Abstract
We study exclusive quarkonium production in the dipole picture at next-to-leading order (NLO) accuracy, using the non-relativistic expansion for the quarkonium wavefunction. This process offers one of the best ways to obtain information about gluon distributions at small $x$, in ultraperipheral heavy ion collisions and in deep inelastic scattering. The quarkonium light cone wave functions needed in the dipole picture have typically been available only at tree level, either in phenomenological models or in the nonrelativistic limit. In this paper, we discuss the compatibility of the dipole approach and the non-relativistic expansion and compute NLO relativistic corrections to the quarkonium light-cone wave function in light-cone gauge. Using these corrections we recover results for the NLO decay width of quarkonium to $e^{+}e^{-}$ and we check that the non-relativistic expansion is consistent with ERBL evolution and with B-JIMWLK evolution of the target. The results presented here will allow computing the exclusive quarkonium production rate at NLO once the one loop photon wave function with massive quarks, currently under investigation, is known.
Highlights
The partonic structure of hadrons and nuclei in the limit of high collision energies, or equivalently small momentum fractions x, is poorly constrained by existing experimental data
The information about the bound state in this formalism is encoded in the light-cone distribution amplitude (DA). This coincides with the light-cone wave function in the limit in which the transverse radius r⊥ goes to zero. This object was already studied in Refs. [29,30,31] using the nonrelativistic expansion; here, we provide an independent computation in light-cone gauge
We have studied the light-cone wave function of a heavy quarkonium in the nonrelativistic limit with a focus on future applications within the dipole model
Summary
The partonic structure of hadrons and nuclei in the limit of high collision energies, or equivalently small momentum fractions x, is poorly constrained by existing experimental data. We are going to compute the leading-order (LO) relativistic corrections to the quarkonium light-cone wave function in the light-cone gauge such that it can be used to obtain NLO predictions in the dipole picture. This will allow us to compute the radiative NLO corrections to the leading nonrelativistic result. We are going to show that, using this wave function, it is possible to compute NLO corrections to exclusive quarkonium production by analyzing the divergence structure and checking that it is consistent with Balitsky-.
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