william horowitz department of physics, columbia university
DESCRIPTION
LHC Predictions 1 from an extended theory 2 with Elastic, Inelastic, and Path Length Fluctuating Jet Energy Loss. William Horowitz Department of Physics, Columbia University 538 W 120 th St., New York, NY 10027, USA Frankfurt Institute for Advanced Studies (FIAS) - PowerPoint PPT PresentationTRANSCRIPT
111/15/06
William Horowitz
LHC Predictions1 from an extended theory2 with Elastic, Inelastic, and Path Length Fluctuating Jet Energy
Loss William Horowitz
Department of Physics, Columbia University538 W 120th St., New York, NY 10027, USA
Frankfurt Institute for Advanced Studies (FIAS)60438 Frankfurt am Main, Germany
November 15, 2006
With thanks to Azfar Adil and Carsten Greiner
1. W.Horowitz et al to be published2. S.Wicks, W.Horowitz, M.Djordjevic and M.Gyulassy, nucl-th/0512076 v3, NPA in press
211/15/06
William Horowitz
Outline
• Energy dependence of jet quenching at the LHC as a test of loss mechanisms– Highly distinct LHC RAA(pT) predictions
– Naturalness of the difference
• Intro to Physics of Nothing– P0 = Exp(-Nc), the probability of no jet
interactions. Nc ~ elL is the average number of elastic collisions
311/15/06
William Horowitz
Modeling Energy Loss– Different models include some effects while
neglecting others• Radiative only loss: (AWS, Majumder, Vitev)
• Convolved radiative and elastic loss (WHDG)
• Inclusion of probability of nothing (separate from probability of emitting no radiation, Pg
0!)
– Nc is the number of elastic collisions suffered while propagating out
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William Horowitz
Probability of Overquench: E > E
– For highly suppressed jets, P(> 1) has a large support for overabsorption. One of two choices is generally made:• Renormalize (reweight) uniformly
• Include an explicit ) term
– We always use the latter
511/15/06
William Horowitz
Our Extended Theory• Convolve Elastic with Inelastic
energy loss fluctuations ( )
• Include path length fluctuations in diffuse nuclear geometry with 1+1D Bjorken expansion
611/15/06
William Horowitz
Simplified Treatment Uses Fixed L
– Estimates of a fixed, single, representative length:
where
and the fitted L is found by varying it until it best reproduces the true geometric average.• There is no a priori method to determine how
much the first two deviate from the actual answer
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William Horowitz
Path Length FluctuationsCan Not be Neglected
• P(L) is a wide distribution– Flavor
independent
• Flavor dependent best fixed length approximation LQ’s not a priori obvious
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
811/15/06
William Horowitz
RHIC Results
• Inclusion of both fluctuating elastic loss and paths is essential to reproduce data
– Fully perturbative
– dNg/dy = 1000 consistent with entropy data for conservative s = .3
• Results are sensitive to changes in dNg/dy and s
– Model is not “fragile”
– Running of s will be an important effect
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
911/15/06
William Horowitz
Suppression of AWS• AWS pQCD-based controlling parameter must be
nonperturbatively large to fit RHIC data-pQCD gives = c 3/4, where c ~ 2; c ~ 8-20 required for RHIC data-Needed because radiative only energy loss (and > 1? R =
(1/2) L3)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
1011/15/06
William Horowitz
LHC Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
• 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 AWS-based energy loss (next slide)
• We wish to understand the origin of this difference
1111/15/06
William Horowitz
Curves of AWS-based energy loss are flat in pT
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
(a) (b)
Comparison of LHC Predictions
1211/15/06
William Horowitz
Why AWS is Flat• Flat in pT curves result from extreme suppression at
the LHC – When probability leakage P( > 1) is large, the (renormalized or
not) distribution becomes insensitive to the details of energy loss
• Enormous suppression due to:– Already (nonperturbatively) large suppression at RHIC for AWS– Extrapolation to LHC assumes 7 times RHIC medium densities
(using EKRT)» Note: even if LHC is only ~ 2-3 times RHIC, still an immoderate ~ 30-
45
• As seen on the previous slide, Vitev predicted a similar rise in RAA(pT) as we do
– Vitev used only radiative loss, Prad(), but assumed fixed path
– WHDG similar because elastic and path fluctuations compensate
1311/15/06
William Horowitz
The Rise of GLV Rad+El+Geom• Use of both Prad AND Pel implies neither has much
weight for E > E at RHIC
• For the dNg/dy values used, high-pT jets at the LHC have asymptotic energy loss:
• LHC RAA(pT) dependence caused by deceasing energy loss not altered by the flat production spectra
Erad/E 3 Log(E/2L)/EEel/E 2 Log((E T)1/2/mg)/E
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
1411/15/06
William Horowitz
Probability of No Energy Loss
• Induced radiative energy loss requires at least one jet interaction in medium with probability
• After at least one elastic collision, the total energy loss is a convolution of the momentum lost to the radiated glue as well as to the scattering centers
– Prad() also contains a P(Ng = 0) () due to the probability of no glue emission
– For fixed s = .3, including P0 physics accounts for 50% of RAA
– Allowing s(T) to run as s(q2=2T(z)) reduces P0 by a factor of 2
– Integration over momentum transfers with s(q2) given by vacuum running formally gives P0=0
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William Horowitz
Conclusions
• LHC RAA(pT) data will distinguish between energy loss models– GLV Rad+El+Geom predicts significant rise in pT
– AWS type models predict flat pT dependence
• Moderate opacity (GLV, WW) RAA predictions sensitive to noninteracting free jets
RAA ~ P0 + (1-P0) RAA(Nc>0), P0 = exp(-elL)