ZPC 1.0.1: a parton cascade for ultrarelativistic heavy ion collisions

Bin Zhang (Columbia University)

REVIEW

ZPC 1.0.1: a parton cascade for ultrarelativistic heavy ion collisions

Nuclear Theory · Submitted 5 Sep 1997 · 13 references

Pith's verdict: A solid, well-documented parton-cascade code release whose headline speedup claim is asserted rather than benchmarked.

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arXiv IDnucl-th/9709009 (version 1)

Pith IDTIEFHH3D, Pith's permanent record of this paper and its review

CitationBin Zhang (Columbia University). "ZPC 1.0.1: a parton cascade for ultrarelativistic heavy ion collisions." arXiv:nucl-th/9709009 (1997). https://pith.science/paper/TIEFHH3D

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Editor's note

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This is a CPC program-library submission, and judged as one it's competent. Bin Zhang ships a working FORTRAN 77 gluon cascade with a space-cell optimization, a local interaction list, a configurable menu of collision-frame and ordering-time prescriptions, three test geometries (3-d, 1-d, box), and OSCAR-standard output. The documentation is unusually complete for this genre: common blocks are described field by field, the input and output formats are fully specified, and a worked zpc.ini with its zpc.res output is printed. If you want to study pre-hadronization transport without writing a solver, this is a reasonable starting point, and the lineage is real. Credit where due: the cell-division idea applied to a parton cascade, with the local interaction list, is the genuinely new engineering here, and the paper is candid that the cascade method itself is not new (it cites Pang's GCP, VENUS, VNI as parallel efforts). The physics simplifications are stated, not hidden: gluon-gluon elastic only (abstract:s1), an s-independent total cross section, and an equilibrium screening mass extrapolated to a nonequilibrium system (Section 2.3). I'd push back on the reader's framing of the screening mass as the weakest link. It's an explicit user input (XMU in PARA2, set in zpc.ini), it's flagged in the text, and it doesn't threaten the code-release claim. The real soft spot is the one the stress-test names: the headline claim in abstract:s5 that cell division gives 'a large factor' speedup with unchanged results is never demonstrated. Section 3.3 says the with/without options exist 'to check the applicability of the optimization,' and the Program Summary repeats that, but no comparison run is reported. The 'Typical running time' entry quotes only the cell-division case. That equivalence isn't automatic either, since the scattering criterion is evaluated in the collision frame while binning is in the global ordering frame, so 'cell size > interaction length' is plausible but unproven. A short table with timings and statistical errors would close it. Two smaller things: Figs. 1-3 carry no error bars, and ref [10] is the author's own in-press work used to support the claim that ordering prescriptions matter, which is a soft citation. There's also a version slip ('seven common blocks in ZPC-0.2.1') that suggests hasty editing. None of this breaks the tool. Who gets value: heavy-ion transport people, and anyone wanting a reference cascade to cross-check a new solver. It deserves a serious referee, mainly to force the benchmark the paper already promises.

Referee report

Significance

If the code performs as advertised, this is a useful and timely release: a documented, portable cascade that lets users generate several thousand minijet gluons per event and study parton transport with finite mean free path built in, at a cost that makes event samples of statistical interest feasible. The paper earns credit for several concrete strengths. The random-number bookkeeping (iseed and i_ran_used in zpc.ini, plus the ending random number and ending iff recorded in zpc.res) makes runs exactly reproducible and resumable, which is more than many codes of this generation provide. The OSCAR1997A output option supports objective comparison across cascade codes. The deliberate provision of with-and-without cell-division modes is the right design for testing an optimization, and the three geometries are a sensible scaffold for systematic study. The physics simplifications (elastic gluon scattering only, s-independent total cross section, equilibrium screening mass) are stated openly rather than hidden, which is the correct posture for a code-release paper.

Major objections (2)

[Abstract (abstract:s5), Program Summary, Section 3.3] The paper's headline quantitative claim is that space-cell division 'improves the speed of the calculation by a large factor' while leaving the physics unchanged, yet neither half of that claim is benchmarked anywhere in the manuscript. Section 3.3 states the sufficient condition ('size should be larger than the interaction length') and says the user 'may want to produce the results without cell division for reference and cross check', and the Program Summary says the with/without options exist 'to check the applicability of the optimization', but the check is never performed. The only timing quoted (6 minutes on a SPARC20, 30 seconds on an alpha workstation) is for the cell-division case alone, so the 'large factor' is never quantified; the factor of roughly twelve between the two entries is a hardware difference, not a speedup. The equivalence is also not automatic: the scattering criterion is evaluated in the collision frame selected by the first digit of IORD_SCH (for I1=0, the two-parton centre-of-mass frame), while cells are binned in the global ordering frame, so 'cell size > interaction length' is a plausible but unargued sufficient condition. I ask for one table: the same initial condition and the same random seed run with and without cell division (i_config = 1 versus 3, and 4 versus 5), reporting wall-clock time, operation count, collision count, and a quantitative comparison of the final dN/dy and dET/dy (bin-by-bin ratios or a two-sample test), together with the measured mean occupancy n and the constant C in the O(C*N*n) estimate.
[Section 3.2, Section 4.6 (ana3), abstract:s3] The paper motivates the three geometries as tools 'for theoretical study of the parton transport and the applicability of the cascade method', and Section 4.6 describes the ana3 directory as holding '1-d expansion semi-analytic tests' whose et*.res files are 'useful in choosing a final freezeout time ... such that dET/dy|_{y=0}(tau) reaches asymptotic value'. No such comparison is actually shown. For a code release whose stated purpose is solving the Boltzmann equation, at least one check against an analytic or independently known limit is load-bearing: for the 1-d expansion, the free-streaming and asymptotic Bjorken behaviour of dET/dy(tau); for the box, approach to the equilibrium distribution starting from the built-in thermal configuration or, better, from a deliberately non-thermal one. Either check would also demonstrate that the collision-frame and ordering-time choices exposed through IORD_SCH do not introduce a measurable artifact, a concern the paper itself raises in Section 3.1 ('This may lead to causality violation'). One figure of this kind would substantially strengthen the paper at modest cost.

Minor objections (9)

[Section 4.3 (COMMON /PARA7/), Section 3.4, zpc.ini description] The polarity of I_OSCAR is documented inconsistently. Section 4.3 states '= 0: write OSCAR standard output' and '= 1: do not write OSCAR standard output', whereas Section 3.4 says 'We can set i oscar = 1 from file zpc.ini to write out the standard output' and the zpc.ini entry is described as '(0,no;1,yes)'. Users will get this backwards; please make the three descriptions agree and state which one matches the code.
[Section 5, example zpc.ini] The example input file sets 'gene ft flag' to 1, which Section 4.3 defines as 'read in formation time from zpc.inp', while simultaneously setting 'read ini flag' to 1, defined as 'do not read the initial conditions'. Since the formation times would have to come from the file that is not being read, the example appears self-contradictory; please clarify what the code does in this combination or correct the example.
[Section 4.3] The text says 'There are seven common blocks in ZPC-0.2.1', but the program described throughout is version 1.0.1. Please confirm the version number and correct the sentence.
[Section 5, zpc.res output] The quoted freezeout times (70119.5, 447736.9, 99267.9) vary by nearly an order of magnitude across events with almost identical collision counts (6914, 6856, 6954). Please state the units explicitly and add a sentence explaining why the freezeout time is so long and so broadly distributed; as printed, a reader cannot tell whether this reflects the physics of the 3-d expansion or a large-time cutoff in the code.
[Figures 1-3] The three physics figures are shown for 10 events with no error bars or uncertainty indication, and dN/dpT spans four decades on a logarithmic axis, so the high-pT bins must contain very few counts. Please state the number of events and particles behind each figure and indicate statistical uncertainties, at least for dN/dpT.
[Section 2.3 and Figures 1-3] Section 2.3 estimates a screening mass of about 4.5 fm^-1 for the RHIC minijet system, while the example zpc.ini and all three figures use mu = 3 fm^-1. Since mu is a user input that regulates every cross section, a sentence on the sensitivity of the results to mu, or a justification for the value used in the figures, would help the reader judge how much the output depends on this choice.
[Section 2.2] The typeset expression for the differential cross section in Section 2.2 should be checked for dimensional consistency, and the relation between the stated s-independent total cross section sigma = 9*pi*alpha_S^2/(2*mu^2) and the preceding dsigma/dt should be shown explicitly. As printed, a reader cannot verify that the two are consistent without reconstructing the integration.
[Abstract (abstract:s5)] The phrase 'makes the code best optimized' is not defined and overstates what a single optimization can establish; 'optimized' or a quantified statement would be more appropriate. Relatedly, the Program Summary lists 'Memory required to execute with typical data: 1,450 words', which seems low for the particle and interaction-list arrays described in Section 4.3; please check the units.
[Abstract and Section 1] There are several typographical errors to correct: 'At presented' in the abstract should read 'At present', 'hard and semihard processes dominant' in Section 1 is missing 'are', and 'labeled prec!' in Section 4.3 should read 'labeled prec*'.

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The paper

The paper claims

ZPC 1.0.1 is a Monte Carlo that solves the parton Boltzmann equation by cascading gluons, and its claim is that dividing space into expanding cells makes thousands-of-gluon events cheap without changing the physics.

The reading

ZPC 1.0.1 is a FORTRAN 77 Monte Carlo program that solves the Boltzmann equation for gluons by cascading them: two partons are taken to scatter when their closest approach falls inside $R = $$\sqrt$($\sigma$/pi)$, and the scattering angle is drawn from a gluon-gluon cross section regularized by a medium-generated screening mass. The paper's load-bearing claim is about cost. A central collision event starts with several thousand minijet gluons, so finding each particle's next collision partner by scanning all $N$ particles makes the work grow like $$N^{2}$$; dividing space into cells that expand with time and keeping per-cell interaction lists reduces the work to roughly $C cdot N cdot n$, where $n$ is the average occupancy of a cell. The author reports roughly 7000 binary collisions per event finishing in about six minutes on a SPARC20 and thirty seconds on an Alpha workstation, and argues that the cell mode returns exactly the same results as the unoptimized mode provided the cell size exceeds the interaction length. Three geometries — three-dimensional expansion, one-dimensional expansion, and particles confined in a box — are supplied so the cascade method itself can be checked against cases with known or semi-analytic behavior.

What carries the argument

The mechanism that carries the argument is the interaction list built on a 10x10x10 grid of space cells that expand with velocities `v1, v2, v3` after a start time `size`. Each particle keeps a next and last operation partner (`NEXT`, `LAST`), a cell pointer, and an encoded cell index; when a collision happens, only the particles in the same and neighbouring cells need to be re-examined to find the new partner. The correctness condition is stated plainly: cell size must exceed the inverse square root of the total cross section over $pi$, i.e. the interaction length, so that no scatterer outside the searched neighbourhood can be within range. Two independent pieces of machinery feed the same lists: the screening-mass-regulated cross section, which sets that interaction length, and the ordering scheme, which decides which of several candidate operations happens next in the global frame. Everything else in the program — the built-in initial conditions at fixed formation proper time $tau_0 = 0.1$ fm, the optional OSCAR standard event output, the analysis routines for $dE_T/dy$, $dN/dy$ and $dN/dp_T$ — is bookkeeping around those two choices.

Extended reading notes

Core claim

The author's aim is to establish that a geometric cascade Monte Carlo is a practical and faithful solver of parton transport at collider multiplicities, and that the approximation that makes it affordable does not alter the answer. The physics input is deliberately minimal: only gluon-gluon elastic scattering, a Yukawa-type differential cross section $d sigma/d t = 9 pi alpha_S^2 s^{-2} (t - mu)^{-2}$ with the total cross section fixed to $9 pi alpha_S^2 / (2 mu^2)$ so that it is independent of $s$, and a screening mass $mu$ estimated at a few inverse fermis for the minijet gluon system expected at RHIC. The engineering input is the paper's real subject: space cell division with expanding cells, plus a collision-ordering scheme exposed as a user parameter (the first digit of `iord_sch` selects the collision frame and scattering space-time point, the second selects whether the earlier, average, or later of the two collision times orders the event). Making the ordering choice a switch rather than a hidden convention is the paper's way of acknowledging that the geometric scattering prescription lets information travel across the distance of closest approach and so can violate causality; the author cites prior work showing that different prescriptions give different results, and provides the options so the spread can be measured rather than assumed away.

Load-bearing premise

Every scattering rate in the code is set by a screening mass computed from an equilibrium formula that the paper explicitly assumes, without independent check, still holds for the far-from-equilibrium gluon system produced right after a collision.

Editorial extensions

If this is right

Events with several thousand initial gluons become tractable on a workstation, which is what makes event-by-event correlation studies at RHIC multiplicities feasible rather than statistics-starved.
Because the cell mode is claimed to reproduce the unoptimized mode exactly above the interaction length, users can cross-check a fast production run against a slow reference run on the same initial condition.
Exposing the collision frame, scattering point, and ordering time as a single switch turns a hidden convention into a measurable systematic, so the sensitivity of transport output to the cascade prescription can be quantified rather than argued.
The screening mass becomes an effective parameter that can in principle be extracted from data, since the paper proposes that measuring it is one way to probe medium screening in the collision.
The three geometries give a ladder of test problems — box, one-dimensional expansion, three-dimensional expansion — on which the cascade method can be validated before being trusted for the full collision.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the cell scheme is exact only above the interaction length, then the speedup is bounded by how dilute the system is: a denser or more strongly interacting parton system shrinks the interaction length only in absolute terms, but occupancy per cell rises, so the $C cdot N cdot n$ cost grows and the optimization buys less precisely where the physics is most interesting.
The ordering-scheme switch is a natural place to look for residual frame dependence: a user comparing the six combinations on identical initial conditions and random seeds would get a direct numerical handle on how much of the final $dE_T/dy$ is cascade artifact rather than transport physics.
Since only elastic gluon scattering is included, the reported multiplicities and energy distributions are a lower bound on the interaction rate once inelastic channels and parton statistics are added; the cell optimization would carry over unchanged but the cross-section table would not.
The same interaction-list structure would transfer almost directly to a hadronic cascade or to a parton system with several species, provided the per-process cutoff $sigma/pi$ used to set the cell size is taken as the largest of the active cross sections.

Original abstract

A Monte Carlo program solving Boltzmann equation for partons via cascade method is presented. At presented, only gluon-gluon elastic scattering is included. The scattering cross section is regulated by a medium generated screening mass. Three different geometric modes (3 dimension expansion, 1-d expansion, and scattering inside a box) are provided for theoretical study of the parton transport and the applicability of the cascade method. Space cell division is available to save the number of computer operations. This improves the speed of the calculation by a large factor and makes the code best optimized for simulation of parton cascade in ultrarelativistic heavy ion collisions.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,773 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.06 · mentions code or data availability 0.17.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

A Monte Carlo program solving Boltzmann equation for partons via cascade method is presented. At presented, only gluon-gluon elastic scattering is included. The scattering cross section is regulated by a medium generated screening mass. Three different geometric modes (3 dimension expansion, 1-d expansion, and scattering inside a box) are provided for theoretical study of the parton transport and the applicability of the cascade method. Space cell division is available to save the number of computer operations. This improves the speed of the calculation by a large factor and makes the code best optimized for simulation of parton cascade in ultrarelativistic heavy ion collisions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A Monte Carlo program solving Boltzmann equation for partons via cascade method is presented.	contribution 0.82	0.91	0.18	asserted 1.00
s1	At presented, only gluon-gluon elastic scattering is included.	limitation 0.98	0.80	0.04	asserted 1.00
s2	The scattering cross section is regulated by a medium generated screening mass.	method 0.98	0.56	0.04	asserted 1.00
s3	Three different geometric modes (3 dimension expansion, 1-d expansion, and scattering inside a box) are provided for theoretical study of the parton transport and the applicability of the cascade method.	method 0.58	0.82	0.07	asserted 0.98
s4	Space cell division is available to save the number of computer operations.	method 0.97	0.82	0.04	asserted 0.97
s5	This improves the speed of the calculation by a large factor and makes the code best optimized for simulation of parton cascade in ultrarelativistic heavy ion collisions.	interpretation 0.45	0.78	0.19	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** 10 events, µ = 3 fm−1 number of collision between particles = 6954, freezeout time= 99267.891489987, ending at the 135343th random number, ending collision iff= -1 ... The data files in directory ana1 give the final dET dy , dN dy and dN dpT . They are shown in

**Figure 2.** 10 events, µ = 3 fm−1 0.0 2.0 4.0 6.0 pT (GeV/c) 1 10 100 1000 10000 dN/dpT (GeV-1c)

Figures reproduced from arXiv:nucl-th/9709009 by the authors.

References

Works cited (13)

[10]

G. Kortmeyer, W. Bauer, K. Haglin, J. Murray and S. Pratt , Phys. Rev. C 52 (1995) 2714; B. Zhang and Y. Pang, nucl-th/9611012, Phys. Rev. C in press

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[1]

P. V. Ruuskanen, Phys. Lett. B 147 (1984) 465

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[2]

H.-T. Elze and U. Heinz, Advanced Series on Directions in High Energy Physics 6 (1990) 117

View on Pith 1990
[3]

For example, Y. Pang, GCP, http://rhic.phys.columbia.edu/rhic/gcp.; Klaus Werner, VENUS, http://www-subatech.in2p3.fr/Sciences/ Theorie/venus/venus.html; Klaus Kinder Geiger, http://rhic.phys.columbia.edu/rhic/vni; Bin Zhang, ZPC, http://nt1.phys.columbia.edu/people/bzhang/ ZPC/zpc.html. 24

View on Pith
[4]

L. Combridge, J. Kripfganz and J. Ranft, Phys. Lett. B 70 (1977) 234; B. L. Combridge, Nucl. Phys. B 151 (1979) 429; E. Eichten, I. Hinchliﬀe, K. Lane and C. Quigg, Rev. of Mod. Phys. 56 (1984) 579

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[5]

M. Gyulassy and X.-N. Wang, Nucl. Phys. B 420 (1994) 583; X.-N. Wang, M. Gyulassy and M. Pl¨ umer,Phys. Rev. D 51 (1995) 3436

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J. D. Bjorken, Phys. Rev. D 27 (1983) 140

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M. Gao, Phys. Rev. D 41 (1990) 626

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T. Biro, B. M¨ uller and X.-N. Wang, Phys. Lett. B 283 (1992) 171

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L. Xiong and E. Shuryak, Proceedings of the Workshop on Pre- Equilibrium Parton Dynamics (1993) 73

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M. Gyulassy, D. H. Rischke and B. Zhang, Nucl. Phys. A 613 (1997) 397

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[12]

http://rhic.phys.columbia.edu/oscar/

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[13]

W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vett erling, Numerical Recipes. 25

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nucl-th 2024-12 conditional novelty 4.0 of 10

In the AMPT model, jet-induced medium excitation enhances the strange-to-non-strange hadron ratio around quenched jets in Pb+Pb collisions, increasing with centrality and radial distance.
Novel Collective Phenomena in High-Energy Proton-Proton and Proton-Nucleus Collisions
nucl-ex 2015-09 accept novelty 3.0 of 10

High-multiplicity proton-proton and proton-lead collisions show heavy-ion-like long-range azimuthal correlations, and neither hydrodynamic nor Color Glass Condensate explanations is yet ruled out by the data.
QGP@50: More than Four Decades of Jet Quenching
hep-ph 2025-08 conditional novelty 2.0 of 10

A historical and technical review of jet quenching in heavy-ion collisions, covering four decades of theory, the RHIC discovery, and modern Bayesian extractions of the jet transport parameter qhat.
Small System Collectivity in Relativistic Hadron and Nuclear Collisions
nucl-ex 2018-01 accept novelty 2.0 of 10

Collective flow-like correlations in small collision systems match viscous hydrodynamic predictions, extending quark-gluon plasma fluid behavior down to femtometer-scale droplets.

How later papers used it

115 later papers cite it

Evidence: substantial. 110 of the citing papers share no author with it, and 77 of those carry a confident label from Pith's citation classifier.

Pith read 27 of the 143 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

12 later papers by other authors are listed below: 12 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool.

Uses its method or tool 13 of 79 papers with this label · 1 by the same authors

Used the improved Zhang's parton cascade with the Green-Kubo relation to calculate the shear viscosity of a massless quark-gluon matter in chemical equilibrium with Boltzmann statistics.

The shear viscosity of quark-gluon matter calculated with parton transport and comparisons with the Chapman-Enskog results (2026) · 0.99 · paraphrased: the licence does not allow quoting
Simulated the dynamical evolution of the parton plasma with Zhang's parton cascade model, which describes elastic partonic collisions among the medium partons and jet partons.

Overall momentum balance and redistribution of the lost energy in asymmetric dijet events in 2.76~ATeV Pb-Pb collisions with a multi-phase transport model (2016) · 1.00 · paraphrased: the licence does not allow quoting
Simulated elastic scatterings between partons using Zhang's parton cascade model, which includes two-body scatterings with a cross section described by a simplified equation.

Investigating the elliptic anisotropy of identified particles in p--Pb collisions with a multi-phase transport model (2023) · 1.00 · paraphrased: the licence does not allow quoting
The interactions among partons are described by the Zhang's parton cascade (ZPC) parton cascade model [ref] , which includes only two-body parton elastic scattering with a $gg →gg$ cross section: [equation] where $α_s$ is the strong coupling constant (taken as 0.33), while $ŝ$ and $t̂$ are the usual Mandelstam variables.

Testing the collectivity in large and small colliding systems with test particles (2022) · A multiphase transport model · 1.00
Treated scatterings among partons according to Zhang's Parton Cascade model, which includes only two-body elastic scatterings with a cross section obtained by an equation.

Anisotropic flow and flow fluctuations for Au + Au at $\sqrt{s_{NN}}$ = 200 GeV in a multiphase transport model (2014) · 0.98 · paraphrased: the licence does not allow quoting
Described the partonic interactions for both default AMPT and string melting AMPT with the ZPC parton cascade model.

Elliptic and Triangular Flow of Identified Particles from the AMPT Model at RHIC Energies (2015) · 0.84 · paraphrased: the licence does not allow quoting
Allowed quarks and antiquarks emitted from string melting to interact with each other as coded within the parton cascade, with an effective parton-parton cross section provided as an input parameter to the code.

Are minimal conditions for collectivity met in e+e- collisions? (2017) · 0.98 · paraphrased: the licence does not allow quoting
Handled the parton scatterings according to Zhang's Parton Cascade model, which contains only two-body elastic scatterings with a cross section defined by an equation.

Investigation of the elliptic flow fluctuations of the identified particles using the A Multi-Phase Transport model (2020) · 1.00 · paraphrased: the licence does not allow quoting
Simulated the evolution of the partonic matter using Zhang's Parton Cascade model.

Elliptic anisotropy of open-charm hadrons from parton scatterings in p--Pb collisions at energies available at the CERN Large Hadron Collider (2024) · 1.00 · paraphrased: the licence does not allow quoting
The dynamical evolution of the partonic stage is described via Zhang’s Parton Cascade (ZPC) [ref] , including two-body elastic collisions with different cross section: [equation] where $t$ denotes the Mandelstam variable corresponding to the four-momentum transfer.

Impact of nuclear deformation on particle production in $Ne+Ne$ collisions at \texorpdfstring{\five}{sqrt(sNN)=5.36 TeV} from AMPT-SM (2026) · A Multi-Phase Transport (AMPT) model and nuclear structure · 0.97
The parton cascade stage is implemented using Zhang's Parton Cascade (ZPC) model, where partons undergo two-body elastic scatterings with a cross section $σ= 9πα_s^2/(2μ^2)$, with $α_s = 0.33$ [ref] .

Investigating forward-backward asymmetry in D-meson production and anisotropic flow in p-Pb collisions at the LHC (2026) · A multiphase transport mode · 1.00
Parton scatterings, and accordingly the space-time evolution of QGP, are determined via ZPC parton cascade model [ref] .

Event-shaped-dependent cumulants in p-Pb collisions at 5.02 TeV (2020) · Materials and Methods · 0.99

By the same authors

Handled the parton evolution with the ZPC parton cascade model.

Recent results from parton cascade and microscopic transport (2008) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

77 arXiv papers cite this in 93 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 27 sentences without a confident label

Contests it 2 papers

This contrasts with the effective one-component gluon gas treatment used in the ZPC and AMPT models [ref] , which oversimplifies the system and underestimates shear viscosity and $η/s$.

Shear Viscosity of Collider-Produced QCD Matter II: Comparing a Multi-Component Chapman-Enskog Framework with AMPT in Full Equilibrium · Conclusion · contest 0.75
However, traditional parton cascade failed to reproduce the QCD equation of state extracted from first principle lattice QCD calculations [ref] .

Deep-learning quasi-particle masses from QCD equation of state · Introduction · contest 0.87

Uses its method or tool 53 papers

We perform all the calculations of the observables within AMPT model [ref] to study the effects of different nuclear deformations on these observables in U+U collisions at $√(s_NN)$ = 193 GeV and Au+Au collisions at $√(s_NN)$ = 200 GeV.

Systematic investigation of the nuclear multiple deformations in U+U collisions with A Multi-Phase Transport model · AMPT model · 1.00
Afterwards, it is allowed to undergo elastic rescatterings utilizing the Zhang's Parton Cascade (ZPC) component of a multi-phase transpot model [ref] .

On the Origin of QCD Collectivity in High-Multiplicity Jets: A Transport Model Study · Introduction · 1.00
The dynamical evolution of the parton plasma is simulated by Zhang's parton cascade (ZPC) model [ref] , which describes elastic partonic collisions among the medium partons and jet partons.

Overall momentum balance and redistribution of the lost energy in asymmetric dijet events in 2.76~ATeV Pb-Pb collisions with a multi-phase transport model · The AMPT Model · 1.00

Compares with it 1 paper

The main difference to existing parton cascade codes [ref] is that it reproduces exactly the AMY kernels for all elastic scattering, splitting and merging processes.

AMY Lorentz invariant parton cascade -- the thermal equilibrium case · Introduction · 0.93

Cites it as background 7 papers

A simultaneous understanding of collective bulk phenomena and jet quenching on the microscopic level remains a challenge, although several partonic transport models [ref] have been developed to address this issue.

Elliptic flow and nuclear modification factor in ultra-relativistic heavy-ion collisions within a partonic transport model · Introduction · 0.86
Many developments of VNI and other parton cascades [ref] have lead to new insights into Quark-Gluon Plasma production.

Recent results from parton cascade and microscopic transport · Introduction · 0.94
Prominent examples include models like Parton cascade Model (PCM) [ref] , Color Glass Condensate (CGC) [ref] , Zhang parton cascade (ZPC) [ref] among others.

Estimation of initial state structures in high energy heavy-ion collisions using Principal Component Analysis (PCA) · Introduction · 0.97

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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