Energy dependence study of directed flow in Au+Au collisions using an improved coalescence in AMPT model
aa r X i v : . [ nu c l - e x ] S e p Energy dependence study of directed flow in Au+Au collisions using animproved coalescence in AMPT model
Kishora Nayak, Shusu Shi, ∗ Nu Xu,
1, 2 and Zi-Wei Lin
1, 3 Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics,Central China Normal University, Wuhan 430079, China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China Department of Physics, East Carolina University, Greenville, NC 27858, USA (Dated: September 20, 2019)The rapidity-odd component of directed flow ( v ) of identified hardons ( π ± , K ± , K S , p , p , φ , Ξ,Ξ, Λ, Λ) and partons ( u , u , d , d , s , s ) in Au+Au collisions at various beam energies ( √ s NN = 7.7,11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, 200 GeV) using a multi-phase transport model is analyzed. Adata driven approach (inspired from the experimental analysis) is performed here to distinguish thetransported and produced quarks which are found to have different directed flow values at variouscollision beam energies. The coalescence sum rule (Number of Constituent Quark scaling) violationis observed at lower energies where hadronic matters dominate. The strange quark ( s ) and φ mesonslope (d v /dy) show a double sign change around 14.5 GeV unlike other partons and hadrons. Itsuggests that strange quark is more sensitive to the softening of Equation of State (EoS). I. INTRODUCTION
The main goal of relativistic heavy-ion collisionexperiments is to understand the properties andevolution of strongly interacting matter, called theQuark-Gluon Plasma, as well as to explore thehadron-quark phase transition. The rapidity-oddcomponent of directed flow ( v ) is an importantprobe to study the in-medium dynamics as it is sen-sitive to the equation of state (EoS) of the producedmedium. Directed flow is generated during the nu-clear passage time (2R/ γ ∼ c at 200 GeV)and it probes the onset of bulk collective dynamics inthe early stage of the collision [1, 2]. As a suggestedsignature of a first order phase transition, directedflow is sensitive to the existance of the critical pointand it plays an important role in the proposed beamenergy scan program[3–8]. The first-order harmonicof the Fourier expansion in momentum distributionof emitted particles is characterized as directed flow, v = h cos( φ − Ψ RP ) i (1)where φ and Ψ RP are the azimuthal angle andreaction plane angle, respectively [9–11]. The v contains both rapidity-odd and rapidity-even com-ponents. Rapidity-odd component ( v odd ( y ) = - v odd ( − y )) is referred to the sideward collective mo-tion of emitted hadrons with respect to collision re-action plane. The rapidity-even component even( v even ( y ) = v even ( − y )) is unrelated to the reactionplane and it originates from event-by-event fluctu-ations in the initial colliding nuclei. In this paper, v ( y ) implicitly refers to the odd component of di- ∗ [email protected] rected flow. The transport and hydrodynamic mod-els calculations suggested that the directed flow ofbaryon v at mid-rapidity (y ∼
0) is sensitive to theequation of state of the system [4, 12]. Severals hy-drodynamic model calculations predict that the neg-ative v -slope near mid-rapidity called as wiggle oranti-flow might be a possible QGP signature [13, 14].Number-of-constituent-quark (NCQ) scaling is anexample of coalescence behavior among quarks. Be-cause of the NCQ scaling, which is observed atRHIC [16, 17] and LHC [18], the higher order flowharmonics like v behaves as if it is developed at thepartonic level [20–22]. There are recent experimen-tal measurement of directed flow of various identifiedhadrons ( π ± , K ± , K S , p, ¯p, φ , Λ, ¯Λ) from the STARcollaboration at RHIC over a wide range of collidingbeam energies (7.7-200 GeV) [15]. Comprehensive v measurement from STAR [15] supports the coa-lescence mechanism as the dominant process in par-ticle formation dynamics. There are several studiesin heavy-ion collisions to understand the hadron andnuclei formation via coalescence and also hadroniza-tion of quarks in heavy-ion collisions [23–30]. In re-cent articles the importance of coalescence mecha-nism and energy dependence directed flow are dis-cussed [31–35] and an experimental review of v canbe found in Ref. [36].The interplay between NCQ scaling and the trans-port of initial-state u and d quarks towards mid-rapidity during the collision offers possibilities fornew insights [37]. The produced strange ( s ) andanti-strange ( s ) quark contribute in the resonance( φ ) formation and hence also play vital role in un-derstanding the particle formation mechanism. Un-derstanding the strange quarks or particles are veryimportant in order to understand the EoS, as the dv /dy of φ meson also shows a hints of sign changesimilar to baryons ( p , Λ) [15]. An approach tostudy v performed in this paper is inspired fromthe STAR experiment at RHIC [15], where a com-prehensive measurement of directed flow of identi-fied hadrons are reported in a range of collision en-ergies. The experimental paper verified the coales-cence sum rule (NCQ scaling) using v measurementalthough the NCQ scaling is well known in ellip-tic flow ( v ) measurement of identified hadrons atRHIC and LHC [16–19]. Our model calculation isalso compared with the experimental results. Thecalculation can reasonably well describe the data formesons over a range of energies. v prediction forΞ and Ξ baryons are also given along with the newenergy 54.4 GeV for various hadron species.The paper is organized in the following sections.Section II provides a brief description about theAMPT event generator [38]. The analysis detailsof calculating directed flow and the results which in-clude the v of partons and hadrons followed by theslope parameter (d v /dy) are discussed in the Sec.III. A summary with final remarks are given in theSec. IV. II. THE AMPT MODEL
A multi-phase transport model especially thestring-melting version (AMPT-SM) is often used tounderstand the experimental heavy-ion collision re-sults. The hot and dense matter formed due to rel-ativistic heavy-ion collisions are expected to be inparton degrees of freedom and the AMPT-SM alsoevolves through the partonic medium, thus makesit a suitable model for interpreting the experimen-tal results. The AMPT-SM version mainly consistsof four parts. The initial conditions are taken fromHeavy Ion Jet Inter-action Generator (HIJING) [39].Scatterings among partons are described by Zhangsparton cascade (ZPC) [40] model and for hadroni-sation it uses the coalescence model. An extendedrelativistic transport (ART) model describes the fi-nal hadronic evolution [41]. HIJING model includestwo body nucleon-nucleon interactions to form ex-cited strings and mini jets via hard and soft pro-cesses. The mini-jet parton undergoes scattering be-fore they fragment to partons and subsequently intohadrons. The partonic interaction in ZPC model isdescribed by two body partonic elastic cross section( σ p ) as given in Eq. 2. σ p = 9 πα S µ (2)In this study the strong coupling constant ( α S )and parton screening mass ( µ ) are set to be 0.33 and3.20 fm − , respectively, leading to σ p = 1.5 mb. Af-ter partons freeze out, the hadronization process inAMPT is described by a quark coalescence model. A meson is formed by combining a quark with anearby anti-quark. Similarly, three quarks (anti-quarks) combine to form a baryon (anti-baryon).Here the formation process of mesons or baryons(anti-baryons) is independent of the relative momen-tum among the coalescening partons. In this coales-cence process, each number of baryons, anti-baryonsand mesons in an event are conserved individually.However, in the present study an improved quark co-alescence method has been used [42]. The constraintwhich forced separate conservation of the baryons,anti-baryons, and mesons number via the quark coa-lescence has been removed in the new method. How-ever, the net-baryons and net-strangeness numbersare still conserved for each event. In the new coales-cence model, for a meson formation, any availablequark searches all available antiquarks and recordsthe closest relative distance ( d M ) as the potential co-alescence partner. The quark also searches all avail-able quarks to find the closest one in distance asa potential coalescence partner to form a baryon,and then searches all other available quarks again tofind the one that gives the smallest average relativedistance ( d B ) among these three quarks. The con-dition d B < d M * r BM has to be satisfied to forma baryon else a meson is formed. A new coalescenceparameter r BM , controls the relative probability ofquark to form a baryon rather than meson. Thelimit of r BM → r BM → ∞ corresponds to noanti-baryon formation (although to keep net-baryonnumber conservation, a minimum number of baryonswould be formed) and almost no meson formation,respectively. Similar coalescence procedure is alsoapplied to all anti-quarks.In this analysis the mean field is not included [43].The new parameter r BM which controls the relativeprobability to form baryon via coalescence of a quarkis set to 0.61. The popcorn parameter PARJ(5)value is changed to 0 from the default value 1.0which controls the relative percentage of the B ¯ B and BM ¯ M channels. This r BM parameter value isable to describe the dN/dy of proton yields at mid-rapidity in central Au+Au collisions at √ s NN = 200GeV and central Pb+Pb collisions at √ s NN = 2.76TeV as shown in the Ref. [42]. III. ANALYSIS AND RESULTS
In this study, an improved version of AMPT-SMmodel σ p = 1.5 mb is used to study the directedflow of identified hadrons in mid-central (10-40%)Au+Au collisions at √ s NN = 7.7, 11.5, 14.5, 19.6,27, 39, 54.4, 62.4, 200 GeV, corresponding to RHICbeam energy scan program (BES-I). The centralityis determined using the charged particle multiplicity( | η | < v measurement has beenperformed and coalescence sum rule is verified. Theeffect of hadronic interaction on directed flow is alsostudied by changing the hadron cascade time ( t max )in the AMPT-SM. The particles reported here areidentified from their PYTHIA-id (PID). The par-ticle selection cuts (e.g. momentum p, transversemomentum p T ) are listed in the Tab. I, which issimilar to the experimental data [15, 44], in order tohave a better comparison. Hadron p T cut (GeV/c) p , ¯ p . < p T < . π ± , K ± p T > .
2, p < . , ¯Λ , K S , Ξ, Ξ 0 . < p T < . φ . < p T < . The directed flow is calculated by averaging theazimuthal angle ( φ ) using the formula v = h cos( φ − Ψ RP ) i with respect to the reaction plane angle,Ψ RP .Figure 1 shows the directed flow of chargedhadrons and φ mesons as a function of rapidityfor t max = 0.4 and 30 fm/ c in 10-40% centrality,Au+Au collisions at 7.7, 14.5, 27, 54.4 and 200 GeV.The v of negatively charged hadrons (and positivelycharged hadrons at higher energies) are found to benot well developed for t max = 0.4 fm/ c , because theparticles could not get enough time to have hadronicinteractions unlike the case of t max = 30 fm/ c . How-ever, positively charged hadrons at lower energiesfor t max = 0.4 fm/ c have relatively significant v as compared to higher energies because of the domi-nant transported quark at low energies. It is also ob-served that the hadronic interaction affects v moreat higher rapidity. The φ mesons in our t max = 30fm/ c results represent those which have not decayedby the time of 30 fm/ c (i.e. φ mesons that have sur-vived to the time of 30 fm/ c ). However, φ mesonlife time is relatively large and hence they representa majority of the total φ mesons. The v of φ mesonfor t max = 0.4 and 30 fm/ c are found to be similarat higher energies i.e unaffected by hadronic inter-actions. This is because the φ meson has a smallhadronic scattering cross section and long life time( ∼
42 fm/ c ), which thus leads to its decay mainlyoutside the fireball [45]. We also find that hadronicscatterings have little effect on the proton and anti-proton v within | y | < . t max = 30 fm/ c . Therapidity dependence of identified hadrons v getsstronger with decreasing collision beam energy. Athighest RHIC energy (200 GeV), particle and anti-particles v values are found to be similar. The v values of baryons and anti-baryons have oppo-site trend and the difference increases with decreasewith energy. The mesons like K ± and K S have simi-lar v values like π + and π − over the measured beamenergies. φ meson v as a function of rapidity is ob-served to be similar to baryons ( p , Λ, Ξ), which havea strong positive slope at lower energy unlike othermesons ( K ± , K S , π ± ).Figure 3 shows the comparison of directed flowas a function of rapidity between experimental datafrom STAR at RHIC [15] and AMPT-SM ( σ p =1.5 mb, t max = 30 fm/ c ) calculation for differentidentified hadrons at various collision energies. TheAMPT-SM model better describes the experimen-tal data of mesons as compared to the baryons andanti-baryons over the studied energy range.The strength of directed flow signal at mid-rapidity is usually characterized by the linear term,F, in the equation v ( y ) = F y + F y [15] or bythe slope ( F ′ ) parameter of the fit function v ( y ) = F ′ y + C [44]. Here, the slope parameter F ′ is de-noted as dv /dy . By using the cubic fit function onecan reduce sensitivity to the rapidity range in whichthe fitting is performed. However, in order to have abetter comparison we have used the linear fit func-tion similar to the experimental STAR result [15].The fitting range for various hadron species are | y | < φ mesonwhich is fitted in the rapidity range, | y | < dv /dy , for baryons ( p , p , Λ, Λ,Ξ, Ξ) and mesons ( π − , π + , K + , K − , K S , φ ) areshown in Fig. 4 (a) and Fig. 4 (b), respectively. The dv /dy of measured baryons such as p , Λ, and Ξ arefound to have similar value and their anti-particles¯ p , ¯Λ, and Ξ have also similar slope within the un-certainty over the measured energy range. All themeasured baryons have positive d v /dy where astheir anti-particles have negative slope values. InAMPT-SM, the sign change of baryons’ ( p and Λ)slope is not observed unlike observed in STAR ex-periment [15]. The dv /dy of π − and π − are simi-lar; K + and K − values are also similar except forlower energies ( < K S meson. All the mesonsexcept φ resonance have negative dv /dy below 39GeV collision energy like the corresponding STARresults [15]. Overall magnitude of baryons and anti-baryons dv /dy are larger than the mesons.Figure 5 shows the φ meson slope calculated by us-ing different fitting ranges for both linear and cubicfunction in Au+Au collisions from √ s NN = 7.7-200 − − − − − − − − − − − − − − − − − − − − − − − AMPT-SM − − − − − − = 30 fm/c max t = 0.4 fm/c max t − − = 7.7 NN s 14.5 27 54.4 200 GeV + h - h φ ) v D i r e c t ed f l o w ( ) y Rapidity (
FIG. 1. Directed flow ( v ) as a function of rapidity (y) for hadron cascade time, t max = 30 fm/ c (solid marker),0.4 fm/ c (open marker). Upper, middle and lower rows correspond to positively, negatively charged hadrons and φ meson, respectively in 10-40% centrality, Au+Au collisions at √ s NN = 7.7, 14.5, 27, 54.4 and 200 GeV usingAMPT-SM. − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − p p Λ Λ
Ξ Ξ + K - K K − + π - π − φ = 7.7 NN s 11.5 14.5 19.6 27 39 54.4 62.4 200 GeV ) v D i r e c t ed f l o w ( ) y Rapidity (
FIG. 2. (Color online) Directed flow ( v ) as a function of rapidity (y) for hadron cascade time, t max = 30 fm/ c fordifferent identified hadrons (rows) in Au+Au collisions at √ s NN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200GeV (columns). − − − − − − − − × Λ − − − − − − − − − − × Λ − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − = 7.7 NN s 11.5 14.5 19.6 27 39 62.4 200 GeV pp ΛΛ + K S0 K -K ) v D i r e c t ed f l o w ( ) y Rapidity (
FIG. 3. (Color online) Directed flow ( v ) as a function of rapidity (y) for different identified hadrons (rows) usingAMPT-SM model (hadron cascade time, t max = 30 fm/ c ) is compared with the experimental data (solid circle) fromSTAR at RHIC [15] in Au+Au collisions at √ s NN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (columns). GeV. The dv /dy shows the sign change in between11.5 to 27 GeV for the fitting range | y | < | y | < | y | < | y | < dv /dy becomes positive within uncer-tainty for all measured energies. There is an hintof slope change as observed in STAR [15] althoughthe statistical significance is poor. The slope changeof φ meson might be due to short range fitting ( | y | < v as a function of rapidity. There is nodifference between the φ meson slope calculated us-ing linear and cubic function even though differentfitting ranges are considered. One can also observedthat there is a sharp increase in the φ meson slopewith decrease in energy ( <
11 GeV) which is similarto the STAR experimental results at RHIC [15].The energy dependence of proton dv /dy receivescontribution mainly in two ways (i) v of trans-ported protons from the initial colliding beam ra-pidity toward the mid-rapidity and (ii) v of pro-tons from pair (particle and anti-particle) produc-tion near mid-rapidity. The importance of pair pro-duction increases with increase in colliding energy.The ”net particle” is a measure of excess particlesyield over its anti-particles. It is used to disentanglethe transported quarks relative to that of producedin the collisions by using Eq. 3.[ v ( y )] p = r ( y )[ v ( y )] ¯ p + [1 − r ( y )][ v ( y )] net − p , (3) − − − p p Λ ΛΞ Ξ = 30 fm/c max t = 1.5 mb, p σ AMPT-SM, (a) y = / d y | v d − − + K - K K + π - π φ (b) (GeV) NN s − net p Λ net net K (c) FIG. 4. (Color online) The slope ( dv /dy ) of baryons,mesons and net- p , net-Λ, net- K are shown in upper, mid-dle and lower panels as a function of beam energy for 10-40% centrality, respectively. The dotted lines are smoothcurves drawn here to guide the eye. (GeV) NN s | y | = / d y d v − − = 30 fm/c max t = 1.5 mb, p σ AMPT-SM, φ Linear Cubic Fit range |y| < 0.6 |y| < 0.8 |y| < 1.0
FIG. 5. (Color online) Beam energy dependence of φ -meson slope parameter obtained using different fittingranges and fit functions for 10-40% centrality. The dot-ted lines are smooth curves drawn here to guide the eye. where r ( y ) is the rapidity dependence of anti-proton to proton ratio at each beam energy. The for-mulae for net- K and net-Λ are defined in the similarway as Eq. 3. Anti-proton v has been proposed asproxy of produced proton v in the Ref [44] and net- p slope is also used to distinguish the transportedbaryonic matter and hydrodynamic effect [15, 44].There are also model calculation which suggests thatthe transported quarks ( u and d from initial collid-ing nuclei) contribute more towards the formation ofhadrons like p , Λ and K + [37]. Figure 4 (c) showsthe net- p , net-Λ and net- K dv /dy as a function ofbeam energy for mid-central (10-40%) Au+Au col-lisions from √ s NN = 7.7-200 GeV. The net- p andnet-Λ have positive and similar dv /dy unlike thenet- K over the measured energy range.In this analysis, there are several (12) hadronswhich allow us to have a comprehensive study ofconstituent quark v . The assumption like v is de-veloped in pre-hadronic stage, each type of quark hasdifferent directed flow and that hadrons are formedvia quark coalescence can be tested here. The coa-lescence sum rule suggests that at smaller azimuthalanisotropy coefficient ( v n ), the detected hadron’s v n is sum of their constituent quark’s v n [15]. The pop-ular example of NCQ scaling observed at RHIC andLHC are followed from the coalescence sum rule [16–18].Figure 6 (upper panel) shows the comparison of¯Λ( uds ) and K − ( us ) + p ( uud ) slope as a functionof beam energy for 10-40% centrality in Au+Au col-lisions from 7.7-200 GeV. The example stated here y = / d y | v d − )uds( Λ )uud(p 31s) + u( - K = 30 fm/c max t = 1.5 mb, p σ AMPT-SM, (GeV) NN s Λ net + sp 31net p - net p + s31net p - )p 31 - - (s = K FIG. 6. (Color online) Upper panel shows the compar-ison of ¯Λ( uds ) and sum rule test for produced quark( K − (¯ us ) + ¯ p ( uud )) slope as a function of beam energy.Lower panel shows another set of sum rule test using net-Λ and net- p for 10-40% centrality in Au+Au collisionsusing AMPT-SM. The solid and dotted lines are smoothcurves drawn here to guide the eye. is the most suitable to test coalescence sum rule be-cause both Λ( uds ) and p ( uud ) are produced unlikethe u and d quarks which could be either produced ortransported. However, by comparing these two caseswe have assumed that s and s have same flow. Thescale factor is due to the assumption that u and d have the same v . But we found that except forhighest energy both of them are found to have differ-ent slope indicating violation of these assumptions.The dv /dy of s and ¯ s are different except for highestRHIC energy as shown in the Fig 8 for AMPT-SM, σ p = 1.5 mb. As per the assumption, one can ob-serve that u and d have similar slope as shown in theFig. 8. The STAR measurement at RHIC also foundthat the slope of ¯Λ( uds ) and scaled p ( uud ) have dif-ferent slope at lower energies [15] and this might bedue to the assumption that s and ¯ s have similar v over all measured energy ranges which may not bevalid for lower energies.Figure 6 (lower panel) shows the first case of co-alescence sum rule involving u and d quarks whichare either transported or produced and hence it iscumbersome to distinguish them in general. How-ever, one can naively expect that at lower beam en- − − − − − − − − − − − − − − − − − − − − − − − − − − − − u u − d d − s s = 7.7 NN s 11.5 14.5 19.6 27 39 54.4 62.4 200 GeV ) v D i r e c t ed f l o w ( ) y Rapidity (
FIG. 7. (Color online) Directed flow ( v ) as a function of rapidity (y) for different quark (anti-quark) solid marker(open marker) are shown in corresponding rows for Au+Au collisions at √ s NN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4,62.4 and 200 GeV (columns) using AMPT-SM. ergy, u and d quarks are mostly transported whereasthese quarks are largely produced at high collidingbeam energy. In this figure, two different coales-cence sum rule scenarios are compared with the net-Λ (open star). First case is the net- p minus u plus s , where u and s quarks are obtained from ¯ p/ K − (¯ us ) − ¯ p ( uud ), respectively as represented byblue diamond symbol. Here, the produced u quarkin net- p is replaced by s quark. However, we donot have the corresponding straight forward expres-sion for representing the transported u and d quarks.The sum rule is found to be in a good agreement withnet-Λ above 39 GeV and start deviating for lower en-ergies. This observation suggests that the fractionof transported quarks in the constituent quarks as-sembly of net- p increases with decrease in collisionbeam energy, which imply that the assumption ofproduced u quark is removed by keeping the term(net- p - ¯ p ) also starts deviating. The observationof getting the transported quark dominance at lowerenergy ( ≤
39 GeV) in 10-40% centrality Au+Au col-lisions using AMPT-SM is qualitatively similar tothat of observed in STAR experiment at RHIC [15].The second case of coalescence sum rule i.e ( net- p + s) is also shown in (red open circle marker)Fig. 6 (lower panel). In this sum rule, it is assumedthat in the limit of low beam energy, the constituentquarks of net protons are dominated by transportedquarks, and s quark replaces one of the transportedquarks. This assumption starts showing disagree-ment for beam energy greater than 19.6 GeV i.e.the disagreement between black and red markers. (GeV) NN s y = / d y | v d − − u ud ds s 0.5 × φ = 30 fm/c max t = 1.5 mb, p σ AMPT-SM,
FIG. 8. (Color online) Slope ( dv /dy ) as a function of √ s NN for quark, anti-quark and φ meson using AMPT-SM for parton-parton cross section ( σ p ) of 1.5 mb. The φ meson slope is divided with corresponding number ofconstituent quarks i.e 2. Figure 7 shows the directed flow of partons ( u , ¯ u , d , ¯ d , s and ¯ s ) systematic evolution in Au+Au colli-sions from low to high energy ( √ s NN = 7.7 to 200GeV). All the anti-quarks are produced unlike the u and d quarks which might be either transported orproduced depending on the collisions beam energy.So, at highest RHIC energy both the quarks andanti-quarks have same v as these are expected to bemostly produced. However, with decrease in beamenergy the v difference between them increases andanti-quarks shows larger directed flow than quarks. v of quarks forming primordial proton have the op-posite sign compared with v of all quarks, and fur-ther study is needed to understand why this is thecase for the quark coalescence in AMPT. Further-more, the v slope of quarks coalescing to primordialproton and the corresponding proton have similarslope. However, the final proton (Fig. 2) which in-cludes decay contribution and hadronic interactionhave similar positive slope like primordial proton butdifferent in magnitude.Directed flow slope parameter of quarks, anti-quarks and φ meson as a function of beam energyis shown in Fig. 8. The slope of u and d quarks isfound to be similar and decreases with increase inbeam energy unlike the s quark. All the light anti-quarks (¯ u , ¯ d and ¯ s ) have more negative slope thantheir corresponding quarks. However, there is a cleardeviation of ¯ s slope from the trend of s quark exceptat the highest energy. The φ meson slope does notscale with the s and s quarks’ slope. IV. SUMMARY AND OUTLOOK
A comprehensive study of rapidity-odd compo-nent directed flow for charged and identified hadronsin Au+Au collisions (10-40% centrality) for a rangeof collision beam energies using an improved coa-lescence AMPT-SM model has been discussed. Thecoalescence sum rule or commonly known as NCQscaling is tested using the directed flow measurementof identified hadrons. The analysis performed hereare summarized in the following.The effect of hadronic interaction on v of chargedhadrons and φ meson are reported. The v ofcharged hadrons are found to be not well developedfor t max = 0.4 fm/ c , because the particles could notget enough time to have hadronic interactions un-like the case for t max = 30 fm/ c , except for posi-tively charged hadrons at lower energies where thetransported quark effect is more dominant. How-ever, the φ -meson v is found to be unaffected byhadronic interaction because of it’s small hadroniccross section and also it decays outside the fireball(life time ∼
42 fm/ c ). The double sign change of φ meson slope in between 11.5 to 27 GeV is observed.This sign change is also found to be an artifact ofsmall fitting ranges while extracting the v slope.The sign change goes away making positive slopefor all measured energies when the linear or cubicfunction is fitted in a larger rapidity range ( | y | < v /dy) in the real data measurement. Prediction for directed flow as function of rapidityand slope parameter of various identified hadrons insemi-central (10-40%) Au+Au collisions at √ s NN = 54.4 GeV are reported. The v calculation of Ξand Ξ baryons is predicted for a range of energy andthe values are found to be similar to protons and Λbaryons. The v results at higher rapidity range arealso shown here, which cover the Event Plane De-tector (EPD) pesudo-rapidity ( η ) range installed inSTAR detector at RHIC for BES-II program.We find that light quarks such as u and d have sim-ilar slope and it decreases with increase in beam en-ergy unlike the s quark. The anti-quarks (¯ u , ¯ d and ¯ s )have more steeper negative slope than correspondinglight quarks and are similar for the measured beamenergy range. The s and s quarks have different v except for the highest energy. There is a clear in-dication that s quark slope start deviating from thetrend of s quark with the decrease in energy. Themeasured baryons ( p , Λ and Ξ) have similar posi-tive slope and increases with decrease in beam en-ergy unlike their corresponding anti-particles. TheAMPT-SM model shows no sign change for p and Λslope unlike that observed in STAR experiment atRHIC [15]. The slopes of π + , π − , K + , K − and K S mesons are positive at the highest RHIC energy thenstart decreasing and becomes negative with decreasein beam energy. The slope of K S is approximatelyaverage of K + and K − slope as observed in STARat RHIC [15].The test of coalescence sum rule using producedquarks are done by comparing the slope of ¯Λ( uds )and K − (¯ ud ) + ¯ p ( uud ). These are found to havedifferent slope and the departure increases with de-crease in energy which might be due to break-downof the assumption that s and ¯ s have same flow overthe measured energy range. The slope of net- p andnet-Λ are similar over the measured energy range.The sum rule (net- p - ¯ p + s ) and net-Λ are foundto be similar for energy higher than 39 GeV. The de-viation at lower energy might be an indication thatthe assumption of produced u quarks effect can beremoved by keeping the term p . This assumptiondoes not hold at lower energies, which is similar tothe observation in STAR at RHIC [15]. The sumrule ( net- p + s ) and net-Λ values starts deviatingat energy higher than 19 GeV. This sum rule as-sumes that at lower energy the transported quarksdominates and one of the transported quark of net- p is replaced by s quark. Hence, this approximationbreaks down in the limit of high beam energy whichis qualitatively similar to the observation in STARat RHIC [15]. V. ACKNOWLEDGMENTS
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