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Jet correlations at RHIC via AdS/CFT. (and entropy production). Amos Yarom, Munich. together with: S. Gubser and S. Pufu. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A. The quark gluon plasma at RHIC. Measuring jets. . - PowerPoint PPT Presentation
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Jet correlations at RHIC via AdS/CFT
Amos Yarom, Munich
together with: S. Gubser and S. Pufu
(and entropy production)
The quark gluon plasma at RHIC
Measuring jets
Measuring jets
Measuring di-jets
Measuring di-jets(STAR, 0701069)
Measuring di-jets(STAR, 0701069)
=
Measuring di-jets(STAR, 0701069)
»
Creation of sound waves(Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)
Creation of sound waves(Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)
Mach cones and di-jets(Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)
»
N=4 SYM plasma via AdS/CFT
AdS/CFT
J. Maldacena
AdS5 CFT
Empty AdS5Vacuum
L4/’2 gYM2 N
L3/2 G5 N2
J. Maldacena hep-th/9711200
T>0
N=4 SYM plasma via AdS/CFT
AdS5 CFT
AdS5 BH Thermal state
L4/’2 gYM2 N
L3/2 G5N2
E. Witten hep-th/9802150
Horizon radius Temperature
Empty AdS5Vacuum
J. Maldacena hep-th/9711200
AdS Black holes
ds2 = L2=z2 ¡¡ g(z)dt2 +dx2
i +dz2=g(z)¢
g(z) = 1¡µ
zz0
¶4
z0
z
0x1xi, t
AdS5 CFT
AdS5 BH Thermal state
L4/’2 gYM2 N
L3/2 G5N2
E. Witten hep-th/9802150
Horizon radius Temperature
z01/ T
AdS/CFT
J. Maldacena
Static quarks
AdS5 CFT
J. Maldacena hep-th/9803002
Heavy quark
Endpoints of an open
string
z0
z
0
S =1
2¼®0
Z(G@X @X )1=2d2¾
±S±X
= 0 X jb = (t;0;0;0;0)
?
(Maldacena, 1996)
?
»(z) =vz0
4
µln
1¡ z=z0
1+z=z0+2arctan
zz0
¶
Moving quarks
AdS5 CFT
J. Maldacena hep-th/9803002
Massive parton
Endpoints of an open
string
z0
z
0
S =1
2¼®0
Z(G@X @X )1=2d2¾
±S±X
= 0 X jb = (t;vt;0;0;0)
?
X = (t;vt +»(z);0;0;z)
(Holzhey, Karch, Kovtun, Kozcaz, Yaffe, 2006, Gubser 2006, Teaney Cassalderrey-Solana, 2006)
The energy momentum tensor
AdS5 CFT
» hTrF 2i©jb
hTmn iGmn jb
z0
z
0
Gubser, Klebanov, Polyakov hep-th/9802109
Witten hep-th/9802150De Haro, Solodukhin, Skenderis,
hep-th/0002230
The energy momentum tensor
AdS5 CFT
» hTrF 2i©jbhTmn iGmn jb
h±Tmn i / Qmn
Gmn = G(0)mn + hmn
AdS black hole Metric fluctuationshmn = :::+Qmnz4 +:::
S = SN G +SE H
SN G =1
2¼®0
Z(G@X @X )1=2d2¾
SE H =1
16¼G5
Z µR +
12L2
¶G1=2d5x
±S±X
= 0±S±G
= 0z0
z
0
Gmnz,k)
Gubser, Klebanov, Polyakov hep-th/9802109
Witten hep-th/9802150De Haro, Solodukhin, Skenderis,
hep-th/0002230
The energy momentum tensor
z0
z
0
S = SN G +SE H
SN G =1
2¼®0
Z(G@X @X )1=2d2¾
±S±X
= 0±S±G
= 0D¹ º ½¾h½¾= J ¹ º
G¹ º = G(0)¹ º +h¹ º +O(h2)
SE H =1
16¼G5
Z µR +
12L2
¶G1=2d5x
X = (t;vt +»(z);0;0;z)
»(z) =vz0
4
µln
1¡ z=z0
1+z=z0+2arctan
zz0
¶
(Friess, Gubser, Michalogiorgakis, Pufu, 2006)
Energy density for v=3/4
Over energy
Under energy
(Gubser, Pufu, AY, 2007Chesler, Yaffe, 2007)
v=0.75 v=0.58
v=0.25
Small momentum approximations
E = ¡3iK 1v(1+v2)
2¼(K 2? +K 2
1(1¡ 3v2))+O(K 0)
D¹ º ½¾h½¾= J ¹ º
h½¾=X
n
K nh(n)½¾
(Friess, Gubser, Michalogiorgakis, Pufu, 2006Gubser, Pufu, AY, 2007)
The hydrodynamic approximation
Large distances – linear hydrodynamic
picture valid
Intermediate distances – nonlinear
hydrodynamics
Short distances – Strong dissipative
effects
(Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)
Thydroi j =
13²±i j ¡
32¡ sik(i Sj )
= <T00>s = 4 /3 Sj = -<T0j>k(iSj) =1/2(ki Sj+kj Si)-1/3 ij kl Sl
ikmThydromn = J hydro
n
ikmTmn = J n
Energy density for v=3/4
0
Short distance asymptoticsc2s = 5
15
(Gubser, Pufu, 2007, AY, 2007)
Wakes
Mach cones, wakes and di-jets(Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)
Mach cones, wakes and di-jets(Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)
(STAR, 0701069)
Mach cones, wakes and di-jets(Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)
(STAR, 0701069)
Jhydro=(e0, g0, 0, 0)
Jhydro=(0, k1, k2, k3)g1
The Poynting vector
z0
z
0
D¹ º ½¾h½¾= J ¹ º
The Poynting vector
V=0.25
S1 S?
V=0.58
V=0.75
(Gubser, Pufu, AY, 2007Chesler, Yaffe, 2007)
Small momentum asymptotics
Sound Waves
S1 = ¡ iK 1(1+v2)
2¼(K 2 ¡ 3K 21v2)
+ i1
2¼K 1+O(K 0)
(Friess, Gubser, Michalogiorgakis, Pufu, 2006 Gubser, Pufu, AY, 2007)
Wake
Comparison with the phenomenological model
(Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)
V=0.75
Energy analysis
S2 = ¡ iK 2(1+ v2) +O(K 2)
2¼(K 2 ¡ 3K 21v2 ¡ iK 2K 1v)
+O(K )
2¼(K 2 ¡ 4iK 1v)
S3 = ¡ iK 3(1+ v2) +O(K 2)
2¼(K 2 ¡ 3K 21v2 ¡ iK 2K 1v)
+O(K )
2¼(K 2 ¡ 4iK 1v)
S1 = ¡ iK 1(1+ v2) +O(K 2)
2¼(K 2 ¡ 3K 21v2 ¡ iK 2K 1v)
+4v+O(K )
2¼(K 2 ¡ 4iK 1v)
² = ¡3iK 1v(1+v2) +O(K 2)
2¼(K 2 ¡ 3K 21v2 +iK 2K 1v)
_² +@iSi = ¡@E@t
Zd3x
limK ! 0
(¡ iK 1v² + iK iSi ) = F 0drag
= F 0drag
(Friess, Gubser, Michalogiorgakis, Pufu, 2006 Gubser, Pufu, AY, 2007)
_² +@iSi = ¡@E@t
Z
d3x
limK ! 0
(¡ iK 1v² + iK iSi ) = F 0drag
= F 0drag
Energy analysis(Friess, Gubser, Michalogiorgakis, Pufu, 2006 Gubser, Pufu, AY, 2007)
z0
z
0 F
?
Just been calculated
limK ! 0
(¡ iK 1v² + iK iSi ) = F 0draglim
K ! 0(¡ iK 1v² + iK iSi )
¯¯wake+ lim
K ! 0(¡ iK 1v² + iK iSi )
¯¯sound
= F 0jwake + F 0jsound
F 0jwake : F 0jsound = ¡ 1 : 1+v2
Energy analysis
_² +@iSi = ¡@E@t
Z
d3x = F 0drag±( ~X ¡ ~vT)
F 0jwake : F 0jsound = ¡ 1 : 1+v2
Energy analysis
=
Energy analysis
=
25-30
(STAR, 0701069)
Other theories(Gubser, AY,2007)
SN G =1
2¼®0
Z(g@X @X )1=2q(ÁI )d2¾
SE H =1
16¼G5
Zg
12 Rd5x
SÁ =1
16¼G5
Zg
12
¡ I J @ÁI @ÁJ +V(ÁI )d5x
¢
z0
z
0
ds2 = ®(z)2 ¡¡ h(z)dt2 +d~x2 +dz2=h(z)
¢
®! L=z
h ! 1
h ! 0
Other theories(Gubser, AY, 2007)
SN G =1
2¼®0
Z(g@X @X )1=2q(ÁI )d2¾
SE H =1
16¼G5
Zg
12 Rd5x
SÁ =1
16¼G5
Zg
12
¡ I J @ÁI @ÁJ +V(ÁI )d5x
¢
z0
ds2 = ®(z)2 ¡¡ h(z)dt2 +d~x2 +dz2=h(z)
¢
0
zD¹ º ½¾h½¾+ D¹ ºI ±ÁI = J ¹ º
F 0jwake : F 0jdrag = ¡ 1: v2
(Yaffe, Chesler, 2007)
Mach cones, wakes and di-jets(STAR, nucl-ex/0701069)(STAR, 0510055)
0.15 GeV<p?<4 GeV
(PHENIX, 0611019)
Mesons(Gubser, Pufu, AY,2007)
z0
z
0
Mesons(Gubser, Pufu, AY,2007)
z0
z
0l v→v→l
Mesons(Gubser, Pufu, AY,2007)
z0
z
0
D¹ º ½¾h½¾= J ¹ º
Mesons(Gubser, Pufu, AY,2007)
z0
z
0
z0
0
h±T? mn i =¦ ? (v; )̀
k2 ¡ 3k21v2
³¿̀(? )mn +v¾? (v; )̀¿(¾)
mn
´+O(k) ;
h±Tk mn i =¦ k(v; )̀
k2 ¡ 3k21v2
³¿̀(k)mn +2v¾k(v; )̀¿(¾)
mn
´+O(k)
¿ » k2i
Mesons (?)(Gubser, Pufu, AY,2007)
M > T
u d
s c
b t
??
General analysis(Gubser, AY,2008)
z0
z
0 J
Dh=J
1) J » O(z-1)
2) rJ=03) “Causal”
Dh=J
10
General analysis(Gubser, AY,2008)
z0
z
0
Dh=J
Thydroi j =
13²±i j ¡
12¼T
ik(iSj )
ikmhTmn i = J (3)n5
hTmm i = J (2)
55J ¹ º = :::+ J (a)
¹ º za +:::
hTmn i = Thydromn + Fmn +Amn
F i j =µZ z0
z
J (i j )
³3 d³¶ (0)
+O(kJ (i j ))Fine print
Fine print
General analysis(Gubser, AY,2008)
z0
z
0
Dh=J
ikmhTmn i = J (3)n5
hTmm i = J (2)
55
hTmn i = Thydromn + Fmn +Amn
ikmThydromn = J (3)
n5 ¡ iknFmn
´ J hydron
General analysis(Gubser, AY,2008)
z0
z
0
Dh=J
Z z0
z
J 0i +O(kJ 0i )³3h(³)
d³ 6= 1Fine print
J (3)n5 = O(kJ i j );
Absence of a wake:
Entropy production
Entropy production
S ¼ 7.5 Ncharged
(PHOBOS, 2003)
Head on collisions in AdS
= ² =3¼3
16L3
G5T4
L2 =
Rx2
? ²d3xR
²d3x
= 35000µ
E200GeV
¶2=3
¼µ
L3
G5
¶1=3
(2ET L)2=3S ¸
(Gubser, Pufu, AY, to appear)
(related work by Romatschke and Grumiller, 2008)
Penrose, unpublishedEardley and Giddings, 2002
A head-on collision
S ¸ 35000µ
E200GeV
¶2=3
(PHOBOS, 2003)
LHC
= 35000µ
E200GeV
¶2=3
S ¸
£ 1.6
Head on collisions in AdS
S & (ET L)2=3S & (ET L)1=2
?
Summary(STAR, 0701069)Data Pheno. model
=
N=4 theory
Summary(STAR, 0701069)Data
=
ALICE
Thank you
Summary(STAR, 0701069)Data Pheno. model
=
N=4 theory ALICE
Thank you