Why soft interaction approximations are not strong enough for jets in the QGP Simon Wicks Work done with Miklos Gyulassy With thanks to Azfar Adil, William.

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Presentation transcript:

Why soft interaction approximations are not strong enough for jets in the QGP Simon Wicks Work done with Miklos Gyulassy With thanks to Azfar Adil, William Horowitz, Ivan Vitev

22 nd November 2007 Simon Wicks Where are we – Rad vs Coll? Qin et al (McGill group + Mustafa)‏ AMY radiative (>> GLV radiative)‏ arXiv:

32 nd November 2007 Simon Wicks Where are we - R AA (p T ) results? S.Wicks, M.Gyulassy (in preparation)‏

42 nd November 2007 Simon Wicks Where are we - R AA (p T ) results? S.Wicks, M.Gyulassy (in preparation)‏

52 nd 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?

62 nd 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

72 nd 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!

82 nd November 2007 Simon Wicks Conclusion Comparisons between energy loss models cannot be summarized in one parameter.

92 nd November 2007 Simon Wicks Conclusion Comparisons between energy loss models cannot be summarized in one parameter.

102 nd November 2007 Simon Wicks Conclusion Comparisons between energy loss models cannot be summarized in one parameter.

112 nd November 2007 Simon Wicks Conclusion Comparisons between energy loss models cannot be summarized in one parameter.

122 nd November 2007 Simon Wicks Why? 1) q hat is a local parameter

132 nd November 2007 Simon Wicks Why? 2) The response of a jet to the medium is a DISTRIBUTION not a single parameter average

142 nd November 2007 Simon Wicks Which distributions? 1) dN/d( Δ E)‏ => Important for collisional energy loss 2) dN/dq perp => Important for radiative energy loss

152 nd 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 q T tails, but make a few implicit q T small assumptions 4) Assume q T << T is all that's important, use this assumption systematically throughout. BDMPS hep-ph/

162 nd November 2007 Simon Wicks BUT...

172 nd November 2007 Simon Wicks BUT...

182 nd 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

192 nd 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

202 nd 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 ?

212 nd November 2007 Simon Wicks 'HTL-S' Delta E: Equivalent to Thoma-Gyulassy or t-channel or Braaten-Thoma q perp : similar to G-W model, with changes as found by Djordjevic (and Jeon, Moore)‏

222 nd 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'

232 nd November 2007 Simon Wicks Multiple collisions Convolution of single collision distribution We are far away from the approach to the central limit theorem

242 nd November 2007 Simon Wicks Results: averages HTL-S GW HTL-X1,X2 (Note: the RAA calc at the beginning used HTL-X1 for collisional)‏ HTL-S

252 nd November 2007 Simon Wicks Results: distributions q T HTL-S GW HTL-X1,X2

262 nd November 2007 Simon Wicks Results: distributions ΔE HTL-S HTL-X1,X2

272 nd November 2007 Simon Wicks So what? Can't we just scale all our results by a constant factor?

282 nd 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.