O. V. Selyugin, J. -R. Cudell
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.
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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.
We present a short summary of parton saturation concepts as seen in deep inelastic scattering.
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 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.
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 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 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.
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 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…
The theory of the perturbative pomeron, due to Lipatov and collaborators, is used to compute the probability of observing parton-parton elastic scattering and rapidity gaps between jets in hadron collisions at SSC and LHC energies.
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{…
We attempt to describe soft hadron interactions in the framework of saturation models, one based upon the Balitsky-Kovchegov non-linear equation and another one due to Golec-Biernat and Wüsthoff. For $pp$, $Kp$, and $πp$ scattering the relevant hadronic wave functions are formulated, and total, elastic cross-sections, and the forward elastic slope are calculated and compared to experimental data. The saturation mechanism leads to reasonable reproduction of the data for the quantities analyzed, except for the forward elastic slope, where the predicted increase with energy is too moderate.
Predictions of the elastic proton-proton cross sections at energies of LHC are calculate on the base of the high energy dynamical model. The growth of $ds/dt$ at fixed transfer momenta are shown. The form of eikonal of elastic hadron scattering at super high energies is discussed.
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…
The problems linked with the extraction of the basic parameters of the hadron elastic scattering amplitude at the LHC are explored. It is shown that one should take into account the saturation regime which will lead to new effects at the LHC.
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.
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
We parametrize TOTEM data for the elastic differential pp cross section at sqrt(s)=7 TeV in terms of two exponentials with a relative phase. We employ two previously derived sum rules for pp elastic scattering amplitude in impact parameter space to check whether asymptotia has been reached at the LHC. A detailed study of the TOTEM data for the elastic differential cross section at sqrt(s)=7 TeV is made and it is shown that, within errors, the asymptotic sum rules are satisfied at LHC. We propose to use this parametrization to study forthcoming higher energy data.
A model of $pp$ and $\bar{p}p$ elastic scattering developed previously to analyze ISR and SPS Collider data is extended to predict $pp$ elastic differential cross section at LHC at c.m. energy of 14 TeV and momentum transfer range $|t|=0$ - 10 GeV$^2$. Role of the gauged linear $σ$-model as an underlying field theory model describing nucleon structure and elastic scattering is discussed. Possibility of finding evidence of a chiral phase transition at large $|t|$ in the proposed TOTEM project at LHC is pointed out.
Predictions for the total, elastic and single diffractive cross sections calculated for the LHC in the framework of the Miettinen-Pumplin model are presented. The total cross section is expected to be 15% smaller than that determined by Donnachie and Landshoff in the model with soft pomeron. The diffractive cross section is almost constant in the Tevatron-LHC energy range.
A QCD interpretation of the scaling observed in the LHC proton-proton elastic cross-sections at moderate transfer momentum
本文用QCD饱和框架解释LHC质子-质子弹性散射在中等转移动量下的标度现象，指出硬振幅经幺正化构成pp振幅，且标度指数支持饱和标度指数约为硬过程二分之一的QCD饱和方法。
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.
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 discuss the possibility of measuring leading neutron production at the LHC. These data could be used to extract from it $π^+ p$ and $π^+π^+$ cross-sections. In this note we give some estimates for the case of elastic cross-sections and discuss related problems and prospects.
We discuss effects of reflective scattering for hadron and heavy nuclei collisions at the LHC and asymptotical energies. It is shown that the reflective scattering might lead to decreasing matter density with energy beyond the LHC energies. Limiting form of energy dependence of hadron density is obtained. Unitarity upper bound for the absolute value of the real part of elastic scattering amplitude and two-particle inelastic binary reactions amplitudes in impact parameter representation is two times less than the corresponding bound for the imaginary part of the elastic scattering amplitude. Th…
In the light of LHC data, we discuss the global description of all high energy elastic and diffractive data, using a one-pomeron model, but including multi-pomeron interactions. The LHC data indicate the need of a $k_t(s)$ behaviour, where $k_t$ is the gluon transverse momentum along the partonic ladder structure which describes the pomeron. We also discuss tensions in the data, as well as the $t$ dependence of the slope of $dσ_{el}/dt$ in the small $t$ domain.
Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all energy region, the behavior of observables in the LHC collisions in the range $\sqrt{s}$= 2.76 - 14 TeV is discussed. Similarly to the case of 7 TeV data, the proposed amplitudes give excellent description of the preliminary 8 TeV data. We discuss the expected energy dependence of the observable quantities, and present predictions for the experiments at 2.76, 13 and 14 TeV.
The possibility to study elastic and diffractive physics in pp collisions at LHC is investigated. For this purpose we have considered detectors close to the beam in conjunction with the magnetic elements of the accelerator to provide a high precision spectrometer for very forward final state protons. The geometrical acceptance is given and momentum resolution is calculated for different spatial resolution detectors.
We demonstrate that rapidity separated di-hadron spectra in high multiplicity proton-proton collisions at the LHC can be quantitatively described by a combination of BFKL and saturation dynamics. Based on these results, we predict the systematics of di-hadron spectra in proton-nucleus collisions at the LHC.
We discuss a model which gives a `global' description of the wide variety of high-energy elastic and diffractive data that are presently available, particularly from the LHC experiments. The model is based on only one pomeron pole, but includes multi-pomeron interactions. Significantly, the LHC measurements require that the model includes the transverse momentum dependence of the intermediate partons as a function of their rapidity, which results in a rapidity (or energy) dependence of the multi-pomeron vertices.
We will recall the main feaatures of an accurate phenomenological model to describe successfully near-forward elastic scattering in a wide energy range, including ISR, SPS and Tevatron colliders. A large step in energy domain is accomplished with the LHC collider, presently running, giving the opportunity to confront the new data with the predictions of our theoretical approach.
Searching for saturation in forward dijet production at the LHC
本文在ITMD框架下回顾了LHC和EIC的前向喷注产生结果，描述了蒙特卡洛实现并讨论了前向双喷注的唯象结果。
Universal properties of elastic pp cross section from the ISR to the LHC
本研究探究从ISR到LHC能区弹性微分pp截面峰谷位之比恒定的唯象学，验证几何标度在LHC的适用性，并分析其对ρ参数和峰谷截面值比的影响。
Under the assumption of total absorption and dominance of the imaginary part of the scattering amplitude, we present a sum rule for any hadronic elastic differential cross-section ${dσ}\over{dt}$: the dimensionless quantity ${{1}\over{2}}\int (dt)\sqrt{{{1}\over π}{{dσ}\over{dt}}} \to 1$, at asymptotic energies. Experimental data from ISR and Tevatron confirm a trend towards its saturation and some estimates are presented for LHC. Its universality and further consequences for the nature of absorption in QCD based models for elastic and total cross-sections are explored.
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.
An empirical model for the $pp$ elastic differential cross section is proposed. Inspired by early work by Barger and Phillips, we parametrize the scattering amplitude in building blocks, comprising of two exponentials with a relative phase, supplementing the dominant term at small $-t$ with the proton form factor. This model suitably applies to LHC7 and ISR data, enabling to make simple predictions for higher LHC energies and to check whether asymptotia might be achieved.
The analyses of elastic collisions of charged nucleons have been based standardly on West and Yennie formula. However, this approach has been shown recently to be inadequate from experimental as well as theoretical points of view. The eikonal model seems to be more pertinent as it enables to determine physical characteristics in impact parameter space. The contemporary phenomenological models cannot give, of course, any definite answer as the elastic collisions may be interpreted differently, as central or peripheral processes. Nevertheless, the predictions for the planned LHC energy have been…
We present the unified description of the existing data on elastic small angle $pp$ and $p \bar p$ scattering at the energies 1.8, 1.96, 2.76, 7, 8 and 13~TeV in the framework of Additive Quark Model. The agreement with the data is quite reasonable.
We provide predictions for the nuclear modification factor R_{pA} for pions and direct photon production in p+A collisions at LHC energy at midrapidity within different saturation models fitted to HERA data. In our approach we have no free parameters to adjust and all model parameters are fitted to other reactions. Our approach gives a rather good description of PHENIX data for R_{pA} for pions. We show that, in various saturation models, the pion Cronin enhancement is replaced by a moderate suppression at LHC energy at midrapidity due to gluon shadowing effects. However, Cronin enhancement of…
It is shown that regime of elastic scattering with maximal odderon contribution is not compatible with unitarity and black disk limits saturation.
We investigate hadrons and direct photon production in pp and pA collisions at the energies of RHIC and LHC within the color-dipole approach employing various saturation models. We show that greatest sensitivity to saturation effects is reached at very forward rapidities for pp collisions at LHC (\sqrt{s}=14 TeV). The ratio of direct-photon to pion production can be about 20-10 (at η=7-8). Therefore, direct photon production at forward rapidities should provide a rather clean probe. We calculate the rapidity dependence of the invariant cross-section and find some peculiar enhancement at forwar…
We investigate the forward-jet energy spectrum within the Color Glass Condensate framework at 5 TeV center-of-mass energy. In particular, we focus on the kinematic range covered by the CMS-CASTOR calorimeter. We show that our saturation-model calculations are compatible with the CASTOR measurements and that to optimally reproduce the data, effects of multi-parton interactions need to be included. We predict a significant nuclear suppression - reaching down to 50% at the lowest considered jet energies $E_{\rm jet} \sim 500 \, {\rm GeV}$.
We predict pp elastic differential cross sections at LHC at c.m. energy 14 TeV and momentum transfer range |t| = 0 - 10 GeV*2 in a nucleon-structure model. In this model, the nucleon has an outer cloud of quark-antiquark condensed ground state, an inner shell of topological baryonic charge (r ~ 0.44F) probed by the vector meson omega, and a central quark-bag (r ~ 0.2F) containing valence quarks. We also predict elastic differential cross section in the Coulomb-hadronic interference region. Large |t| elastic scattering in this model arises from valence quark-quark scattering, which is taken to …
Taking into account the electromagnetic and gravitational form factors, calculated from a new set of $t $-dependent GPDs, a new model including the soft and hard pomerons is build. In the framework of this model the ualitative description of all existing experimental data at $\sqrt{s} \leq 52.8 $ GeV, including the Coulomb range and large momentum transfers, is obtained with only 4 free parameters. Predictions for LHC energies are made.
High energy elastic $p p$ scattering at the Large Hadron Collider (LHC) at c.m. energy 14 TeV is predicted using the asymptotic behavior of $σ_{tot}(s)$ and $ρ(s)$ known from dispersion relation calculations and the measured elastic $\bar p p$ differential cross section at $\sqrt{s} = 546 {\rm GeV}$. The effective field theory model underlying the phenomenological analysis describes the nucleon as having an outer cloud of quark-antiquark condensed ground state, an inner core of topological baryonic charge of radius $\simeq 0.44F$ and a still smaller valence quark-bag of radius $\lesssim 0.1 {\…
A recent Schwinger Generating Functional based formulation, by H.M.Fried,Y.Gabellini,T.Grandou and Y-M.Sheu and P.H.Tsang provided gauge-invariant, exact, non-perturbative solutions for QCD. After choosing a renormalization scheme and assuming a simpler 2 body quark-quark scattering problem, this formalism is tested against experimental elastic proton-proton scattering at LHC energies (7, 8, 13 TeV). This formulation was previously compared with ISR energies at (23.5 - 62.5 GeV). The full scattering amplitude with infinite gluons summed, infinite loops summed and their interference terms are n…
We study the behaviour of elastic and diffractive proton dissociation cross sections at high energy. First, we describe what would be expected to be observed at the LHC based on conventional Regge theory. We emphasize the tension between these expectations and the recent LHC measurements, and we discuss the possibilty to modify the classic Reggeon Field Theory in a physically-motivated way so as to accommodate the tendencies observed at the LHC. As a result, we show that we are able to achieve a `global' description of the wide variety of high energy elastic and diffractive data that are prese…
Geometric scaling of elastic $pp$ cross section at the LHC
该研究利用交叉性与解析性分析弹性 $pp$ 散射，证明 ISR 时期发现的几何标度在 LHC 仍成立，并刻画凹陷—凸起结构及 $\ ho$ 参数等规律。
The TOTEM Collaboration has measured the differential cross section of elastic proton-proton scattering $\mathrm{d}σ/\mathrm{d}|t|$ at $\sqrt{s} = 2.76$, 7, 8, and 13 TeV. It is observed that all $\mathrm{d}σ/\mathrm{d}|t|$ data points vary in the same way as a function of the center-of-mass energy in the so-called "dip" and "bump" regions. These features hint at possible universal properties of elastic scattering. Based on these empirical observations, and taking inspiration from saturation models, we propose a simple scaling law for proton-proton elastic scattering at LHC energies. We find t…
We discuss prompt production of $J/ψ$ mesons in proton-proton collisions at the LHC within NRQCD $k_t$-factorization approach using Kimber-Martin-Ryskin (KMR) unintegrated gluon distributions (UGDF). We include both direct color-singlet production ($g g \to J/ψg$) as well as a feed-down from $χ_c \to J/ψγ$ and $ψ' \to J/ψX$ decays. The production of the decaying mesons ($χ_c$ or $ψ'$) is also calculated within NRQCD $k_t$-factorization approach. The corresponding matrix elements for $g g \to J/ψ$ g, $g g \to ψ'g$ and $g g \to χ_c$ include parameters of the nonrelativistic space wave functions …
We investigate saturation effects in $ep$ scattering as well as in ultraperipheral $p$A and AA collisions at small $x$ with four variants of the impact parameter dependent color dipole model: with and without gluon saturation and with and without a novel mechanism that suppresses unphysical dipole radii above the confinement scale, a problem not addressed by most implementations. We show that $ep$ scattering at HERA can be very well described by any of the four variants. When going from $ep$ to $e$A scattering, saturation effects are expected to increase as $\sim$A$^{1/3}$. In lieu of an elect…
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