Abstract
In the scattering of a small onium off a large nucleus at high center-of-mass energies, when the parameters are set in such a way that the cross section at fixed impact parameter is small, events are triggered by rare partonic fluctuations of the onium, which are very deformed with respect to typical configurations. Using the color dipole picture of high-energy interactions in quantum chromodynamics, in which the quantum states of the onium are represented by sets of dipoles generated by a branching process, we describe the typical scattering configurations as seen from different reference frames, from the restframe of the nucleus to frames in which the rapidity is shared between the projectile onium and the nucleus. We show that taking advantage of the freedom to select a frame in the latter class makes possible to derive complete asymptotic expressions for some boost-invariant quantities, beyond the total cross section, from a procedure which leverages the limited available knowledge on the properties of the solutions to the Balitsky-Kovchegov equation that governs the rapidity-dependence of total cross sections. We obtain in this way an analytic expression for the rapidity-distribution of the first branching of the slowest parent dipole of the set of those which scatter. This distribution provides an estimator of the correlations of the interacting dipoles, and is also known to be related to the rapidity-gap distribution in diffractive dissociation, an observable measurable at a future electron-ion collider. Furthermore, our result may be formulated as a more general conjecture, that we expect to hold true for any one-dimensional branching random walk model, on the branching time of the most recent common ancestor of all the particles that end up to the right of a given position.
Highlights
Onium-nucleus scattering is an outstanding process to understand theoretically: first, because it is the simplest interaction process between a hadron and a nucleus, and second, for its potential phenomenological applications
The latter will be measured at the future electron-ion collider (EIC) [3], which will be built at the Brookhaven National Laboratory within the decade, and at still higher-energy proposed DIS experiments, such as the Large Hadron-Electron Collider (LHeC) at CERN and the Future Circular Collider (FCC) in electron-hadron mode (FCC-eh) [4]
Where the momentum QA, called the “saturation momentum,” is characteristic of the nucleus. (Its value is of the order of 1 GeV for a large nucleus.) In this model, the amplitude T1 ≡ 1 − S is steeply falling from 1 to 0 as r becomes smaller, especially since the relevant scale for the dipole sizes is logarithmic: as a matter of fact, it is a Gaussian function of this variable
Summary
Onium-nucleus scattering is an outstanding process to understand theoretically: first, because it is the simplest interaction process between a (model) hadron and a nucleus, and second, for its potential phenomenological applications. Boost invariance is a fundamental symmetry of scattering amplitudes, and it is interesting to understand theoretically how it is realized microscopically in this particular regime of QCD, in which the interacting objects may be thought of as sets of independent partons generated by a branching process. It is already well-known that using boostinvariance of the scattering amplitudes helps to. The main outcome of our work is a partonic picture of the scattering in different frames, which turns out to enable the derivation of an expression of the asymptotics of the probability distribution of the rapidity at which the slowest ancestor of all dipoles that interact with the nucleus has branched. Appendix A outlines the evaluation of a useful integral, and Appendix B presents an alternative numerical model
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