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