# Presentation: 023438

## Falsifying AdS/CFT Drag or pQCD Heavy Quark Energy Loss with A+A at RHIC and LHC

- William Horowitz
- Columbia University
- Frankfurt Institute for Advanced Studies (FIAS)
- November 2, 2007

- With many thanks to Miklos Gyulassy,
- Simon Wicks, and Ivan Vitev

## Shameless Web Self Promotion

- Scary!

- Hello Online Viewers!

## pQCD Success at RHIC:

- Consistency: RAA()~RAA()

- Null Control: RAA()~1

- GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dN/dy

- (circa 2005)

## wQGP not ruled out, but what if we try strong coupling?

- Trouble for wQGP Picture

## Strong Coupling Calculation

- The supergravity double conjecture:
-                 QCD  SYM  IIB
_***IF***_ super Yang-Mills (SYM) is not too different from QCD, &
_***IF***_ Maldacena conjecture is true
- Then a tool exists to calculate strongly-coupled QCD in SUGRA

##  sstrong=(3/4) sweak, similar to Lattice

-  sstrong=(3/4) sweak, similar to Lattice

-  /sAdS/CFT ~ 1/4 << 1 ~ /spQCD

-  *e*- RAA ~ ,  RAA; *e*- RAA(**)

- T. Hirano and M. Gyulassy, Nucl. Phys. **A69**:71-94 (2006)

- Qualitative AdS/CFT Successes:

## Quantitative AdS/CFT with Jets

- Langevin model
- Collisional energy loss for heavy quarks
- Restricted to low pT
- pQCD vs. AdS/CFT computation of *D*, the diffusion coefficient
- ASW model
- Radiative energy loss model for all parton species
- pQCD vs. AdS/CFT computation of
- Debate over its predicted magnitude
- ST drag calculation
- Drag coefficient for a massive quark moving through a strongly coupled SYM plasma at uniform T
- not yet used to calculate observables: let’s do it!

## Energy Loss Comparison

- ST Drag
- dpT/dt = -(T2/2Mq)pT

- Compare to Bethe-Heitler
- dpT/dt ~ -(T3/Mq2) pT
- Compare to LPM
- dpT/dt ~ -LT3 log(pT/Mq)

## Use future detectors’ identification of c and b to distinguish between pQCD, AdS/CFT
RAA ~ (1-(pT))n(pT), where pf = (1-)pi (i.e.  = 1-pf/pi)
Asymptotic pQCD momentum loss:

String theory drag momentum loss:

Independent of pT and strongly dependent on Mq!
T2 dependence in exponent makes for a very sensitive probe
Expect: pQCD      0 vs. AdS indep of pT!!
dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST

- RAA ~ (1-(pT))n(pT), where pf = (1-)pi (i.e.  = 1-pf/pi)
- Asymptotic pQCD momentum loss:
- String theory drag momentum loss:
- Independent of pT and strongly dependent on Mq!
- T2 dependence in exponent makes for a *very* sensitive probe
- Expect: pQCD      0 vs. AdS _***indep***_ of pT!!
- dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST

- Looking for a Robust, Detectable Signal

- ST  1 - Exp(- L),         = T2/2Mq

- S. Gubser, Phys.Rev.**D74**:126005 (2006); C. Herzog *et al.* JHEP 0607:013,2006

## Model Inputs for LHC Predictions

- AdS/CFT Drag: nontrivial mapping of QCD to SYM
-  “Obvious”: s = SYM = const., TSYM = TQCD
- D/2T = 3 inspired: s = .05
- pQCD/Hydro inspired: s = .3   (D/2T ~ 1)
-  “Alternative”:  = 5.5, TSYM = TQCD/31/4
-  Start loss at thermalization time 0; end loss at Tc
- WHDG convolved radiative and elastic energy loss
-  s = .3
- WHDG radiative energy loss (similar to ASW)
-      = 40, 100
- Use realistic, diffuse medium with Bjorken expansion
- PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900)

## LHC c, b RAA pT Dependence

- Large suppression leads to flattening
- Use of realistic geometry and Bjorken expansion allows saturation below .2

- Significant rise in RAA(pT) for pQCD Rad+El

- Naïve expectations born out in full numerical calculation:
-                          dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST

- LHC *c*, *b* RAA pT Dependence

- LHC Prediction Zoo: What a Mess!
- Let’s go through step by step

- WH, M. Gyulassy, nucl-th/0706.2336

## An Enhanced Signal

- But what about the interplay between mass and momentum?
- Take ratio of *c* to *b* RAA(pT)
- pQCD: Mass effects die out with increasing pT
- Ratio starts below 1, asymptotically approaches 1.  Approach is slower for higher quenching
- ST: drag independent of pT, inversely proportional to mass.  Simple analytic approx. of uniform medium gives
- R*cb*pQCD(pT) ~ *n*bMc/*n*cMb ~ Mc/Mb ~ .27
- Ratio starts below 1; independent of pT

- R*cb*pQCD(pT)  1 - s *n*(pT) L2 log(Mb/Mc) (   /pT)

## LHC RcAA(pT)/RbAA(pT) Prediction

- LHC R*c*AA(pT)/R*b*AA(pT) Prediction

- Recall the Zoo:

- Taking the ratio cancels most normalization differences seen previously
- pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates)
- AdS/CFT ratio is flat and many times smaller than pQCD at only moderate pT

- WH, M. Gyulassy, nucl-th/0706.2336

- WH, M. Gyulassy, nucl-th/0706.2336

## Speed limit estimate for applicability of AdS/CFT 
	drag computation
  < crit = (1 + 2Mq/1/2 T)2
                 ~ 4Mq2/(T2)
Limited by Mcharm ~ 1.2 GeV
Similar to BH    LPM
 crit ~ Mq/(T)
Ambiguous T for QGP
 smallest crit for largest 
         T = T(0, x=y=0): “(”
 largest crit for smallest T = Tc: “]”

- 	drag computation
-   < crit = (1 + 2Mq/1/2 T)2
-                  ~ 4Mq2/(T2)
- Limited by Mcharm ~ 1.2 GeV
- Similar to BH    LPM
-  crit ~ Mq/(T)
- Ambiguous T for QGP
-  smallest crit for largest
-          T = T(0, x=y=0): “(”
-  largest crit for smallest T = Tc: “]”

- But There’s a Catch

- D3 Black Brane

- D7 Probe Brane

- Q

- Worldsheet boundary Spacelikeif  > crit

- Trailing
- String
- “Brachistochrone”

## LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits)

- LHC R*c*AA(pT)/R*b*AA(pT) Prediction(with speed limits)

- T(0): (O), corrections unlikely for smaller momenta
- Tc: (|), corrections likely for higher momenta

- WH, M. Gyulassy, nucl-th/0706.2336

## Measurement at RHIC

- Future detector upgrades will allow for identified ***c*** and ***b*** quark measurements

- NOT slowly varying
- No longer expect
-     pQCD dRAA/dpT > 0
- Large *n* requires corrections to naïve
-    Rcb ~ Mc/Mb

- RHIC production spectrum significantly harder than LHC

## RHIC c, b RAA pT Dependence

- Large increase in *n*(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well

- WH, M. Gyulassy, *to be published*

## RHIC Rcb Ratio

- Wider distribution of AdS/CFT curves due to large *n*: increased sensitivity to input parameters
- Advantage of RHIC: lower T => higher AdS speed limits

- WH, M. Gyulassy, *to be published*

- pQCD

- AdS/CFT

- pQCD

- AdS/CFT

## Conclusions

- Year 1 of LHC could show qualitative differences between energy loss mechanisms:
- dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
- Ratio of charm to bottom RAA, Rcb, will be an important observable
- Ratio is: flat in ST; approaches 1 from below in pQCD partonic
-     E-loss
- A measurement of this ratio NOT going to 1 will be a clear sign of new physics: pQCD predicts ~ 2-3 times increase in Rcb by 30 GeV—this can be observed in year 1 at LHC
- Measurement at RHIC will be possible
- AdS/CFT calculations applicable to higher momenta than at LHC due to lower medium temperature