We report the first measurement of the semileptonic decay D s + → K 0 μ + ν μ , using a sample of e + e − annihilation data corresponding to an integrated luminosity of 7.33 fb − 1 collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector at the BEPCII collider. The branching fraction of the decay is measured to be B ( D s + → K 0 μ + ν μ ) = ( 2.89 ± 0.2 7 stat ± 0.1 2 syst ) × 10 − 3 , where the first uncertainty is statistical and the second is systematic. Based on a simultaneous fit to the partial decay rates in q 2 intervals measured in D s + → K 0 μ + ν μ and D s + → K 0 e + ν e decays, the product value of the form factor f + K 0 ( 0 ) and the Cabibbo-Kobayashi-Maskawa matrix element | V c d | is measured to be f + K 0 ( 0 ) | V c d | = 0.140 ± 0.00 8 stat ± 0.00 3 syst , which is the most precise determination to date. In addition, lepton flavor universality is tested for the first time with D s + → K 0 ℓ + ν ℓ decays in full and separate q 2 intervals. No violation is found.

We introduce a parton and hadron cascade model PACIAE 3.0 based on PYTHIA 6.428 and the PACIAE 2.2 program series. The simulation framework of C-, B-, and A-loops are designed for the high energy ($\sqrt{s_{NN}}\geq 3$ GeV) and low energy ($\sqrt{s_{NN}}<3$ GeV) nuclear collisions, respectively, in PACIAE 3.0. In the C-loop simulation, the parton-parton inelastic scattering processes are added in the partonic rescattering process. The single string structure and multiple string interaction mechanism have been introduced investigating the strangeness enhancement in C- and B-loop. An improved mapping relation between the centrality percentage definition and the impact parameter definition is proposed responding the observation of $b_{max}\approx 20$ fm from ALICE, ATLAS, and CMS collaborations. We have extensively modified the phenomenological coalescence hadronization model. The PACIAE 3.0 model simulated results of particle yield, transverse momentum distribution, and rapidity distribution well reproduce, respectively, the experimental data measured at FOPI, E895, RHIC, and LHC energies.

The lepton charge asymmetry in [Formula: see text] production in the nuclear collisions at [Formula: see text][Formula: see text]TeV is investigated with a parton and hadron cascade model PACIAE. Recently published ALICE and the ATLAS data of lepton charge asymmetry are well reproduced. An interesting linear scaling behavior is observed in the lepton charge asymmetry as a function of the collision system valence quark number asymmetry among different sizes of nuclear collision systems at [Formula: see text][Formula: see text]TeV. This linear scaling behavior may serve as an additional constraint on the PDF (nPDF) extractions.

We have systematically studied the connection between hadron and its quark component nuclear modification factors and the flavor (mass) ordering at both parton and hadron levels in the nucleus-nucleus collisions at the LHC energies by the PACIAE model. It turns out that these two physical phenomena explored in our last publication (J. Phys. G 49 065104, 2022) are generally held, irrespective of the rapidity, centrality, reaction energy, and the collision system size. The mass ordering at hadron level in nuclear modification factor seems to be really existed, which should be studied further both theoretically and experimentally.

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, Npart, and Ncoll 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 distri-butions in Pb-Pb collisions at root sNN = 5.02 TeV simulated by PACIAE 2.2.2 well reproduce the ALICE experimental data.New version program summaryProgram Title: PACIAE version 2.2.2CPC Library link to program files: https://doi .org /10 .17632 /w3g68dj4d9 .4Licensing provisions: CC By 4.0Programming language: FORTRANJournal reference of previous version: Comput. Phys. Commun. 224 (2018) 417Does the new version supersede the previous version?: YesReasons for the new version: Recently ALICE, ATLAS and CMS collaborations reported that the maximum impact parameter bmax should be extended to 20 fm in the nuclear-nuclear collisions at relativistic en-ergies. 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 = root cx bmax, where c refers to the centrality percentile and bmax is assumed to be bmax= RA+RB+f x d. In above equation RA (RB) is the radius of nuclear A (B), d = 0.546 fm describes the tail of the nu-clear 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. Mean-while, 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 pa-rameter, bmax, 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.(c) 2022 Elsevier B.V. All rights reserved.

In this paper, the centrality dependent and production and the isospin effect in production are investigated with a parton and hadron cascade model PACIAE in Pb–Pb collisions at =5.02 TeV. ALICE data of production in Pb–Pb collisions at =5.02 TeV are found to be reproduced fairly well. The prediction on production in the same collision system is given as well. An interesting isospin effect is observed in exploring the charge asymmetry between and as a function of the asymmetry between number of valence u- and d-quarks varied from small to large collision systems at center-of-mass energy 5.02 TeV. The results serve as a important benchmarks for understanding the initial conditions of heavy-ion collisions.

. We have systematically studied the connection between hadron and its quark component nuclear modification factors and the flavor (mass) ordering at both parton and hadron levels in the nucleus-nucleus collisions at the LHC energies by the PACIAE model. It turns out that these two physical essences explored in our last publication (J. Phys. G 49 065104, 2022) are generally held, irrespective of the rapidity, centrality, reaction energy, and the collision system size. The mass ordering at hadron level in nuclear modification factor seems to be really existed, which should be studied further both theoretically and experimentally.

In this work, we propose a method qualitatively connecting the hadron nuclear modification factor to its quark component nuclear modification factor. A parton and hadron cascade model, PACIAE, based on PYTHIA6 is then employed calculating the hadron (in final hadronic state) and its quark component (in final partonic state) nuclear modification factors in the 0%-5% most central Pb + Pb collisions at. root S-NN = 2.76 TeV. It turns out that the hadron nuclear modification factor is usually smaller than its quark component factor. On the other hand, the flavor (mass) ordering of the nuclear modification factor is investigated for a hadron in the final hadronic state and a quark in the final partonic state. It is found that the nuclear modification factor is more likely to be identified with the quarks and mesons but not with the baryons.

We present a systematic study of the strange and multistrange particle production in Pb + Pb collisions at root S-NN = 2.76 TeV based on PACIAE model simulations. Two different mechanisms, namely the single string structure variations and multiple string interactions, are implemented in the simulations. These modifications give rise to an enhancement of the string tension value involved in the Lund string fragmentation framework and generate more strange particles in the hadronic final state. By comparing the simulation results with the ALICE experimental data, it turns out that the inclusion of the variable effective string tension in the PACIAE model results in an improved agreement between theory and experiment on the strangeness production in Pb + Pb collisions.

We propose a forward method based on PYTHIA6.4 to study the jet properties in ultra-relativistic pp collisions. In the forward method, the partonic initial states are first generated with PYTHIA6.4 and then hadronized in the Lund string fragmentation model, and finally the hadronic jets are constructed from the created hadrons. Jet properties calculated with the forward method for pp collisions at <i =7 TeV are comparable to those calculated with the usual anti- algorithm (backward method) in PYTHIA6.4. The comparison between the backward and forward methods may contribute to the understanding of the partonic origin of jets in the backward method.

In this work, we propose a method to show the correspondence between hadron and its quark component nuclear modification factors. A parton and hadron cascade model PACIAE based on the PYTHIA6.4 is employed to calculate the hadron and its quark component nuclear modification factors in the 0-5% most central Pb+Pb collisions at √(s_NN)=2.76 TeV. It turns out that the hadron nuclear modification factor is usually smaller than that of its quark component. On the other hand, it is shown in our study that the "dead cone effect" is more likely to be identified with the quarks and mesons but not with the baryon states obviously.

Based on transportation networks of mobile agents, this paper discusses the condition under which the communication radii of mobile agents obey the power-law distribution. The analysis of network structure indicates that out-degrees obey a power-law distribution, while in-degrees follow a Poisson distribution. Simulation results reveal that: (i) there exists a critical value of package generate rate Pc, which defines the free-flow state and congested state. (ii) In the free-flow regime, the average traveling time T is small and independent of the packet generation rate P, but the average path length L increases with the growth of P and is related to a traffic awareness parameter h. (iii) The larger the heterogeneous exponent α of the communication radii is, the lower the transport efficiency of the network would be. (iv) There exists an optimal traffic awareness parameter h that maximizes the critical value Pc. (v) The critical value Pc decreases with the heterogeneous exponent α, increases with the network size N, and decreases with the speed v until v reaches an appropriate value.

We present a systematic study on the strange particle production at the Large Hadron Collider (LHC) in proton-proton (pp) collisions at $\sqrt{s}=$ 7 TeV based on PACIAE simulations. Two different mechanisms accounting for single string structure variations and multiple string interactions are implemented in the simulations. These modifications give rise to increased effective string tension in the Lund fragmentation model and generate more strange particles in the hadronic final state. By comparing the results with a wealth of the LHC data, it is turned out that the inclusion of variable effective string tension is capable to reach an improved agreement between theory and experiment, especially on the recently observed multiplicity dependence of strangeness enhancement in pp collisions. This approach provides us a new method to understand the microscopic picture of the novel high multiplicity pp events collected at the LHC in the string fragmentation framework.

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the differential cross section of phi(1020)-meson production at forward rapidity in p + p collisions at root s = 510 GeV via the dimuon decay channel. The partial cross section in the rapidity and P-T ranges 1.2 < vertical bar y vertical bar < 2.2 and 2 < p(T) < 7 GeV/c is sigma(phi) = [2.28 +/- 0.09(stat) +/- 0.14(syst) +/- 0.27(norm)] x 10(-2) mb. The energy dependence of sigma(phi) (1.2 < vertical bar y vertical bar < 2.2,2 < p(T) < 5 GeV/c) is studied using the PHENIX measurements at root s = 200 and 510 GeV and the Large Hadron Collider measurements at root s = 2.76 and 7 TeV. The experimental results arc compared to various event generator predictions (PYTHIA6, PYTHIA8, PHOJET, AMPT, EPOS3, and EPOS-LHC).

We present measurements of the transverse-momentum dependence of elliptic flow upsilon(2) for identified pions and (anti)protons at midrapidity (vertical bar eta vertical bar < 0.35), in 0%-5% central p + Au and He-3 + Au collisions at ,root s(NN) = 200 GeV. When taken together with previously published measurements in d + Au collisions at root s(NN) = 200 GeV, the results cover a broad range of small-collision-system multiplicities and intrinsic initial geometries. We observe a clear mass-dependent splitting of upsilon(2) (p(T)) in d + Au and He-3 + Au collisions, just as in large nucleus-nucleus (A + A) collisions, and a smaller splitting in p + Au collisions. Both hydrodynamic and transport model calculations successfully describe the data at low p(T) (<1.5 GeV/c), but fail to describe various features at higher p(T). In all systems, the upsilon(2) values follow an approximate quark-number scaling as a function of the hadron transverse kinetic energy per constituent quark (KET/n(q)), which was also seen previously in A + A collisions.

An analytic formula is proposed to characterize the variance propagation from correlated input variables to the model response, by using multi-variate Taylor series. With the formula, partial variance contributions to the model response are then straightforwardly evaluated in the presence of input correlations. Additionally, an arbitrary variable is represented as the sum of independent and correlated parts. Universal expressions of the coefficients that specify the correlated and independent sections of a single variable are derived by employing linear correlation model. Based on the coefficients, it is nature to quantify the independent, correlated and coupling contributions to the total variance of model response. Numerical examples suggest the effectiveness and validation of our analytic framework for general models. A practical application of the analytic framework is also proposed to the sensitivity analysis of a deterministic HIV model.

”Each individual will adopt a course of action that will involve the expenditure of the probably least average of his work.” This statement was named ”the principle of least effort”. The principle of least effort is often known as a ”deterministic description of human behavior”. In this paper, we present a brief introduction of this principle. Applications of the principle in different fields are also summarized. As the principle of least effort is proposed by Zipf, it is also called Zipf’s law. We then discuss the correlation between three widely considered distributions: Zipf distribution, Pareto distribution and probability distribution. With empirical investigations, it is often stated that, most social behaviors are controlled by the pure Zipf’s law that corresponds to the Zipf distribution of exponent -1. We summarily present the discovery of Zipf’s law in different social behaviors. Some empirical studies are also given as examples, verifying that, in most countries, the distribution of city size by population follows Zipf’s law, and the exponent of Zipf distribution of individual income is about -0.5, the same as Zipf predicted in theory.

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 summaryProgram Title: PACIAE version 2.1 & 2.2Program Files doi: http://dx.doi.org/10.17632/w3g68dj4d9.1 Licensing provisions: CC By 4.0Programming language: FORTRAN 77Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 1476, 193 (2015) 89.Does the new version supersede the previous version?: YesNature 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 pT. In the PACIAE 2.0 it is sampled on the circle with radius of pT, but on the circumference of ellipse with half major and minor axes of pT(1+δp) and pT(1−δp), 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.

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (mu_B > 500 MeV), effects of chiral symmetry, and the equation-of-state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2022, in the context of the worldwide efforts to explore high-density QCD matter.