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Why soft interaction approximations are not strong enough for jets in the QGP
Simon WicksWork done with Miklos GyulassyWith thanks to Azfar Adil, William Horowitz, Ivan Vitev
22nd November 2007 Simon Wicks
Where are we – Rad vs Coll?Qin et al (McGill group + Mustafa)
AMY radiative(>> GLV radiative)
arXiv:0710.0605
32nd November 2007 Simon Wicks
Where are we - RAA
(pT) results?
S.Wicks, M.Gyulassy (in preparation)
42nd November 2007 Simon Wicks
Where are we - RAA
(pT) results?
S.Wicks, M.Gyulassy (in preparation)
52nd November 2007 Simon Wicks
Question:
Can perturbative processes explain both the pion and electron high pT data?
What are the uncertainties in our models?
What do the parameters that we extract from the 'fitting' actually mean?
62nd November 2007 Simon Wicks
Outline
1) What do I mean by 'soft'?
2) Concluding remarks
3) Introduction, the models etc
Why soft interaction approximations are not strong enough for jets in the QGP
72nd November 2007 Simon Wicks
Soft vs hard collisions
Soft = soft relative to the medium
Hard = hard relative to the medium
Note: hard relative to the medium can still be soft relative to the jet!
82nd November 2007 Simon Wicks
Conclusion
Comparisons between energy loss modelsComparisons between energy loss models
cannot be summarized cannot be summarized
in one parameter.in one parameter.
92nd November 2007 Simon Wicks
Conclusion
Comparisons between energy loss modelsComparisons between energy loss models
cannot be summarized cannot be summarized
in one parameter.in one parameter.
102nd November 2007 Simon Wicks
Conclusion
Comparisons between energy loss modelsComparisons between energy loss models
cannot be summarized cannot be summarized
in one parameter.in one parameter.
112nd November 2007 Simon Wicks
Conclusion
Comparisons between energy loss modelsComparisons between energy loss models
cannot be summarized cannot be summarized
in one parameter.in one parameter.
122nd November 2007 Simon Wicks
Why?
1) q hat is a local parameter
132nd November 2007 Simon Wicks
Why?
2) The response of a jet to the medium is aDISTRIBUTION
not a single parameter average
142nd November 2007 Simon Wicks
Which distributions?
1) dN/d(ΔE)=> Important for collisional energy loss
2) dN/dqperp
=> Important for radiative energy loss
152nd November 2007 Simon Wicks
Some examples (radiative)
1) Use GW model, but assume in deep LPM regime where many, many scatterings reduce (by central limit theorem) to Gaussian.
2) Assume only very soft scatterings matter, make expansion of interaction for small q
T, use free parameter to fit.
3) Use full GW model including large qT tails, but make a few
implicit qT small assumptions
4) Assume qT << T is all that's important, use this assumption
systematically throughout.
BDMPShep-ph/9604327
162nd November 2007 Simon Wicks
BUT ...
172nd November 2007 Simon Wicks
BUT ...
182nd November 2007 Simon Wicks
The model Simple model: t-channel on-shell 2->2
scattering
Evaluate the distribution for one collision, convolute for multiple collisions.
Take several approximations, look at the effect on the resulting distributions
192nd November 2007 Simon Wicks
Models
Note: C_ab's can be related to the imaginary part of the (medium modified) propagator.
Note: the full dk integrals can be done analytically => polylogs
202nd November 2007 Simon Wicks
Coefficients
1) Strict HTL – neglect (omega,q)/(E or k) everywhere=> 'HTL-S'
2) HTL eXtrapolation – include the extra terms in the coefficients
?
212nd November 2007 Simon Wicks
'HTL-S'
Delta E: Equivalent to Thoma-Gyulassyor t-channel or Braaten-Thoma
qperp
: similar to G-W model, with changes as found by Djordjevic (and Jeon, Moore)
222nd November 2007 Simon Wicks
Models II For HTL eXtrapolation, what do we use as
the propagators? HTL propagators? free space propagators?
=> 'HTL-X1', 'HTL-X2'
232nd November 2007 Simon Wicks
Multiple collisions
Convolution of single collision distribution
We are far away from the approach to the central limit theorem
242nd November 2007 Simon Wicks
Results: averages
HTL-S GW
HTL-X1,X2HTL-X1,X2
(Note: the RAA calc at the beginning used HTL-X1 for collisional)
HTL-S
252nd November 2007 Simon Wicks
Results: distributions qT
HTL-S
GW
HTL-X1,X2
262nd November 2007 Simon Wicks
Results: distributions ΔE
HTL-S
HTL-X1,X2
272nd November 2007 Simon Wicks
So what?
Can't we just scale all our results by a constant factor?
282nd November 2007 Simon Wicks
Conclusion The details of the distributions will affect:
mass dependence energy dependence
of our results.
Must take into account recoil! Do not (only) make soft interaction approximations.
The rarer, harder interactions are at least comparable in importance in our considerations of jet energy loss.
There are many aspects to consider to reconcile the different energy loss models.