Impact Parameter Dependent Saturation Research Articles

Single inclusive hadron production at the LHC with an improved impact parameter dependent saturation model* *Supported by the National Natural Science Foundation of China (12165004, 11765005, 11947119); the Guizhou Provincial Science and Technology Projects (ZK[2023]027, [2019]5103); the Education Department of Guizhou Province, China (KY[2021]131); the National Key Research and Development Program of China (2018YFE0104700, CCNU18ZDPY04)

To obtain a reasonable description of the hadron production at the LHC energies, the impact parameter dependent saturation model is modified by inclusion of an anomalous dimension γ, which controls the slope of the scattering amplitude in the transition from the dilute region to the saturation region. We calculate the transverse momentum distribution and nuclear modification factor of the and charged hadrons with the improved model, and the results are consistent with measurements performed at the LHC. Moreover, we use the original impact parameter dependent model to study the aforementioned measurements performed at the LHC by adjusting its parameters. We find that the improved model is more consistent with the experimental data than the original one, as the anomalous dimension plays a significant role in the suppression of the evolution of the scattering amplitude.

Beyond DGLAP improved saturation model

We present a modification of the DGLAP improved saturation model with respect to the nonlinear correction (NLC). The GLR-MQ improved saturation model is considered by employing the parametrization of proton structure function due to the Laplace transforms method, which preserves its behavior success in the low and high Q^{2} regions. We show that the geometric scaling holds for the GLR-MQ improved model in a wide kinematic region rQ_{s}. These results are comparable with other models in a wide kinematic region rQ_{s}. The behavior of the dipole cross sections, with respect to the GLR-MQ improved saturation model, are comparable with the Color Glass Condensate (CGC) model. The model describes the dipole cross sections in the inclusive and diffractive processes. We also compare the nonlinear corrections to the impact-parameter dependent saturation (IP-Sat) model with the impact-parameter dependent color glass condensate (b-CGC) dipole model. Finally, we consider the linear and nonlinear corrections to the IP Non-Sat model. These results provide a benchmark for further investigation of QCD at small x in future experiments such as the Large Hadron Collider and Future Circular Collider projects.

Diffractive incoherent vector meson production off protons: a quark model approach to gluon fluctuation effects

Fluctuations play an important role in diffractive production of vector mesons. It was in particular recently suggested, based on the Impact-Parameter dependent Saturation model (IPSat), that geometrical fluctuations triggered by the motion of the constituent quarks within the protons could explain incoherent diffractive processes observed at HERA. We propose a variant of the IPSat model which includes spatial and symmetry correlations between constituent quarks, thereby reducing the number of parameters needed to describe diffractive vector meson production to a single one, the size of the gluon cloud around each valence quark. The application to J/varPsi , rho and phi diffractive electron and photon production cross sections reveal the important role of geometrical fluctuations in incoherent channels, while other sources of fluctuations are needed to fully account for electroproduction of light mesons, as well as photo production of J/varPsi mesons at small momentum transfer.

In depth analysis of the combined HERA data in the dipole models with and without saturation

We present an updated impact parameter dependent saturation model determined through a fit to the combined HERA I and $\mathrm{I}+\mathrm{II}$ reduced cross section data. The same HERA data are used to fit the linearized version of the applied dipole amplitude, which makes it possible to estimate the magnitude of the saturation effects in various experiments. We find that both parametrizations provide comparable descriptions of the considered data when an effective confinement scale dynamics is incorporated with quark masses. Moreover, it is possible to consistently determine the light and charm quark masses. The role of potentially nonperturbatively large dipoles is examined in detail, with the result that, especially in the case of the structure function ${F}_{2}$, their contribution is numerically significant. The potential to discriminate between the two models in future $e+p$ and $e+A$ experiments is also illustrated.

CGC/saturation approach: an impact-parameter dependent model for diffraction production in DIS

In the paper we discussed the evolution equations for diffractive production in the framework of CGC/saturation approach, and found the analytical solutions for several kinematic regions. The most impressive features of these solutions are, that diffractive production does not manifest geometric scaling behaviour i.e. being a function of one variable. Based on these solutions, we suggest an impact parameter dependent saturation model, which is suitable for describing diffraction production both deep in the saturation region, and in the vicinity of the saturation scale. Using the model we attempted to fit the combined data on diffraction production from H1 and ZEUS collaborations. We found that we are able describe both x_{I!!P} and beta dependence, as well as Q behavior of the measured cross sections. In spite of the sufficiently large chi ^2/d.o.f. we believe that our description provides an initial impetus to find a fit of the experimental data, based on the solution of the CGC/saturation equation, rather than on describing the diffraction system in simplistic manner, assuming that only quark-antiquark pair and one extra gluon, are produced.

Impact-parameter dependent color glass condensate dipole model and new combined HERA data

The Impact-Parameter dependent Color Glass Condensate (b-CGC) dipole model is based on the Balitsky-Kovchegov non-linear evolution equation and improves the Iancu-Itakura-Munier dipole model by incorporating the impact-parameter dependence of the saturation scale. Here we confront the model to the recently released high precision combined HERA data and obtain its parameters. The b-CGC results are then compared to data at small-x for the structure function, the longitudinal structure function, the charm structure function, exclusive vector meson (J/\psi, \phi, \rho) production and Deeply Virtual Compton Scattering (DVCS). We also compare our results with the Impact-Parameter dependent Saturation model (IP-Sat). We show that most features of inclusive DIS and exclusive diffractive data, including the Q^2, W, |t| and x dependence are correctly reproduced in both models. Nevertheless, the b-CGC and the IP-Sat models give different predictions beyond the current HERA kinematics, namely for the structure functions at very low x and high virtualities Q^2, and for the exclusive diffractive vector meson and DVCS production at high t. This can be traced back to the different power-law behavior of the saturation scale in x, and to a different impact-parameter b dependence of the saturation scale in these models. Nevertheless, both models give approximately similar saturation scale Q_S<1 GeV for the proton in HERA kinematics, and also both models lead to the same conclusion that the typical impact-parameter probed in the total \gamma^{*}p cross-section is about b\approx 2\div 3 GeV^{-1}. Our results provide a benchmark for further investigation of QCD at small-x in heavy ion collisions at RHIC and the LHC and also at future experiments such as an Electron-Ion Collider and the LHeC.

Analysis of combined HERA data in the impact-parameter dependent saturation model

The Impact-Parameter dependent Saturation Model (IP-Sat) is a simple dipole model that incorporates key features of the physics of gluon saturation and matches smoothly to the perturbative QCD dipole expression at large Q^2 for a given x. It was previously shown that the model gives a good description of HERA data suggesting evidence for gluon saturation effects at small x. The model has also been applied to proton-proton and proton-nucleus collisions and provides the basis for the IP-Glasma model of initial conditions in heavy ion collisions. Here we present a reanalysis of available data in electron-proton collisions at small Bjorken-x, including the recently released combined data from the ZEUS and H1 collaborations. We first confront the model to the high precision combined data for the reduced cross-section and obtain its parameters. With these parameters fixed, we compare model results to data for the structure function F_2, the longitudinal structure function F_L, the charm structure function F_2^{c\bar{c}}, exclusive vector meson (J/\psi, \phi and \rho) production and Deeply Virtual Compton Scattering (DVCS). Excellent agreement is obtained for the processes considered at small x in a wide range of Q^2. Our results strongly hint at universality of the IP-Sat dipole amplitude and the extracted impact-parameter distribution of the proton. They also provide a benchmark for further refinements in studies of QCD saturation at colliders.

Event-by-event gluon multiplicity, energy density, and eccentricities in ultrarelativistic heavy-ion collisions

The event-by-event multiplicity distribution, the energy densities and energy density weighted eccentricity moments ${\ensuremath{\epsilon}}_{n}$ (up to $n=6$) at early times in heavy-ion collisions at both the BNL Relativistic Heavy Ion Collider (RHIC) ($\sqrt{s}=200\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$) and the CERN Large Hardron Collider (LHC) ($\sqrt{s}=2.76\phantom{\rule{0.16em}{0ex}}\mathrm{TeV}$) are computed in the IP-Glasma model. This framework combines the impact parameter dependent saturation model (IP-Sat) for nucleon parton distributions (constrained by HERA deeply inelastic scattering data) with an event-by-event classical Yang-Mills description of early-time gluon fields in heavy-ion collisions. The model produces multiplicity distributions that are convolutions of negative binomial distributions without further assumptions or parameters. In the limit of large dense systems, the $n$-particle gluon distribution predicted by the Glasma-flux tube model is demonstrated to be nonperturbatively robust. In the general case, the effect of additional geometrical fluctuations is quantified. The eccentricity moments are compared to the MC-KLN model; a noteworthy feature is that fluctuation dominated odd moments are consistently larger than in the MC-KLN model.

Fluctuating Glasma Initial Conditions and Flow in Heavy Ion Collisions

We compute initial conditions in heavy ion collisions within the color glass condensate framework by combining the impact parameter dependent saturation model with the classical Yang-Mills description of initial Glasma fields. In addition to fluctuations of nucleon positions, this impact parameter dependent Glasma description includes quantum fluctuations of color charges on the length scale determined by the inverse nuclear saturation scale Q(s). The model naturally produces initial energy fluctuations that are described by a negative binomial distribution. The ratio of triangularity to eccentricity ε(3)/ε(2) is close to that in a model tuned to reproduce experimental flow data. We compare transverse momentum spectra and v(2,3,4)(p(T)) of pions from different models of initial conditions using relativistic viscous hydrodynamic evolution.

Impact parameter dependent color glass condensate dipole model

We show that the color glass condensate dipole model of Iancu, Itakura, and Munier, improved to include the impact parameter dependence, gives a good fit to the total ${\ensuremath{\gamma}}^{*}p$ cross section measured at HERA if the anomalous dimension at the saturation scale, ${\ensuremath{\gamma}}_{s}$, is treated as a free parameter. We find that the optimum value of ${\ensuremath{\gamma}}_{s}=0.46$ is close to the value determined from numerical solution of the Balitsky-Kovchegov equation. The impact parameter dependent saturation scale is generally less than $0.5\text{ }\text{ }{\mathrm{GeV}}^{2}$ in the HERA kinematic regime for the most relevant impact parameters $b\ensuremath{\sim}2--3\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$. We compare predictions of the model to data on the longitudinal and heavy flavour structure functions, exclusive diffractive vector meson production, and deeply virtual Compton scattering at HERA. The model is found to be deficient for observables sensitive to moderately small dipole sizes, where an alternative model with explicit Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution performs better. The energy dependence of exclusive diffractive processes is shown to provide an important discriminator between different dipole model cross sections.

Exclusive diffractive processes at HERA within the dipole picture

We present a simultaneous analysis, within an impact parameter dependent saturated dipole model, of exclusive diffractive vector meson (J/psi, phi and rho) production, deeply virtual Compton scattering and the total gamma* p cross section data measured at HERA. Various cross sections measured as a function of the kinematic variables Q^2, W and t are well described, with little sensitivity to the details of the vector meson wave functions. We determine the properties of the gluon density in the proton in both longitudinal and transverse dimensions, including the impact parameter dependent saturation scale. The overall success of the description indicates universality of the emerging gluon distribution and proton shape.