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Background & Motivation ; PART a! Evolution of the system ; PART b! Dilepton production ; PART c! SummaryqqK* Background & Motivation 60!0 +  /  8  9  ,  -  6  7  1  2  {   0` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴` 333fSf3f` 3f3fSf3f` 33fSf3f` 3Sff>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> L0 (    6Pz  " `}   LUSQdkYkHrh7h_     0|  " `   8USQdkYkHre,g7h_ ,{N~ ,{ N~ ,{V~ ,{N~    08  "   ^*   0  "w    `*   0  "   `* 3f   tA޽h ? YN ^g-GNN"@` 3f___PPT10i.V@ۛ+D=' B = @B +  ؞!jg 0 ~v`T(  T T 0dA  P     P*   T 0V       \* d T c $ ?    T 0\   0   8USQdkYkHre,g7h_ ,{N~ ,{ N~ ,{V~ ,{N~   T 61  _P    Z*  T 6e  _    \* H T 0޽h ? 3380___PPT10.\[  0 L0 `.9(  ) ) # l LRxfd ?" ,  GDILEPTONS FROM A CHEMICALLY EQUILIBRATING QGP AT FINITE BARYON DENSITYHH&!# * 3 r  MMMԔ?"6@ NNN?NPj J C Guan-Nana (2 b + T@  "` -7   B - ZDԔMMMԔ?"0@NNN?NS GS % . 3 r  MMMԔ?"6@ NNN?N  EOUTLINE"(2fH  0޽h ? 3Sff___PPT10i.  H HA ? ?< K`x dA  H BA ??Mx d  H BA ??*Fzx d8  H0 TA ? ?<Wl   1 H 3 rp  Ԕ?"6@ NNN?Nd QEvolution of the systemf! H C xlt  MMMԔ?"6@ NNN?N M , |A set of coupled relaxation equations describing evolutions of temperature and quark chemical potential and fugacities .0} 2zfdp ` H c $A ??8 d   H c A ? MMMԔ?"6@ NNN?NC -  ^L" H 3 r{ GHIJKL-MBN0MMMԔ?"6@ `NNN?NP   lAssuming that elastic parton scattering is rapid enough to maitain local thermal equilib- rium, the evolution of the parton densities can be given by the master equations .: u2fdb2r H ZMMMԔ?"6@ `NNN?N Jjv& H 3 rȄ  MMMԔ?"6@ NNN?NW F Combining: 2 fd !H S ~A ? MMMԔ?"6@ NNN?N x d{d "H S ~A ? MMMԔ?"6@ NNN?Nx dAH H 0޽h ?/ H#H 3Sff___PPT10i.V+D='  = @B +\   0 L0 [ S p p (  pd p c .A! evol"`T T p C x  MMMԔ?"6@ NNN?NP * n.The evolutions of QGP for initial values $/(``F aj p M&/l p S ~A ,? MMMԔ?"6@ NNN?Na<bx ,dAl  p S ~A -? MMMԔ?"6@ NNN?N<tx -dAl  p S ~A" .? MMMԔ?"6@ NNN?Nmjx .dAl  p S ~A# /? MMMԔ?"6@ NNN?NgSx /dA  p C x  MMMԔ?"6@ NNN?NP    with initial quark chemical potential (a) the fugacity of quark(anti-quark) and gluon; (b) quark chemical potential and temperature.8,bu``"A B`  p c $A 0??8 d  0d p S ~A$ 1? MMMԔ?"6@ NNN?N S9 x 1dAH p 0޽h ? 3f___PPT10i.\ݝ+D='  = @B +w  0 L0  t_(  tV t C A%mut"`1 & k t C x\  MMMԔ?"6@ NNN?NTpn OThe relation of quark chemical potential and the temperature at the same time.PPb t 3 rЪ  MMMԔ?"6@ NNN?N`  > 2` d t S ~A& 5? MMMԔ?"6@ NNN?N x 5dA'  t 3 rl  MMMԔ?"6@ NNN?N/S) GInitial values: 2b  t 3 r  MMMԔ?"6@ NNN?N6 p  [The quark phase life-time increases with the initial quark chemical potencial going higher.\ 2\bD H t 0޽h ? 3f80___PPT10.iӛ  0 L0 !4`f(  48 /V 4Me > 4 BA ? ?C"?/Tm 8 4 <A ??C"?mV 8 @ /  4"P > 4 BA ? ?C"?@ m 8 4 <A ??C"?@ /m   4 < ?y` ICompton-like scattering:   4 B8 '0  wDilepton production processes :" 0Z bG 4 N  MMMԔ?"6@ NNN?N't  ;Bremsstrahlung of a quark and annihilation with scattering:< 2<`.` 4 c $A ??8 d   4 S ~A ? MMMԔ?"6@ NNN?No   C 4  `  MMMԔ?"6@ NNN?N+\  uQuark-antiquark annihilation:` y 4 3 r  MMMԔ?"6@ NNN?Ng &  -(i denotes a quark, an antiquark or a gluon)... 2d+d  4 NX  MMMԔ?"6@ NNN?NR 9  C Gluon fusion: 2`1 4 N  MMMԔ?"6@ NNN?NE , uQuark-antiquark annihilation: 2`  4 S ~A ? MMMԔ?"6@ NNN?NZ f   4 S ~A ? MMMԔ?"6@ NNN?NN 7Y AY !4 c   Ԕ?"6@ NNN?Nk gDilepton productionf! H 4 0޽h ? 3f3f___PPT10i.0OO+D='  = @B +  0 L0 :2 @(  @ @ TMMMԔ?"6@ NNN?N  @ BA ? ?j < @ <A ??)   @ <A ?? x d^ @ B  q  : the step function, s, t and u : the Mandelstam variables. 2A&;@l  @ c P  MMMԔ?"6@ NNN?NZ\ A z*Dileptons from annihilation -reaction (0):++` " @ c l  MMMԔ?"6@ NNN?N9M Dileptons from annihilation  reaction (1) and Compton-like processes (2)and (3) :RR` I @ S ~A ? MMMԔ?"6@ NNN?N qJ7   @ S ~A ? MMMԔ?"6@ NNN?N  7   @ C x  MMMԔ?"6@ NNN?N # Inserting the Jttner distribution functions of partons and the squared matrix elements for reaction processes into the equation, integrate over`,Zx @ <A %??S %& @ 3 rD>  MMMԔ?"6@ NNN?N Fto get the rate. 2`H @ 0޽h ? 3f80___PPT10.0B|  0 L0 Phd(  h h 3 r>  MMMԔ?"6@ NNN?NZ7 ]Landau-Pomeranchuk-Migdal resummation for dilepton production from bremsstrahlung of a quark:^ 2^bP  S h 3 r >  MMMԔ?"6@ NNN?NM,4 s=(Multiple scattering plays an important role in the process.)> 2>`F h N> MMMԔ?"6@ NNN?N , ,P. Aurenche, G. D. Moore, JHEP12 (2002) 006. - 2-f" h c $A $??]W A $ h 3 r>  MMMԔ?"6@ NNN?NP   hThey developed a simple method to compute the imaginary part of the retarded current-current correlator.i 2ib] g  h C x>  MMMԔ?"6@ NNN?N B  MWe further integrate these rates over the space-time volume of the reaction.:NN`  h c $A &?? @ x &dg8 ' j  h) ' @  h 3 r>  MMMԔ?"6@ NNN?N' j  X"We consider central collisions of # 2#`l  h S ~A (? MMMԔ?"6@ NNN?N] ~ d x (dc h 3 r #>  MMMԔ?"6@ NNN?NP j  {#, so the final dilepton spectra is:$ 2$`  h S ~A )? MMMԔ?"6@ NNN?N 4 G )AB h ZDԔMMMԔ?"0@NNN?N% % H h 0޽h ? 3f80___PPT10.MP<  0 L0 &`l(  ll l c 6A'Graph569"` k   l C x+>  MMMԔ?"6@ NNN?N  OThe calculated dilepton spectra from various processes. Curves 0-7 represent :PP`9j  l c A 6? MMMԔ?"6@ NNN?N^ ) x 6dAj  l c A 7? MMMԔ?"6@ NNN?N jf x 7dAj l c A" 8? MMMԔ?"6@ NNN?Nz  V x 8dAj l c A# 9? MMMԔ?"6@ NNN?N  x 9dAd l S ~A$ :? MMMԔ?"6@ NNN?N gx :dA 8 @m lN /V l Cm28 l <A ;? ?C"?/Tm ;2 l 6A <??C"?mV <N @ / l C` % 8 l <A =? ?C"?@ m =2 l 6A >??C"?@ /m > l S ~A* C? MMMԔ?"6@ NNN?N@R F  C l S ~A @? MMMԔ?"6@ NNN?Np V  @ l S ~A A? MMMԔ?"6@ NNN?Np   AA0 l 3 r;>  MMMԔ?"6@ NNN?NC  H(7) Total of 0-6 2d' l 3 r@A>  MMMԔ?"6@ NNN?N :  GInitial values: 2bH l 0޽h ? 3f80___PPT10.#0/  0 L0 #T (  Tf T C 0A(Graph-total"`|  T C xl~>  MMMԔ?"6@ NNN?N#  The calculated total dilepton yields for differentinitial quark chemical potential, curves 1- 4 represent the total spectra for:`, H 8 ] "T p  T <F> 0 M00g d  T <t> ! M00g d  T <h>  O0.001.ed T <> r O0.284.ed T <> 0 Oq2g d T <x> ! Oq2g d T <>  iGeV0ed T <> r iGeV0ed T <> ]p Mm0ed T <,> ]a Mm0ed T <> Bp K=.ed T <> Ba K=.ed 8 ]n  !T2p  T <P> } M00g d  T <>  n  M00g d T <> d O0.569.ed T <> U  O0.852.ed T <`> } Oq2g d T < >  n  Oq2g d T <> d iGeV0ed T <> U  iGeV0ed T <8> ]S Mm0ed T <> ]D  Mm0ed T <> BS K=.ed  T <8> BD  K=.ed #T 3 r>  MMMԔ?"6@ NNN?N 3  uWe can see from the figure that the dilepton production goes up with the increasing initial quark chemical potential.v 2vb$JH T 0޽h ? 3f80___PPT10.1of  0 L0 XN(  X7 X c >  Ԕ?"6@ NNN?Nwg  ESummary"(f! 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Background & Motivation ; PART a! Evolution of the system ; PART b! Dilepton production ; PART c! SummaryqqK* Background & Motivation 60!0 +  /  8  9  ,  -  6  7  1  2  V   0 L0 U M p p (  pd p c .A! evol"`T N p C x MMMԔ?"6@ NNN?N  h(The evolution of QGP for initial values $)'``F aj p M&/l p S ~A ,? MMMԔ?"6@ NNN?Na<bx ,dAl  p S ~A -? MMMԔ?"6@ NNN?N<tx -dAl  p S ~A" .? MMMԔ?"6@ NNN?Nmjx .dAl  p S ~A# /? MMMԔ?"6@ NNN?NgSx /dA  p C xL MMMԔ?"6@ NNN?NP    with initial quark chemical potential (a) the fugacity of quark(anti-quark) and gluon; (b) quark chemical potential and temperature.8,bu``"A B`  p c $A 0??8 d  0d p S ~A$ 1? 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Background & Motivation ; PART a! Evolution of the system ; PART b! Dilepton production ; PART c! 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Background & Motivation ; PART a! Evolution of the system ; PART b! Dilepton production ; PART c! SummaryqqK* Background & Motivation 60!0 +  /  8  9  ,  -  6  7  1  2  V   0 L0 U M p p (  pd p c .A! evol"`T N p C x MMMԔ?"6@ NNN?N  h(The evolution of QGP for initial values $)'``F aj p M&/l p S ~A ,? MMMԔ?"6@ NNN?Na<bx ,dAl  p S ~A -? MMMԔ?"6@ NNN?N<tx -dAl  p S ~A" .? MMMԔ?"6@ NNN?Nmjx .dAl  p S ~A# /? MMMԔ?"6@ NNN?NgSx /dA  p C xL MMMԔ?"6@ NNN?NP    with initial quark chemical potential (a) the fugacity of quark(anti-quark) and gluon; (b) quark chemical potential and temperature.8,bu``"A B`  p c $A 0??8 d  0d p S ~A$ 1? 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