# Presentation: 224087

## Why soft interaction approximations 
are not strong enough 
for jets in the QGP

**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

## Where are we – Rad vs Coll?

- Qin et al (McGill group + Mustafa)‏

- AMY radiative
- (>> GLV radiative)‏

- arXiv:0710.0605

**Notes:**
Recent paper from McGill group confirms the physical conclusions from WHDG
(just with a different radiative formalism and different geometry modelling)‏

## Where are we - RAA(pT) results?

- S.Wicks, M.Gyulassy (in preparation)‏

**Notes:**
Note: not going to touch low pt
Assume eikonal, vacuum fragmentation ...

The model: GLV + (collisional with proper fluctuations for finite small number of collisions, phenomenological magnetic screening = mu_D), basic medium integration

Vary alpha, see what we get for fixed density, can also do the other way around

## Where are we - RAA(pT) results?

- S.Wicks, M.Gyulassy (in preparation)‏

**Notes:**
Large uncertainties in heavies from:
1) production
2) x_LC vs x_P vs x_E, but calc not work well when these are different (ie bottom quark < 5 GeV or so)‏

## 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?

**Notes:**
Without introducing any new mechanisms (eg collisional dissocation)‏

Of course, c:b uncertainty. 

But running with what we have, what about intrinsic in the energy loss mechanisms?

Heavy quarks-> motivation to go back and look again at our uncertainties in our energy loss models

## 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**

**Notes:**
Note: most of what I will discuss will be applied to light quarks. 

However, it is also directly relevant to heavy quarks, and to the consistency between heavy and light quarks.

## 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***!

**Notes:**
ie Soft <~ 0.5 GeV

Hard >= 1 GeV

## Conclusion

- Comparisons between energy loss models
- cannot be summarized
- in one parameter.

## Conclusion

_**Comparisons between energy loss models**_
_**cannot be summarized **_
_**in one parameter.**_

## Conclusion

- Comparisons between energy loss models
- cannot be summarized
- in one parameter.

## Conclusion

- Comparisons between energy loss models
- cannot be summarized
- in one parameter.

## Why?

- 1) q hat is a local parameter

**Notes:**
It's like asking 'what is the temperature of the QGP'?

but at least 'temperature' has an (energy loss) model independent definition.

But when we say temperature, we immediately understand that the averaging is all important – what time? where? How do we turn temperature into energy loss?

## Why?

- 2) The response of a jet to the medium is a
- DISTRIBUTION
- not a single parameter average

**Notes:**
Different energy loss models use different approximations for this distribution

(as well as different treatments for the radiation, but here look at the medium interaction vertices)‏

We must compare models at the level of the distributions, not the 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 qT, 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.

- BDMPS
- hep-ph/9604327

**Notes:**
Assumes that the ONLY important region is << mu,T.

Not saying that this region is unimportant. But that region q~mu,T and q>mu,T is comparable in importance

We cannot make sense of the parameters without considering it.

## BUT ...

**Notes:**
Area under q_T curve => <qT^2>

Area under omega curve =><omega>

## 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-Gyulassy
- 					or 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 distributionWe are far away from the approach to the central limit theorem

**Notes:**
Of course, this is hand wavy. Have not explicitly showed it. 

Could do an effective separation: (infinite number) of soft collisions in a diffusion equation, the few hard collisions in a convolution.

BUT the soft collisions do not contribute much energy loss (or fluctuation), only RAA->0.9 or so (max)‏

## Results: averages

- HTL-S

- GW

- HTL-X1,X2

- HTL-X1,X2

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

- HTL-S

**Notes:**
But it's very difficult to see the physics if we only look at the averages

Why is HTL-S >> others?

## Results: distributions qT

- HTL-S

- GW

- HTL-X1,X2

**Notes:**
All HTLs agree for q_T <~ mu, different for large momentum transfer

HTL-S does not take into account exponential suppression by medium – a cutoff by hand does not cover the physics.

GW - ??

Difference between HTL-X1 and HTL-X2 is estimate of uncertainty

Rad calc with HTL-S overestimates the rad energy loss for fixed params (compare to coll)‏

## Results: distributions ΔE

- HTL-S

- HTL-X1,X2

**Notes:**
Again, HTL-S ok for om<~mu

Is ok for energy loss for om >> mu.

But, is bad for energy gain region (distribution goes negative – have cut off series too early)‏

If we calc this without looking at the distribution, we will overestimate the average loss.

## 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 dependenceof 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.