hard photon production in a chemically equilibrating qgp at finite baryon density
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Hard Photon Production in a Chemically Equilibrating QGP at Finite Baryon Density. Zejun He Shanghai Institute of Applied Physics Research Chinese Academy of Sciences. I. INTRODUCTION. - PowerPoint PPT PresentationTRANSCRIPT
Hard Photon Production in a Hard Photon Production in a Chemically Equilibrating QGP Chemically Equilibrating QGP
at Finite Baryon Densityat Finite Baryon Density
Zejun HeZejun He
Shanghai Institute of Applied Physics Research Shanghai Institute of Applied Physics Research
Chinese Academy of SciencesChinese Academy of Sciences
I. INTRODUCTION
Lattice QCD results show: hadronic matter undergoes a phase transition into QGP. RHIC and LHC provide the opportunity to study the formation and evolution of the QGP.
QGP exists: for several fm, in about 100 fm3 . Indirect signatures have to be used for its detection, such as dileptons strangeness, and photon.
The QGP is regarded as a thermodynamic equilibrium system, dileptons are suppressed with increasing the initial quark chemical potential.
In recent years, some authors indicate:
The partons suffer many collisions in ( :0.3~0.7fm), the system may attain kinetic equilibrium, but away from the chemical equilibrium.
From this, K.Geiger, T.S.Biro et al have studied the effect of the chemical equilibration on the dilepton production in baryon-free QGP.
N.Hammon, K.Geiger indicated: the initial system has finite baryon
density.
C.Gale et al. have discussed the dileptons from QGP with finite baryon density.
Thus one may study the effect of the chemical equilibration on the dilepton production in a QGP with finite baryon density.
Distributions of partons in a chemically non-equilibrated system:
Jüttner distributions:
for quarks (anti-quarks)
for gluons
Boltzmann form error of the order of 40%
Factorized distribution for quarks (anti-quarks)
for gluons
T.S.Biro et al. pointed out: the calculated thermal screening mass in the
intermediate region of the the deviation from that calculated via the Jüttner
distributions quite large.
)( )(/)(
)()( qqTp
qqqqqef
)()( /g
Tpgg epf
Tpqqqq ef /)(
)()(
)1( /)()()( Tp
qqqqqef
)1()( / Tpgg epf
g
Nucl. Phys. A724 (2003) 477;
Phys. Rev. C68 (2003) 042902;
Phys. Rev. C69 (2004) 034906;
Chin. Phys. Lett. 20 (2003) 836;
Chin. Phys. Lett. 21 (2004) 795;
《物理学报》 . 52 (2003) 145.
In this work we mainly study the PHOTON PRODUCTION.
From Jüttner distribution, studied the evolution of the chemically equilibrating
QGP (CEQGP) system with finite baryon density, and calculate the dilepton
yields from processes: , , and Compton-like
, and discuss strangeness for and .
llqq ccgg ccqq
lqlqg ssgg ssqq
II. EVOLUTION OF THE SYSTEM
A.THERMODYNAMIC RELATIONS OF THE SYSTEM Expanding densities of quarks (antiquarks)
(1)
over quark chemical potential , to get the baryon density
(2)
Tpqq
qqqq
qqqe
dppgn
/)()(
2
)(2
)()( 2
q
)(2)([6
11
11
221
21
32, qqqqq
qqb QQTQQT
gn
)]11
(3
1)( 30
101
2
q
q
q
qqqqq QQT
and corresponding energy density including the contribution of s quarks
(3)
and : degeneracy factors of quarks (antiquarks) and gluons, the integral factors appearing in the above:
(4)
the integration related to the mass of the s quark .
2221
21
331
31
42
3)(3)([2
TQQTQQTg
qqqqqqq
QGP
)11
(3
1)()(Q 40
101
311
11
q
q
q
qqqqqqq QQTQ
]2 03
14
qg
q
g
g
BGT
g
g
)(qqg gg
mg
z
nnm e
dZZG
)(
mzq
nnm e
dZZQ
)(
mzq
nn
m e
dZZQ
)(
nmS
B. EVOLUTION EQUATION OF THE SYSTEM
Considering chemical equilibration processes:
, , and ,
taking ,
combining the master equations together with equation of energy-
momentum conservation and of baryon number conservation, one can
get a set of coupled relaxation equations describing evolutions of the T,
and for quarks and for gluons on the basis of the above
thermodynamic relations of the system with finite baryon density
(5)
ssgg ggggg ssqq qqgg qq
q q g
22
12
21
321
22 )
)3(2(1[2]
)3(21[
13)
1(
GR
GR
T
T
G
G qggg
g
]1
))3(2
(1[2]1
.2
22
122
gss
sssg
gqq
nn
nn
GR
nn
nn
(6)
(7)
(8)
)()(2)([ 02
01
211
11
222
21
3 QQTQQTQQT qqqqqq
11
201
211
21
22
3 2[]43[])1(
1
3
1QTQTQQTT qqqqqqq
]1
))3(2
(1[]1
22
22
12
00
201
gqq
qqqgg
q
q
qqqq nn
nn
GRn
nTQ
])(1[2 22
ss
ss
q
qsq
nn
nn
n
nR
22
12
00
2
222
122
22
13 )
)3(2(1[)3()(
GRn
nSmSTTSST sg
gs
essss
])(1[]1
. 22
02
ss
ss
q
qsqq
gss
ss
nn
nn
n
nRn
nn
nn
qqqqq
qqqq QTTQTQQT
11
2112
311
11
2 4[8])1(
1
3
2)(4[
]13
24[
1]
)1(2 31
122
q
qqqq
q
qq QT
11
2232
31
432
31
4 (6)(2[)( QTQQTGGTg
gqqqg
q
gg
(9)
is at , , , and
The gluon, quark and g-s production rates
, and are:
(10)
(11)
(12)
(13)
: the Debye screening mass, , and the function of and are from thermal masses of quarks and s quarks, respectively.
31
311
231
32
421 4128[]
)1(
1
4
2) GT
g
gTQQTTQ g
q
gqqq
qqq
qqqqqess
q
s QTQTSmSTTg
g
3
1431
122
323
12 2[
1]
1212[)]4(
2
])1
(6 32
431
411
22 STg
gGT
g
gQT s
q
sg
q
g
q
qqq
)(qqn)(qqn 1)( qq )
2(
20
q
gnn )
2(
20
g
gg
gnn MeVB 2504/1
0 20206.1)3(
TR /3 TR qg /2 TR sg /2
),,,(]29
)4([
3
32 242
20
2
13 qqg
DD
g
s TITg
MsM
aTR
)/65.1ln(24
22
1
211
2q
sgsfgqg N
G
GgTR
)/65.1ln(24
22
1
211
2s
sgsfgsg N
G
GgTR
)]1
()(22[3 21
1112
222
q
qqqfgD T
QNGTg
M
2DM 2
12
1 2 Gga g ),,( , qqg TI .,, qq T
,gq s
III. PHOTON PRODUCTION
Considering Compton scattering , and annihilation , we have rate:
taking
(14)
thus
(15)
qgq gqq
)](1)[()(16
1
)2( 2132211212
73EEEfEfEfdEdEMdtds
E
N
Pd
dRE ii
2/11
2121 ))(( cbEaEEEE
qTE
q
qeEf
/)(11 1
)(q
TE
q
qeEf
/)(22 2
)(
gTEEE
g
eEEEf
/)(213 21
)(
qTE
qTE
qsi
qq eedEdE
ut
tudtds
EsPd
dRE
/)(/)(21
222
3 21
11
36
5
2/11
2121/)( ))((]1[
21
cbEaEEEE
e gTEEE
g
qqg
For Compton scattering
(16)
should be a quantity, or
qgq
gTE
qTE
gqsi
eedEdE
us
sudtds
EPd
dRE
q
//)(21
22
53 21
11
36
5
2/11
2121/)( ))((]1[
21
cbEaEEEE
e qTEEE
q
q
).()(),)((2,)( 222 tEEstsstctEEstsbtsa
;22cc ktks .2 2 skc
)2/(22.02 2222qgqc Tgmk
2ck .//// 2 skc .02 ck
IV. CALCULATED RESULTS AND DISCUSSIONS
Fig 1: The calculated evolution paths of the system in the phase
diagram.
0.0 0.2 0.4 0.60.0
0.2
0.4
0.6
0.8
q [G
eV]
T [GeV]
Fig 2: The calculated equilibration rates.
0 2 4 6 8
0.0
0.2
0.4
0.6
0.8
g, q
[fm]
Fig 4: Photon spectra
1 2 3
10-8
10-7
10-6
10-5
10-4
dn/
d2 p T [G
eV -
2 ]
pT [GeV
-2]
1 2 3
10-7
10-6
10-5
10-4
10-3
dn/
d2 p T [G
eV -
2 ]
pT [GeV
-2]
1 2 3
10-8
10-7
10-6
10-5
10-4
10-3
dn/d
2 p T [G
eV -
2 ]
pT [GeV
-2]
1 2 3
10-7
10-6
10-5
10-4
10-3
dn/d
2 p T [G
eV -
2 ]
pT [GeV
-2]
gqq qgq
totalqqg
V. CONCLUSION
(1)The photon production is heightened with increasing the quark
chemical potential;
(2) The Photon production sensitively depends on the initial
conditions of the QGP system;
(3) The photon production of a thermodynamic equilibrium QGP
system is much faster than that of a chemically equilibrating
system. Thus from the production we can understand the
thermodynamic properties of the QGP.
The increase of the initial quark chemical potential will change the hydrodynamic behavior of the system to cause both the quark phase life-time to increase and the evolution path of the system in the phase diagram to become even longer. These effects are to heighten the photon yield of these three processes to compensate the photon suppression of the process .gqq
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