顆粒性粒子發(fā)射源的視像(Imaging)分析

顆粒性粒子發(fā)射源的視像(Imaging)分析張衛(wèi)寧楊志滔任延宇1,2

大連理工大學(xué)物理與光電工程學(xué)院2)哈爾濱工業(yè)大學(xué)物理系22Phys.Rev.C80(2009)044908一、引言強(qiáng)度干涉學(xué)(HBT)已被廣泛應(yīng)用于獲取高能重離子碰撞產(chǎn)生的粒子發(fā)射源的時(shí)空信息。在高能重離子碰撞的傳統(tǒng)強(qiáng)度干涉學(xué)分析中，人們是對(duì)實(shí)驗(yàn)(或模擬)產(chǎn)生的2粒子(如2π)關(guān)聯(lián)函數(shù)用參量化的公式進(jìn)行擬合，得到有關(guān)時(shí)空結(jié)構(gòu)定量結(jié)果。例如，一維高斯參量化公式擬合，得到的定量結(jié)果是模型依賴的。在高能重離子碰撞產(chǎn)生的π發(fā)射源可能并不是簡(jiǎn)單的高斯分布。例如，為解釋實(shí)驗(yàn)觀察上小的λ參量，人們提出了源的Core-Halo分布模型；為解釋RHIC的HBT之謎，提出了顆粒源模型。-0-+對(duì)這樣的非高斯源，高斯擬合得到的源半徑不能反映源的空間特征，得到的參量也會(huì)畸變。視像分析可以從關(guān)聯(lián)函數(shù)得到相對(duì)源函數(shù)，(一維,Brown&Danielewicz;三維,Danielewicz&Pratt)。笛卡爾諧函數(shù)基由視像分析得到的是模型無關(guān)的，從中獲取的有關(guān)源的定量信息也與模型無關(guān)。因而適合用于對(duì)非高斯源的分析。π對(duì)質(zhì)心系中相對(duì)動(dòng)量和坐標(biāo)二、源的模型無關(guān)特征量之前對(duì)實(shí)驗(yàn)imaging的研究主要集中于對(duì)源函數(shù)形狀的討論和利用參數(shù)化函數(shù)擬合

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定義相對(duì)距離r的n階矩r的各階“矩”是描述發(fā)射源的模型無關(guān)的特征量。引入對(duì)靜態(tài)源的分析表明：對(duì)非高斯源，視像法得到的更接近于真實(shí)值，能更好地體現(xiàn)非高斯源在大r的分布，而反映了源分布與高斯分布的差異。對(duì)高斯源三、改進(jìn)的QGP顆粒源模型形成QGP顆粒源的可能因素：大的初始漲落+快速膨脹+表面張力效應(yīng)PRC74(2006)024908QGP在接近相變時(shí)快速增加的體粘滯性PRC77(2008)034903NeXus過去QGP顆粒源的結(jié)果：(W.N.Zhang,Y.Y.Ren,C.Y.Wong,PRC74,024908,2006)V2隨PT增加V2飽和初始顆粒的速度滿足Bjorken條件對(duì)模型的改進(jìn)：初始顆粒的大小滿足高斯分布考慮了直接產(chǎn)生和衰變產(chǎn)生的介子中心快度區(qū)域（|y|<ym)速度假定系統(tǒng)在碎裂，顆粒的初始速度為顆粒按流體力學(xué)演化，初始半徑滿足高斯分布，初始位置分布滿足態(tài)方程π介子凍結(jié)溫度滿足分布模型參量：四、顆粒源的多維視像分析一維視像三維視像x—out方向，y—side方向，z—long方向，kT=|p1T-p2T|/2X方向有長(zhǎng)的尾巴,隨kT增加,與y方向不同.Z方向小kT有長(zhǎng)的尾巴。定義i方向n階矩引入考慮了洛侖茲變換后，顆粒源的視像結(jié)果R與傳統(tǒng)HBT的半徑結(jié)果符合，且可以解釋HBT實(shí)驗(yàn)的半徑結(jié)果。五、總結(jié)與傳統(tǒng)的強(qiáng)度干涉學(xué)相比，視像法得到的源函數(shù)S(r)具有模型獨(dú)立的特性。從原函數(shù)可以得到r的各階矩，它們是描述粒子發(fā)射源時(shí)空和相干性的模型獨(dú)立的特征量。我們的研究表明，與零階矩相關(guān)的給出有關(guān)源相干性的信息，與一階矩有關(guān)的給出源的平均尺寸，而可以反映源分布與高斯分布的差異。對(duì)非高斯源，這些模型獨(dú)立的特征量比通常HBT的結(jié)果更能反映源的實(shí)際情況。顆粒源模型能夠再現(xiàn)實(shí)驗(yàn)HBT的主要特性。對(duì)顆粒源的視像分析表明，相對(duì)原函數(shù)在out方向的分布要比side方向?qū)?，其值隨粒子對(duì)橫動(dòng)量的增加而增加。而在long方向，小橫動(dòng)量時(shí)相對(duì)原函數(shù)有長(zhǎng)的尾巴。在考慮了洛侖茲收縮后，視像分析的結(jié)果與通常HBT分析的結(jié)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.)

高能重離子碰撞系統(tǒng)演化碎裂機(jī)制碎裂信號(hào)X1X2

Intensitive

interferometry（HBT）Life