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

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


Where are we - RAA

(pT) results?

S.Wicks, M.Gyulassy (in preparation)


Where are we - RAA

(pT) results?

S.Wicks, M.Gyulassy (in preparation)


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?


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


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!


Conclusion

Comparisons between energy loss modelsComparisons between energy loss models

cannot be summarized cannot be summarized

in one parameter.in one parameter.


Conclusion





Conclusion





Conclusion





Why?

1) q hat is a local parameter


Why?

2) The response of a jet to the medium is aDISTRIBUTION

not a single parameter average


Which distributions?

1) dN/d(ΔE)=> Important for collisional energy loss

2) dN/dqperp

=> Important for radiative energy loss


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


BUT ...


BUT ...


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


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


Coefficients

1) Strict HTL – neglect (omega,q)/(E or k) everywhere=> 'HTL-S'

2) HTL eXtrapolation – include the extra terms in the coefficients

?


'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)


Models II For HTL eXtrapolation, what do we use as

the propagators? HTL propagators? free space propagators?

=> 'HTL-X1', 'HTL-X2'


Multiple collisions

Convolution of single collision distribution

We are far away from the approach to the central limit theorem


Results: averages

HTL-S GW

HTL-X1,X2HTL-X1,X2

(Note: the RAA calc at the beginning used HTL-X1 for collisional)

HTL-S


Results: distributions qT

HTL-S

GW

HTL-X1,X2


Results: distributions ΔE

HTL-S

HTL-X1,X2


So what?

Can't we just scale all our results by a constant factor?


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.

Documents

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