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Recently, seven produced hadron species have been used to construct multiple hadron sets with given differences in the net electric charge (∆q) and strangeness (∆S) between the two sides. A nonzero directed flow difference △v₁has been proposed as a consequence of the electromagnetic field produced in relativistic heavy ion collisions. Previously, we have shown with quark coalescence that Av1 and the slope difference △v′₁depend linearly on both △qand ∆Swith zero intercept. Here we emphasize that a two-dimensional function or fit is necessary for extracting the △q- and △S-dependences of △v₁. On the other hand, a one-dimensional fit gives a different value for the slope parameter of the ∆q- or ∆S-dependence. Furthermore, a one-dimensional fit is incorrect because its slope parameter depends on the arbitrary scaling factor of a hadron set and is thus ill-defined. We use test data of △v₁to explicitly demonstrate these points. 

Abstract We study the production of$$D^0$$ $D^0$meson inp+pandp-Pb collisions using the improved AMPT model considering both coalescence and independent fragmentation of charm quarks after the Cronin broadening is included. After a detailed discussion of the improvements implemented in the AMPT model for heavy quark production, we show that the modified AMPT model can provide a good description of$$D^0$$ $D^0$meson spectra inp-Pb collisions, the$$Q_{\textrm{pPb}}$$ $Q_{\text{pPb}}$data at different centralities and$$R_{\textrm{pPb}}$$ $R_{\text{pPb}}$data in both mid- and forward (backward) rapidities. We also studied the effects of nuclear shadowing and parton cascade on the rapidity dependence of$$D^{0}$$ $D^0$meson production and$$R_{\textrm{pPb}}$$ $R_{\text{pPb}}$. Our results indicate that using the same strength of the Cronin effect (i.e$$\delta $$ $\delta$value) as that obtained from the mid-rapidity data leads to a considerable overestimation of the$$D^0$$ $D^0$meson spectra and$$R_{\textrm{pPb}}$$ $R_{\text{pPb}}$data at high$$p_{\textrm{T}}$$ $p_{\text{T}}$in the backward rapidity. As a result, the$$\delta $$ $\delta$is determined via a$$\chi ^2$$ ${\chi }^2$fitting of the$$R_{\textrm{pPb}}$$ $R_{\text{pPb}}$data across various rapidities. This work lays the foundation for a better understanding of cold-nuclear-matter (CNM) effects in relativistic heavy-ion collisions. 

Abstract In this work, we investigate the collective flow development in high energy proton proton (pp) collisions with a multiphase transport model (AMPT) based on PYTHIA8 initial conditions with a sub-nucleon structure. It is found that the PYTHIA8 based AMPT model can reasonably describe both the charged hadron productions and elliptic flow experimental data measured in pp collisions at$$\sqrt{s}=13$$ $\sqrt{s}=13$TeV. By turning on the parton and hadron rescatterings in AMPT separately, we find that the observed collective flow in pp collisions is largely developed during the parton evolution, while no significant flow effect can be generated with the pure hadronic rescatterings. It is also shown that the parton escape mechanism is important for describing both the magnitude of the two-particle cumulant and the sign of the four-particle cumulants. We emphasize that the strong mass ordering of the elliptic flow results from the coalescence process in the transport model and can thus be regarded as unique evidence related to the creation of deconfined parton matter in high energy pp collisions. 

Recently, the rapidity-odd directed flow (v1) of produced hadrons (K−, ϕ, p¯, Λ¯, Ξ¯+, Ω−, and Ω¯+) has been studied. Several combinations of these produced hadrons, with very small mass differences but differences in the net electric charge (Δq) and net strangeness (ΔS) on the two sides, have been considered. A difference in v1 between the two sides of these combinations (Δv1) has been proposed as a consequence of the electromagnetic field produced in relativistic heavy-ion collisions, especially if Δv1 increases with Δq. Our study is performed to understand the effect of the coalescence sum rule (CSR) on Δv1. We point out that the CSR leads to Δv1=cqΔq+cSΔS, where the coefficients cq and cS reflect the Δv1 of produced quarks. Equivalently, one can write Δv1=cqΔq+cBΔB, involving the difference in the net baryon number ΔB, where the CSR gives cB=−3cS. We then propose two methods to extract the coefficients for the Δq and ΔS dependences of Δv1.