Study of Dynamical Fluctuations and Levy Stability in Silicon-Nucleus Collisions at High Energy

1. Study of Dynamical Fluctuations and Levy Stability in Silicon-Nucleus Collisions at High Energy Mustafa Abdusalam Nasr Department of Physics 7th October University, Misurata-Libya E-mail: bayio@yahoo.com

2. Out Lines of this Talk Introduction Experimental Details Experimental results Conclusions

3. Introduction Systematic and thorough study of fluctuations in multiparticle production in high energy hadronic collisions started since the observation of a relatively high multiplicity cosmic ray event known as JACEE[1] event. In order to explain the observed fluctuations in the rapidity distribution for this event, Bialas and Peschanski proposed[2,3]scaled factorial moments(SFMs) approach to investigate dynamical fluctuations in multiparticle production in high energy nuclear collisions. The qth order factorial moment, Fq, is defined as Where M is the partition number in the available space into which a given rapidity interval is binned and nm is the number of particles falling in the mth bin and the symbol < ….. > represents vertical average obtained for the entire event. If the averaging is done over the whole data sample, the average value of qth order factorial moment is calculated from:

4. Where denotes the total number of events in the sample. Many experiments have reported that exhibit anomalous scaling behaviour exemplified by Where a small pseudorapidity interval is partitioned into M bins each of equal size, . It is of interest to note that" intermittency" in particle physics refers to the power-law behaviour exhibited by with decreasing bin size. Since the occurrence of fluctuation or power-law behaviour in relativistic nuclear collisions has been quite frequently observed, it therefore suggests that multi-hadronic final states in these collisions possess self-similar fractal. Hence one should carry out a study of Levy stability and multifractal spectrum analysis for the fractal systems.

5. Experimetal Details A random sample comprising of 555 interactions having , where represents the number of charged particles produced in an event with relative velocities, , produced in Silicon-Emulsion collisions, is used for carrying out the present analysis. The emission angles of all the relativistic charged particles were measured and their pseudorapidities were determined. All other relevant details about the stacks used, criteria employed for selecting the events and the method of measuring the emission angles may be found elsewhere. Furthermore, for comparing the experimental results with the corresponding values predicted by the Lund model, FRITIOF, a sample consisting of 5000 events, identical to the experimental ones were simulated.

6. Experimental results Fig.1 Variation of with It is observed that increases linearly with for both the data samples.

7. Fig.2Variation of with for AgBr, CNO and Emulsion group of nuclei It is seen that for the three categories of interactions, CNO, emulsion and AgBr, a linear rise in the SFMs with decreasing bin width , is observed.

8. In Fig.3 a linear increase is clearly discernible in the value of Φq with the order of the moments, q. Fig.3 Variation of Φq with q

9. Fig.4 Variation of with q Fig.5 Variation of with q It is seen fromthis figure that value of dq is found to increase with q. It is interesting to note that exactly similar trends of variations of with q are observed for the experimental as well as FRITIOF data

10. Fig.6 Variation of with It is observed from this figure that the slope of the best fit to the data defines the specific heat of the system of multiparticle final state in relativistic nuclear collisions. The values of the specific heats for the experimental and FRITIOF data are found to be 0.607±0.017 and 0.816±0.206 respectively.

11. Fig.7 Variation of with q Fig.8 Variation of with q It is observed fromthis figure that value of is found to increase with q. It is observed fromthis figure that value of is found to decrease with the order of the moments q.

12. Fig.9 Variation of f(α) with α The plotted against is observed to have a maximum around =5 for experimental as well as simulated data.

13. Table 1. calculated values of intermittency indices , for the interactions of 1 silicon nuclei with CNO and AgBr groups of targets. From Table 1 it is clearly evident that amongst the three groups of targets, the values of are relatively higher for the collisions due to CNO targets.

14. Conclusions Results obtained in the present study reveal the presence of Intermittency and multifractality in the data on silicon-nucleus collisions. Moreover, analyses for the experimental and simulated data show good compatibility.

15. Thank you