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Register a new userCollinearly improved kernel suppresses Coulomb tails in the impact-parameter dependent Balitsky-Kovchegov evolution
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We solved the impact-parameter dependent Balitsky-Kovchegov equation with the recently proposed collinearly imporved kernel. We find that the solutions do not present the Coulomb tails that have affected previous studies. We also show that once choosing an adequate initial condition it is possible to obtain a reasonable description of HERA data on the structure function of the proton, as well as on the cross section for the exclusive production of a $mathrm{J/}psi$ vector meson off proton targets. As a further application of the solutions, we computed the impact-parameter dependent Weiszacker-Williams gluon distribution.
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The solution to the impact-parameter dependent Balitsky-Kovchegov equation with the collinearly improved kernel is studied in detail. The solution does not present the phenomenon of Coulomb tails at large impact parameters that have affected previous studies. The origin of this behaviour is explored numerically. It is found to be linked to the fact that this kernel suppresses large daughter dipoles. Solutions based on a physics motivated form of the initial condition are used to compute predictions for structure functions of the proton and the exclusive photo- and electroproduction of vector mesons. A reasonable agreement is found when comparing to HERA and LHC data.
In this work we present dipole scattering amplitudes, including the dependence on the impact-parameter, for a variety of nuclear targets of interest for the electron-ion colliders (EICs) being currently designed. These amplitudes are obtained by numerically solving the Balitsky-Kovchegov equation with the collinearly improved kernel. Two different cases are studied: initial conditions representing the nucleus under consideration and the solutions based on an initial condition representing a proton complemented by a Glauber-Gribov prescription to obtain dipole-nucleus amplitudes. We find that the energy evolution of these two approaches differ. We use the obtained dipole scattering amplitudes to predict ($i$) nuclear structure functions that can be measured in deep-inelastic scattering at EICs and ($ii$) nuclear suppression factors that reveal the energy evolution of shadowing for the different cases we studied. We compare our predictions with the available data.
{In this paper we propose a new impact-parameter dependent CGC/saturation model. We introduce two new features in the model that make it consistent with what we know theoretically about the deep inelastic scattering. They are: the use of the exact form of the solution to the non-linear (BK) equation, whereas in all previous attempts only the form of $r^2Q^2_s$ dependence, has been taken into account; and the large impact parameter dependence, through the $b$-dependence of the saturation momentum which reproduce the correct behaviour of the amplitude at large impact parameters $b$ ($A propto expLb - mu bRb$) as well as at large momentum transferred $Q_T$ ($A $ decreases as a power of $Q_T$ as it follows from perturbative QCD). These improvement compared to all previous attempts to build such models, allows us to claim, that the experimental data are in accord with the prediction of CGC/saturation approach while previously, based on similar models, we could only conclude that the DIS data, perhaps, can be described by introducing the shadowing corrections at small photon virtualities.
The variational approach to QCD in Coulomb gauge developed previously by the Tubingen group is improved by enlarging the space of quark trial vacuum wave functionals through a new Dirac structure in the quark-gluon coupling. Our ansatz for the quark vacuum wave functional ensures that all linear divergences cancel in the quark gap equation resulting from the minimization of the energy calculated to two-loop order. The logarithmic divergences are absorbed in a renormalized coupling which is adjusted to reproduce the phenomenological value of the quark condensate. We also unquench the gluon propagator and show that the unquenching effects are generally small and amount to a small reduction in the mid-momentum regime.
This paper is the first attempt to build CGC/saturation model based on the next-to-leading order corrections to linear and non-linear evolution in QCD. We assume that the renormalization scale is the saturation momentum and found that the scattering amplitude has geometric scaling behaviour deep in the saturation domain with the explicit formula of this behaviour at large $tau = r^2 Q^2_s$. We built a model that include this behaviour, as well as the ingredients that has been known: (i) the behaviour of the scattering amplitude in the vicinity of the saturation momentum, using the NLO BFKL kernel, (ii) the pre-asymptotic behaviour of $lnLb Q^2_sLb Y RbRb$, as function of $Y$ and (iii) the impact parameter behaviour of the saturation momentum, which has exponential behaviour $propto expLb -, m, bRb$ at large $b$.We demonstrated that the model is able to describe the experimental data for the deep inelastic structure function. Despite this, our model has difficulties that are related to the small value of the QCD coupling at $Q_sLb Y_0Rb$ and the large values of the saturation momentum, which indicate the theoretical inconsistency of our description.
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