of the light-cone Hamiltonian in the presence of valence charges

Abstract

We derive the evolution of a hadronic light cone wave function with energy at weak coupling. Our derivation is valid both in the high and the low partonic density limit, and thus encompasses both the JIMWLK and the KLWMIJ evolution. The hadronic wave function is shown to evolve by the action of the Bogoliubov-type operator, which diagonalizes on the soft gluon sector the light-cone hamiltonian in the presence of an arbitrary valence charge density. We find explicitly the action of this operator on the soft as well as the valence degrees of freedom of the theory.