W. A. Horowitz
The Ohio State University
January 19, 2010
With many thanks to Brian Cole, Miklos Gyulassy, Ulrich Heinz, and Yuri Kovchegov
4/16/2020 LBL Nuclear Theory Seminar 1

• Running a s
– b
-fcn
• SU(N c
= 3)
PDG
ALEPH, PLB284, (1992)
• N f
(E)
– N f
(RHIC) ≈ 2.5
Griffiths Particle Physics
2 4/16/2020 LBL Nuclear Theory Seminar

4/16/2020
Long Range Plan, 2008
LBL Nuclear Theory Seminar 3

T Hirano, Colliding Nuclei from AMeV to ATeV
4/16/2020 LBL Nuclear Theory Seminar
STAR
4

Past, Present, and Future Questions
• Bulk properties
– Deconfinement
– Thermalization, density
– EOS, h
/s
– QGP DOF
• Weakly vs. Strongly coupled plasma
– G
= U/T: <<1 or >>1?
• Weakly vs. Strongly coupled theories
– a s
~ 0.3 << 1?
l = √(g
YM
2 N c
) ~ 3.5 >> 1?
• New computational techniques
– AdS?
4/16/2020 LBL Nuclear Theory Seminar 5

Methods of QCD Calculation I: Lattice
Long Range Plan, 2008
Kaczmarek and Zantow, PRD71 (2005) Davies et al. (HPQCD), PRL92 (2004)
4/16/2020 LBL Nuclear Theory Seminar
• All momenta
• Euclidean correlators
6

Methods of QCD Calculation II: pQCD
Jäger et al., PRD67 (2003)
4/16/2020 d’Enterria, 0902.2011
• Any quantity
• Small coupling (large momenta only)
LBL Nuclear Theory Seminar 7

Methods of QCD Calculation III: AdS(?)
Maldacena conjecture: SYM in d  IIB in d +1
Gubser, QM09
• All quantities
• N c
→ ∞
• SYM, not QCD: b
= 0
4/16/2020
– Probably not good approx. for p+p; maybe A+A?
LBL Nuclear Theory Seminar 8

• Tomography in medicine
T
One can learn a lot from a single probe …
and even more with multiple probes
4/16/2020
PET Scan
SPECT-CT Scan uses internal g photons and external X-rays http://www.fas.org/irp/imint/docs/rst/Intro/P art2_26d.html
LBL Nuclear Theory Seminar 9

• Requires wellcontrolled theory of:
– production of rare, highp
T probes
• g, u, d, s, c, b
– in-medium E-loss
– hadronization
• Requires precision measurements of decay fragments f
Invert attenuation pattern => measure medium properties p
T
, g
, e -
4/16/2020 LBL Nuclear Theory Seminar 10

• Learn about E-loss mechanism
– Most direct probe of DOF
4/16/2020 LBL Nuclear Theory Seminar 11

• p+p • Au+Au
YS Lai, RHIC & AGS Users’ Meeting, 2009
4/16/2020
PHENIX
LBL Nuclear Theory Seminar 12

T
Naively: if medium has no effect, then R
AA
= 1
Common variables used are transverse momentum, p
T
, and angle with respect to the reaction plane, f
Fourier expand R
AA
: f p
T
, g
, e -
4/16/2020 LBL Nuclear Theory Seminar 13

• Bremsstrahlung Radiation
– Weakly-coupled plasma
• Medium organizes into Debye-screened centers
– T ~ 250 MeV, g ~ 2
• m
~ gT ~ 0.5 GeV
• l mfp
~ 1/g 2 T ~ 1 fm
• R
Au
~ 6 fm
– 1/ m
<< l mfp
<< L
• mult. coh. em.
– LPM dp
T
/dt ~ -LT 3 log(p
T
/M q
)
– Bethe-Heitler dp
T
/dt ~ -(T 3 /M q
2 ) p
T
14 4/16/2020 LBL Nuclear Theory Seminar

(circa 2005)
Y. Akiba for the PHENIX collaboration , hep-ex/0510008
– Consistency:
R
AA
( h
)~R
AA
( p
)
– Null Control:
R
AA
( g
)~1
– GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dN g
/dy~dN p
/dy
4/16/2020 LBL Nuclear Theory Seminar 15

• v
2
• e e -
4/16/2020
WAH, Acta Phys.Hung.A27 (2006)
Djordjevic, Gyulassy, Vogt, and Wicks, PLB632 (2006)
LBL Nuclear Theory Seminar 16

• Appreciable!
• Finite time effects small
4/16/2020
Mustafa, PRC72 (2005)
LBL Nuclear Theory Seminar
Adil, Gyulassy, WAH, Wicks, PRC75 (2007)
17

Quantitative Disagreement Remains
– v
2 too small – NPE supp. too large p
0 v
2
WHDG
NPE v
2
C. Vale, QM09 Plenary (analysis by R. Wei)
Wicks, WAH, Gyulassy, Djordjevic, NPA784 (2007)
Pert. at LHC energies?
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
4/16/2020 LBL Nuclear Theory Seminar 18

Strongly Coupled Qualitative Successes
AdS/CFT
Blaizot et al., JHEP0706
T. Hirano and M. Gyulassy, Nucl. Phys. A69 :71-94 (2006)
PHENIX, PRL98, 172301 (2007)
4/16/2020 LBL Nuclear Theory Seminar 19
Betz, Gyulassy, Noronha, Torrieri, PLB675 (2009)

• Model heavy quark jet energy loss by embedding string in AdS space dp
T
/dt = m p
T m
= pl 1/2
T 2 /2M q
– Similar to Bethe-Heitler dp
T
/dt ~ -(T 3 /M q
2 ) p
T
J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 (2007)
– Very different from LPM dp
T
/dt ~ -LT 3 log(p
T
/M q
)
4/16/2020 LBL Nuclear Theory Seminar 20

• String drag: qualitative agreement
4/16/2020
WAH, PhD Thesis
LBL Nuclear Theory Seminar 21

PHENIX 0-5% p
0
4/16/2020 dp q /dt ~ E 1/3 dp g /dt ~ (2E) 1/3
LBL Nuclear Theory Seminar
WAH, in preparation
22

STAR
AdS/CFT pQCD
WAH, in preparation
– Distinguishing measurement?
4/16/2020 LBL Nuclear Theory Seminar
STAR
AdS/CFT pQCD
23

• Plethora of Predictions:
WAH, M. Gyulassy, PLB666 (2008)
– Taking the ratio cancels most normalization differences
– pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates)
WAH, M. Gyulassy, PLB666 (2008)
– AdS/CFT ratio is flat and many times smaller than pQCD at only moderate p
T
4/16/2020 LBL Nuclear Theory Seminar 24

– Speed limit estimate for applicability of AdS drag
• g
< g crit
= (1 + 2M q
/ l
1/2 T) 2
~ 4M q
2 /( l
T 2 )
– Limited by M charm
~ 1.2 GeV
• Similar to BH LPM
– g crit
~ M q
/( l
T)
– No Single T for QGP
• smallest g crit
• largest g crit for largest T
T = T( t
0
, x=y=0): “(” for smallest T
T = T c
: “]”
4/16/2020 LBL Nuclear Theory Seminar
D7 Probe Brane
Worldsheet boundary
Spacelike if g
> g crit x
5 Trailing
String
“Brachistochrone”
D3 Black Brane
Q
25
“z”

LHC R c
AA
(p
T
)/R b
AA
(p
T
) Prediction
(with speed limits)
WAH, M. Gyulassy, PLB666 (2008)
– T( t
0
): “(”, corrections likely small for smaller momenta
– T c
: “]”, corrections likely large for higher momenta
4/16/2020 LBL Nuclear Theory Seminar 26

cb
pQCD pQCD
AdS/CFT AdS/CFT
4/16/2020
WAH, M. Gyulassy, JPhysG35 (2008)
• Wider distribution of AdS/CFT curves due to large n : increased sensitivity to input parameters
• Advantage of RHIC: lower T => higher AdS speed limits
LBL Nuclear Theory Seminar 27

• How universal are th. HQ drag results?
– Examine different theories
– Investigate alternate geometries
• Other AdS geometries
– Bjorken expanding hydro
– Shock metric
• Warm-up to Bj. hydro
• Can represent both hot and cold nuclear matter
4/16/2020 LBL Nuclear Theory Seminar 28

Constant T Thermal Black Brane
Albacete, Kovchegov, Taliotis,
JHEP 0807 , 074 (2008)
4/16/2020
DIS
Shock Geometries
Nucleus as Shock
Embedded String in Shock
P Chesler,
Quark Matter 2009
Before z x v shock
Q
After z
LBL Nuclear Theory Seminar
Q v shock x
WAH and Kovchegov, PLB680 (2009)
29

z = 0
• Three t-ind. solutions (static gauge):
X m
= (t, x(z), 0,0, z)
– x(z) = x
0
, x
0
± m ½ z 3 /3
Q v shock x
0
- m ½ z 3 /3 x
0
+ m ½ z 3 /3 z =
 x
0 x
• Constant solution unstable
• Time-reversed negative x solution unphysical
• Sim. to x ~ z 3 /3, z << 1, for const. T BH geom.
4/16/2020 LBL Nuclear Theory Seminar 30

• For L typical momentum scale of the medium
–Recall for BH:
–Shock gives exactly the same drag as BH for
L
= p
T
• We’ve generalized the BH solution to both cold and hot nuclear matter E-loss
4/16/2020 LBL Nuclear Theory Seminar 31

• Local speed of light (in HQ rest frame)
– Demand reality of point-particle action
• Solve for v = 0 for finite mass HQ
– z = z
M
= l ½
/2 p
M q
– Same speed limit as for BH metric when L
= p
T
4/16/2020 LBL Nuclear Theory Seminar 32

Back to pQCD: Quant. and Falsifiable
– Requires rigorous pQCD estimates, limits:
– Different pQCD formalisms, different results
4/16/2020
Bass et al., Phys.Rev.C79:
024901,2009 LBL Nuclear Theory Seminar 33

• Want to rigorously:
– falsify theories
– quantify medium
• Therefore need:
– Precise observables
– Precise theory
• Distinguish between systematic uncertainties:
– between formalisms
• Due to diff. physics assumptions
– within formalisms
• Due to simplifying approximations
• Focus specifically on opacity expansion
– GLV; ASW-SH
4/16/2020 LBL Nuclear Theory Seminar 34

– R
AA
• E f
~ ∫(1-ϵ) n P( ϵ) dϵ
= (1ϵ)E i
– Opacity expansions finds single inclusive gluon emission spectrum
• dN g
/dxdk
T dq
T
4/16/2020 LBL Nuclear Theory Seminar 35

Gyulassy, Levai, and Vitev NPB594 (2001)
• Find P(ϵ) by convolving dN g
/dx
– Approximates probabilistic multiple gluon emission, Sudakov
• assume independent emissions
– NB: ϵ is a momentum fraction
4/16/2020 LBL Nuclear Theory Seminar 36

• Want to find dN g
/dx
– Make approximations to simplify derivation
• Small angle emission: k
T
<< xE
– Note: ALL current formalisms use collinear approximation
– Derived dN g
/dxdk
T violates collinear approx
4/16/2020
• Both IR and UV safe
• Enforce small angle emission through UV cutoff in k
T
LBL Nuclear Theory Seminar 37

• Derived dN g
/dxdk
T maximally violates collinear approximation
– dN g
/dx depends sensitively on k
T cutoff
• Despite UV safety
– For effect on extracted prop., must understand x
• Discovered through
TECHQM Brick Problem
WAH and B Cole, arXiv:0910.1823
4/16/2020 LBL Nuclear Theory Seminar 38

4/16/2020
P
• ASW-SH: xE
– Energy fraction
• GLV: x+
– Plus momentum fraction
NB: gluon always on-shell
LBL Nuclear Theory Seminar 39

– Same in the limit k
T
/xE → 0!
• UV cutoff given by restricting maximum angle of emission
P q
– Previous comparisons with data took q max
= p
/2
– Vary q max to estimate systematic theoretical uncertainty
4/16/2020 LBL Nuclear Theory Seminar 40

• ϵ is fraction of longitudinal momentum
– Need dN g
/dx
E to find P( ϵ)
– A Jacobian is required for x = x
+ interpretation
4/16/2020 LBL Nuclear Theory Seminar 41

• UV
WAH and B Cole, arXiv:0910.1823
• What about IR?
4/16/2020 LBL Nuclear Theory Seminar 42

• Massless gluons:
– Large IR cutoff sensitivity
• Gluons with thermal mass
BDMS, JHEP 0109 (2001)
~
Larger x better respects k
T
<< xE
4/16/2020 LBL Nuclear Theory Seminar
WAH and B Cole, arXiv:0910.1823
43

• Quantitatively compare to PHENIX data
WAH and B Cole, arXiv:0910.1823
– Assumed infinite Elastic precision
4/16/2020 LBL Nuclear Theory Seminar 44

• Dependence on parton energy
• Uncertainty on qhat
WAH and B Cole, arXiv:0910.1823
4/16/2020
– Assume all formalisms equally affected
LBL Nuclear Theory Seminar 45

– pQCD and AdS/CFT enjoy qualitative successes, concerns in high-p
T
HIC
• RHIC suppression of lights and heavies
• Future LHC measurements
– Quantitative comparisons with rigorous theoretical uncertainty estimates needed for falsification/verification
• Theoretical work needed in both in pQCD and AdS
– In AdS, control of jet IC, large p
T required
– In pQCD, wide angle radiation very important, not under theoretical control
4/16/2020 LBL Nuclear Theory Seminar 46