1. 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

2. 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

3. Parton multiple scattering: In the plane  the beam. 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)

4. Simulation results: p trigger =4.5 Sample tracks: Superposition of many events, 1 track per event. (a)Exit tracks: When successive steps are bending away from the center, the track length is shorter, is likely to get out. (b)Absorbed tracks: When successive steps swing back and forth, the track length is longer, more energy loss. The track is likely to be absorbed. (c)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)

5. Model prediction for parton P trig =9.5; and P assoc : 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

6. 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 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.

7. 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 / (f 1 ) 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: f 1 = N/M = (1/M)  j n j (red line). An event: N pcles in M bins Fq’s & event averaged ’s are basic bg-suppressed measures

8. 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

9. vs M plots for q= 2, 3, and 4. Bg events: ~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.

10. Measurement of fluctuations between two  - regions The 2 regions could be I:  0. Difference: F I -F II measures fluctuation. Introduce =. Here raising to the pth power further enhances the measure. To track the relative normalization, one also needs the corresponding sums: =. Now one can look at features in D vs S plots.

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

12. 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 B q = /<S q. The curve of Bq vs  c contains information on  -dependence of the signal. -c-c cc III

13. 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.

14. Event-average of NFM: F q of the bg example (a): F 3 vs i, for 500 events. Event-avg line: ~ 1 Fluctuations about the line (b): Distributions of Fq’s dN/F 3 vs F 3 (red) dN/F 2 vs F 2 (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 =  i Fq(i) /Nevt Background Events (a)

15. B q 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) B 4 for [i], [j], [k] Case [j]: Red Curve (c): Bg+1j: low plateau on a high bg. (d) Corresponding 1-B 4 vs  c curve has the features of broad peak in (a) and large background in (c). Bg+1j 1j Signal/Noise ratios of [i], [j] and [k]: Bg=20, 2, 0.2, S/N ~ 1%, ~10%, ~100%.