Poduction Mechnism of Quk Gluon Plsm in Hevy Ion Collision Amb Jin And V.Rvishnk
Pimy im of theoeticlly studying URHIC is to undestnd Poduction of quks nd gluons tht fom the bulk of the plsm ( ) t 0 Thei spce-time evolution leding to t c t h () Equilibtion ( ) (b) Hdoniztion ( ) The behviou of hevy ptons in the bove medium s function of spce-time In othe wods we wish to study the Y-M esponse functions
The dution of the bove pocesses e estimted to vy fom fction of femi to sevel femis. It is ntul fo the timescles mentioned bove to be ovelpping. Tht is poduction, evolution, nd the equilibtion e not disjoint pocesses. We need simple but obust fmewok to study the bove mentioned spects. In doing tht we seek diections fom Lttice esults (such s detemining the fom of f eq ), QCD nd Clssicl Plsm Physics. Note tht we e studying non-equilibium phenomenon nd stndd themodynmic esults cnnot be used.
Fmewok A fmewok does exist nd tht is the semi-clssicl fomultion of poduction nd equilibtion. Typiclly one wites tnspot eqution in extended phse-spce o its geneliztion to multipticles. f t + f v. + f F. p + Q f Q = Σ + collision tem Whee Σ is the souce tem. This hs long histoy dting bck to the wok of Lndu, Femi nd Pomenchuk (950 s). A moe ecent discussion is by Cuthes nd Zchisen*. This ppoch ws fist invoked fo QGP by Bjoken. * Reviews of Moden Physics, 55 (), Jnuy 983
Slient Fetues of Tnspot Eqution f f (, p, Q ) is descibed in n extended phsespce P = R 6 G Fi = Q [ Ei + ( v B ) i ] whee is guge covint quntity Q Q hee, unlike the Mxwell chges, e dynmicl vibles. In fct they stisfy: dq d = f bc τ Note tht they e sensitive not to the field tenso diectly but to the guge potentils themselves. Q b A µ c u µ
We hve souce tem which is defined ove the phse spce..this is nomlly bsent in the clssicl plsms. P Since poduction of ptons fom vcuum is not clssicl phenomenon, this hs to be detemined quntum mechniclly. Following methods hve been employed in the litetue: pqcd ( stuctue functions & S-mtix ppoch) Effective ppoches ( we will come bck to it lte) Similily Collision tem is lso complicted becuse one cnnot tke ove the Boltzmnn nstz without futhe nlysis In this tlk I will concentte entiely on souce tems fo gluons & quks
Souce Tem Detemintion of the souce tem cnnot be done independently of the kind of tnspot eqution we use. Self consistency is the key wod. We do not employ the pqcd ppoch fo following eson: No method to employ multiple ovelpping time scles. The equied souce tem is fo the bulk of the plsm which is composed of soft nd semi-hd ptons. It is unlikely tht pqcd will be vlid ppoximtion. Moeove even t equilibtion we do not hve n idel gs o smll petubtion ove tht.
Theefoe we need n effective model. Colo Flux Tube Model is one such model, which povides ntul setting fo discussing quk confinement, in tems of colo stings, which e Chomo Electic Field (CEF) flux tubes teminting on two ptons. Fo effective Schwinge mechnism bsed models, which e stictly vlid fo constnt nd unifom electic field: Rte t given time m = ge( t)exp ge( t) This is clely wong, fo, this is not tue even fo clssicl dition theoy in Electodynmics. Clssicl dition fom pticle in LINAC, fo exmple, depends on complete histoy of the pticle nd not meely on instntneous field stength.
We need mechnism which is Inheently Non-Mkovin Reflects the dynmicl ntue of the vcuum Also eflects the qusi-pticle ntue of excittions We popose mechnism, which hs inheently ll the bove mentioned fetues. We obtin it by employing time dependent petubtion theoy. Non-petubtive spects e modeled in the fmewok of Colo Flux Tube Model. We illustte it fo pton poduction t the lowest ode.
Poduction Mechnism Afte the two nuclei collide, nd stt eceding fom ech othe, colo stings e fomed between them. These stings mege to fom colo ope (i.e. CEF is fomed). Consequently the poduction pocess educes to the instbility of the QCD vcuum in the pesence of clssicl CEF which is in genel spce-time dependent. We study both the g nd qq poduction in the extenl Y-M field. Gluon cse is pticully inteesting becuse it is nonbelin with no countept in QED.
Fomlism Gluons: Expnd guge potentils s sum of clssicl vlues nd thei fluctutions: L A µ = A µ + φ µ = C µ + φµ Expnding YM Lgngin, we find tems esponsible fo gluon poduction to be: g = g f bc µ b νc µ b νc [( µ Cν ν C µ ) φ φ + ( µ φν νφ µ )( C φ + φ whee tems e kept up to qudtic in fluctutions. Mking suitble choice of bckgound field, poduction te could be detemined. µ b C νc )]
Keeping in mind the model nd invoking guge covince of CEF, we choose the guge potentil to be, with the guge goup SU(3) in mind, of the following fom : ) ), ( ), ( ( 8,,3 0, t f t f A δ δ δ µ µ + = We poject the stte to the two gluon stte nd the mplitude is given by: ; ; c c s s p p ψ (t) ) ; ; ( ~ ) ( ). ( ) ( ) ( 0 ) ( 0 3 t p p E E C f p p E E E E ig t T f c c s s + + = ε ε π whee + + = ), ' ( ' ~ 0 ). ( 3 0 ' ) ( 0 t C e d e dt C p p i t t E E i
Similly fo quks: f g m + ~ T( t) 0 = u ( p ) v ( p) T, C0 ( E E; p p; t) 3 s s c c + + (π ) E E The finl sttes e not stndd symptotic fee sttes. They hve ovelpping pojection with the unphysicl degees of feedom. We distinguish physicl pis by pojecting the sttes onto the physicl subspce. The pobbility tht pi is poduced ny time duing the intevl (0,t) is given by: f T (t) 0 The poduction te t ny time t is thus given by its deivtive t tht instnt; howeve this quntity not gunteed to be nonnegtive.
A Model Exmple nd Results We will now illustte the esults with the help of n model exmple dwn fom its behviou expected in el situtions. Let CEF be given by: E i = δ δ i, ze0( δ,3 +,8) e ( t z )/ t 0 with initil field stength given by E 0. This itself is not n boost invint desciption but it cptues ll the essentil fetues.
Gluon pobbility distibution in longitudinl momentum spce p =.0 & t =.0 = 3. 0 & t =. 0 T p T
Quk pobbility distibution in longitudinl momentum spce p =.0 & t =. 0 = 5.0 & t =. 0 T p T
Gluon poduction tes fo s = 0.6 & p T = 0. (+,-) chnnel (+,+) chnnel
Gluon poduction tes fo s =.0 & p T = 0.4 (+,-) chnnel (+,+) chnnel
Quk poduction tes fo s = 0.6 & p T = 0. (+,-) chnnel (+,+) chnnel
Quk poduction tes fo s =.0 & p T = 0.4 (+,-) chnnel (+,+) chnnel