# Presentation: 297198

## Away-side distribution ina parton multiple-scattering model   and background-suppressed measures

**Charles B. Chiu**
- Center for Particle Physics and Department of Physics                          University of Texas at Austin

- Hardprobes,  Asilomar,  June 9-16, 2006

## The dip-bump structure in the away-side distribution

**Collective response of medium:**
- Cherenkov radiation of gluon,
- Mach Cone structure ...
- Sonic boom,
- (Casadelerrey-Solana05, Koch05, Dremin05,Shurryak...)
**Our work:**                     This structure is due to   the effect of parton multiple-scattering.

- Jia (PHENIX nucl-ex/0510019)
- Au+Au, 0-5%
- (2.5-4)  (1-2.5) GeV/c
- _Dip-bump structure_
-  Dip  (=  -  ) ~ 0
-  Bumps:   ~ 1 rad

## Parton multiple scattering:  In the plane  the beam.
	     p ~P ~ E, 
      in units of GeV.

- 	     p ~P ~ E,
-       in units of GeV.

- In 1-5 GeV region pQCD not reliable.
**We use a simple model** to simulate effect of multiple scattering.
- Process is carried out in an expanding medium.
**At each point, a **_**random angle **_**is selected fom a gaussian distribution of the **_**forward cone**_**. **
- There is successive energy loss and  the decrease in step size.
- There is a cutoff in energy:
- If parton energy decreases below the cutoff, it is absorbed by the medium.
- Parton with  a sufficient energy exits the medium.

- Exit

- x

- x

- x

- x

- x

- Trigger

- Recoil

- Part I.  Simulation based on a parton multiple-scattering model (Chiu and Hwa,  preliminary)

## Simulation results: ptrigger=4.5

**Sample tracks: **Superposition of many events, 1 track per event.
**Exit tracks**: When successive steps are _bending away from the center_, the track length is shorter, is likely to get out.
**Absorbed tracks**: When successive steps _swing back and forth_, the track length is longer, more energy loss. The track is likely to be absorbed.
**Comparison with the data:**
- Parameters are adjusted to qualitatively reproduce the dip-bump structure.
- Dashed line indicates the thermal bg related to the parton energy-loss.

- (c)

- (a)

- (b)

## Model prediction for

- parton  Ptrig=9.5; and  Passoc: 4-6.
- For momenta specified, our model predicts a negligible thermal bg. To display comparison with experimental peak, model curve is plotted above the bg line.

**STAR nucl -exp 0604108**

## So far we have compared event-averaged data. Next we must also look at the implication of the event by event description of the model.  

**Parton multiple-scattering**:
- In a given event, there is _only one-jet of associated particles_.
- It takes _large event-to-event fluctuations about ____=0_ to build up the dip-bump structure.
**Mach-cone-type models:**
- Collective medium response suggests a simultaneous production of particles in <0 and >0 regions.
- _Less event-by-event fluctuation about ____=0 _is expected.

- This leads to the second part my talk, where  the implication of these two event- by-event descriptions will be explored.

## Part II. Use of background-suppressed measures to analyze away-side distribution  (Chiu&Hwa nucl-th/0605054)

**Factorial Moment (FM)**
_**FM of order q**_:
-  fq= (1/M)****j nj(nj-1)..(nj -q+1),
- only terms with positive last factor contribute to the sum.
_**NFM**__:_
-   	Fq= fq / (f1)q.
**Theorem:**_ Ideal statistical limit_
- (Poisson-like fluctuation, large N limit)
**Fq’s ********1, **for all relevant q’s and M’s.

**A sample bg-event**

- _Factorial moment of order 1_ is the avg-multiplicity-per-bin:                  f1= N/M = (1/M) **j** n**j** (red line).

**An event: N pcles in M bins**

**Fq’s & event averaged <Fq>’s** are basic bg-suppressed measures

## A toy model to illustrate the use of FM-method

_**Signal **__is defined_ _as a cluster of several particles_ spread over a small ******-**interval. We will loosely refer it as a “**jet**”.
_**3 types of events**_
**bg**: Particles randomly distributed in the full -range of interest.
**bg+1j**: 1j is randomly distributed over the range indicated.               It _mimics_ parton-ms model, i.e. it takes large fluctuations about =0 to build the 1j-spectrum.
**bg+2j**_:_ The 2j-spectrum shown is symmetric about =0. It meant to _mimic_ Mach–cone-type models.

-       1j: 5pcles,  bg: 60 pcles
-      bg+1j : 65 pcles
-      bg+2j: 70  pcles

## <Fq> vs M plots for q= 2, 3, and 4. 

- Bg events: <Fq>~1, independent on M and q values.
- bg+1j, bg+2j events: For q>2, deviations from unity becomes noticeable. Increase of M and q, lead to further increase in <Fq>. ** **

## Measurement of fluctuations between two -regions

- The 2 regions could be
- 	I: <0, and II: >0.
- Difference: FI-FII measures fluctuation. Introduce
-      <D(p,q)> =<(F**q****I**-F**q****||****)****p**>.
- Here raising to the pth power further enhances the measure. To track the relative normalization, one also needs the corresponding sums:
-         <S(p,q)> =<(Fq| +Fq||)p>.
- Now one can look at features in D vs S plots.

## <D(p,q)>  vs  <S(p,q)> plots

**Common pattern**:
- bg: well localized and suppressed.
- bg+1j, bg+2j: fanning out with distinct slopes
**     **for** **pts:M=20,30,40,50
**<D> vs <S> plots** can be used to distinguish:      _bg+1j_ parton-ms model
- 	_bg+2j_ Mach-cone-type models
**These plots are obtained without bg subtraction!**

## FM-measures which contain -dependent information can also be constructed using the 2-regions approach.  

- Use parameter ****c to setup two regions:
-  region **I**(****c): ****<|******c**|
-  region **II**(****c): ****>|******c** |
- Determine Bq=<Dq > /<Sq.
- The curve of Bq vs ****c contains information on -dependence of the signal.

**-******c

****c

- I

- II

- II

## Conclusion (part II)

**We have investigated FM-method to analyze away-side ********-distribution.**
- Advantages in using FM-measures.
- They are insensitive to statistical fluctuation of bg.
- Sensitive to  “jet” (localized cluster)-signal.
- No explicit bg subtraction is needed.
- We suggest that FM-method has the potential to provide a _common framework _to compare results from different experiments and various subtraction schemes.

## Event-average of NFM: <Fq>

**F****q ****of the bg example**
- (a):   **F****3**** vs i**, for 500 events.
- Event-avg line: <F3> ~ 1
- Fluctuations about the line
- (b):   **Distributions of Fq’s**
- dN/F3 vs F3 (red)
- dN/F2 vs F2 (blue)
- Width of the dispersion curve increases with q.
- In Poissonian large N limit the width  0.

- (b)

- Event-Avrage over  i=1,2,..Nevt
- <Fq > =  i Fq(i) /Nevt

**Background Events**

- (a)

## Bq of bg+1j case  for                       different -peak structure

- (a) [i], [j], [k] cases: 1j+bg
-      Only 1j part is shown. bg: [i]=20, [j]=2,[k]=0.2
- (b) B4 for [i], [j], [k]
**Case [j]: Red Curve**
- (c): Bg+1j: low plateau on a high bg.
- (d) Corresponding         1-B4 vs ******c ** curve has the features of broad peak in (a) and large background in (c).

- Bg+1j

- Bg+1j

- Bg+1j

- 1j

- Signal/Noise ratios of [i], [j] and [k]:
- Bg=20, 2, 0.2, S/N ~ 1% , ~10%,  ~100%.