Parton cascades at DLA: the role of the evolution variable
Carlota Andrés, Liliana Apolinário, Néstor Armesto, André Cordeiro, Fabio Dominguez, José Guilherme Milhano
备注：
4 pages, 3 figures. Proceedings for a parallel presentation at Quark Matter 2023 in Houston, Texas, United States of America from 3-9 September 2023. arXiv admin note: text overlap with arXiv:2307.08410
The theoretical treatment of jet quenching lacks a full description of the interplay between vacuum-like emissions, usually formulated in momentum space, and medium induced ones that demand an interface with a space-time picture of the expanding medium and thus must be formulated in position space. In this work we build a toy Monte-Carlo parton shower ordered in formation time, virtual mass, and opening angle, which are equivalent at leading logarithmic accuracy. Aiming to explore a link with jet substructure, we compute the Lund plane distributions for the different ordering prescriptions. Further, we investigate the sensitivity of ordering prescriptions to medium effects by counting the number of events eliminated by a decoherence condition.
The multiparton density matrices of the QCD gluon cascade are investigated. The generating functional and master equation for momentum space multiparton density in the double logarithmic approximation (DLA) are proposed.
The structure of the QCD gluonic cascade in configuration space is investigated. The explicit form of the inclusive single particle density in configuration space transverse coordinates is derived in the double logarithmic approximation (DLA) of QCD. The possible simplification of the multiparton density matrix formalism for DLA approach is found and discussed.
The structure of the QCD gluonic cascade in configuration space is investigated. The explicit form of the inclusive single particle density in configuration space transverse coordinates is derived in the double logarithmic approximation (DLA) of QCD. The possible simplification of the multiparton density matrix formalism for DLA approach is found and discussed.
Based on parametric reasoning, we provide a simple dynamical picture of how a perturbative parton cascade, in interaction with a QCD medium, fills phase space as a function of time.
This comment is hereby withdrawn, because the paper by D. Seibert, KSUCNR-005-94 and nucl-th/9403005 was withdrawn and it was acknowleged that the parton cascade model does approach chemical equilibrium correctly. Therefore our reply to Seibert's paper is now obsolete.
Parton cascade models have been surprisingly successful in describing heavy-ion reactions at RHIC energies -- surprising because in spite of their QCD bells and whistles, they essentially embody classical many-particle dynamics. The procedure to determine the sequence of the binary parton interactions, however -- an essential aspect of all such models -- is by necessity a phenomenological (and somewhat arbitrary) feature of these codes. This has been recognized early on as a serious drawback of non-covariant cascade models. While in the Poincare-Covariant Parton Cascade code "pcpc" the interac…
The shear viscosity is calculated by means of the perturbative kinetic partonic cascade BAMPS with CGC initial conditons for various saturation momentum scale Q_s. eta/s ~ 0.15 stays approximately constant when going from RHIC to LHC.
We present a new cascade-type microscopic simulation of nucleus-nucleus collisions at RHIC energies. The basic elements are partons (quarks and gluons) moving in 8N-dimensional phase space according to Poincare-covariant dynamics. The parton-parton scattering cross sections used in the model are computed within perturbative QCD in the tree-level approximation. The Q^2 dependence of the structure functions is included by an implementation of the DGLAP mechanism suitable for a cascade, so that the number of partons is not static, but varies in space and time as the collision of two nuclei evolve…
The angular correlation function of partons in a jet, as derived from perturbative QCD, is nonanalytic at a critical angle which separates a multiparticle regime with scaling properties from a regime with few particles near the hadronisation scale. Some phenomenological consequences are discussed.
An analytical method is presented to solve generalized QCD evolution equations for the time development of parton cascades in a nuclear environment. Closed solutions for the spectra of produced partons with respect to the variables time, longitudinal momentum and virtuality are obtained under some idealizing assumptions about the composition of the nuclear medium. Several characteristic features of the resulting parton distributions are discussed. One of the main conclusions is that the evolution of a parton shower in medium is dilated as compared to free space and is accompanied by an enhance…
We present a new cascade-type microscopic simulation of Nucleus-Nucleus Collisions at RHIC energies. The basic elements are partons (quarks and gluons) moving in 8N-dimensional phase space according to Poincaré-covariant dynamics. The parton-parton scattering cross sections used in the model are computed within perturbative QCD in the tree-level approximation. The $Q^2$ dependence of the structure functions is included by an implementation of the DGLAP mechanism suitable for a cascade, so that the number of partons is not static, but varies in space and time as the collision of two nuclei evol…
Evolution equations for multiplicities in QCD cascades can, both in the parton and dipole picture, be used to estimate corrections beyond the formal accuracy of the modified leading log approximation (MLLA). The differences between the two pictures, and other uncertainties beyond first order MLLA corrections, are here investigated in some detail. For example, I discuss how some colour suppressed corrections, which cannot be determined without better knowledge of non-perturbative QCD, are related to the question of colour reconnection. A generalized evolution equation for the dipole cascade is …
The new version of the parton shower module APACIC++ for the SHERPA event generator framework is presented. It incorporates some features, that are specific for the consistent merging with multi-particle matrix elements at tree-level. This publication also includes some exemplary results and a short description of the upgraded class structure of APACIC++, version 2.0.
Employing a newly developed pQCD inspired parton cascade we simulate the space time evolution of gluons which are produced initially in a heavy ion collision at RHIC energy. The inelastic $gg \leftrightarrow ggg$ interactions are for the first time implemented obeying full detailed balance. The numerical results show that thermalization of gluons is mainly driven by the inelastic gluonic interactions and reaches equilibrium at $1\sim 2$ fm/c. In simulations for noncentral collisions considerable partonic elliptic flow $v_2$ is generated being comparable with the experimental data.
These lecture notes are a combination of two lectures and a contribution to the celebration of Andrzej Białas' birthday at the LI Cracow School of Theoretical Physics in June 2011. I here discuss the dynamics of particle production in high energy reactions. It includes parton cascades and hadronization in e+e--ann., small x evolution including the Double Leading Log approximation and the BFKL equation, saturation at high densities and the BK equation, and finally the Lund Dipole Cascade model for high energy collisions, which is implemented in the DIPSY MC.
We elaborate on a new 3+1 dimensional Monte Carlo parton cascade solving kinetic Boltzmann processes including - for the first time - inelastic multiplication processes (gg <-->ggg) in a unified manner. The back reaction channel is treated fully consistently, exactly obeying detailed balance. The algorithm can handle, in principle, any specified initial conditions for the freed partons, the latter being on their kinetic mass shell. First full simulations with minijet initial conditions demonstrate that the inclusion of the inelastic channels leads to a very fast kinetic and chemical equilibrat…
New properties of the multiplicity distributions predicted by higher order QCD and their physical origin are discussed briefly. Several studies which can be performed at HERA are proposed.
Parton Cascade Models (PCM), which describe the full time-evolution of a system of quarks and gluons using pQCD interactions are ideally suited for the description of jet production, including the emission, evolution and energy-loss of the full parton shower in a hot and dense QCD medium. The Landau-Pomeranchuk-Migdal (LPM) effect, the quantum interference of parton wave functions due to repeated scatterings against the background medium, is likely the dominant in-medium effect affecting jet suppression. We have implemented a probabilistic implementation of the LPM effect within the PCM which …
Going beyond the simplified gluonic cascades, we introduce both gluon and quark degrees of freedom for partonic cascades inside the medium. We then solve the set of coupled evolution equations numerically with splitting kernels calculated for static, exponential, and Bjorken expanding media to arrive at medium-modified parton spectra for quark and gluon initiated jets. Using these, we calculate the inclusive jet $R_{AA}$ where the phenomenologically driven combinations of quark and gluon jet fractions are included. Then, the rapidity dependence of the jet $R_{AA}$ is examined. We also study th…
In this talk the newly developped Monte-Carlo event generator {\tt APACIC++} suitable to describe multijet-events in high-energetic electron-positron annihilations is presented. A new ansatz to match the corresponding matrix elements for the production of jets via the strong and electroweak interactions to the subsequent parton shower modelling the inner-jet evolution is discussed in some detail. Results obtained with {\tt APACIC++} are compared to other QCD event generators and to some representative experimental data.
A solution of the CCFM equation for a description of both the structure function $F_2$ and the cross section of forward jet production as measured by the HERA experiments is obtained on the basis of the parton level Monte Carlo program SMALLX. The treatment of the non - Sudakov form factor and the so - called "consistency constraint" are discussed. Following this a backward evolution scheme according to CCFM is developed which then is used to construct an efficient hadron level Monte Carlo program CASCADE. The results from the forward evolution and the backward evolution Monte Carlos are compa…
A Dual Parton Model with a formation zone intranuclear cascade in the spectators of the projectile and target nuclei is studied. The hadrons produced in the formation zone cascade contribute to Feynman-$x_F$ and lab-$x$ distributions in the fragmentation regions of the target and projectile nuclei. We discuss the consequences of this model in the secondary cosmic ray production, by analyzing the calculated spectrum weighted moments for pion and kaon production. We show that the proposed model leads to significant differences with respect to a simple superposition model, where the nucleus-nucle…
We studied the evolution of jets within a medium that contains both, transverse kicks as well as medium induced coherent radiation. In this framework parton branching occurs simultaneously to scatterings within the medium, leading to the interference effects that reproduce the well known BDMPS-Z emission rates and sizeable transverse momentum broadening. We examined the relative importances of transverse momentum broadening from the coherent splittings and different types of in-medium scatterings and found a clear hierarchy of the influences from different scattering effects and deflections du…
The explanation of the suppression of high-pT hadron yields at RHIC in terms of jet-quenching implies that the multiplicity distributions of particles inside a jet and jet-like particle correlations differ strongly in nucleus-nucleus collisions at RHIC or at the LHC from those observed at e+e- or hadron colliders. We present a framework for describing the medium-induced modification, which has a direct interpretation in terms of a probabilistic medium-modified parton cascade, and which treats leading and subleading partons on an equal footing. We show that our approach can account for the stro…
Highly energetic particles in the medium of a quark gluon plasma undergo processes of coherent medium induced radiation and scatterings off medium particles. We solved the evolution equations for particle fragmentation functions that describe in-medium evolution via these two in-medium processes numerically via Monte-Carlo algorithms. We study the in-medium broadening of the distribution over momentum components transverse to the jet-axis for different cases of jet-medium interactions and different values of average transverse momentum transfer.
This comment is withdrawn, as the figure on which it was based is inconsistent with other figures in the text and thus probably incorrect. Using the other figures, I find that the parton cascade model does approach chemical equilibrium correctly.
APACIC++ is a Monte-Carlo event-generator dedicated for the simulation of electron-positron annihilations into jets. Within the framework of APACIC++, the emergence of jets is identified with the perturbative production of partons as governed by corresponding matrix elements. In addition to the build-in matrix elements describing the production of two and three jets, further programs can be linked allowing for the simultaneous treatment of higher numbers of jets. APACIC++ hosts a new approach for the combination of arbitrary matrix elements for the production of jets with the parton shower, wh…
VNI is a general-purpose Monte-Carlo event-generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. It uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme, as well as the development of hadron cascades after hadronization. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time-development of the phase-space densities of partons, pre-hadronic parton clusters, and final-state hadrons…
It is the central goal of our studies to describe parton fragmentation in the hot and dense medium of a quark gluon plasma (QGP). Under the assumption that the medium is not static and homogeneous, knowledge about the temporal evolution of the processes involved can be of essential importance. Therefore, parton fragmentation has been studied with a Monte-Carlo algorithm that approximates the DGLAP-evolution of fragmentation functions via a set of parton cascades. The presented work consists mainly of implementations of this kind of algorithm and the application of a simple approximation, which…
We argue that the evolution of coloured partons into colour-singlet hadrons has approximate factorization into an extended parton-shower phase and a colour-singlet resonance--pole phase. The amplitude for the conversion of colour connected partons into hadrons necessarily resembles Regge-pole amplitudes since qq-bar resonance amplitudes and Regge-pole amplitudes are related by duality. A `Regge-cascade' factorization property of the N-point Veneziano amplitude provides further justification of this protocol. This latter factorization property, in turn, allows the construction of general multi-…
We study the production of bottom quarks in $pp$ collisions at Large Hadron Collider energies using previously developed parton cascade model to explore the impact of Landau Pomeranchuk Midgal (LPM) effect on their dynamics. In contrast to the case for charm quarks reported recently, we find only a marginal impact of the suppression of multiple scatterings of partons due to the LPM effect on their production. It is felt that this happens as they are only produced in very hard collisions.
We investigate the radiative break-up of a highly energetic quark or gluon in a high-temperature QCD plasma. Within an inertial range of momenta $T \ll ω\ll E$, where $E$ denotes the energy of the original hard parton (jet) and $T$ the temperature of of the medium, we find that, as a result of the turbulent nature of the underlying parton cascade, the quark to gluon ratio of the soft fragments tends to a universal constant value that is independent of the initial conditions. We discuss implications of this result to jet quenching physics and the problem of thermalization of the quark-gluon pla…
The high density of scattered partons predicted in nuclear collisions at very high energy makes color screening effects significant. We explain how these screening mechanisms may suppress nonperturbative, soft QCD processes, permitting a consistent calculation of quark-gluon plasma formation within the framework of perturbative QCD. We present results of a model calculation of these effects including predictions for the initial thermalized state for heavy nuclei colliding at RHIC and LHC.
We introduce a backward evolution Monte Carlo algorithm implementation of the CCFM equation and present latest developments in phenomenology of hadron-hadron collisions for the Monte Carlo generator Cascade.
We report on re-calculation of the next-to-leading order DGLAP evolution kernels performed in a scheme suited for Monte Carlo simulations of parton cascades (parton showers).
ALP photo-production in the parton and hadron cascade model PACIAE
Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室及粒子物理研究所）；School of Mathematics and Statistics, Wuhan Textile University（武汉纺织大学数学与统计学院）；School of Physics and Electronic Science, Guizhou Normal University（贵州师范大学物理与电子科学学院）；School of Physics and Information Technology, Shaanxi Normal University（陕西师范大学物理学与信息工程学院）；College of Physics, Sichuan University（四川大学物理学院）；China Institute of Atomic Energy（中国原子能科学研究院）
We calculate the probability for rapidity gaps in the parton cascade for different approximations within the perturbative QCD and compare the results with recent measurements. The aim is to find out whether the dual connection between the parton and hadron final states -- observed so far in various inclusive measurements -- holds as well for the extreme kinematic configurations with colour sources separated by large rapidity gaps. A description of the data is possible indeed choosing the parameters of the cascade in the range suggested by recent analyses of the energy spectra (the $k_\perp$ cu…
We have updated the parton and hadron cascade model PACIAE 2.0 for relativistic nuclear collisions (cf. Comput. Phys. Comm. 183(2012)333) to the new issue of PACIAE 2.1. The PACIAE model is based on PYTHIA. In the PYTHIA model, once the generated particle/parton transverse momentum $p_T$ is randomly selected, its component of $[p_x,p_y]$ was originally put on the circle with radius $p_T$ randomly. It is now replaced by put on the circumference of ellipse with half major and minor axes of $p_T(1+δ_p)$ and $p_T(1-δ_p)$, respectively, in order to investigate better the transverse momentum anisotr…
We discuss the dynamics of parton cascades that develop in dense QCD matter, and contrast their properties with those of similar cascades of gluon radiation in vacuum. We argue that such cascades belong to two distinct classes that are characterized respectively by an increasing or a constant (or decreasing) branching rate along the cascade. In the former class, of which the BDMPS, medium-induced, cascade constitutes a typical example, it takes a finite time to transport a finite amount of energy to very soft quanta, while this time is essentially infinite in the latter case, to which the DGLA…
We illustrate a study based on a veto technique to match parton showers and matrix elements in the Cascade Monte Carlo event generator, and present a numerical application to gluon matrix elements for jet production.
Different treatments for the inclusion of higher-order perturbative QCD corrections in parton based transport models of relativistic heavy-ion collisions are studied and their influence on experimental observables is investigated. At RHIC, particle multiplicities may vary by more than 30%, depending on the correction scheme. A detailed analysis of the squared relative momentum transfers to be expected in parton (re)scatterings at RHIC casts doubt on the applicability of pQCD based transport approaches at the SPS and rules out the application of higher-order correction schemes based on a rescal…
The parton and hadron cascade model PACIAE 2.1 (cf. Comput. Phys. Commun.184 (2013) 1476) has been upgraded to the new issue of PACIAE 2.2. By this new issue the lepton-nucleon and lepton-nucleus (inclusive) deep inelastic scatterings can also be investigated. As an example, the PACIAE 2.2 model is enabled to calculate the specific charged hadron multiplicity in the $e^-$+p and $e^-$+D semi-inclusive deep-inelastic scattering at 27.6 GeV electron beam energy. The calculated results are well comparing with the corresponding HERMES data. Additionally, the effect of model parameters αand βin the …
In this paper a solution is given to the nonlinear equation which describes the evolution of the parton cascade in the case of the high parton density. The related physics is discussed as well as some applications to heavy ion-ion collisions.
We introduce a Monte Carlo space-time model for high-energy collisions with nuclei, involving the dynamical interplay of perturbative QCD parton production and evolution, with non-perturbative parton-cluster formation and `afterburner' cascading of formed pre-hadronic clusters plus hadron excitations. This approach allows us to trace the space-time history of parton and hadron degrees of freedom of nuclear collisions on the microscopical level of parton and hadron cascades in both position and momentum space, from the instant of nuclear overlap to the final yield of particles. In applying this…
Longitudinal broadening along $Δη$ direction on near side in two-dimensional ($Δϕ\times Δη$) di-hadron correlation distribution has been studied for central Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, within a dynamical multi-phase transport model. It was found that the longitudinal broadening is generated by a longitudinal flow induced by strong parton cascade in central Au+Au collisions, in comparison with p+p collisions at $\sqrt{s_{NN}}$ = 200 GeV. The longitudinal broadening may shed light on the information about strongly interacting partonic matter at RHIC.
Interest in studying the inclusive photon induced processes of Deep-Inelastic Scattering (DIS) and Diffractive DIS (DDIS) at high energies includes their experimental investigation and thorough theoretical description. The conventional instrument for theoretical investigation of DIS at large x is DGLAP. It describes the Q^2-evolution. Description of DIS in the small-x region requires accounting for the both Q^2 and x -evolution at the same time. Combining DGLAP with total resummation of double logarithms of x and Q^2, we present a description of structure function F_1 at large Q^2 and arbitrar…
Cascade solutions of the Boltzmann equation suffer from causality violation at large densities and/or scattering cross sections. Although the particle subdivision technique can reduce the causality violation, it alters event-by-event correlations and fluctuations and is also computationally expensive. Here we evaluate and then improve the accuracy of the ZPC parton cascade for elastic scatterings inside a box without using parton subdivision. We first test different collision schemes for the collision times and ordering time and find that the default collision scheme does not accurately descri…
There seems to be a general consensus now that a first glimpse of a QGP-like effect has become visible in the beautiful NA50 data on J/ψproduction and the `anomalous supression' phenomenon. On the other hand, it is still widely believed that the dynamics of heavy-ion collisions at CERN SPS energy is predominantly governed by soft, non-perturbative physics. This is ironic: after all, it is unlikely that a QGP could be formed if the underlying dynamics were essentyially soft, rather than that it requires intense quark-gluon production with sufficient cascade-like reinteractions which drive the m…
In this work, we introduce both gluon and quark degrees of freedom for describing the partonic cascades inside the medium. We present numerical solutions for the set of coupled evolution equations with splitting kernels calculated for the static, exponential and Bjorken expanding media to arrive at medium-modified parton spectra for quark and gluon initiated jets respectively. We discuss novel scaling features of the partonic spectra between different types of media. Next, we study the inclusive jet $R_{AA}$ by including phenomenologically driven combinations of quark and gluon fractions insid…
We report on a possible application of the HBT phenomenon in testing the existence of two hypothetical phenomena. First, it is argued that the existence of a rapidly developing parton cascade in the earliest stages of a high energy nuclear collision process can be tested by studying two-photon HBT correlations over a wide longitudinal momentum scale - corresponding to the early photon emission time from the hypothetical parton system. This method provides the needed selectivity for the early emitted photons, since the photons emitted at later times correlate over progressively narrower momentu…
We present a study of three-particle correlations among a trigger particle and two associated particles in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV using a multi-phase transport model (AMPT) with both partonic and hadronic interactions. We found that three-particle correlation densities in different angular directions with respect to the triggered particle (`center', `cone', `deflected', `near' and `near-away') increase with the number of participants. The ratio of `deflected' to `cone' density approaches to 1.0 with the increasing of number of participants, which indicates that partoni…
We present a new parton-shower algorithm. Borrowing from the basic ideas of dipole cascades, the evolution variable is judiciously chosen as the transverse momentum in the soft limit. This leads to a very simple analytic structure of the evolution. A weighting algorithm is implemented, that allows to consistently treat potentially negative values of the splitting functions and the parton distributions. We provide two independent, publicly available implementations for the two event generators Pythia and Sherpa.
We evaluate the spectra of produced particles (pions, kaons, antiprotons) from partonic cascades which may develop in the wake of heavy-ion collisions at CERN SPS energies and which may hadronize by formation of clusters which decay into hadrons. Using the experimental data obtained by NA35 and NA44 collaborations for S+S and Pb+Pb collisions, we conclude that the Monte Carlo implementation of the recently developed parton-cascade/cluster-hadronization model provides a reasonable description of the distributions of the particles produced in such collisions. While the rapidity distribution of t…
The longitudinal long-range correlations of the triangular flow event plane angles are calculated in a Boltzmann + hydrodynamics hybrid approach. The potential to disentangle different energy deposition scenarios is explored by utilizing two different transport approaches for the early non-equilibrium evolution. In the hadronic transport approach the particle production in high energy heavy ion reactions is mainly governed by string excitation and fragmentation processes which are absent in the parton cascade approach. We find that in both approaches the initial state shows a strong longitudin…
