Particle Multiplicities in Nuclear Collisions at the LHC from Saturation Physics
Javier L. Albacete
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4 pages and 2 figures. To appear in the proceedings of Quark Matter 2008: 20th International Conference On Ultra-relativistic Nucleus Nucleus Collisions (QM08), Jaipur, India, 4-10 Feb. 2008
The inclusion of running coupling effects in the BK-JIMWLK evolution equations considerably reduces the energy dependence of the saturation scale with respect to previous estimates based on fits to HERA data. We discuss how such slowdown affects the expectations for particle multiplicities in Pb-Pb collisions at LHC energies. Our prediction is based on the use of k_t-factorization and on the use of unintegrated gluon distributions taken from the numerical solutions of the BK equation with running coupling. We obtain a central value dN/dη(sqrt{s}=5.5 TeV)(η=0)~1390.
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.
We present our predictions on multiplicities and $J/ψ$ suppression at LHC energies. Our results take into account shadowing effects in the initial state and final state interactions with the hot medium. We obtain 1800 charged particles at LHC and the $J/ψ$ suppression increases by a factor 5 to 6 compared to RHIC.
Experiments at the Large Hadron Collider (LHC) have measured multiplicity distributions in p+p and p+Pb collisions at a new domain of collision energy. Based on considering an energy-dependent broadening of the nucleon's density distribution, charged hadron multiplicities are studied with the phenomenological saturation model and the evolution equation dependent saturation model. By assuming the saturation scale have a small dependence on the 3-dimensional root mean square (rms) radius at different energy, the theoretical results are in good agreement with the experimental data from CMS and AL…
The mid-rapidity charged particle multiplicities in pp and AA collisions at LHC energies are described in the framework of a generalized eikonal model with shadowing corrections incorporated in AA. We show that the pp data require a Pomeron intercept close to 1.2, higher than the conventional one close to 1.1. An $s^{0.11}$ energy dependence is obtained in the LHC range and beyond. The size and centrality dependence of the AA multiplicity at $\sqrt{s} = 2.76$ TeV is reproduced and its energy dependence is predicted.
Atomic number ($A$) and energy ($\roots$) scaling exponents of multiplicity and transverse energy in heavy ion collisions are analytically derived in the perturbative QCD + saturation model. The exponents depend on the small-$x$ behaviour of gluon distribution functions at an $x$-dependent scale. The relation between initial state and final state saturation is also discussed.
We discuss the recent claim that hadron multiplicities measured at RHIC energies are directly described in terms of gluon degrees of freedom fixed from the initial conditions of central heavy ion collisions. The argument is based on the parton saturation scenario expected to be valid at high parton densities and on the assumption of conserved gluon number. Alternatively we conjecture that "bottom-up" equilibration before hadronization modifies this picture, due to nonconservation of the number of gluons.
An addendum to our previous papers in Phys. Lett. B539 (2002) 46 and Phys. Lett. B502 (2001) 51, contributed to the CERN meeting "First data from the LHC heavy ion run", March 4, 2011
Predictions for the pseudorapidity density of charged particles produced in Pb-Pb central collisions at $\sqrt{s_{NN}}=5.5$ TeV are presented. Particle production in such collisions is computed in the framework of k_t-factorization, using running coupling non-linear evolution to determine the transverse momentum and rapidity dependence of the nuclear unintegrated gluon distributions.
We present predictions for the pseudo-rapidity density of charged particles produced in central Pb-Pb collisions at the LHC. Particle production in such collisions is calculated in the framework of k_t-factorization. The nuclear unintegrated gluon distributions at LHC energies are determined from numerical solutions of the Balitsky-Kovchegov equation including recently calculated running coupling corrections. The initial conditions for the evolution are fixed by fitting RHIC data at collision energies \sqrt{s}}=130 and 200 GeV per nucleon. We obtain dN^{Pb-Pb}_{ch}/dη(\sqrt{s}=5.5 TeV, η=0)\ap…
We compute the particle multiplicities and transverse energies at central and nearly central AA collisions at RHIC and LHC. The initial state is computed from perturbative QCD supplemented by the conjecture of saturation of produced partons. The expansion stage is described in terms of hydrodynamics assuming longitudinal boost invariance and azimuthal symmetry. Transverse flow effects, a realistic list of hadrons and resonance decays are included. Comparison with the data of the multiplicities at $\sqrt s=56$ AGeV and 130 AGeV from RHIC is done and predictions for the full RHIC energy and LHC …
Minijet production in ultra-relativistic heavy-ion collisions is discussed by taking semi-hard parton rescatterings explicitly into account. At both RHIC and LHC energies we find sizable effects on global characteristics of the nuclear collision like the initial multiplicity and transverse energy of the minijets. The dependence of these quantities on the cutoff that separates soft and hard interactions becomes much smoother after the inclusion of the rescatterings. This allows to define an energy and centrality dependent saturation cutoff and to push perturbative computations to rather low val…
We bring the EKRT framework, which combines perturbative QCD (pQCD) minijet production with gluon saturation and hydrodynamics, to next-to-leading order (NLO) in pQCD as rigorously as possible. We chart the model uncertainties, and study the viability and predictive power of the model in the light of the RHIC and LHC measurements in central $A+A$ collisions. In particular, we introduce a new set of measurement functions to define the infrared- and collinear-safe minijet transverse energy, $E_T$, in terms of which we formulate the saturation. We update the framework with the EPS09 NLO nuclear p…
The upcoming p+Pb run at the LHC will probe the nuclear gluon distribution at very small Bjorken x (from $x \sim 10^{-4}$ at mid-rapidity down to $x \sim 10^{-6}$ in the proton fragmentation region) and will allow to test approaches based on parton saturation. Here, we present the predictions of the KLN model for hadron multiplicities and multiplicity distributions in p+Pb collisions at a center-of-mass energy of 4.4 TeV. We also compare the model to the existing pp, dA and AA data from RHIC and LHC.
We consider a search strategy for new physics at the Large Hadron Collider which focuses on the signature of many jets and missing transverse energy, but no charged leptons. We show that this signature can be useful in probing a wide class of models, including natural supersymmetry, in which dark matter is produced in conjunction top quarks. As an example, we apply this strategy to a simplified supersymmetric model with a light gluino, light stop and light neutralino. The efficacy of this strategy is comparable to (and in some cases better than) that of other strategies which require charged l…
Within the framework of a modified Balitsky-Kovchegov equation, we calculated and provide estimates of non-linear saturation effects expected in the LHC range of energies.
The phenomenology of gluon saturation at small parton momentum fraction, Bjorken-x, in the proton and in the nucleus is introduced. The experimentally-accessible kinematic domains at the nucleus-nucleus colliders RHIC and LHC are discussed. Finally, the saturation hints emerging from measurements at RHIC and the perspectives for LHC are described.
The effects of saturation and unitarization for hadron-hadron scattering at LHC energies are explored in several models. It is shown that different choices of saturation parameters lead to sizable differences in the energy dependence of total cross sections, and to dramatic changes in elastic differential cross sections.
We compute the initial energy density and net baryon number density in 5% most central Pb+Pb collisions at $\sqrt s=5.5$ TeV from pQCD + (final state) saturation, and describe the evolution of the produced system with boost-invariant transversely expanding hydrodynamics. In addition to the total multiplicity at midrapidity, we give predictions for the multiplicity of charged hadrons, pions, kaons and (anti)protons, for the total transverse energy and net-baryon number, as well as for the $p_T$-spectrum of charged hadrons, pions and kaons. We also predict the region of applicability of hydrodyn…
Analyses of the centrality binned identified hadron multiplicities at SPS and RHIC within the statistical-thermal model point to strangeness saturation with increasing centrality and energy.
Recent ALICE data for the multiplicity distributions in the central rapidity bins at LHC energies are compared with the results from two default versions of the PYTHIA 8 generator. We find that, contrary to the earlier versions of PYTHIA, the model overestimates the increase of average multiplicity with energy. Tuning two of the model parameters one obtains reasonable agreement with data. The dependence of the normalized moments of the distribution on the rapidity bin width and on energy is also qualitatively correct.
We consider possible saturation effects in the structure function $F_L$ at fixed W in HERA energy range and in $b\bar b-$production at LHC energies in the framework of $k_T-$facrorization approach.
A new geometrical scaling method with gluon saturation rapidity limit is proposed to study the gluon saturation feature of the central rapidity region of relativistic nuclear collisions. The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. We take advantage of the gluon saturation model with geometric scaling of the rapidity limit to investigate the net baryon distributions, nuclear stopping power and gluon saturation features in the SPS and RHIC energy regions. Predictions for net-baryon rapidity distribution…
Unitarization schemes can be reduced to non-linear equations which saturate at small $b$ the evolution of the elastic amplitude with $s$, and which mimic parton saturation in the non-perturbative regime. These equations enable us to study the effect of saturation on total and elastic cross sections for various models, and to evaluate the uncertainties on $σ_{tot}$ and $ρ(s,t)$ at the LHC in the presence of a hard pomeron.
The problems linked to the extraction of the basic parameters of the hadron elastic scattering amplitude at the LHC are explored. The impact of the Black Disk Limit (BDL)$-$ which constitutes a new regime of the scattering processes - on the determination of these values is examined.
We analyse the centrality dependence of thermal parameters deduced from hadron m ultiplicities in Au + Au collisions at $\sqrt{s_{NN}} = 130 GeV$. While the chemical freeze-out temperature and chemical potentials are found to be roughly centrality-independent, the strangeness saturation factor $γ_S$ increases with participant number towards unity, supporting the assumption of equilibrium freeze-out conditions in central collisions.
We calculate the unintegrated gluon distribution at low intrinsic transverse momenta and its parameters are found from the best description of the SPS and LHC data on the $pp$ collision in the soft kinematical region. It allows us to study the saturation of the gluon density at low $Q^2$ more carefully and find the saturation scale.
In this paper we demonstrate that our model which is based on the CGC/saturation approach, is able to describe the soft interaction collisions including the new TOTEM prelimenary data at 13 TeV. We believe that this strengthens the argument that the CGC/saturation approach is the only viable candidate for an effective theory for high energy QCD.
First results on charged hadron transverse momentum spectra in pp collisions obtained by the CMS Collaboration at LHC were analyzed in z-scaling approach. The first LHC data confirm z-scaling. The saturation regime of the scaling function psi(z) observed in pp and antp-pp interactions at lower energy sqrt s = 19-1960 GeV is verified. The saturation of psi(z) for charged hadrons is found down to z=0.05 at the highest energy sqrt s = 2360 GeV reached till now at colliders. A microscopic scenario of hadron production is discussed in connection with search for new signatures of phase transitions i…
In this paper we demonstrate that the selection of events with different multiplicities of produced particles, leads to the violation of the azimuthal angular symmetry, $ϕ\to π- ϕ$. We find for LHC and lower energies, that this violation can be so large for the events with multiplicities $n \geq 2 \bar{n}$, where $\bar{n}$ is the mean multiplicity, that it leads to almostno suppression of $v_n$, with odd $n$. However, this can only occur if the typical size of the dipole in DIS with a nuclear target is small, or $Q^2 \,>\,Q^2_s\Lb A, Y_{\rm min},b\Rb$, where $Q_s$ is the saturation momentum of…
In view of recent perturbative and nonperturbative evidence that the peak of the Higgs resonance saturates as the coupling increases, we examine the potential of the future Large Hadron Collider to discover a heavy Higgs resonance by gluon fusion.
The pseudorapidity density of charged particles produced at LHC collisions are predicted by using two complementary production mechanisms with a set of consistent integrated and unintegrated parton distributions. We discuss the limiting fragmentation hypothesis and its possible violation, and we compare our model with other partonic models.
The forthcoming LHC measurement of hadron multiplicity in proton-nucleus collisions is a crucial test of the k_t factorization and gluon saturation based models. Here, we provide quantitative predictions for the pseudorapidity distribution of charged particles produced in minimum bias proton-nucleus collisions at the LHC based on the idea of gluon saturation in the color-glass condensate framework. Our formulation gives good descriptions of the LHC and RHIC data for the charged-hadron multiplicities in both proton-proton and nucleus-nucleus collisions, and also the deep inelastic scattering at…
The production of $c\bar{c}c\bar{c}$, $b\bar{b}b\bar{b}$ and $c\bar{c}b\bar{b}$ pairs considering double parton scattering at LHC energies is investigated. We estimate the contribution of saturation effects to the different final states and predict the energy dependence of the cross sections. Moreover, we estimate the ratio between the double and single parton scattering cross sections for the full rapidity range of the LHC and for the rapidity range of the LHCb experiment. For the full rapidity range we confirm a previous prediction, namely that for charm production the double parton scatteri…
We review the recent results from the computation of saturated next-to-leading order perturbative QCD minijet intial conditions combined with viscous hydrodynamical evolution of ultrarelativistic heavy-ion collisions at the LHC and RHIC. Comparison with experimental data is shown.
We study the transverse spectra of hadrons in nearly central $AA$ collisions at RHIC and LHC in a broad transverse momentum range Low-$p_T$ spectra are calculated by using boost-invariant hydrodynamics with initial energy and net-baryon densities from the EKRT pQCD+saturation model. High-$p_T$ spectra are obtained from pQCD jet calculation including the energy loss of the parton in the matter prior to its fragmentation to final hadrons.
The Color Glass Condensate picture of the nuclear wave function at small-x successfully predicted the suppressed production of high-pT particles at forward rapidities in deuteron-gold collisions at RHIC. This triggered more efforts which resulted in theoretical improvements and predictions for different observables which will provide further phenomenological tests. I review recent theoretical developments and discuss the resulting predictions.
We compute in QCD perturbation theory the transverse energy carried by gluons, quarks and antiquarks with $p_T\ge p_0\approx 2$ GeV in Pb+Pb collisions at $\sqrt{s}=5500$ $A$GeV by using structure functions compatible with the small-$x$ increase observed at HERA. This gives a perturbative estimate for the energy and entropy density of the bulk system at times $τ\sim 0.1$ fm. The predicted initial gluon entropy density gives a lower limit of about 2200...3400 for the final charged multiplicity. Sources of further entropy increase are discussed.
A broad class of scenarios for new physics involving additional strongly-interacting fields generically predicts signatures at hadron colliders which consist solely of large numbers of jets and substantial missing transverse energy. In this work, we investigate the prospects for discovery in such scenarios using a search strategy in which jet multiplicity and missing transverse energy are employed as the primary criteria for distinguishing signal from background. We examine the discovery reach this strategy affords in an example theory (a simplified supersymmetric model whose low-energy spectr…
The average charged hadron multiplicities induced by top quark decays are calculated in pQCD at LHC energies. Different modes of top production are considered. Proposed measurements can be used as an additional test of pQCD calculations independent on a fragmentation model.
We show that saturation can manifest itself in central-forward dijet production in p-A collisions. In spite of large transverse momenta of the jets, the almost back-to-back dijet configurations are able to probe gluon density at low x and low kt. We perform our study in the framework of high energy factorization with the unintegrated gluon density given by a nonlinear QCD evolution equation. We show that the formalism can successfully account for features measured in e-p and p-p data and it predicts significant suppression of the central-forward jet decorrelations in p-Pb compared to p-p, whic…
We calculate initial conditions for the hydrodynamical evolution in ultrarelativistic heavy-ion collisions at the LHC and RHIC in an improved next-to-leading order perturbative QCD + saturation framework. Using viscous relativistic hydrodynamics, we show that we obtain a good simultaneous description of the centrality dependence of charged particle multiplicities, transverse momentum spectra and elliptic flow at the LHC and at RHIC. In particular, we discuss how the temperature dependence of the shear viscosity is constrained by these data.
We have developed a model in which the quantum fluctuations of the proton structure are characterised by hot spots, whose number grows with decreasing Bjorken-$x$. Our model reproduces the $F_2(x,Q^2)$ data from HERA at the relevant scale, as well as the exclusive and dissociative $\mathrm{J/}ψ$ photoproduction data from H1 and ALICE. Our model predicts that for $W_{γ\mathrm{p}} \approx 500$ GeV, the dissociative $\mathrm{J/}ψ$ cross section reaches a maximum and then decreases steeply with energy, which is in qualitatively good agreement to a recent observation that the dissociative $\mathrm{…
This paper investigates the configurational entropic content of hadron-nucleus collisions. Hadron multiplicities and Au nuclei are employed to compute the critical points of the configurational entropy as a function of the saturation scale in deep inelastic scatterings, in QCD. The results match phenomenological data to the precision of 0.39%.
Time evolution of a "little bang" created in heavy ion collisions can be divided into two phases, the pre-equilibrium and hydrodynamic. At what moment the evolution becomes hydrodynamic and is there any universality in the hydrodynamic flow? To answer these questions we briefly discuss various versions of hydrodynamics and their applicability conditions. In particular, we elaborate on the idea of "universal" (all-order resumed) hydrodynamics and propose a simple new model for it. The model is motivated by results obtained recently via the AdS/CFT correspondence. Finally, charged hadron multipl…
Unintegrated gluon distributions sensitive to the transverse spatial distribution of gluons in the proton are extracted from data on exclusive and diffractive final states at HERA in the dipole approach. These unintegrated gluon distributions can be used to compute inclusive hadron production in p+p collisions at the LHC. In this paper, we consider a number of saturation models with differering dynamical assumptions that give good fits to the available HERA data. We apply these models to study the rapidity and transverse momentum dependence of the LHC data up to $\sqrt{s} = 7$ TeV. We examine …
The forthcoming p+Pb run at the LHC will provide crucial in formation on the initial state effects of heavy ion collisions and on the gluon saturation phenomena. In turn, most of the saturation inspired phenomenology in heavy ion collisions borrows substantial empiric information from the analysis of e+p data, where abundant high quality data on the small-x kinematic region is available. Indeed, the very precise combined HERA data provides a testing ground in which the relevance of novel QCD regimes, other than the successful linear DGLAP evolution, in small-x inclusive DIS data can be ascerta…
We have previously predicted multiplicities and transverse momentum spectra of hadrons for the most central LHC Pb+Pb collisions at $\sqrt{s_{NN}}=5.5$ TeV using initial state for hydrodynamic evolution from pQCD + final state saturation model. By considering binary collision and wounded nucleon profiles we extend these studies to non-central collisions, and predict the $p_{T}$ dependence of minimum bias $v_{2}$ for pions at the LHC. For protons we also show how the $p_{T}$ dependence of $v_2$ changes from RHIC to the LHC.
We compute how the initial energy density and produced gluon, quark and antiquark numbers scale with atomic number and beam energy in ultrarelativistic heavy ion collisions. The computation is based on the argument that the effect of all momentum scales can be estimated by performing the computation at one transverse momentum scale, the saturation momentum. The initial numbers are converted to final ones by assuming kinetic thermalisation and adiabatic expansion. The main emphasis of the study is at LHC and RHIC energies but it is observed that even at SPS energies this approach leads to resul…
The centrality dependence of thermal parameters describing hadron multiplicities and intermediate-mass dilepton spectra in heavy-ion collisions at SPS and RHIC is analyzed. From experimental hadron multiplicities we deduce evidence for strangeness saturation at high energy and maximum centrality. The observed dilepton spectra can be parameterized by a centrality independent temperature.
In recent years the Tsallis statistics is gaining popularity in describing charged particle produc- tion and their properties, in particular pT spectra and the multiplicities in high energy particle collisions. Motivated by its success, an analysis of the LHC data of proton-proton collisions at ener- gies ranging from 0.9 TeV to 7 TeV in different rapidity windows for charged particle multiplicities has been done. A comparative analysis is performed in terms of the Tsallis distribution, the Gamma distribution and the shifted-Gamma distribution. An interesting observation on the inapplicability…
DPMJET-III with chain fusion is used to calculate inclusive distributions of Pb-Pb collisions at LHC energies. We present rapidity distributions as well as scaled multiplicities at mid-rapidity as function of the collision energy and the number of participants.
Selected aspects of the theory and phenomenology of production of forward jets at the LHC and RHIC are overviewed. In the theory part we discuss basics of frameworks originating from the BFKL dynamics while in the phenomenology part we present results for forward-central jet correlations at the LHC and forward di-jet production at RHIC.
Two-particle momentum correlations of $N$ identical bosons are studied in the quantum canonical ensemble. We define the latter as a properly selected subensemble of events associated with the grand canonical ensemble which is characterized by a constant temperature and a harmonic-trap chemical potential. The merits of this toy model are that it can be solved exactly, and that it demonstrates some interesting features revealed recently in small systems created in $p+p$ collisions at the LHC. We find that partial coherence can be observed in particle emission from completely thermal ensembles of…
We report results of our ongoing nonperturbative numerical study of a classical effective theory describing low-x partons in the central region of a heavy-ion collision. In particular, we give estimates of the initial transverse energies and multiplicities for a wide range of collision regimes, including those at RHIC and at LHC.
We investigate hadrons and direct photon production in pp collisions at the LHC energy within the color-dipole approach. We show that greatest sensitivity to gluon saturation effects is reached at very forward rapidities in pp collisions at LHC (\sqrt{s}=14 TeV). The discrepancies among various saturation models (fitted to HERA data) results can be about a factor of 2-3 at forward rapidities. We found that the ratio of direct-photon to pion production can be about 20-10 at forward rapidities η=7-8. Therefore, direct photon production at forward rapidities should provide a rather clean probe as…
We study the effects of low-$p_T$ collective flow on radiative energy loss from high-$p_T$ partons traversing the QCD medium created in high-energy nucleus-nucleus collisions. We illustrate this idea through three examples. Due to longitudinal flow, jet profiles at the LHC present marked asymmetries in the $η\times ϕ$-plane, and widths in $η$ and $ϕ$ of particle distributions associated with a high-$p_T$ trigger at RHIC become different. Finally, transverse flow implies an increase of high-$p_T$ $v_2$ at RHIC.
We make quantitative predictions for the rapidity and centrality dependencies of hadron multiplicities in dA collisions at RHIC basing on the ideas of parton saturation in the Color Glass Condensate.
