Geometric scaling for the total gamma(*)p cross section in the low x region

Nuclear Modification Factor in Small System Collisions within Perturbative QCD including Thermal Effects

In this paper, the nuclear modification factors, RxA, are investigated for pion production in small system collisions, measured by PHENIX experiment at RHIC (Relativistic Heavy Ion Collider). The theoretical framework is the parton transverse momentum kT-factorization formalism for hard processes at small momentum fraction, x. Evidence for collective expansion and thermal effects for pions, produced at equilibrium, is studied based on phenomenological parametrization of blast-wave type in the relaxation time approximation. The dependencies on the centrality and on the projectile species are discussed in terms of the behavior of Cronin peak and the suppression of RxA at large transverse momentum, pT. The multiplicity of produced particles, which is sensitive to the soft sector of the spectra, is also included in the present analysis.

Pursuing the Precision Study for Color Glass Condensate in Forward Hadron Productions

With the tremendous accomplishments of RHIC and the LHC experiments and the advent of the future electron-ion collider on the horizon, the quest for compelling evidence of the color glass condensate (CGC) has become one of the most aspiring goals in the high energy quantum chromodynamics research. Pursuing this question requires developing the precision test of the CGC formalism. By systematically implementing the threshold resummation, we significantly improve the stability of the next-to-leading-order calculation in CGC for forward rapidity hadron productions in pp and pA collisions, especially in the high p_{T} region, and obtain reliable descriptions of all existing data measured at RHIC and the LHC across all p_{T} regions. Consequently, this technique can pave the way for the precision studies of the CGC next-to-leading-order predictions by confronting them with a large amount of precise data.

Mining for Gluon Saturation at Colliders

Quantum chromodynamics (QCD) is the theory of strong interactions of quarks and gluons collectively called partons, the basic constituents of all nuclear matter. Its non-abelian character manifests in nature in the form of two remarkable properties: color confinement and asymptotic freedom. At high energies, perturbation theory can result in the growth and dominance of very gluon densities at small-x. If left uncontrolled, this growth can result in gluons eternally growing violating a number of mathematical bounds. The resolution to this problem lies by balancing gluon emissions by recombinating gluons at high energies: phenomena of gluon saturation. High energy nuclear and particle physics experiments have spent the past decades quantifying the structure of protons and nuclei in terms of their fundamental constituents confirming predicted extraordinary behavior of matter at extreme density and pressure conditions. In the process they have also measured seemingly unexpected phenomena. We will give a state of the art review of the underlying theoretical and experimental tools and measurements pertinent to gluon saturation physics. We will argue for the need of high energy electron-proton/ion colliders such as the proposed EIC (USA) and LHeC (Europe) to consolidate our knowledge of QCD knowledge in the small x kinematic domains.

Geometrical scaling of prompt photons in heavy ion collisions

We discuss geometrical scaling (GS) for the prompt (direct) photons produced in heavy ion collisions. To this end we first introduce the concept of GS and illustrate its emergence on the example of charged particles. Next, we analyse direct photon data from RHIC and from the LHC. We show that thedata supportthehypothesisofGSin termsof participant number relatedto different centrality classes. We also study GS at different energies, however a more detailed study will be possible only when data for at least three different energies from one experiment will be available and also when we use the data obtained from the collisions of large systems (Cu+Cu, Au+Au, Pb+Pb) and small systems (p+p,d+Au,p+Au).

Diffractive Electron-Nucleus Scattering and Ancestry in Branching Random Walks

We point out an analogy between diffractive electron-nucleus scattering events and realizations of one-dimensional branching random walks selected according to the height of the genealogical tree of the particles near their boundaries. This correspondence is made transparent in an event-by-event picture of diffraction, emphasizing the statistical properties of gluon evolution, from which new quantitative predictions straightforwardly follow: we are able to determine the distribution of the total invariant mass produced diffractively, which is an interesting observable that can potentially be measured at a future electron-ion collider.

The Weizsäcker-Williams distribution of linearly polarized gluons (and its fluctuations) at small x

The conventional and linearly polarized Weizsäcker-Williams gluon distributions at small x are defined from the two-point function of the gluon field in light-cone gauge. They appear in the cross section for dijet production in deep inelastic scattering at high energy. We determine these functions in the small-x limit from solutions of the JIMWLK evolution equations and show that they exhibit approximate geometric scaling. Also, we discuss the functional distributions of these WW gluon distributions over the JIMWLK ensemble at rapidity Y ~ 1/αs. These are determined by a 2d Liouville action for the logarithm of the covariant gauge function g2tr A+(q)A+(-q). For transverse momenta on the order of the saturation scale we observe large variations across configurations (evolution trajectories) of the linearly polarized distribution up to several times its average, and even to negative values.

High gluon densities in heavy ion collisions

The early stages of heavy ion collisions are dominated by high density systems of gluons that carry each a small fraction x of the momenta of the colliding nucleons. A distinguishing feature of such systems is the phenomenon of 'saturation' which tames the expected growth of the gluon density as the energy of the collision increases. The onset of saturation occurs at a particular transverse momentum scale, the 'saturation momentum', that emerges dynamically and that marks the onset of non-linear gluon interactions. At high energy, and for large nuclei, the saturation momentum is large compared to the typical hadronic scale, making high density gluons amenable to a description with weak coupling techniques. This paper reviews some of the challenges faced in the study of such dense systems of small x gluons, and of the progress made in addressing them. The focus is on conceptual issues, and the presentation is both pedagogical, and critical. Examples where high gluon density could play a visible role in heavy ion collisions are briefly discussed at the end, for illustration purpose.

Evolution to the quark-gluon plasma

Theoretical studies on the early-time dynamics in the ultra-relativistic heavy-ion collisions are reviewed, including pedagogical introductions on the initial condition with small-[Formula: see text] gluons treated as a color glass condensate, the bottom-up thermalization scenario, plasma/glasma instabilities, basics of some formulations such as the kinetic equations and the classical statistical simulation. More detailed discussions follow to make an overview of recent developments on the fast isotropization, the onset of hydrodynamics, and the transient behavior of momentum spectral cascades.

Longitudinal coherence in a holographic model of asymmetric collisions

As a model of the longitudinal structure in heavy ion collisions, we simulate gravitational shock wave collisions in anti-de Sitter space in which each shock is composed of multiple constituents. We find that all constituents act coherently, and their separation leaves no imprint on the resulting plasma, when this separation is ≲0.26/T_{hyd}, with T_{hyd} the temperature of the plasma at the time when hydrodynamics first becomes applicable. In particular, the center-of-mass of the plasma coincides with the center-of-mass of all the constituents participating in the collision, as opposed to the center-of-mass of the individual collisions. We discuss the implications for nucleus-nucleus and proton-nucleus collisions.

Violation of geometric scaling in deep inelastic scattering due to Coulomb corrections

We compute the Coulomb correction to the total and diffractive cross sections for virtual photon scattering off a heavy nucleus at low x. We show that it violates the geometric scaling in a wide range of photon virtualities and is weakly x independent. In heavy nuclei at low Q2, the Coulomb correction to the total and diffractive cross sections is about 20% and 40%, correspondingly.

Improved geometrical scaling at the LHC

We show that geometrical scaling exhibited by the p(T) spectra measured by the CMS Collaboration at the LHC is substantially improved if the exponent λ of the saturation scale depends on p(T). This dependence is shown to be the same as the dependence of small x exponent of F(2) structure function in deep inelastic scattering taken at the scale p(T) ≃ Q/2.

AdS black disk model for small-x deep inelastic scattering

Using the approximate conformal invariance of QCD at high energies we consider a simple anti-de Sitter black disk model to describe saturation in deep inelastic scattering. Deep inside saturation the structure functions have the same power law scaling, F{T}∼F{L}∼x{-ω}, where ω is related to the expansion rate of the black disk with energy. Furthermore, the ratio F{L}/F{T} is given by the universal value 1+ω/3+ω, independently of the target. For γ{*}-γ{*} scattering at high energies we obtain explicit expressions and ratios for the total cross sections of transverse and longitudinal photons in terms of the single parameter ω.

Baryon stopping as a new probe of geometric scaling

We suggest using net-baryon rapidity distributions in central relativistic heavy-ion collisions at energies reached at the CERN Super Proton Synchrotron, BNL Relativistic Heavy-Ion Collider (RHIC), and CERN LHC in order to probe saturation physics. Within the color glass condensate framework based on small-coupling QCD, net-baryon rapidity distributions are shown to exhibit geometric scaling. In a comparison with RHIC data in Au+Au collisions at sqrt[sNN=62.4 GeV and 200 GeV the gradual approach to the gluon saturation regime is investigated. Predictions for net-baryon rapidity spectra and the mean rapidity loss in central Pb+Pb collisions at LHC energies of sqrt[sNN=5.52 TeV are made.

Geometric scaling from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution

We show that the geometric scaling of the total virtual photon-proton cross section data can be explained using standard linear Dokshitzer-Gribov-Altarelli-Parisi perturbative evolution with generic boundary conditions in a wide kinematic region. This allows us to single out the region where geometric scaling may provide evidence for parton saturation.

Relating high-energy Lepton-Hadron, proton-nucleus, and nucleus-nucleus collisions through geometric scaling

A characteristic feature of small-x lepton-proton data from HERA is geometric scaling: the fact that in the region of small Bjorken variable x, x less, similar 0.01, all data can be described by a single variable Q(2)/Q(2)(s,p)(x), with all x dependence encoded in the so-called saturation momentum Q(s,p)(x). Here, we observe that the same scaling ansatz accounts for nuclear photoabsorption cross sections and favors the nuclear dependence Q(2)(s,A) proportional, variant A(alpha)Q(2)(s,p), alpha approximately 4/9. We then make the empirical finding that the same A dependence accounts for the centrality evolution of the multiplicities measured in Au+Au collisions at RHIC. It also allows one to parametrize the high-p(t) particle suppression in d+Au collisions at forward rapidities. If these geometric scaling properties have a common dynamical origin, then this A dependence of Q(2)(s,A) should emerge as a consequence of the underlying dynamical model.

Evolution of the nuclear modification factors with rapidity and centrality in d + Au collisions at (sqrt)[N(S)N]=200 GeV

We report on a study of the transverse momentum dependence of nuclear modification factors R(dAu) for charged hadrons produced in deuteron + gold collisions at sqrt[s(NN)]=200 GeV, as a function of collision centrality and of the pseudorapidity (eta=0, 1, 2.2, 3.2) of the produced hadrons. We find a significant and systematic decrease of R(dAu) with increasing rapidity. The midrapidity enhancement and the forward rapidity suppression are more pronounced in central collisions relative to peripheral collisions. These results are relevant to the study of the possible onset of gluon saturation at energies reached at BNL RHIC.

Geometric scaling as traveling waves

We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale.

Geometric scaling in inclusive charm production

We show that the cross section for inclusive charm production exhibits geometric scaling in a large range of photon virtualities. In the DESY ep collider HERA kinematic domain the saturation momentum Q(2)(sat)(x) stays below the hard scale micro(2)(c)=4m(2)(c), implying charm production probing mostly the color transparency regime and unitarization effects being almost negligible. We derive our results considering two saturation models which are able to describe the HERA data for the proton structure function at small values of the Bjorken variable x. A striking feature is the scaling on tau identical with Q(2)/Q(2)(sat)(x) above te saturation limit, corroborating recent theoretical studies.

Geometric scaling in inclusive eA reactions and nonlinear perturbative QCD

We report on geometric scaling in inclusive eA scattering data from the NMC and E665 experiments. This scaling and nuclear shadowing follows the pattern expected from nonlinear perturbative QCD for zero impact parameter at sufficiently small x(bj) and is compatible with geometric scaling in ep.

Coherent gluon production in very-high-energy heavy-ion collisions

The early stages of a relativistic heavy-ion collision are examined in the framework of an effective classical SU(3) Yang-Mills theory in the transverse plane. We compute the initial energy and number distributions, per unit rapidity, at midrapidity, of gluons produced in high-energy heavy-ion collisions. We discuss the phenomenological implications of our results in light of the recent Relativistic Heavy-Ion Collider data.