颗粒性粒子发射源的视像(Imaging)分析

颗粒性粒子发射源的视像(Imaging)分析张卫宁杨志滔任延宇1,2

大连理工大学物理与光电工程学院2)哈尔滨工业大学物理系22Phys.Rev.C80(2009)044908一、引言强度干涉学(HBT)已被广泛应用于获取高能重离子碰撞产生的粒子发射源的时空信息。在高能重离子碰撞的传统强度干涉学分析中，人们是对实验(或模拟)产生的2粒子(如2π)关联函数用参量化的公式进行拟合，得到有关时空结构定量结果。例如，一维高斯参量化公式拟合，得到的定量结果是模型依赖的。在高能重离子碰撞产生的π发射源可能并不是简单的高斯分布。例如，为解释实验观察上小的λ参量，人们提出了源的Core-Halo分布模型；为解释RHIC的HBT之谜，提出了颗粒源模型。-0-+对这样的非高斯源，高斯拟合得到的源半径不能反映源的空间特征，得到的参量也会畸变。视像分析可以从关联函数得到相对源函数，(一维,Brown&Danielewicz;三维,Danielewicz&Pratt)。笛卡尔谐函数基由视像分析得到的是模型无关的，从中获取的有关源的定量信息也与模型无关。因而适合用于对非高斯源的分析。π对质心系中相对动量和坐标二、源的模型无关特征量之前对实验imaging的研究主要集中于对源函数形状的讨论和利用参数化函数拟合

imagedsources。S.S.Afanasiev

etal.,(PHENIXCollaboration),Phys.Rev.Lett.100,232301(2008)

S.S.Adleretal.,(PHENIXCollaboration),Phys.Rev.Lett.98,132301(2007)

Zhi-TaoYang,Wei-NingZhang,L.Huo,Jing-BoZhang,J.Phys.G36,015113(2009)ImagingModel-independent定义相对距离r的n阶矩r的各阶“矩”是描述发射源的模型无关的特征量。引入对静态源的分析表明：对非高斯源，视像法得到的更接近于真实值，能更好地体现非高斯源在大r的分布，而反映了源分布与高斯分布的差异。对高斯源三、改进的QGP颗粒源模型形成QGP颗粒源的可能因素：大的初始涨落+快速膨胀+表面张力效应PRC74(2006)024908QGP在接近相变时快速增加的体粘滞性PRC77(2008)034903NeXus过去QGP颗粒源的结果：(W.N.Zhang,Y.Y.Ren,C.Y.Wong,PRC74,024908,2006)V2随PT增加V2饱和初始颗粒的速度满足Bjorken条件对模型的改进：初始颗粒的大小满足高斯分布考虑了直接产生和衰变产生的介子中心快度区域（|y|<ym)速度假定系统在碎裂，颗粒的初始速度为颗粒按流体力学演化，初始半径满足高斯分布，初始位置分布满足态方程π介子冻结温度满足分布模型参量：四、颗粒源的多维视像分析一维视像三维视像x—out方向，y—side方向，z—long方向，kT=|p1T-p2T|/2X方向有长的尾巴,随kT增加,与y方向不同.Z方向小kT有长的尾巴。定义i方向n阶矩引入考虑了洛仑兹变换后，颗粒源的视像结果R与传统HBT的半径结果符合，且可以解释HBT实验的半径结果。五、总结与传统的强度干涉学相比，视像法得到的源函数S(r)具有模型独立的特性。从原函数可以得到r的各阶矩，它们是描述粒子发射源时空和相干性的模型独立的特征量。我们的研究表明，与零阶矩相关的给出有关源相干性的信息，与一阶矩有关的给出源的平均尺寸，而可以反映源分布与高斯分布的差异。对非高斯源，这些模型独立的特征量比通常HBT的结果更能反映源的实际情况。颗粒源模型能够再现实验HBT的主要特性。对颗粒源的视像分析表明，相对原函数在out方向的分布要比side方向宽，其值随粒子对横动量的增加而增加。而在long方向，小横动量时相对原函数有长的尾巴。在考虑了洛仑兹收缩后，视像分析的结果与通常HBT分析的结果相符。Thankyou!----------------------------------------------------------------------

ReportoftheReferee--CJ10161/Zhang

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Thisisaninterestingpaperthatexpoundsonsomelong-standingideas

abouthowdropletsorgranularitymightmanifestthemselvesin

correlationmeasurements.Themethodswellsurpassthequalityof

previousanalyses,andwarrantpublicationinPRC.Theauthorsmight

wanttoreferencesomeolderpaperswhichpresentthesameideas,but

certainlydonotcompetewiththepresentpaperintheir

sophistication,e.g.,S.Pratt,PRC49,2722(1994).

Thepaperisclearandeasytoread.Irecommendpublishingwithout

changes,unlesstheauthorswishtoaddreferencetothepaperabove.

a.Granulardropletsmayoccurin

first-orderphasetransitionsE.Witten,Phy.RevD30,272(1984)ThereasonfortheoccurrenceofGranularSourceofQGPb.InitialStateEffect

Inhigh-energyheavy-ioncollisonsonanevent-by-eventbasis,theinitialtransverseenergydensityishighlyfluctuating(a)(b)

(a)

(NeXus)H.J.Drescher,F.M.Liu,S.Ostapchenko,T.Pierog,K.Werner,PRC65,054902,2002;(b)Y.Hama,QM2005talk,hep-ph/0510096;

Thelargeinitialfluctuationsofmatterdensity,togetherwithviolentexpansionandsurfacetensioneffectsmayleadtoformationofgranulardroplets!

Dynamicalexpansionofahighlyfluctuatingdistrbution

mayleadtodropletformation(orfragmentation)

(TubesofdenseQGPmatter)(Longtubesbreakupintodroplets)(Highlyfluctuatingtransversedensitydistribution)ModelCalculationPhysicsResultsFragmentationandformationofgranulardropletsComparingwithexperimentsAveragingModelCalculationAveragingResultsWhyHBT

Puzzle？Theshortlifetimesforgranularsourcesareleftfromtheaveraging---〉HBTpuzzle!TransversedistributionsofenergydensityoftheeventsevolvingwithEOS-I((a)--(d))andEOS-II

((a‘)--(d’))at

differenttimesfor

b=0fm.Thesystemsareinhomoge-neousinspaceandtimebothfortheeventsevolvingwiththeEOS-IandtheEOS-II.Therearemany``lumps“inthesystems.Thelumploca-tionsaredifferentevent-by-event.Transversedistributionsofenergydensityoftheeventsfor

b=5and10fm.ThesystemsevolvewithEOS-I((a)--(d))andEOS-II((a')--(d')).Thenumberofthelumpsinthesystemdecreaseswithimpactparameterincreasing.

ThesystemsevolvingwiththetwokindsofEOSshavethe

similarspace-timestructure.Wewillconsideronlythe

EOS-IIinourcalculationslater.Single-eventHBTcorrelationfunctionsTwo-pioncorrelationfunc-tionsfortheNEXSPHERIOeventswithdifferentimpactparameters.Tf

=150MeV.Thecorrelationfunctionsforsingleeventsexhibitfluctuations.Thefluctua-tionsarelargerforbiggerimpactparameter.Inlongitudinaldirectionthecorrelationfunctionsexhibitoscillationswhichcannotbesmoothedoutbyeventmixing.Single-eventsMixed-eventsByapplyinganadditionalcutfortheinitialrapidityofthe``smoothedparticles“,$\eta_0>0$,wefindthattheosci-llationsofthemixed-eventcorrelationfunctionsaresmoo-thedoutasshowninFig.5(c).Observablesforsingle-eventHBTcorrelationsWeshownthatthetwo-pioncorrelationfunctionsofsingleventsexhibitevent-by-eventfluctuations.BecauseofstatisticstraditionalHBTmeasurementsarebasedonmixed-eventanalysis.Theevent-by-eventfluctuationsaresmoothedoutinthiscase.Inordertoobservetheevent-by-eventfluctuations,wenextinvestigatethedistributionofthedifferencesbetweenthecorrelationfunctionsofsingleandmixedevents,withtheirerrorsasweights,dN/df,,i–side,out,long.

Thedistributionsofffor40eventswithFIC&SIC.Fluctuatinginitialconditions(FIC)Smoothedinitialconditions(SIC)Uppanels:thedistributionsforFICaremuchwiderthanthecorrespondingresultsforSIC.Downpanels:onecanalsoseethedistributionsforFICarewiderthanthoseforSIFinthiscase.Becauseofstatistics,sometimeswehavetoreducevariablenum-bersinanalysis,althoughitwilllosesomedetails.(i–side,out,long,trans.)Thedistributionsaregoodobservablesforthe“granularsource”.(W.N.Zhang,S.X.Li,C.Y.Wong,M.J.Efaaf,PRC71,064908,2005.)

高能重离子碰撞系统演化碎裂机制碎裂信号X1X2

Intensitive

interferometry（HBT）Life