Speaker
Description
Within the Color Glass Condensate (CGC) framework and using the light cone wave function (LCWF) formalism, we compute the differential cross section for single inclusive gluon production at central rapidity at next-to-leading order (NLO) in the small-$x$ regime. In the CGC approach, the LCWF factorizes into valence and soft sectors residing in separate Hilbert spaces, separated by an arbitrary momentum scale. The dependence on this separation scale generates a renormalization group equation that defines the high energy evolution operator $\Omega$, which constructs the soft gluon dressing the valence degrees of freedom. The explicit structure of $\Omega$ beyond leading order is not known in closed form. In this work, we derive $\Omega$ at NLO using light cone perturbation theory through a systematic normal ordered operator expansion and construct its action on the valence Hilbert space to the accuracy required for the NLO cross section, including the necessary NNLO components. Using this operator, we diagonalize the QCD light cone Hamiltonian to the corresponding order and obtain corrections to the energy eigenvalues. The operator is fixed by matching to perturbative results and imposing unitarity. With the resulting evolution operator, we compute the single inclusive gluon production cross section and identify the contributions associated with final state interactions, running coupling corrections and small-$x$ evolution effects. This work provides a consistent operator level formulation of NLO gluon production at central rapidity within the LCWF framework.