study of dynamical fluctuations and levy stability in silicon-nucleus collisions at high energy
DESCRIPTION
Study of Dynamical Fluctuations and Levy Stability in Silicon-Nucleus Collisions at High Energy. Mustafa Abdusalam Nasr Department of Physics 7 th October University, Misurata-Libya E-mail: [email protected]. Out Lines of this Talk. Introduction. Experimental Details. - PowerPoint PPT PresentationTRANSCRIPT
Mustafa Abdusalam Nasr
Department of Physics
7th October University, Misurata-Libya E-mail :[email protected]
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:
M
mq
m
mmmq n
qnnn
MF
1
1 )1.....().........(1
evtN
M
mqmmm
EVT
q
q N
qnnn
N
MF
1
11 )1...().........(
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.
evtN
qF
q
qF
][ 0
M
qF
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.
2snsn
7.0 15.14 AGeVc
It is observed that increases linearly with for both the data samples.It is observed that increases linearly with for both the data samples.
qFln ln
Fig.1 Variation of with qFln ln
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.
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.
qFln ln
Fig.2 Variation of with for AgBr, CNO and Emulsion group of nuclei
In Fig.3 a linear increase is clearly discernible in the value of
Φq with the order of the moments, q . In Fig.3 a linear increase is clearly discernible in the value of
Φqwith the order of the moments, q .
Fig.3 Variation of Φq with q
It is seen from this figure that value of dq is found to increase with q.
Fig.4 Variation of with q qd Fig.5 Variation of with q 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
qd
)1( qq dD 1
ln
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.
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.
It is observed from this figure that value of is found to increase with q.
It is observed from this figure that value of is found to decrease with the order of
the moments q.
Fig.7 Variation of with q q Fig.8 Variation of with q qD
q qD
The plotted against is observed to have a maximum around =5
for experimental as well as simulated data. The plotted against is observed to have a maximum around =5
for experimental as well as simulated data. )(f
Fig.9 Variation of f(α) with α
Order of the moment(q) (CNO)(Em.)(AgBr)
2
3
4
5
6
Table 1. calculated values of intermittency indices , for the interactions of
1 silicon nuclei with CNO and AgBr groups of targets. 15.4 AGeVc
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 .
q
046.0382.0 038.0331.0 042.0315.0
133.0915.0 138.0833.0 164.0752.0
143.0403.1 169.0368.1 160.0278.1
151.0136.2 133.0005.2 042.0922.1
142.0744.2 0117628.2 172.0473.2
q qq
sq'
Results obtained in the present study reveal the presence of Intermittency and multifractality in the data on silicon-nucleuscollisions. Moreover, analyses for the experimental and simulateddata show good compatibility.
