Zeroth Order Heavy Quark
Photon/Gluon Bremsstrahlung
William Horowitz
Columbia University
Frankfurt Institute for Advanced Studies (FIAS)
May 2, 2008
With many thanks to Miklos Gyulassy, Simon Wicks,
Ivan Vitev, Hendrik van Hees
5/2/08
Yale-Columbia Fest 2008
William Horowitz
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A Talk in Two Parts
pQCD vs. AdS/CFT Drag
0th Order Production Radiation
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Testing pQCD vs. AdS/CFT Drag
Energy Loss Mechanisms
(In Five Slides)
arXiv:0706.2336 (LHC predictions)
arXiv:0710.0703 (RHIC predictions)
5/2/08
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(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
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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
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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
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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
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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
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Some Investigations of
th
0 Order Production Radiation
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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
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New Fragmentation g Data
A. Hanks, QM2008
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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
5/2/08
S. Wicks, WH, M. Djordjevic, M Gyulassy,
Nucl.Phys.A783:493-496,2007
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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
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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:
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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 (
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) violated
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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:
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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
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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
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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
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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%
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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
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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?
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Backups
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Reasonable Consistency with Magda
c
b
M. Djordjevic and M. Gyulassy,
Phys.Rev.C68:034914,2003
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0th Order % Differences
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