Jing Yang·Wei-Ning Zhang,2

Interferometry analyses of pion and kaon for the granular sources for Au+Au collisions at=200 GeV

Jing Yang1·Wei-Ning Zhang1,2

Pion interferometry.Kaon interferometry. Granular sources.Absorption effect

1 Introduction

2 Granular source model

The granular sources are assumed to be formed at a later time of the QGP expansion in relativistic heavy ion collisions.The lumps of the QGP after this time are consideredto be spherical droplets for simplicity and evolve in hydrodynamics separately[6-11].The strong interactions of the QGP matter before forming the granular source are assumed to lead to the anisotropic initial velocities of the QGP droplets in the granular source model[6-11].

where r0iis x0,y0,or z0for i=1,2,or 3,and sign（r0i）denotes the signal of r0i,which ensures an outward droplet velocity.In Eq.(2),Ri=（RT，RT，Rz）,the quantities ai=（ax，ay，az）,and bi=（bx，by，bz）are the magnitude and exponent parameters of droplet initial velocity in x,y,and z directions.In the model calculations in this paper,we take the values of the source parameters as the same in Ref.[7].

In the granular source model,the droplets evolve in relativistic hydrodynamics and with the equation of state (EOS)of the S95p-PCE-v0[15].The final identical pions and kaons are considered to be emitted from the surfaces of the droplets with the momenta obeying Bose-Einstein distribution in the local frame at freeze-out temperature,Tf. To include the resonance-decayed particles later as well as the directly produced pions at chemical freeze-out early,a wide region of Tfis considered with the probability[6,7]

where fdiris the fraction of the direct emission around the chemical freeze-out temperature Tchem,and ΔTdirand ΔTdecare the temperature widths for the direct and decay emissions,respectively.In the calculations,we take ΔTdir=10 MeV and ΔTdec=90 MeV as in Refs.[6,7].The value of Tchemis taken to be 165 MeV as in the EOS of S95p-PCE-v0 [15].Theparameterfdiristakentobe0.75forpionasinRefs. [6,7]and is taken to be 1 for kaon for its early freeze-out.

Unlikeacontinuoussourcewhichisemittingparticlesfrom source surface,the particles are freezed out on the droplet surfacesforthegranularsource,andtheparticleemittedfrom a droplet may also be absorbed by other droplets in the granularsource.Because the particleemitted early(orathigh Tf)from a droplet in the granular source is more possible to meet the other droplets with higher temperatures and be absorbedwhenpropagatinginwardinthegranularsource,we apply simply the cut,

to forbid the particle which freezes out at the higher temperatures Tf＞?and has a momentum p with negative (p.rT)or(p.rz)value in our model calculations for the case withabsorption,whereristhecoordinatevectoroftheparticle freeze-out point in the frame of the granular source.The particleabsorption in high-density(temperature)mediumisa complicatedproblem.Thecrosssectionofparticleabsorption isrelatednot onlytothe mediumenvironment,but alsotothe particle property.In the present consideration,the absorption effect is related to the values of?parameter used in the calculations.We take=150 and 155 MeV in the calculations for pion and kaon,respectively,by the comprehensive comparisons of the model-calculated HBT radii with experimental data.

3 Pion and kaon interferometry analyses

Two-particle HBT correlation function is defined as the ratio of the two-identical-particle momentum spectrum P（p1，p2）to the productofthe two single-particle momentum spectra P（p1）P（p2）.In the interferometry analyses in high-energy heavy ion collisions,the two-particle correlation functions are usually fitted by the Gaussian-parameterized formula

Fig.1(Color online)Transverse-momentum spectra of pion and kaon for the granular sources for the Au+Au collisions at=200 GeV and in 10-20%centrality region.The dashed and solid lines are for the granular source results without and with the consideration of the particle absorptions in the granular sources.The experimental data are measured by the PHENIX collaboration[16] and the STAR collaboration[17]

where qout,qside,and qlongare the Bertsch-Pratt variables [18-20],which denote the components of the relative momentum q=p1-p2in transverse‘out’(parallel to the transverse momentum of the pion pair kT),transverse‘side’(in transverse plane and perpendicular to kT),and longitudinal(‘long’)directions,respectively.In Eq.(4),λ is chaoticity parameter,and Rout,Rside,and Rlongare the HBT radii in the out,side,and long directions.

Fig.2(Color online)Two-pion interferometry results for the granular sources for the Au+Au collisions at=200 GeV. The dashed and solid lines are for the cases without and with the consideration of the particle absorption in the granular sources.The symbols are the experimental data in the Au+Au collisions measured by the PHENIX collaboration[12]and the STAR collaboration[14],respectively

Fig.3(Color online)Two-kaon interferometry results for the granular sources for the Au+Au collisions at?=200 GeV. The dashed and solid lines are for the cases without and with the consideration of the particle absorption in the granular sources.The symbols are the experimental data in the Au+Au collisions measured by the PHENIX collaboration[12]

4 Summary and conclusions

We have performed pion and kaon interferometry analyses in the granular source model of QGP droplets [6,7].The effect of particle absorption on the HBT radii of pion and kaon is investigated based on a consideration of forbidding inward emission for the particles freezed out earlier(or at higher temperature).This absorption effect is important in the kaon interferometry analyses.It leads to the decreases of the kaon HBT radii.In our analyses,the particle-emitting sources of pion and kaon have the same initial source parameters,but different freeze-out temperature regions.Although it is only a simple consideration for the particle absorption,the HBT radii of pion and kaon of the granular sources are in better agreement with the experimental data of the Au+Au collisions at=200 GeV at the RHIC after considering the particle absorption.Further investigations of the particle absorption in the granular source model and its influence on final-particle multiple observables will be of interest.

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Received:16 August 2016/Revised:22 September 2016/Accepted:27 September 2016

©Shanghai Institute of Applied Physics,Chinese Academy of Sciences,Chinese Nuclear Society,Science Press China and Springer Science+Business Media Singapore 2016

This work was supported by the National Natural Science Foundation of China(No.11275037).

✉ Wei-Ning Zhang

wnzhang@dlut.edu.cn

1School of Physics and Optoelectronic Technology,Dalian University of Technology,Dalian 116024,China

2Department of Physics,Harbin Institute of Technology, Harbin 150006,China