Zeroth Order Heavy Quark
Photon/Gluon Bremsstrahlung
William Horowitz
Columbia University
Frankfurt Institute for Advanced Studies (FIAS)
April 9, 2008
With many thanks to Miklos Gyulassy, Simon Wicks,
Ivan Vitev, Hendrik van Hees
4/9/08
WWND 2008
William Horowitz
1
A Talk in Two Parts
pQCD vs. AdS/CFT Drag
0th Order Production Radiation
4/9/08
WWND 2008
William Horowitz
2
Testing pQCD vs. AdS/CFT Drag
Energy Loss Mechanisms
(In Five Slides)
arXiv:0706.2336 (LHC predictions)
arXiv:0710.0703 (RHIC predictions)
4/9/08
WWND 2008
William Horowitz
3
(Proper) Subset of Mechanisms
• DGLV, AdS/CFT Drag, Diffusion…
LPM: dpT/dt ~ -LT3 log(pT/Mq)
dpT/dt ~ -(T2/Mq) pT
• Use heavy quark RAA to test these two
4/9/08
WWND 2008
William Horowitz
4
LHC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv:0706.2336
– Significant
NaïvePrediction
LHC
Unfortunately,
Large
suppression
expectations
rise large
inZoo:
Rleads
met
suppression
What
(pTin
to
) for
full
flattening
a Mess!
pQCD
numerical
pQCD
Rad+El
similar
calculation:
to AdS/CFT
AA
– Use
Let’sofgorealistic
through
dRAA
geometry
step
(pT)/dp
by step
> 0 Bjorken
=> pQCD;
expansion
dRAA(pTallows
)/dpT <
saturation
0 => ST below .2
Tand
4/9/08
WWND 2008
William Horowitz
5
LHC RcAA(pT)/RbAA(pT) Prediction
• Recall the Zoo:
WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]
– Taking the ratio cancels most normalization differences seen previously
– pQCD ratio asymptotically approaches 1, and more slowly so for increased
quenching (until quenching saturates)
WH, M.times
Gyulassy,
arXiv:0706.2336
– AdS/CFT ratio is flat and many
smaller
than[nucl-th]
pQCD at only moderate pT
4/9/08
WWND 2008
William Horowitz
6
RHIC Rcb Ratio
pQCD
pQCD
AdS/CFT
AdS/CFT
WH, M. Gyulassy, arXiv:0710.0703
• Wider distribution of AdS/CFT curves at RHIC due to large n
power law production: increased sensitivity to input parameters
• Advantage of RHIC: lower T => higher AdS speed limits
4/9/08
WWND 2008
William Horowitz
7
Conclusions
• AdS/CFT Drag observables calculated
• Generic differences (pQCD vs.
AdS/CFT Drag) seen in RAA
– Masked by extreme pQCD
• Enhancement from ratio of c to b RAA
– Discovery potential in Year 1 LHC Run
• Understanding regions of selfconsistency crucial
• RHIC measurement possible
4/9/08
WWND 2008
William Horowitz
8
Some Investigations of
th
0 Order Production Radiation
4/9/08
WWND 2008
William Horowitz
9
Motivation
• Previous work: test pQCD or AdS/CFT
energy loss
– Heavy quark RQAA and RcAA/RbAA
• Future goal: additional energy loss test
using photon bremsstrahlung
• Zeroth Order Calculation
– Recent p + p fragmentation g data
– Good warm-up and test problem
• Investigate running a, low-pT, etc.
– Reevaluate magnitude of Ter-Mikayelian
4/9/08
WWND 2008
William Horowitz
10
New Fragmentation g Data
A. Hanks, QM2008
4/9/08
WWND 2008
William Horowitz
11
Motivating Example: Running as
– Fixed as is
simplification to
speed up code
• Not a free parameter
– Running as will most
likely introduce a
large error
– Want to understand
systematics in 0th
Order
4/9/08
S. Wicks, WH, M. Djordjevic, M Gyulassy,
Nucl.Phys.A783:493-496,2007
WWND 2008
William Horowitz
12
Quark and Gluon/Photon Mass Effects
• Quark mass => Dead cone
– Ultrarelativistic “searchlight” rad. pattern
q ~ Mq/E
Y. Dokshitzer and D. Kharzeev,
Phys.Lett.B519:199-206,2001
• Gluon mass => Longitudinal modes,
QCD Ter-Mikayelian
M. Djordjevic and M. Gyulassy,
Phys.Rev.C68:034914,2003
– Reduction of production radiation
compared to vacuum
• Alters DGLAP kernel
4/9/08
WWND 2008
William Horowitz
13
Previous Calculation of Ter-Mikayelian
M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003
• Reduction of E-loss for charm quarks by ~ 30%
• E-loss from full HTL well approx. by fixed mg = m∞
• Small-x pQCD 0th Order result:
4/9/08
WWND 2008
William Horowitz
14
Compare Classical E&M to “pQCD”
– Classical E&M
• Recall Jackson:
• Soft photon limit =>
– Note charge conserved
– Usual pQCD approach
– Charge explicitly not conserved
=> Ward identity (
4/9/08
WWND 2008
) violated
William Horowitz
15
Classical/QFT Inconsistency
– For mQ = mg = 0 and in the small x, large E+
limit, both are equal:
– For mQ, mg ≠ 0 and the small x, large E+
limit, they differ:
4/9/08
WWND 2008
William Horowitz
16
Not a Classical Error
– Wrong classical calculation?
• Plugged in massive 4-vectors into massless formulae
• Rederive classical result using Proca Lagrangian
– After several pages of work…
• Identical to
4/9/08
WWND 2008
William Horowitz
17
Error from QFT Ward Violation
• Identical expressions are not a surprise
• QFT Calculation
– Photon momentum carried away crucial
for cancellation of photon mass
• Classical case neglects both; effects cancel
4/9/08
WWND 2008
William Horowitz
18
Resulting Expression
– To lowest order in 1/E+
– New:
• (1-x)2 prefactor: naturally kills hard gluons
• mg2 in numerator: fills in the dead cone!?!
– What are the sizes of these effects?
Call this LO
4/9/08
WWND 2008
William Horowitz
19
LO Gluon Production Radiation
– Numerics includes kT and x limits
» x large enough to create mg
» x small enough that EJet > Mq
– Fixed m = .5 GeV and as = .5
» Similar to Magda full HTL
propagator with running as
• Prefactor => 50-150% effect
– Implications for in-medium
radiative loss?
• Filling in dead code => 5-20%
4/9/08
WWND 2008
William Horowitz
20
LO vs. All Orders Production Rad.
• Ter-Mikayelian similar
for both
• Different normalizations
• All orders calculation
self-regulates for mg = 0
and pT → 0
– 0-60% effect
4/9/08
WWND 2008
William Horowitz
21
Conclusions
• No single satisfactory energy loss model
• Search for tests sensitive to mechanism
– Ratio of charm to bottom RAA for pQCD vs.
AdS/CFT
– Future tests using photon bremsstrahlung
• Inclusion of away-side jet fills in dead cone
– Ultimately leads to a relatively small (5-20%) effect
• Radiative calculations integrate over all x;
importance of large x behavior?
4/9/08
WWND 2008
William Horowitz
22
Backups
4/9/08
WWND 2008
William Horowitz
23
Reasonable Consistency with Magda
c
b
M. Djordjevic and M. Gyulassy,
Phys.Rev.C68:034914,2003
4/9/08
WWND 2008
William Horowitz
24
0th Order % Differences
4/9/08
WWND 2008
William Horowitz
25
Testing AdS/CFT Drag and pQCD
Heavy Quark Energy Loss
William Horowitz
Columbia University
Frankfurt Institute for Advanced Studies (FIAS)
February 9, 2008
arXiv:0706.2336 (LHC predictions)
arXiv:0710.0703 (RHIC predictions)
With many thanks to Miklos Gyulassy and Simon Wicks
4/9/08
WWND 2008
William Horowitz
26
Motivation
– Many heavy quark energy loss models
– Hope to distinguish between two broad
classes:
• Standard Model pQCD
• AdS/CFT Drag
– Comparison difficult:
• nontrivial mapping of AdS/CFT to QCD
• predictions for LHC
– Look for robust signal
4/9/08
WWND 2008
William Horowitz
27
pQCD Success at RHIC:
(circa 2005)
Y. Akiba for the PHENIX collaboration,
hep-ex/0510008
– Consistency:
RAA(h)~RAA(p)
– Null Control:
RAA(g)~1
– GLV Prediction: Theory~Data for reasonable
fixed L~5 fm and dNg/dy~dNp/dy
4/9/08
WWND 2008
William Horowitz
28
• v2 too large
Trouble for wQGP Picture
e- RAA too
• wQGP
notsmall
ruled out, but what if we try
strong coupling?
all
A. Drees, H. Feng, and J. Jia, P
(first by E. Shuryak, Phys. Rev
M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett.
B632:81-86 (2006)
4/9/08
WWND 2008
William Horowitz
29
Intro to AdS/CFT
Large Nc limit of d-dimensional conformal field
theory dual to string theory on the product of
d+1-dimensional Anti-de Sitter space with a
compact manifold
3+1 SYM

z=0
4/9/08
WWND 2008
William Horowitz
30
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 stronglycoupled QCD in classical SUGRA
4/9/08
WWND 2008
William Horowitz
31
Qualitative AdS/CFT Successes:
-R1~
sMach
=(3/4)
wave-like
s
structures
,
similar
• h/s
e-strong
RAA
~
p,
h
R
;
e
)to Lattice
~
1/4p
<<
weak
AA
AA(fh/s
AdS/CFT
pQCD
AdS/CFT
J. P. Blaizot,
S. S. Gubser,
E. Iancu,
S. S.U.
Pufu,
Kraemmer,
and A. Yarom,
A. Rebhan,
arXiv:0706.0213
hep-ph/0611393
T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
4/9/08
WWND 2008
William Horowitz
32
AdS/CFT Energy Loss Models
• 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!
4/9/08
WWND 2008
William Horowitz
33
AdS/CFT Drag
• Model heavy quark jet energy loss by
embedding string in AdS space
dpT/dt = - m pT
m = pl1/2 T2/2Mq
4/9/08
WWND 2008
William Horowitz
34
Energy Loss Comparison
D7 Probe Brane
t

– AdS/CFT Drag:
zm = 2pm / l1/2
dpT/dt ~ -(T2/Mq) pT
zh = pT
z=0
Q, m
v
x
3+1D Brane
Boundary
D3 Black Brane
(horizon)
Black Hole
– Similar to Bethe-Heitler
dpT/dt ~ -(T3/Mq2) pT
– Very different from LPM
dpT/dt ~ -LT3 log(pT/Mq)
4/9/08
WWND 2008
William Horowitz
35
RAA Approximation
– Above a few GeV, quark production
spectrum is approximately power law:
• dN/dpT ~ 1/pT(n+1), where n(pT) has some
momentum dependence
y=0
RHIC
– We can approximate RAA(pT):
• RAA ~ (1-e(pT))n(pT),
where pf = (1-e)pi (i.e. e = 1-pf/pi)
LHC
4/9/08
WWND 2008
William Horowitz
36
Looking for a Robust, Detectable Signal
– Use LHC’s large pT reach and identification of c
and b to distinguish between pQCD, AdS/CFT
• Asymptotic pQCD momentum loss:
erad ~ as L2 log(pT/Mq)/pT
• String theory drag momentum loss:
eST ~ 1 - Exp(-m L),
m = pl1/2 T2/2Mq
S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006
– Independent of pT and strongly dependent on Mq!
– T2 dependence in exponent makes for a very sensitive probe
– Expect: epQCD
0 vs. eAdS indep of pT!!
• dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
4/9/08
WWND 2008
William Horowitz
37
Model Inputs
– AdS/CFT Drag: nontrivial mapping of QCD to SYM
• “Obvious”: as = aSYM = const., TSYM = TQCD
– D 2pT = 3 inspired: as = .05
– pQCD/Hydro inspired: as = .3 (D 2pT ~ 1)
• “Alternative”: l = 5.5, TSYM = TQCD/31/4
• Start loss at thermalization time t0; end loss at Tc
– WHDG convolved radiative and elastic energy loss
• as = .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)
4/9/08
WWND 2008
William Horowitz
38
LHC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv:0706.2336
– Significant
NaïvePrediction
LHC
Unfortunately,
Large
suppression
expectations
rise large
inZoo:
Rleads
met
suppression
What
(pTin
to
) for
full
flattening
a Mess!
pQCD
numerical
pQCD
Rad+El
similar
calculation:
to AdS/CFT
AA
– Use
Let’sofgorealistic
through
dRAA
geometry
step
(pT)/dp
by step
> 0 Bjorken
=> pQCD;
expansion
dRAA(pTallows
)/dpT <
saturation
0 => ST below .2
Tand
4/9/08
WWND 2008
William Horowitz
39
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
RcbpQCD(pT) ~ 1 - as n(pT) L2 log(Mb/Mc) ( /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
RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27
– Ratio starts below 1; independent of pT
4/9/08
WWND 2008
William Horowitz
40
LHC RcAA(pT)/RbAA(pT) Prediction
• Recall the Zoo:
WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]
– Taking the ratio cancels most normalization differences seen previously
– pQCD ratio asymptotically approaches 1, and more slowly so for increased
quenching (until quenching saturates)
WH, M.times
Gyulassy,
arXiv:0706.2336
– AdS/CFT ratio is flat and many
smaller
than[nucl-th]
pQCD at only moderate pT
4/9/08
WWND 2008
William Horowitz
41
Not So Fast!
– Speed limit estimate for
applicability of AdS drag
• g < gcrit = (1 + 2Mq/l1/2 T)2
~ 4Mq2/(l T2)
– Limited by Mcharm ~ 1.2 GeV
• Similar to BH
LPM
Q
Worldsheet boundary
Spacelike if g > gcrit
x5
Trailing
String
“Brachistochrone”
– gcrit ~ Mq/(lT)
– No Single T for QGP
• smallest gcrit for largest T
T = T(t0, x=y=0): “(”
• largest gcrit for smallest T
T = Tc: “]”
4/9/08
D7 Probe Brane
WWND 2008
D3 Black Brane
“z”
William Horowitz
42
LHC RcAA(pT)/RbAA(pT) Prediction
(with speed limits)
WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]
– T(t0): (O), corrections unlikely for smaller momenta
– Tc: (|), corrections likely for higher momenta
4/9/08
WWND 2008
William Horowitz
43
Measurement at RHIC
– Future detector upgrades will allow for identified c
and b quark measurements
– RHIC production spectrum significantly
harder than LHC
•
• NOT slowly varying
y=0
RHIC
– No longer expect
pQCD dRAA/dpT > 0
• Large n requires
corrections to naïve
Rcb ~ Mc/Mb
4/9/08
LHC
WWND 2008
William Horowitz
44
RHIC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv:0710.0703 [nucl-th]
• Large increase in n(pT) overcomes reduction in
E-loss and makes pQCD dRAA/dpT < 0, as well
4/9/08
WWND 2008
William Horowitz
45
RHIC Rcb Ratio
pQCD
pQCD
AdS/CFT
AdS/CFT
WH, M. Gyulassy, arXiv:0710.0703 [nucl-th]
• Wider distribution of AdS/CFT curves due to large n:
increased sensitivity to input parameters
• Advantage of RHIC: lower T => higher AdS speed limits
4/9/08
WWND 2008
William Horowitz
46
Conclusions
• AdS/CFT Drag observables calculated
• Generic differences (pQCD vs.
AdS/CFT Drag) seen in RAA
– Masked by extreme pQCD
• Enhancement from ratio of c to b RAA
– Discovery potential in Year 1 LHC Run
• Understanding regions of selfconsistency crucial
• RHIC measurement possible
4/9/08
WWND 2008
William Horowitz
47
Backups
4/9/08
WWND 2008
William Horowitz
48
Geometry of a HI Collision
Medium density and jet production
are wide, smooth distributions
Use of unrealistic geometries strongly
bias results
S. Wicks, WH, M. Djordjevic, M. Gyulassy,
Nucl.Phys.A784:426-442,2007
1D Hubble flow => r(t) ~ 1/t
=> T(t) ~ 1/t1/3
M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005
4/9/08
WWND 2008
William Horowitz
49
Langevin Model
– Langevin equations (assumes gv ~ 1 to neglect
radiative effects):
– Relate drag coef. to diffusion coef.:
– IIB Calculation:
AdS/CFT here
• Use of Langevin requires relaxation time be large
compared to the inverse temperature:
4/9/08
WWND 2008
William Horowitz
50
But There’s a Catch (II)
• Limited experimental pT reach?
ALICE Physics Performance Report, Vol. II
– ATLAS and CMS do not seem to be limited in this
way (claims of year 1 pT reach of ~100 GeV) but
systematic studies have not yet been performed
4/9/08
WWND 2008
William Horowitz
51
LHC p Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic,
in preparation
4/9/08
• Our predictions show a
significant increase in RAA as a
function of pT
• This rise is robust over the
range of predicted dNg/dy for
the LHC that we used
• This should be compared to
the flat in pT curves of AWSbased energy loss (next slide)
• We wish to understand the
origin of this difference
WWND 2008
William Horowitz
52
Asymptopia at the LHC
Asymptotic pocket formulae:
DErad/E ~ a3 Log(E/m2L)/E
DEel/E ~ a2 Log((E T)1/2/mg)/E
4/9/08
WH, S. Wicks, M.
Gyulassy,
WWND
2008M. Djordjevic, in preparation
William Horowitz
53
K. J. Eskola, H. Honkanen, C. A. Salgado, and U.
A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
K. J. Eskola, H. Honkanen, C. A. Salgado, and
U. A. Wiedemann, Nucl. Phys. A747:511:529
(2005)
4/9/08
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
WWND 2008
William Horowitz
54
Pion RAA
• Is it a good measurement for tomography?
– Yes: small experimental error
– Maybe not: some models
appear “fragile”
• Claim: we should not be so immediately dismissive of the pion RAA as a tomographic tool
4/9/08
WWND 2008
William Horowitz
55
Fragility:
A Poor Descriptor
• All energy loss models with a formation time
saturate at some RminAA > 0
• The questions asked should be quantitative :
– Where is RdataAA compared to RminAA?
– How much can one change a model’s controlling
parameter so that it still agrees with a measurement
within error?
– Define sensitivity, s = min. param/max. param that
is consistent with data within error
4/9/08
WWND 2008
William Horowitz
56
Different Models have Different
Sensitivities to the Pion RAA
• GLV:
s<2
• Higher Twist:
s<2
• DGLV+El+Geom:
s<2
• AWS:
s~3
4/9/08
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
WWND 2008
William Horowitz
57
T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007)
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
4/9/08
WWND 2008
William Horowitz
58
A Closer Look at ASW
The lack of sensitivity needs to be more closely examined
because (a) unrealistic geometry (hard cylinders) and no
expansion and (b) no expansion shown against older data (whose
error bars have subsequently shrunk
(a)
(b)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
4/9/08
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
WWND 2008
William Horowitz
59
Surface Bias vs. Surface Emission
– Surface Emission: one phrase explanation of fragility
• All models become surface emitting with infinite E loss
– Surface Bias occurs in all energy loss models
• Expansion + Realistic geometry => model probes a large
portion of medium
A. Majumder, HP2006
4/9/08
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
WWND 2008
William Horowitz
60
A Closer Look at ASW
– Difficult to draw conclusions on
inherent surface bias in AWS
from this for three reasons:
• No Bjorken expansion
• Glue and light quark contributions
not disentangled
• Plotted against Linput (complicated
mapping from Linput to physical
distance)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
4/9/08
WWND 2008
William Horowitz
61