We present a formalism for gluon-gluon elastic scattering in the presence of the classical color field of the protons in high energy collision. The classical field is obtained by solving the classical Yang-Mills equation in the covariant gauge and treated as a prescribed background for the quantum gluons involved in the scattering process. The interaction between the classical field and the quantum gluon modifies the gluon propagator, and, in turn, the $gg\rightarrow gg$ amplitude. The modified gluon propagator is derived to the first non-zero order of the classical field using the Gaussian approximation in Color Glass Condensate and shown to satisfy the generalized Slavnov-Taylor identity. This formalism is the theoretical basis for our recently proposed classical color field modified minijet model where we show that the $pp$ and $\pbar p$ cross section data from $\sqrt{s}=5$ GeV to 30 TeV can be satisfactorily fitted and the model predicts a $(\ln s)^2$ behavior for large $s$, which saturates the asymptotic behaviour of Froissart bound.
Towards a fluid-dynamic description of an entire heavy-ion collision: from the colliding nuclei to the quark-gluon plasma phase
Duke University（杜克大学）；GSI Helmholtzzentrum für Schwerionenforschung（GSI亥姆霍兹重离子研究中心）；Università di Firenze（佛罗伦萨大学）；INFN Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）
Elastic scattering data gained for proton-proton collisions at high energies are being analyzed at the present practically only with the help of purely phenomenological mathematical models. And the question exists whether in the impact parameter plane the elastic processes may be interpreted as central or peripheral. From realistic point of view the peripherality should be preferred and one may expect that nucleon dimensions should manifest in some way in elastic data. It will be demonstrated that the elastic pp data at the energy of 53 GeV in the interval |t| from (0., 4.) [GeV^2] may be inte…
Saturation of small-x gluons in a nucleus, which has the form of transverse momentum broadening of projectile gluons in pA collisions in the nuclear rest frame, leads to a modification of the parton distribution functions in the beam compared with pp collisions. The DGLAP driven gluon distribution turns out to be suppressed at large x, but significantly enhanced at x<<1. This is a high twist effect. In the case of nucleus-nucleus collisions all participating nucleons on both sides get enriched in gluon density at small x, which leads to a further boosting of the saturation scale. We derive rec…
We propose a novel formalism for simultaneously describing both, the hard and soft parton dynamics in ultrarelativistic collisions of nuclei. The emission of gluons from the initially coherent parton configurations of the colliding nuclei and low-$p_t$ color coherence effects are treated in the framework of a Yang-Mills transport equation on a coupled lattice-particle system. A collision term is added to the transport equation to account for the remaining intermediate and high-$p_t$ interactions in an infrared finite manner.
Interaction with a nucleus in pA collisions enhances the higher Fock components in the projectile proton. Effectively, this corresponds to an increase of the hard scale of the process by the saturation momentum Q^2 -> Q^2+Q_{sA}^2, which leads to an increased gluon distribution function at small x (but suppressed at x -> 1) compared to that in pp collisions. In the case of AA collisions the gluon distributions of bound nucleons in both nuclei turn out to be enhanced, i.e. to be boosted to higher saturation scales compared to pA collisions. A set of bootstrap equations relating the saturation s…
We present the potential to determine the polarised gluon density from boson-gluon fusion processes with di-jet events at future high energy ep-colliders. These include HERA at DESY operated with polarised electrons and protons, polarised protons from HERA colliding on polarised electrons from a future linear collider, and polarised protons from RHIC at BNL colliding on electrons from a future electron accelerator.
The main contribution to hard elastic scattering comes from components of wave functions of colliding hadrons that contain minimum number of partons. We discuss this mechanism in regge and parton approaches and estimate the probabilities that colliding hadrons are in such bare states. The behavior of cross-sections in this regime at various energies can give nontrivial information on high energy dynamics.
Elastic gluon-gluon-quark (gluon-gluon-antiquark) scattering is studied in perturbative QCD with 123 Feynman diagrams at the tree level. Individually squared amplitudes and interference terms of the Feynman diagrams are derived. With the elastic gluon-gluon-quark scattering and the elastic gluon-gluon-antiquark scattering transport equations are established. In the thermalization process of initially created quark-gluon matter, this matter is governed by elastic 2-to-2 scattering and elastic 3-to-3 scattering. Solutions of the transport equations show that initially created quark-gluon matter …
We study the behavior of the differential cross section for vector meson photoproduction at large momentum transfer in the two-gluon exchange model. We focus on the treatment of two-quark correlation function in the proton and on gluon propagators with a dynamically generated mass. We find that only the large t region is sensitive to the particular details of these inputs.
The energy dependence of the total hadronic cross sections is caused by gluon bremsstrahlung which we treat nonperturbatively. It is located at small transverse distances about 0.3 fm from the valence quarks. The cross section of gluon radiation is predicted to exponentiate and rise with energy as s^Δ with Δ=0.17 +/- 0.01. The total cross section also includes a large energy independent Born term which corresponds to no gluon radiation. The calculated total cross section and the slope of elastic scattering are in good agreement with the data.
We describe the dynamics of gluons and quarks in a relativistic nuclear collision, within the framework of classical mean-field transport theory, by the coupled equations for the classical Yang-Mills field and a collection of colored point particles. The particles represent the valence quarks in the colliding nuclei. We explore the time evolution of the gauge field in a numerical simulation of the collision of two Lorentz-boosted ``nuclei'' on a long three-dimensional gauge lattice. We report first results on soft gluon scattering and coherent gluon radiation.
A Linear Boltzmann Transport model within perturbative QCD is developed for the study of parton propagation inside the quark-gluon plasma. Both leading partons and thermal recoil partons are tracked so that one can also study jet-induced medium excitations. In this study, we implement the complete set of elastic parton scattering processes and investigate elastic parton energy loss, transverse momentum broadening and their nontrivial energy and length dependence. We further investigate medium modifications of the jet shape and fragmentation functions of reconstructed jets. Contributions from t…
The next-to-leading order of the differential cross-section of the subprocess of Compton scattering of quark-gluon of prompt photon production in proton-proton collisions at NICA energies
Baku State University（巴库国立大学）；Institute for Physical Problems, Baku State University（巴库国立大学物理问题研究所）
The nonlinear effect of gluon depletion in the collision of large nuclei can be large. It is due to multiple scatterings among comoving partons initiated by primary scattering of partons in the colliding nuclei. The effect can give rise to substantial suppression of $J/ψ$ production in very large nuclei, even if the linear depletion effect is insignificant for the collisions of nuclei of smaller sizes. This mechanism offers a natural explanation of the enhanced suppression in the Pb-Pb data recently observed by NA50.
The goal of this paper is to extend the results of Ref. [1], where formulae were derived for gluonic radiation for a high energy nucleus colliding with a classical colored particle. In Ref. [1], we computed the amplitudes for radiation in the fragmentation region of the particle for a dilute gluonic field. In this paper, we compute the radiation by solving the fluctuation equations of the dense background field in a specific gauge which makes it simple to solve the asymptotic radiation from an initial condition immediately after the passage of the nucleus. We identify and compute two component…
We argue that the classical evolution of small x modes in the collision of two ultrarelativistic nuclei is described on a transverse lattice by the Kogut--Susskind Hamiltonian in 2+1-dimensions coupled to an adjoint scalar field. The initial conditions for the evolution are provided by the non--Abelian Weizsäcker--Williams fields which constitute the classical parton distributions in each of the nuclei. We outline how lattice techniques developed for real time simulations of field theories in thermal equilibrium can be used to study non--perturbatively, thermalization and classical gluon radia…
We derive expressions for various correlators of the gauge field and find the propagators in Hamiltonian dynamics which employs a new gauge $A^τ=0$. This gauge is a part of the wedge form of relativistic dynamics suggested earlier as a tool for the study of quantum dynamics in ultra-relativistic heavy ion collisions. We prove that the gauge is completely fixed. The gauge field is quantized and the field of radiation and the longitudinal fields are unambiguously separated. The new gauge puts the quark and gluon fields of the colliding hadrons in one Hilbert space and thus allows one to avoid fa…
The elastic scattering of gqq, gqqbar and gqbarqbar and the thermalization of quark-gluon matter are studied. According to Feynman diagrams at the tree level, squared amplitudes for the elastic gqq scattering and the elastic gqqbar scattering are derived in perturbative QCD. Transport equations including the squared amplitudes for the elastic gqq, gqqbar and gqbarqbar scattering are established. Corresponding to anisotropic gluon and quark distributions created in central Au-Au collisions at RHIC, solutions of the transport equations show that thermalization time of quark matter can be shorten…
The early thermalization is crucial to the quark-gluon plasma as a perfect liquid and results from many-body scattering. We calculate squared amplitudes for elastic parton-parton-parton scattering in perturbative QCD. Transport equations with the squared amplitudes are established and solved to obtain the thermalization time of initially produced quark-gluon matter and the initial temperature of quark-gluon plasma. We find that the thermalization times of quark matter and gluon matter are different.
Exploiting recently obtained analytic solutions of classical Yang-Mills equations for higher order perturbations in the field of the dilute object (proton), we derive the complete first saturation correction to the single inclusive semi-hard gluon production in high energy proton-nucleus collisions by applying the Lehmann-Symanzik-Zimmermann reduction formula. We thus finalize the program started by Balitsky (see Ref.~\cite{Balitsky:2004rr}) and independently by Chirilli, Kovchegov and Wertepny (see Ref.~\cite{Chirilli:2015tea}) albeit using a very different approach to carry out our calculati…
We show that soft gluons exchanged between the two colliding protons in multiparton scattering processes can be decoupled, such that their effects are described by the vacuum expectation values of Wilson lines. Our argument relies on nonabelian Ward identities and generalises the proof of factorisation for single Drell-Yan production given by Collins, Soper and Sterman.
Similar to the radiative parton energy loss due to gluon bremsstrahlung, elastic energy loss of a parton undergoing multiple scattering in a finite medium is demonstrated to be sensitive to interference effect. The interference between amplitudes of elastic scattering via a gluon exchange and that of gluon radiation reduces the effective elastic energy loss in a finite medium and gives rise to a non-trivial length dependence. The reduction is most significant for a propagation length $L< 4/πT$ in a medium with a temperature $T$. Though the finite size effect is not significant for the average …
The application of a modified gluon propagator and an infrared frozen running co upling constant in the description of the proton-proton elastic scattering is in vestigated. The model based on the exchange of the Pomeron as a pair of non-pert urbative gluons is modified to include the frozen coupling constant in the infra red kinematic region. A good fit to the data of the differential cross section f or different center of mass energies (53 GeV and 1.8 TeV) is obtained.
In this talk we report on recent calculation of high energy baryon scattering amplitudes in QCD. Elastic baryon impact factors for two, three and four gluons are presented and their energy evolution is described that incorporates unitarity corrections. We find that the baryon couples directly to the BFKL Pomeron, to the BKP odderon and to a new state, a three-gluon BKP Pomeron. The new state may decay into four gluons with a new 3 -> 4 transition vertex. This vertex defines the transition amplitude of the three-gluon BKP Pomeron state into two BFKL Pomerons.
The elastic hadronic amplitude is calculated using the nonperturbative light-cone dipole representation for gluon bremsstrahlung. The data for large mass diffraction demand a two-scale structure of light hadrons: the gluon clouds of the valence quarks with a size of 0.3fm and the hadronic size 1fm. The presence of the two scales unavoidably leads to a specific form for the total hadronic cross section which consists of a steeply rising \propto s^Δ (Δ=0.17 +/- 0.01) term related to gluon radiation, and a large constant term originating from soft interactions which does not induce any gluon emis…
It is shown that the amplitude for the scattering of a heavy quarkonium system from a nucleon near threshold is completely determined by the fraction of angular momentum, as well as linear momentum, carried by gluons in the nucleon. A form for the quarkonium-nucleon non-relativistic potential is derived.
We apply the Low's theorem to soft gluon emission from heavy quark scattering in the nonperturbative strongly interacting quark-gluon plasma (sQGP). The sQGP is described in terms of the dynamical quasi-particles and adjusted to reproduce the EoS from lQCD at finite temperature and chemical potential. Since the emitted gluon is soft and of long wavelength, it does not provide information on the detailed structure of the scattering, and only the emission from incoming and outgoing partons is enough. It simplifies the calculations making the scattering amplitude factorizable into the elastic sca…
We discuss the two-gluon exchange contribution (formally three-loops) to elastic photon-photon scattering in the high-energy approximation. The elastic $γγ\to γγ$ amplitude is given in the impact-factor representation for all helicity configurations and finite quark masses. We discuss the importance of including the charm quark, which contribution, due to interference, can enhance the cross section considerably. We investigate the contribution to the $γγ\to γγ$ amplitude from the soft region, by studying its dependence on nonperturbative gluon mass. Helicity-flip contributions are shown to be …
I derive expressions for various correlators of the gauge field and find propagators in a new gauge A^τ=0. This gauge is a part of the wedge form of relativistic dynamics suggested earlier as the tool for the study of quantum dynamics in collisions of hadrons at extremely high energies and in ultrarelativistic heavy ion collisions. The new gauge puts the quark and gluon fields of the colliding hadrons in one Hilbert space and thus allows one to avoid factorization.
We discuss the role of elastic and inelastic collisions and their interplay in the thermalization of the quark-gluon plasma. We consider a simplified situation of a static plasma, spatially uniform and isotropic in momentum space. We focus on the small momentum region, which equilibrates first, and on a short time scale. We obtain a simple kinetic equation that allows for an analytic description of the most important regimes. The present analysis suggests that the formation of a Bose condensate, expected when only elastic collisions are present, is strongly hindered by the inelastic, radiative…
We prove that the inclusive single-gluon production cross section for a hadron colliding with a high-density target factorizes into the gluon distribution function of the projectile, defined as usual within the DGLAP collinear approximation, times the cross section for scattering of a single gluon on the strong classical color field of the target. We then derive the gluon-proton (nucleus) inelastic cross section and show that it is (up to logarithms) infrared safe and that it grows slowly with center of mass energy. Furthermore, we discuss jet transverse momentum broadening for the case of nuc…
Using previously described functional techniques for exact, non-perturbative, gauge-invariant renormalized QCD processes, a simplified version of the amplitudes - in which forms akin to Pomerons naturally appear - provides fits to ISR Elastic pp scattering data. Extension of this work to LHC reactions is presently underway.
We analyze the differences between the $pp$ and $p\bar{p}$ differentia l elastic cross section measurements by the D0 and TOTEM Collaborations at the Tevatron, Fermilab, and the LHC, CERN that lead to a significance larger than 3$σ$ of the existence of the colourless $C$-odd three-gluon state, the odderon.
We discuss heavy-quark dynamics in the quark-gluon plasma under a strong magnetic field induced by colliding nuclei. By the use of the diagrammatic resummation techniques for Hard Thermal Loop and the external magnetic field, we show analytic results of heavy-quark diffusion coefficient and drag force which become anisotropic due to the preferred spatial orientation in the magnetic field. We argue that the anisotropic diffusion coefficient gives rise to an enhancement/suppression of the heavy-quark elliptic flow depending on the transverse momentum.
The Yang Mills equations provide a classical mean field description of gauge fields. In view of developing a coherent description of the formation of the quark gluon plasma in high energetic nucleus-nucleus collisions we study pure gauge field dynamics in 3+1 dimensions. In collisions of wave packets, numerically simulated on a SU(2) gauge lattice, we study transverse and longitudinal energy currents. For wave packets with different polarizations in color space, we observe a time delayed fragmentation after the collision resulting in a rapid expansion into transverse directions. We call this p…
Deep-elastic pp scattering at c.m. energy 14 TeV at LHC in the momentum transfer range 4 GeV*2 < |t| < 10 GeV*2 is planned to be measured by the TOTEM group. We study this process in a model where the deep-elastic scattering is due to a single hard collision of a valence quark from one proton with a valence quark from the other proton. The hard collision originates from the low-x gluon cloud around one valence quark interacting with that of the other. The low-x gluon cloud can be identified as color glass condensate and has size ~0.3 F. Our prediction is that pp differential cross section in t…
We construct an analytical expression for the distribution of gluons in the state immediately following a heavy ion collision in the quasi-classical limit of QCD given by McLerran-Venugopalan model. The resulting gluon number distribution function includes the effects of all multiple rescatterings of gluons with the nucleons of both colliding nuclei. The typical transverse momentum k of the produced gluons is shown to be of the order of the saturation scale of the nuclei Qs, as predicted by Mueller. We analyze the properties of the obtained distribution and demonstrate that due to multiple res…
The KN and KbarN low-energy elastic scattering is consistently studied in the framework of the QCD-inspired quark potential model. The model is composed of the t-channel one-gluon exchange potential, the s-channel one-gluon exchange potential and the harmonic oscillator confinement potential. By means of the resonating group method, nonlocal effective interaction potentials for the KN and KbarN systems are derived and used to calculate the KN and KbarN elastic scattering phase shifts. By considering the effect of QCD renormalization, the contribution of the color octet of the clusters (qqbar) …
We compute by numerical integration of the Dirac equation the number of quark-antiquark pairs initially produced in the classical color fields of colliding ultrarelativistic nuclei. While the number of qqbar pairs is parametrically suppressed in the coupling constant, we find that in this classical field model their production rate is comparable to the thermal ratio of gluons/pairs = 9 N_f/32. After isotropization one thus would have quark-gluon plasma in chemical equilibrium.
We present exploratory studies of the proton content via unpolarized and polarized transverse-momentum-dependent gluon distributions in the proton at leading twist. We make use of an enhanced spectator-model approach to encode in our densities both small- and moderate-$x$ effects. These studies are relevant to the investigation of the inner structure of hadrons via tomographic analyses at new-generation colliding machines.
Unraveling the inner dynamics of gluons and quarks inside nucleons is a primary target of studies at new-generation colliding machines. Finding an answer to fundamental problems of Quantum ChromoDynamics, such as the origin of nucleon mass and spin, strongly depends on our ability of reconstructing the 3D motion of partons inside the parent hadrons. We present progresses and challenges in the extraction of TMD parton densities, with particular attention to the ones describing polarization states of gluons, which still represent an largely unexplored field. Then, we highlight connections with c…
We examine the significance of $2 \rightarrow 2$ partonic collisions as the suppression mechanism of high-energy partons in the strongly interacting medium formed in ultrarelativistic heavy ion collisions. For this purpose, we have developed a Monte Carlo simulation describing the interactions of perturbatively produced, non-eikonally propagating high-energy partons with the quarks and gluons from the expanding QCD medium. The partonic collision rates are computed in leading-order perturbative QCD (pQCD), while three different hydrodynamical scenarios are used to model the medium. We compare o…
We perform explorative analyses of the 3D gluon content of the proton via a study of (un)polarized twist-2 gluon TMDs, calculated in a spectator model for the parent nucleon. Our approach encodes a flexible parametrization for the spectator-mass density, suited to describe both moderate and small-$x$ effects. All these prospective developments are relevant in the investigation of the gluon dynamics inside nucleons and nuclei, which constitutes one of the major goals of new-generation colliding machines, as the EIC, the HL-LHC and NICA.
Sufficiently inclusive processes, like the deep inelastic scattering (DIS), are described in terms of scale-dependent parton distributions, which correspond to the density of partons with a given longitudinal momentum fraction, integrated over the parton transverse momentum. For less inclusive processes, one needs to consider densities unintegrated over the transverse momentum. This work focuses on the unintegrated gluon distribution (UGD), describing the probability that a gluon can be emitted by a colliding proton, with definite longitudinal fraction and transverse momentum. Through the lept…
In ultra-relativistic heavy-ion collisions, the strong electric field can be produced by the colliding nuclei. The magnitude of the electric field $E$ is on the order of $eE\sim m_π^2$ at the early stage of the collision. In quark gluon plasma (QGP), such a strong electric field can have a significant impact on the evolution of charmonia. We employ the time-dependent Schrödinger equation to study the evolution of charmonium states in the strong electric field generated by the moving charges. The electric field can result in transitions between charmonium states with different angular momenta. …
Colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high energies, elastic scattering contributes considerably (18-25%) to the total cross section. Its share first decreases and then increases at higher energies. Small-angle scattering prevails at all energies. Some characteristic features are seen that provide informationon the geometrical structure of the colliding particles and the relevant dynamical mechanisms. The st…
All contemporary phenomenological models of elastic hadronic scattering have been based in principle on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved in particle physics cannot be applied to short-ranged strong interactions. The analysis of corresponding collision experiments is to be done under new basic assumptions. The actual progress in description of hadronic collision processes might then exist only if the initial states are specified on the basis of impact parameter values of col…
We study the kinetic equilibration of gluons produced in the very early stages of a high energy heavy ion collision in a ``self-consistent'' relaxation time approximation. We compare two scenarios describing the initial state of the gluon system, namely the saturation and the minijet scenarios, both at RHIC and LHC energies. We argue that, in order to characterize kinetic equilibration, it is relevant to test the isotropy of various observables. As a consequence, we find in particular that in both scenarios elastic processes are not sufficient for the system to reach kinetic equilibrium at RHI…
Gluon distributions of colliding hadrons saturate as a result of the non-linear evolution equations of QCD. As a consequence there exists the so called saturation momentum, which is related to the gluon density per unit rapidity per transverse area. When saturation momentum is the only scale for physical processes, different observables exhibit geometrical scaling (GS). We show a number of examples of GS and its violation in different reactions.
Nuclei colliding at very high energy create a strong, quasi-classical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromo-electric and chromo-magnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. Our res…
We compute by numerical integration of the Dirac equation the number of quark-antiquark pairs produced in the classical color fields of colliding ultrarelativistic nuclei. Results for the dependence of the number of quarks on the strength of the background field, the quark mass and time are presented. We also perform several tests of our numerical method. While the number of qqbar pairs is parametrically suppressed in the coupling constant, we find that in this classical field model it could even be compatible with the thermal ratio to the number of gluons.
We discuss how the main features of the recent LHC data on elastic scattering can be described by a QCD-inspired formalism with a dynamical infrared mass scale. For this purpose new developments on a dynamical gluon mass approach are reported, with emphasis on a method to estimate uncertainty bounds in the predictions for the high-energy scattering observables. We investigate the effects due to the correlations among the fixed and free parameters involved and show that the band of predictions are consistent with the recent data from the TOTEM experiment, including the forward quantities and th…
