Saturation 2005 (mini-review)
This talk was given at DIS'05 (Madison, April 27-May 2, 2005). It is a brief review of ups and downs of high density QCD during the past year.
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arXiv subjects
Eugene Levin
Publications and source records attributed to Eugene Levin.
Balitsky's hierarchy from Mueller's dipole model and more about target correlations
High energy scattering is considered within the framework of the QCD dipole model formulated as a classical branching process. Starting from Mueller's generating functional we derive the high energy evolution law for the scattering amplitude. The amplitude's evolution is given by an infinite hierarchy of linear equations equivalent to Balitsky's chain reduced to dipole operators. This new derivation of the hierarchy is the central result of the paper. We comment about target correlations which prevent the hierarchy from being expressed as a closed form Balitsky-Kovchegov equation.
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CGC, QCD Saturation and RHIC data (Kharzeev-Levin-McLerran-Nardi point of view)
This is the talk given at the Workshop:"Focus on Multiplicitioes", Bari, Italy, 17-19 June,2004.. In this talk, we are going to discuss ion-ion and deuteron - nucleus RHIC data and show that they support, if not more, the idea of the new QCD phase: colour glass condensate with saturated parton density. .
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Color Glass Condensate at the LHC: hadron multiplicities in $pp$, $pA$ and $AA$ collisions
We make quantitative predictions for the rapidity and centrality dependencies of hadron multiplicities in $AA$, $pA$ and $pp$ collisions at the LHC energies basing on the ideas of parton saturation in the Color Glass Condensate.
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Jet Azimuthal Correlations and Parton Saturation in the Color Glass Condensate
We consider the influence of parton saturation in the Color Glass Condensate on the back-to-back azimuthal correlations of high $p_T$ hadrons in $pA$ (or $dA$) collisions. When both near--side and away--side hadrons are detected at mid-rapidity at RHIC energy, the effects of parton saturation are constrained to transverse momenta below the saturation scale $p_T \leq Q_s$; in this case the back-to-back correlations do not disappear but exhibit broadening. However when near-side and away-side hadrons are separated by several units of rapidity, quantum evolution effects lead to the depletion of back-to-back correlations as a function of rapidity interval between the detected hadrons (at fixed $p_T$). This applies to both $pp$ and $pA$ (or $dA$) collisions; however, due to the initial conditions provided by the Color Glass Condensate, the depletion of the back-to-back correlations is significantly stronger in the $pA$ case. An experimental study of this effect would thus help to clarify the origin of the high $p_T$ hadron suppression at forward rapidities observed recently at RHIC.
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High energy amplitude as an admixture of "soft" and "hard" Pomerons
In this paper an attempt is made to find an interface of the perturbative BFKL Pomeron with the non-perturbative Pomeron originating from non-perturbative QCD phenomena such as QCD instantons and/or scale anomaly. The main idea is that the non-perturbative Pomeron involves a large scale ($M_0 \approx 2 GeV $), which is larger than the scale from which perturbative QCD is applicable. One key result is that even for processes involving a large hard scale (such as DIS) the low $x$ behavior is determined by an effective Pomeron with an intercept having an essential non-perturbative QCD contribution.
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QCD Saturation and $γ^*-γ^*$ Scattering
Two photon collisions at high energy have an important theoretical advantage: the simplicity of the initial state, which gives us a unique opportunity to calculate these processes for large virtualities of both photons in perturbative QCD approach. In this paper we study QCD saturation in two photon collisions in the framework of the Glauber-Mueller approach. The Glauber-Mueller formula is derived emphasizing the impact parameter dependence ($b_t$) of the dipole-dipole amplitude. It is shown that non-perturbative QCD contributions are needed to describe large $b_t $-behaviour, and the way how to deal with them is suggested. Our approach can be viewed as the model for the saturation in which the entire impact parameter dependence is determined by the initial conditions. The unitarity bound for the total cross section, its energy dependence as well aspredictions for future experiments are discussed.It is argued that the total cross section increases faster than any power of $ \log(1/x)$ in a wide range of energy or $x$, namely $σ(γ^*-γ^*) \propto (1/Q^2) exp(a \sqrt{\ln(1/x)}) \leq 1/m^2_π$ where $exp(a \sqrt{\ln(1/x)})$ reflects the $x$ dependence of the gluon density $xG \propto exp(2 a \sqrt{\ln(1/x)})$ and $m_π$ is the pion mass.
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Instantons in the Saturation Environment
We show that instanton calculations in QCD become theoretically well defined in the gluon saturation environment which suppresses large size instantons. The effective cutoff scale is determined by the inverse of the saturation scale. We concentrate on two most important cases: the small-x tail of a gluon distribution of a high energy hadron or a large nucleus and the central rapidity region in a high energy hadronic or heavy ion collision. In the saturation regime the gluon density in a single large ultrarelativistic nucleus is high and gluonic fields are given by the classical solutions of the equations of motion. We show that these strong classical fields do not affect the density of instantons in the nuclear wave function compared to the instanton density in the vacuum. A classical solution with non-trivial topological charge is found for the gluon field of a single nucleus at the lowest order in the instanton perturbation theory. In the case of ultrarelativistic heavy ion collisions a strong classical gluonic field is produced in the central rapidity region. We demonstrate that this field introduces a suppression factor of exp{-c ρ^4 Q_s^4 / [8 α^2 N_c (Q_s τ)^2]} in the instanton size distribution, where Q_s is the saturation scale of both (identical) nuclei, τis the proper time and c = 1 is the gluon liberation coefficient. This factor suggests that gluonic saturation effects at the early stages of nuclear collisions regulate the instanton size distribution in the infrared region and make the instanton density finite by suppressing large size instantons.
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Soft Pomeron in QCD
This is a talk, given at Diffraction'2000, Sept. 2 - 7, Centraro, Italy. This talk is a brief presentation of our view on the Pomeron, as a non-perturbative QCD phenomenon but from sufficiently short distances. Our approach is based on the scale anomaly of QCD and emphasizes the r{ô}le of semi-classical QCD vacuum fields. We show that both the intercept and the slope of Pomeron trajectory appear to be determined by the energy density of non-perturbative QCD vacuum. The particular example of semi-classical QCD vacuum fields is discussed based on a new type of instanton-induced interactions (``instanton ladder'') that leads to the rising with energy cross section $σ\sim s^{Δ_P}$ of Regge type (the Pomeron).
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Low x Physics
This is a talk, given at Diffraction'2000, Sept. 2 - 7, Centraro, Italy. In this talk, we present the arguments, that a new QCD regime - gluon saturation, has been reached at HERA.
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A manifestation of a gluon saturation in e-A DIS
This is a short presentation of our talks given at eRHIC Workshop at the BNL. We give here a status report of our attempts to understand how gluon saturation will manifest itself in deep inelastic scattering with nuclei. This summary reflects our current understanding and shows directions of our research rather then a final answer to the question. Nevertheless, we are able to share with our reader our tentative answer to the question:``Why do we need to measure DIS with nuclei and why these data will be complementary to the information obtained from proton DIS".
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QCD Instantons and the Soft Pomeron
We study the role of semi-classical QCD vacuum solutions in high energy scattering by considering the instanton contribution to hadronic cross sections. We propose a new type of instanton-induced interactions (``instanton ladder'') that leads to the rising with energy hadronic cross section of Regge type (the Pomeron). We argue that this interaction may be responsible for the structure of the soft Pomeron. The intercept is calculated. It has a non-analytic dependence on the strong coupling constant, allowing a non-singular continuation into the non-perturbative region. We derive the Pomeron trajectory, which appears to be approximately linear in some range of (negative) momentum transfer t, but exhibits a curvature at small t. Possible role of instantons in multiparticle production is also discussed.
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Cost of Survival for Large Rapidity Gaps
In this talk, given at "RunII QCD and weak boson WS", we report on calculations of the survival probability of the large rapidity gap (LRG) processes and its energy behaviour.
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Higgs and Heavy Quarks Diffractive Production
In this talk, given at "RunII QCD and weak boson WS", we give the highest of reasonable estimates for the value of cross section of the double Pomeron Higgs meson production and suggest a new mechanism for heavy quark diffractive production which will dominate at the Tevatron energies.
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Large Scale Rapidity Correlations in Heavy Ion Collisions
We discuss particle production mechanisms for heavy ion collisions. We present an argument demonstrating how the fluctuations of the number of produced particles in a series of classical emissions can account for KNO scaling. We predict rapidity correlations in the particle production in the event by event analysis of heavy ion collisions on the rapidity scales of the order of one over the strong coupling constant.
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Diffractive Dissociation Including Multiple Pomeron Exchanges in High Parton Density QCD
We derive an evolution equation describing the high energy behavior of the cross section for the single diffractive dissociation in deep inelastic scattering on a hadron or a nucleus. The evolution equation resums multiple BFKL pomeron exchanges contributing to the cross section of the events with large rapidity gaps. Analyzing the properties of an approximate solution of the proposed equation we point out that at very high energies there is a possibility that for a fixed center of mass energy the cross section will reach a local maximum at a certain intermediate size of the rapidity gap, or, equivalently, at some non-zero value of the invariant mass of the produced particles.
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Low x News for Monte Carlo
This talk,given at Monte Carlo Workshop, is a review of news in low $x$ physics which, I think, would be useful for writing of the Monte Carlo codes. The following topics are discussed here: (i) the next-to-leading order BFKL Pomeron; (ii) two indications for shadowing corrections (SC) in DIS from HERA data; (iii) matching of "soft" and "hard" photon - proton interactions; and (iv) survival probability for large rapidity gap (LRG) processes in hadron-hadron scattering and DIS. I hope, that our current understanding of these topics will allow us to narrow the gap between the MC codes and our microscopic theory - QCD.
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The dependence of the emission size on the hadron mass
The size of the emission volume of pions and kaons, r_{ππ} and r_{KK}, were measured in the hadronic Z^0 decays through the two-pion and two-kaon Bose-Einstein correlations near threshold. Recently the emitter size of the two identical baryons, ΛΛ(\bar Λ\bar Λ), was evaluated from the dependence of the fraction of the spin S=1 state on the energy near threshold where it is affected by the Pauli exclusion principle. Here we show that the r dependence on the particle masses, namely the hierarchy r_{ππ} > r_{KK} > r_{ΛΛ} observed in the Z^0 hadronic decays, is well described in terms of the Heisenberg uncertainty principle. A good description can also be obtained via the virial theorem when applied to a general QCD potential. Other available approaches are also discussed.
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