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We replace the old PACIAE 2.1 and PACIAE 2.2 program series with new ones, respectively. In the new program series, the method of creation of the partonic initial state is changed, an option for calling PYEVNT or PYEVNW in PYTHIA is added, and the few bugs in the calculation for the reduction of strange quark suppression are corrected. New version program summary Program Title: PACIAE version 2.1 & 2.2 Program Files doi: http://dx.doi.org/10.17632/w3g68dj4d9.1 Licensing provisions: CC By 4.0 Programming language: FORTRAN 77 Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 1476, 193 (2015) 89. Does the new version supersede the previous version?: Yes Nature of problem: PYEVNT is the subroutine in PYTHIA to administer the generation of a high-pT event via calls a number of subroutines. PYEVNW is the new subroutine in PYTHIA to administer the generation of an event for new multiple interactions scenario. In previous PACIAE versions only PYEVNT is called, while both PYEVNT and PYEVNW can be called in this new version. Solution method: There has been added a parameter of mstp81 in PACIAE programs and input files of usux.dat (for 21a or 22a) and usu.dat (for 21b, 21c ,22b and 22c). The PACIAE will call PYEVNT when mstp81=1( default) and call PYEVNW when mstp81=21. Reasons for the new version: The method of creation of the partonic initial state is changed, an option for calling PYEVNT or PYEVNW in PYTHIA is added, and the few bugs in the calculation for the reduction of strange quark suppression are corrected in the new version. Summary of revisions: The PACIAE model [1] is a parton and hadron cascade model based on PYTHIA [2]. PACIAE model consists of four stages of the parton initiation, the parton evolution (rescattering), the hadronization, and the hadron evolution (rescattering). The stage of parton initiation is just by means of PYTHIA model and the rest are modeled by us [1]. PYTHIA model is for the high energy elementary particle collisions such as hadron–hadron and lepton–hadron collisions, but PACIAE model is also for high energy lepton–nucleus, hadron–nucleus and nucleus–nucleus collisions. So far, the PACIAE model has three series of PACIAE 2.0 (catalogue identifier: AEKI_v1_0) [1], PACIAE 2.1 (AEKI_v2_0) [3], and PACIAE 2.2 (AEKI_v2_2) [4]. The discrepancy between PACIAE 2.0 and PACIAE 2.1 is just the sampling of momentum x and y components at fixed p T . In the PACIAE 2.0 it is sampled on the circle with radius of p T , but 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 PACIAE 2.1. Including the reaction of lepton–nucleon and lepton–nucleus is the distinction of PACIAE 2.2 series from the PACIAE 2.1. Each series of PACIAE 2.0, PACIAE 2.1 and PACIAE 2.2 consists of a, b, and c packages. The package of PACIAE 2.1a, for instance, is for the high energy elementary collisions, while the PACIAE 2.1b as well as PACIAE 2.1c for the high energy hadron–nucleus and nucleus–nucleus collisions. We refer to [1] for the difference between PACIAE 2.0b and PACIAE 2.0c (PACIAE 2.1b and PACIAE 2.1c as well as PACIAE 2.2b and PACIAE 2.2c). In this replacement the modifications are as follows: 1. The method of creation of a partonic initial state is changed from setting mstj(1)=0 (or mstp(111)=0) before “CALL PYINIT” to adding a “RETURN” statement before the statement of “CALL PYEXEC” in subroutine PYEVNT (PYEVNW) in p21b.f. 2. Correcting the mistakes in the calculation for the mechanism of reduction of strange quark suppression. 3. Calling PYEVNT or PYEVNW is controlled by mstp(81) (=1 or 21) instead of calling PYEVNT only originally. References [1] Ben-Hao Sa, Dai-Mei Zhou, Yu-Liang Yan, Xiao-Mei Li, Sheng-Qin Feng, Bao-Guo Dong, and Xu Cai, Comput. Phys. Comm. 183 (2012) 333. [2] Sjöstrand T, Mrenna S, Skands P, J. High Energy Phys., 05 (2006) 026, arXiv:hep-ph/0603175. [3] Ben-Hao Sa, Dai-Mei Zhou, Yu-Liang Yan, Bao-Guo Dong, and Xu Cai, Comput. Phys. Comm. 184 (2013) 1476. [4] Dai-Mei Zhou, Yu-Liang Yan, Xing-Long Li, Xiao-Mei Li, Bao-Guo Dong, Xu Cai, and Ben-Hao Sa, Comput. Phys. Comm. 193 (2015) 89. [ABSTRACT FROM AUTHOR]

We improve the centrality definition in impact parameter in PACIAE model responding the fact reported by the ALICE, ATLAS, and CMS collaborations that the maximum impact parameter in heavy ion collisions should be extended to 20 fm. Meanwhile the PACIAE program is updated to a new version of PACIAE 2.2.2 with convenience of studying the elementary nuclear collisions, proton-nucleus collisions, and the nucleus-nucleus collisions in one unified program version. The new impact parameter definition together with the optical Glauber model calculated impact parameter bin, N part , and N coll in proton-nucleus and nucleus-nucleus collisions at relativistic energies are consistent with the improved MC-Glauber model ones within the error bar. The charged-particle pseudorapidity and the transverse momentum distributions in Pb-Pb collisions at s NN = 5.02 TeV simulated by PACIAE 2.2.2 well reproduce the ALICE experimental data. Program Title: PACIAE version 2.2.2 CPC Library link to program files: https://doi.org/10.17632/w3g68dj4d9.4 Licensing provisions: CC By 4.0 Programming language: FORTRAN Journal reference of previous version: Comput. Phys. Commun. 224 (2018) 417 Does the new version supersede the previous version?: Yes Reasons for the new version: Recently ALICE, ATLAS and CMS collaborations reported that the maximum impact parameter b m a x should be extended to 20 fm in the nuclear-nuclear collisions at relativistic energies. The impact parameter formula in PACIAE model has to be improved correspondingly. Meanwhile the PACIAE model is updated to PACIAE 2.2.2 with the convenience of studying the elementary nuclear collisions, proton-nucleus collisions, and the nucleus-nucleus collisions in one unified program version. Summary of revisions: The impact parameter b in PACIAE model is calculated by geometrical model of b = c × b m a x , where c refers to the centrality percentile and b m a x is assumed to be b m a x = R A + R B + f × d. In above equation R A (R B) is the radius of nuclear A (B), d = 0.546 fm describes the tail of the nuclear density profile. Originally, the coefficient f is set to be equal to 2 and 1 for nucleus-nucleus and proton-nucleus collisions, respectively. Now they are assumed to be equal to 4 and 2, respectively. Meanwhile, the PACIAE model is updated to the version of PACIAE 2.2.2 with the convenience of studying the elementary nuclear collisions, proton-nucleus collisions, and the nucleus-nucleus collisions in a unified program version. Nature of problem: The ALICE, ATLAS and CMS collaborations reported that the maximum impact parameter, b m a x , in heavy-ion collisions at relativistic energies should be extended to 20 fm where the interaction is really approaching to zero. The impact parameter centrality determination in heavy-ion collisions at relativistic energies has to be revised accordingly in the PACIAE model. Solution method: A new f coefficient sets in the impact parameter formula in PACIAE model, sequentially the new b bin corresponding to a given centrality percentile bin is introduced in the new version of PACIAE 2.2.2. [ABSTRACT FROM AUTHOR]

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 α and β in the Lund string fragmentation function on the multiplicity is studied. Program summary Program title: PACIAE version 2.2 Catalogue identifier: AEKI_v2_2 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKI_v2_2.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 297,665 No. of bytes in distributed program, including test data, etc.: 2,063,650 Distribution format: tar.gz Programming language: FORTRAN 77. Computer: DELL Studio XPS and/or others with a FORTRAN 77 compiler. Operating system: Linux with FORTRAN 77 compiler. RAM: ≈ 1 GB Classification: 11.1, 17.8. Does the new version supersede the previous version?: Yes Catalogue identifier of previous version: AEKI_v2_0 Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 1476 Nature of problem: The lepton inclusive and semi-inclusive deep inelastic scattering (DIS and SIDIS) off nuclear target have greatly contributed to the parton structure of hadron, the parametrization of parton distribution function (PDF), and the extraction of fragmentation function (FF). Unfortunately, the PACIAE 2.1 model is unable to describe the lepton–nucleon and lepton–nucleus DIS (SIDIS), the corresponding upgrade is highly required. Solution method: The parton and hadron cascade model of PACIAE 2.1 is upgraded to PACIAE 2.2 with the possibility of investigating the lepton–nucleon and lepton–nucleus DIS (SIDIS). In the PACIAE 2.2 model the lepton–nucleon and lepton–nucleus DIS are treated the same as proton–nucleon and proton–nucleus collisions in PACIAE 2.1, respectively. However, the lepton–nucleon DIS cross section is used instead of the nucleon–nucleon cross section in the initiation stage of the PACIAE model. Reasons for new version: In order that the PACIAE 2.2 model is now also able to simulate the lepton–nucleon and lepton–nucleus DIS. Summary of revisions: In the PACIAE 2.2 model the lepton–nucleon and lepton–nucleus DIS are dealt in the same way as the proton–nucleon and proton–nucleus collisions in PACIAE 2.1, respectively. However, the lepton–nucleon DIS cross section is employed instead of nucleon–nucleon cross section. Restrictions: Depend on the problem studied. Running time: PACIAE 2.2 has three versions of PACIAE 2.2a, 2.2b, and 2.2c. PACIAE 2.2a is for the elementary collision, such as p p , pp, and e + e − collisions, as well as the lepton–nucleon DIS, with input file of usux.dat. PACIAE 2.2b and PACIAE 2.2c are for the nuclear-nucleus collision of p+A and A+B as well as the lepton–nucleus DIS with input file of usu.dat. PACIAE 2.2b and 2.2c are similar in the physical contents but are different in the topological structure (see text for the details). • Using the attached input file of usux.dat to run 1000 events for the s = 200 GeV Non Single Diffractive pp collision by PACIAE 2.2a takes 0.5 min. • Using the attached input file of usu.dat to run 10 events for the 10%–40% most central Au + Au collisions at s N N = 200 GeV by PACIAE 2.2b takes 4 min. • Using the attached [ABSTRACT FROM AUTHOR]

Abstract: We have updated the parton and hadron cascade model PACIAE 2.0 (cf. Ben-Hao Sa, Dai-Mei Zhou, Yu-Liang Yan, Xiao-Mei Li, Sheng-Qin Feng, Bao-Guo Dong, Xu Cai, 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 hadron transverse momentum is randomly sampled in the string fragmentation, the and components are originally put on the circle with radius randomly. Now it is put on the circumference of ellipse with half major and minor axes of and , respectively, in order to better investigate the final state transverse momentum anisotropy. New version program summary : Manuscript title: PACIAE 2.1: An updated issue of the parton and hadron cascade model PACIAE 2.0 Authors: Ben-Hao Sa, Dai-Mei Zhou, Yu-Liang Yan, Bao-Guo Dong, and Xu Cai Program title: PACIAE version 2.1 Journal reference: Catalogue identifier: Licensing provisions: none Programming language: FORTRAN 77 or GFORTRAN Computer: DELL Studio XPS and others with a FORTRAN 77 or GFORTRAN compiler Operating system: Linux or Windows with FORTRAN 77 or GFORTRAN compiler RAM: ≈ 1GB Number of processors used: Supplementary material: Keywords: relativistic nuclear collision; PYTHIA model; PACIAE model Classification: 11.1, 17.8 External routines/libraries: Subprograms used: Catalogue identifier of previous version: aeki_v1_0* Journal reference of previous version: Comput. Phys. Comm. 183(2012)333. Does the new version supersede the previous version?: Yes* Nature of problem: PACIAE is based on PYTHIA. In the PYTHIA model, once the hadron transverse momentum is randomly sampled in the string fragmentation, the and components are randomly placed on the circle with radius of . This strongly cancels the final state transverse momentum asymmetry developed dynamically. Solution method: The and component of hadron in the string fragmentation is now randomly placed on the circumference of an ellipse with half major axis of and the half minor axis of instead of the circle. Reasons for the new version: PACIAE is based on PYTHIA, where once the hadron transverse momentum is randomly sampled in the string fragmentation, the and components are randomly placed on the circle with radius of . This is not only strongly canceling the final state transverse momentum asymmetry developed dynamically, but also inconsistent with the ATLAS observation of the final state charged particle transverse sphericity being less than unity [8]. Summary of revisions: The main revision is executed by randomly placing and components of the hadron transverse momentum , in the string fragmentation, on the circumference of an ellipse with half major axis of and half minor axis of instead of a circle. Restrictions: Depend on the problem studied. Unusual features: Additional comments: Email addresses: zhoudm@phy.ccnu.edu.cn (D.-M. Zhou), yanyl@ciae.ac.cn (Y.-L. Yan). Running time: [•] Using the attached input file of usux.dat (where the string fragmentation is selected and the elastic parton–parton interactions are considered only, the same later) to run 1000 events for the Non Single Diffractive pp collision by 21a.tar.gz takes 0.5 min. [•] Using the attached input file of usu.dat to run 10 events for the 10%–40% most central Au+Au collisions at by 21b.tar.gz takes 5 min. [•] Using the attached input file of usu.dat to run 10 events for the 10%–40% most central Au+Au collisions at by 21c.tar.gz takes 17 min. 1. The large azimuthal anisotropy (the large second harmonic coefficient ) of the emitted particle is an important feature of the hot and dense medium created in the ultra-relativistic nuclear collisions. This large has contributed to the observation of a strongly coupled quark–gluon plasma (sQGP) in the nucleus–nucleus collisions at the RHIC energies [1–4]. The nuclear overlap zone created in a nucleus–nucleus collisions at a given impact parameter possesses an almond-like spatial asymmetry. Because of the strong parton rescattering, the local thermal equilibrium and asymmetric pressure gradient may build up in this initial fireball. The asymmetric pressure gradient then drives a collective anisotropic expansion. The expansion along the almond minor axis (along the large pressure gradient) is faster than the one along the major axis. This results in a strong asymmetric transverse momentum azimuthal distribution and hence a large elliptic flow coefficient of the final hadronic state. As mentioned in [6], PACIAE is a parton and hadron cascade model for the ultra-relativistic nuclear collisions and is based on PYTHIA [7]. In the PACIAE model, a nucleus–nucleus collision is decomposed into a sequence of nucleon–nucleon (NN) collisions according to the collision geometry and the NN total cross section. Each NN collision is performed, in turn, by the PYTHIA model with the string fragmentation switched-off temporarily and the diquark (anti-diquark) broken into quark pairs (anti-quark pairs) randomly. The parton rescattering then proceeds. This parton evolution stage is followed by the hadronization at the moment of partonic freeze-out (exhausting the partonic collisions). The Lund string fragmentation regime and/or phenomenological coalescence model is provided for the hadronization. Then the rescattering among produced hadrons is dealt with by the usual two body collision model [6]. In the PYTHIA model [7] once the transverse momentum of a final state hadron generated from the string fragmentation and/or the unstable particle decay is randomly sampled, the and components are randomly placed on the circle with radius of . This and determination may strongly cancel the final state transverse momentum anisotropy developed dynamically. The charged particle transverse sphericity [8–10] may reach to unity (isotropic). This is inconsistent with the experimental observation that the charged particle transverse sphericity is less than unity [8]. Therefore we randomly placed the generated final state hadrons on the circumference of an ellipse with half major axis of and a half minor axis of instead of a circle. This change is also introduced in the particle/parton production process of hard scattering, multiple interactions, initial- and final-state parton showers, for the nucleus–nucleus collisions [7]. This change is even introduced in the deexcitation of energetic quark (anti-quark) when the phenomenological coalescence model [6] is selected for hadronization. Of course, a new should be recalculated by and after this change. Then the transverse momentum distribution of the final state hadron may be modified. However, if the deformation parameter is less than unity (a small perturbation) the change in transverse momentum distribution may be weak. From ideal hydrodynamic calculations [11] one knows that the integrated elliptic flow parameter is directly proportional to the initial spatial eccentricity of the nuclear overlap zone. Therefore, if the nuclear overlap zone is assumed to be an ellipse with major axis of and minor axis of for a symmetry nucleus–nucleus collision with nuclear radius of , we may assume where is an extra model parameter. corresponds to the original case of and put on the circle randomly. In order to calculate we first calculate the reaction plane eccentricity [12] according to the participant nucleons spatial distributions inside the nuclear overlap zone [6] in the PACIAE simulation. In the above equation, (the same for ) and () denotes an average of () over particles in a single event. The event average reaction plane eccentricity reads On the other hand, the geometric eccentricity [13] of the ellipse-like nuclear overlap zone is Letting , one approximately obtains The calculated charged particle at mid-rapidity () in the 10%–40% most central Au+Au collision at is compared with the corresponding STAR data [5] in Fig. 1. In this figure the STAR data are denoted by solid symbols: the black circles are measured with the event plane method (EP), red squares with Lee–Yang zero point method (L–YZ), and green triangles with four particle cumulant method (4 cumulant). The PACIAE results are given by open symbols: the black circles calculated with , red squares with , and green triangles with . One sees in this figure that the STAR data [5] on the charged particle are able to be reproduced by the PACIAE calculations with . The PACIAE results are too small compared to the STAR data. Display Omitted A similar comparison for charged particle () in the 10%–40% most central Au+Au collision at is given in Fig. 2. Here one sees again that the STAR data on the charged particle  [5] are able to be reproduced by the PACIAE calculations with . We have to mention here that in Fig. 3 of Ref. [5] the PHOBOS data [14] were introduced to compare with the STAR data and to complement the lack of the STAR data in region. Because the PHOBOS data were measured for the 0%–40% most central Au+Au collisions at the same energy but in the full phase space, it is not suitable to compare the PHOBOS data with the STAR data. Therefore we do not include the PHOBOS data [14] in Fig. 2 here. Display Omitted We give the calculated charged particle transverse momentum distribution in 10%–40% most central Au+Au collisions at in Fig. 3. Fig. 3(a) and (b) are drawn for the full and partial () pseudo-rapidity phase space, respectively. In panels (a) and (b) the solid black circles, open red circles, open green triangles, and the blue line are calculated with , 3, 2, and 0, respectively. We see in this figure that the charged particle transverse momentum distribution is really not sensitive to the parameter both in the full and partial phase space, provided the deformation parameter is less than unity (a small perturbation). Display Omitted In addition, an extra switching parameter of is introduced in the new issue of PACIAE 2.1. We assume that the is for the elastic parton–parton rescattering only and for otherwise. [Copyright &y& Elsevier]

We have updated the parton and hadron cascade model PACIAE for the relativistic nuclear collisions, from based on JETSET 6.4 and PYTHIA 5.7 to based on PYTHIA 6.4, and renamed as PACIAE 2.0. The main physics concerning the stages of the parton initiation, parton rescattering, hadronization, and hadron rescattering were discussed. The structures of the programs were briefly explained. In addition, some calculated examples were compared with the experimental data. It turns out that this model (program) works well. Program summary: Program title: PACIAE version 2.0 Catalogue identifier: AEKI_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKI_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 297 523 No. of bytes in distributed program, including test data, etc.: 2 051 274 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: DELL Studio XPS and others with a FORTRAN 77 or GFORTRAN compiler Operating system: Unix/Linux RAM: 1 G words Word size: 64 bits Classification: 11.2 Nature of problem: The Monte Carlo simulation of hadron transport (cascade) model is successful in studying the observables at final state in the relativistic nuclear collisions. However the high suppression, the jet quenching (energy loss), and the eccentricity scaling of etc., observed in high energy nuclear collisions, indicates the important effect of the initial partonic state on the final hadronic state. Therefore better parton and hadron transport (cascade) models for the relativistic nuclear collisions are highly required. Solution method: The parton and hadron cascade model PACIAE is originally based on the JETSET 7.4 and PYTHIA 5.7. The PYTHIA model has been updated to PYTHIA 6.4 with the additions of new physics, the improvements in existing physics, and the embedding of the JETSET model, etc. Therefore we update the PACIAE model to the new version of PACIAE 2.0 based on the PYTHIA 6.4 in this paper. In addition, some improvements in physics have been introduced in this new version. Restrictions: Depends on the problem studied. Running time: [•] Running 1000 events for inelastic pp collisions at by program PACIAE 2.0a to reproduce PHOBOS data of rapidity density at mid-rapidity, [1], takes ≈3 minutes. [•] Running 0–6% most central Au+Au collision at by program PACIAE 2.0b and PACIAE 2.0c to reproduce PHOBOS data of charged multiplicity of 5060 [2] takes ≈13 seconds/event and ≈265 seconds/event, respectively. References: [[1]] B. Alver, et al., PHOBOS Collab., Phys. Rev. C 83 (2011) 024913, arXiv:1011.1940v1. [[2]] B.B. Back, et al., PHOBUS Collab., Phys. Rev. Lett. 91 (2003) 052303. [ABSTRACT FROM AUTHOR]