Dynamical fluctuation of compound multiplicity in nucleus-nucleus interactions at 4.5 AGeV Evidence of projectile dependence of azimuthal asymmetry
Dipak Ghosh, Argha Deb, Subrata Biswas, Pasupati Mandal & Prabir Kumar Haldar Nuclear and Particle Physics Research Centre, Department of Physics, Jadavpur University, Kolkata 700 032
Received 3 June 2006; accepted 16 August 2007
Azinmuthal fluctuations in compound multiplicity (pions + target protons) spectrum emitted from nucleus-nucleus interactions initiated by 24Mg-AgBr and 12C-AgBr both at 4.5 AgeV have been studied. The data exhibit the existence of emission asymmetry in the azimuthal plane for both the interactions. Asymmetry is found to depend on the number of compound multiplicity produced.
Keywords: Relativistic nucleus-nucleus collisions, Compound multiplicity, Azimuthal asymmetry IPC Code: G01T
1 Introduction
Various experiments have been performed mainly with the lepton-lepton, lepton-nucleus, hadron- hadron, hadron-nucleus and nucleus-nucleus interactions at relativistic and ultra relativistic energies to know the ultimate structure of matter. The observations from these experiments reveal the existence of non-statistical fluctuations during multiparticle production process. The existence of intermittent type of fluctuations speaks in favour of the presence of non-statistical fluctuations in high energy interactions. Hence, the non-statistical fluctuations in particle density distribution have become a subject of major interest.
A lot of methodologies have been developed to study the large non-statistical fluctuations. Some well known physical phenomena like correlation, intermittency, etc. may be considered as the manifestation of the fact that the production of pions is dominated by large fluctuations arising out of dynamical reasons. Recently, fluctuation studies have been reported for the pions in pseudorapidity space1-15 .Azimuthal asymmetry is a very simple but useful tool for studying the non-statistical fluctuations. The method of azimuthal asymmetry have been employed earlier16-23 in different types of interactions.
In the high energy nuclear collisions, investigations are carried out on the produced pions with a common belief that these particles are the most informative about the collisional dynamics and thus, could be effective in revealing the underlying physics of high
energy relativistic interactions. Limited attention has been given on the medium energy (30–400 MeV) knocked out target protons, which are also supposed to carry some information about the interaction mechanism because the time scale of emission of these particles is of the same order ( ≈10-22 s) as that of the produced particles. These target protons, which manifest themselves as grey tracks in nuclear emulsion, are the low energy part of the inter nuclear cascade formed in high energy interactions. If the number of fast target fragments, generally, known as the grey particles in emulsion media are combined with produced pions, known as the shower tracks in the same media, in a collision, a new parameter named as compound multiplicity (nc= ng+ ns where nc
= compound multiplicity, ng = number of grey tracks and ns = number of shower tracks ) is formed which can play an important role in understanding the reaction dynamics in high energy nuclear interactions.
However, the physics of nuclear interactions is completely known and therefore, all the available probes need to be thoroughly exploited towards meaningful analysis of experimental data. It is essential to analyze the behaviour of the compound multiplicity spectra thoroughly using the available tools in order to get more information about the inner dynamics of the particle production in high energy nuclear interactions.
The objective of this paper is to investigate the dynamical fluctuations in the azimuthal angle distribution of compound multiplicity spectrum
emitted from 24Mg-AgBr and 12C-AgBr interactions both at 4.5 AGeV. We have also performed similar studies in case of shower multiplicity in our earlier publication23 for both the interactions.
2 Experimental Details
The data set used in this present analysis are obtained by exposing NIKFI-BR2 emulsion plates by
24Mg beam and 12C beam with incident energy 4.5 AGeV at JINR Dubna, Russia. The scanning of the plates is carried out with the help of a high resolution Leitz metalloplan microscope provided with semi automatic scanning and measuring system. The scanning is done using objective 10X in conjunction with a 25X ocular lens. To increase the scanning efficiency, two independent observers scanned the plates independently. For measurement , 100X oil- immersion objective was used in conjunction with 25X ocular lens. The measuring system fitted with it has 1 µm resolution along the X and Y axes and 0.5
µm resolution along the Z axis.
The events were chosen according to the following criteria:
The incident beam track should lie within 3° angles to the mean beam direction of the pellicle. It is done to ensure that we have taken the real projectile beam;
the events, which are within 20µm thickness from the top or bottom surface of the plate, should be rejected. It is done to reduce the loss of tracks as well as to reduce the error in angle measurement; the events, primary beam tracks of which are observed to be a secondary track of other interaction should not be analyzed and are rejected.
According to the emulsion terminology24, the particles emitted after interactions are classified as:
a. Black particles:- Black particles consist of both single and multiple charged fragments. They are target fragments of various elements such as carbon, lithium, beryllium etc. with ionization greater than or equal to 10 I0, I0 being the minimum ionization of a singly charged particle.
These black particles having maximum ionizing power are less energetic and consequently, they are short ranged. Their range is less than 3 mm in emulsion medium. They have velocities less than 0.3 c and energy less than 30 MeV, c is the velocity of light in vacuum. In the emulsion experiments, it is very difficult to measure the charge of the fragments. So, identification of the exact nucleus is not possible.
b. Grey particles- They are mainly fast target recoil protons with energy up to 400 MeV. They have ionization 1.4 I0 ≤ I< 10 I0. These particles have range greater than 3mm in emulsion medium and having velocities 0.7c≥V≥0.3c.
c. Shower particles- The relativistic shower tracks with ionization I less than or equal to 1.4I0 are mainly produced by pions and are not generally confined within the emulsion pellicle. These shower particles have energy in the GeV range.
d. Projectile fragments- Along with these tracks there are a few projectile fragments. In high energy nuclear collisions, the projectile beam which collides with the target nucleus also undergoes fragmentation. These particles have constant ionization, long range and small emission angle. They, generally, lie within 3°
with respect to the main beam direction. Great care should be taken to identify these projectile fragments.
To ensure that the targets in the emulsion are silver or bromine nuclei, we have chosen only the events with at least eight heavy ionizing tracks of (black + grey) particles. i.e central and quasi-central events are taken. The events that have the number of heavy tracks less than eight, are due to the collision of the projectile beam with carbon, nitrogen and oxygen nucleus present in the emulsion. These types of events are called CNO events.
For our present analysis , the combination of grey and shower tracks for formation of compound multiplicity has been considered. According to the above selection procedure, we have chosen 800 events25 of 24Mg-AgBr and 800 events26 of 12C-AgBr interactions both at 4.5 AGeV. The azimuthal angle (φ) is measured for each track with respect to the beam direction by taking the readings of the coordinates of the interaction point (X0, Y0, Z0), the coordinates (X1, Y1, Z1) at the end of the linear portion of each secondary track and the coordinates (Xi, Yi, Zi) of a point on the incident beam. The variable used for this analysis is azimuthal angle (φ).
The experimental resolution of the azimuthal angle is of the order 5°.
Nuclear emulsion covers 4
π
geometry and provides very good accuracy in the measurements of angles of produced particles and fragments due to high spatial resolution and thus, is suitable as a detector for the study of fluctuations in the fine resolution of the phase space considered.3 Method of Study
To search asymmetry in the distribution of compound multiplicity for both the interactions in azimuthal angle space, we have divided the whole azimuthal plane having 2
π
angular range into two equal angular intervals and the difference in the number of particles emitted in the two intervals for each of the events is found out. We repeat the process and continue it by shifting the line of division over the azimuthal plane by 10°and by taking the difference in the number of compound multiplicity in the two halves, each time. This process is carried out till the position of the line of division is repeated. The maximum difference obtained for each event is taken as ∆nci, i, indicates the event. The probability of azimuthal asymmetry for the i-th event27 is defined as:Wi= ∆nci / nci … (1)
where nci is the total number of compound multiplicity in the i-th event of the group of events in a particular Nc interval. For a group of m events in an Nc interval, the probability of azimuthal asymmetry is then given as :
W=
∑
i
Wi / m … (2)
To calculate the asymmetry parameter (W) , the whole data sample for both the interactions, is divided into groups such that all the events in a particular group have equal or almost equal number of compound multiplicity. Then, W for different Nc
intervals for both magnesium and carbon interactions have been calculated. For any particular Nc interval, the weighted average of Nc is given by the relation:
Nc= ∑
Nc
P Nc … (3)
where
Nc
P represents the probability of getting an event with Nc number of compound multiplicity.
4 Results and Discussion
For studying the variation of the azimuthal asymmetry with the number of compound multiplicity, the calculated values of the probability W of azimuthal asymmetry and their corresponding weighted averages Ncfor experimental data sets in
24Mg-AgBr and 12C-AgBr interactions both at 4.5 AGeV are given in Table1. We have plotted W against Nc for the experimental data sets in [24Mg- AgBr and 12C-AgBr interactions and they are shown in Figures1 and 2, respectively. The Figs 1 and 2 for both the data sets reveal that W depends on the Nc interval. W decreases with the increase of Nc indicates that asymmetry decreases with the increase of number of compound multiplicity.
The observed asymmetrical behaviour is due to the statistical fluctuations and inner dynamics of multiparticle production has nothing to do with it. To counter such an argument and ensure that the observed asymmetrical behaviour is not due to
Table 1—Values of the probability W of azimuthal asymmetry in different Nc intervals in compound multiplicity distributions of
24Mg-AgBr and 12C-AgBr interactions at 4.5 AGeV for both the experimental and randomized data sets Interaction
Nc Nc Experimental values
(W )
Randomized values (W )
24Mg-AgBr (4.5 AGeV)
1-6 7-10 11-15 16-21 22-32
4.47 8.82 13.64 17.96 26.88
0.82 ± 0.04 0.60 ± 0.06 0.46 ± 0.02 0.45 ± 0.02 0.36 ± 0.01
0.70 0.46 0.42 0.38 0.32
12C-AgBr (4.5 AGeV)
1-5 6-9 10-15 16-18 19-29
3.66 7.36 11.97 16.11 22.00
0.77 ± 0.02 0.65 ± 0.06 0.60 ± 0.05 0.50 ± 0.01 0.46 ± 0.04
0.72 0.55 0.50 0.47 0.36
statistical fluctuations, we have redistributed all the particles of each event for both the interactions randomly throughout the considered phase space interval and the same analysis has been performed. W calculated from both the randomized data sets of magnesium and carbon have also been presented in
Table 1. We have plotted ΥWagainst Nc for the randomized data sets in 24Mg-AgBr and 12C-AgBr interactions and they are also shown in Figs1 and 2, respectively.
The results for the randomized data sets show that the probability of azimuthal asymmetry for most of the points differ appreciably from that of the experimental values (considering the error bars) for both heavier (24Mg ) and lighter (12C) projectile. In fact the azimuthal asymmetry for randomized events is less than that of experimental events. Such an outcome obviously confirms the existence of non- statistical fluctuations in compound multiplicity distribution. From Table1, it is evident that for Nc the probability W depends upon the number of compound multiplicity.
We have plotted the probability W against Nc for the experimental data of heavier (24Mg ) and lighter (12C) projectileand they are shown in Figures 3 and 4,
Fig.1—Plot of the probability W of azimuthal asymmetry against Nc intervals for both experimental and randomized data in
24Mg-AgBr interactions at 4.5 AgeV
Fig.2—Plot of the probability W of azimuthal asymmetry against Nc intervals for both experimental and randomized data in 12C- AgBr interactions at 4.5 AGeV
Fig. 3—Plot of the probability W of azimuthal asymmetry against Nc intervals for the experimental data of 24Mg-AgBr interactions along with the power law best-fit curve
respectively. The W -Nc plots reveal that the experimental data sets follow a power law of the form:
W = p.Nc q … (4)
The values of p and q are obtained from best fit curve of W versus Nc plot for both the interactions and the values are presented in Table 2. We have noted for every fit in W vesus Nc plot
χ
2/ DOF (degrees of freedom) is less than 1. It is seen from Table 2 that the values of p and q obtained from the best fit curves of compound multiplicity data emitted from magnesium and carbon are not the same. In fact ,the value of q determines how rapidly the azimuthal asymmetry decreases with the number of compound multiplicity.Larger value of q indicates the value of W decreases more rapidly. The rate of decrement of azimuthal asymmetry is faster in case of 24Mg-AgBr interactions than that in case of 12C-AgBr interactions for compound multiplicity (Table 2) .
Thus the above analysis indicates the following interesting results:
1. Compound multiplicity, for both 24Mg-AgBr and 12C-AgBr interactions, are emitted asymmetrically in azimuthal angle space.
2. The degrees of asymmetry depend on the number of compound multiplicity and it decreases with the increase of number of multiplicity.
3. The values of p and q for compound multiplicity in heavier (24Mg) projectile are greater than that for lighter (12C) projectile.
This suggests that the variation depends on the projectile mass at the same incident energy.
4. However, for the same incident energy 4.5 AGeV, for compound multiplicity the degree of azimuthal asymmetry decreases faster for the heavier projectile than that of lighter projectile.
Acknowledgement
We thank Prof. K D Tolstov of JINR, Dubna, Russia, for his extreme generosity in providing us with the exposed and developed emulsion plates for this work.
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