Dipole picture and the nonrelativistic expansion

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. I. INTRODUCTIONThe 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. It is believed that at high enough energies the properties of small-x gluons are dominated by gluon saturation, i.e. the dominance of nonlinear interactions in the gluon field. In order to fully understand the behavior of small x gluons, a variety of different experimental measurements are needed. Of particular importance here is exclusive quarkonium production mediated by real or virtual photons. Such measurements are currently made in ultraperipheral heavy ion collisions [1] at the LHC and at RHIC. Exclusive measurements will also be an important part of the program at a future electron-ion-collider [2]. Exclusive quarkonium production is an important process for several reasons. As an exclusive process it depends on the gluon density quadratically and is thus more sensitive to nonlinearities than inclusive cross sections. Exclusive processes can, depending on exactly what final state of the target one measures, be sensitive to separately the average and the fluctuations of the gluon density in the target [3][4][5][6]. On the other hand, the heavy quark masses cut away nonperturbative long distance contributions and make the use of a weak coupling framework safer than for light quark processes [7,8].The dipole picture of DIS [9-13] (a specialization of the light cone perturbation theory framework of [14] to the DIS process) provides a convenient framework to study deep inelastic scattering at high energy. In particular one expresses both inclusive and exclusive cross sections in terms of the same fundamental quantity, the dipole scattering amplitude, which gives this picture more predictive power than collinear factorization. With light quarks several recent advances have taken cal...

Relativistic corrections to the vector meson light front wave function

“…In addition to the corrections in velocity, it would be important to include perturbative corrections in the strong coupling α s in the calculation of exclusive vector meson production. Indeed some recent advances [94,115] are gradually making it possible to do so in the dipole picture. However, a study of the phenomenological implications of these α s corrections remains to be done.…”

“…In a strict NRQCD power counting sense in α s , the α s corrections could be considered more important. Although steps have been taken to take them into account in the dipole picture exclusive cross section calculations [94] (see also recent work in a different formalism [95]), fully including them in the cross section is not yet possible at this point since the full photon to heavy quark pair wave function is not known to one-loop accuracy. Thus we will leave a computation that includes also the perturbative α s calculations to future work and continue with our focus on the velocity corrections to the wave function here.…”

“…Since our cross section calculation does not include pure α s corrections, taking the wave function to be given by just the operator hO 1 i J=ψ in (22) would lead to an inconsistent treatment of the α s corrections between the decay width and the cross section. Even in a more general sense, the α s contributions that appear as corrections to the decay widths or cross sections expressed in terms of nonrelativistic wave functions should, in light cone perturbation theory, be thought of as perturbative corrections to the light cone wave function itself [39,94]. This can be understood in the sense that the degrees of freedom in the nonrelativistic wave function are constituent quarks as opposed to bare quarks in the light cone wave function; see the discussion in [39].…”

The dipole picture and the non-relativistic expansion

“…where K L,T (z, z 0 ) is the ERBL kernel. We have checked explicitly in [4], both in longitudinal and transverse polarization, that the distribution amplitudes obtained by our wave functions fulfil this requirement. Now we move to the discussion of our second cross-check.…”

“…In section 4 we discuss the application of these results to the computation of exclusive quarkonium production in the limit Q � m. Finally, in section 5 we give the conclusions. A more extended discussion of these results can be found in [4].…”