Soft Gluon Wave Function and Evolution Operator in the CGC at Next-to-Leading Order

2026/07/20 by Ramkumar Radhakrishnan
#hep-ph #hep-th #nucl-th

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Abstract

We construct the soft gluon light cone wave function of a fast moving hadron and the associated unitary evolution operator Ω up to O(g²) in pure Yang Mills theory (N_f = 0), within the Color Glass Condensate (CGC) framework. Working in light cone gauge, we perform a Born Oppenheimer separation between fast valence and soft modes and implement the eikonal approximation, which allows Ω to be written as a fully normal ordered series in soft gluon creation and annihilation operators. The expansion coefficients are functionals of the non-commuting valence color charge density operators ρ. We fix the coefficients by using the unitarity and explicit diagrammatic calculations within light-cone perturbation theory (LCPT). As an application, we diagonalize the pure Yang Mills soft Hamiltonian through orders g and g² and show that the off diagonal mixing elements between Fock sectors cancel leading to the coherent background field energy proportional to ρ².

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