fulltext

New method to analyze super-family events

observed with emulsion chambers

M. AMENOMORI

Department of Information Science, Faculty of Science, Hirosaki University Hirosaki 036, Japan

(ricevuto il 22 Marzo 1996; revisionato il 22 Aprile 1997; approvato il 18 Giugno 1997)

Summary. — We have developed a clustering method to analyze family events observed with emulsion chambers at high mountains. The main purpose of this analysis is to estimate the main production height of individual events, angular spread of gamma-rays in each event and so on. These enable us to investigate hadronic interactions at energies over 1016_{eV, inaccessible by the present} high-energy accelerators. We examined our clustering method using Monte Carlo events, and found that for the family events whose production height is low (within 2–3 km above the observation point in air), their production heights and lateral spreads are well reproduced. We further applied our method to the super-family events (

!

above sea-level). The results seem to suggest that particle production with large transverse momentum occurs with considerable frequency even in the fragmentation region in the energy region over 1016_eV.

PACS 94.40 – Cosmic rays.

1. – Introduction

It is well known that emulsion chamber experiments at high mountain altitude provide information about nuclear interactions by cosmic rays with energies over

1015_{eV, and are considered to be a unique means for direct observation of such}

phenomena in such ultrahigh-energy region [1]. The emulsion chamber (EC) essentially consists of absorber (lead or iron) plates and photosensitive layers, which are piled up alternately. Each photosensitive layer contains high sensitive X-ray films or both X-ray films and nuclear emulsion plates. This detector allows detection and energy estimation of high-energy particles produced in the nuclear interactions with good accuracy. By exposing this detector on a large scale to cosmic rays at high mountain altitudes for a duration of one year or more, one can observe many instances of the type of event called a “family”, which is a bundle of high-energy particles coming from the same direction in the atmosphere. A family is generally composed of both gamma-rays (hereafter this means electromagnetic components) and hadrons which

M.AMENOMORI 672

are products of nuclear and electromagnetic cascade processes in the atmosphere originating from the same primary particle with sufficient energy. High-energy particles such as gamma-rays and hadrons, which constitute a family, can be detected with emulsion chamber in the form of cascade showers. When the energy of showers exceeds about 1 TeV, cascade development is recorded as a series of black spots on the X-ray films ranging over several layers in the emulsion chamber. The energy of each shower is easily estimated by measuring the change of optical density of shower spots and by comparing it with a calculation based on the cascade theory. The study of these family events is the key subject of emulsion chamber experiments at mountain altitude. The emulsion chamber experiments have been carried out on Mt. Kanbala (5500 m above sea level) in Tibet, China [2], Mt. Chacaltaya (5200 m) in Bolivia [3], the Pamir Highland (4300 m) in the former Soviet Union [4], and the summit of Mt. Fuji (3750 m) in Japan [5, 6]. A large-scale emulsion chamber experiment has been continued on Mt. Kanbala in collaboration with Chinese researchers [2]. Using the data obtained from this experiment, we have investigated the nuclear interactions and primary cosmic rays

in the energy region over 1014_{eV and the following have become evident [2]: 1) The}

inelastic cross-sections of nuclear interactions increase as the primary energy increases. i.e. sinelp-airP E00.05-0.06, where E0 is the energy of primary particles. 2) The average behavior of particle production can almost be explained by a smooth extrapolation from the accelerator energy region in energy. 3) The transverse momentum of the secondary particles on average increases slowly with increasing primary energy. 4) The proton component in the primary cosmic rays decreases

gradually in the knee region between 1015_–1016_{eV, and the heavy components such as}

iron become predominant there. 5) Several examples of the family events with a peculiar structure were observed. Hadronic interactions can fundamentally be described by quantum chromodynamics (QCD), but rigorous calculations for soft processes such as multiple particle production are almost impossible because of the large coupling constant, which precludes use of the perturbation theory. At present, although the multiple production is basically based on QCD, a considerable part of its description is still dependent on a phenomenological model [7]. The recent problem is whether any anomalous events are to be seen or not in the hadronic interactions in the

energy region over 1016_{eV. It is expected that such phenomena would be found in the}

family events with energies over 1000 TeV, and therefore detailed analysis of such big events is very important. In case of the family analysis so far made, importance has been placed on the study of their total behavior, and no detailed analysis of individual events has been made except for peculiar events. We have already been successful in

observing 10 or more big family events with

!

introduced a new method of family analysis based on the clustering method to analyze individual events. The clustering method is actually applied to the big family events observed in the Mt. Kanbala experiment.

2. – Experiment

The emulsion chamber (EC) used for the experiment on Mt. Kanbala is the equipment composed alternately of absorber and photosensitive layers. In this experiment 2 kinds of absorber are used. One is the lead chamber, as generally used in mountain experiments, and another is the iron one which is exposed to obtain hadronic components with higher detection efficiency. The cascade showers in the individual

events observed in the emulsion chamber are classified statistically into 2 groups, i.e. gamma-rays and hadrons. Here, the showers whose starting depth (Dt) in EC is less than 6 r.l.

(

₎

are defined as gamma-rays, while those with Dt D 6 r.l. are defined as hadrons. The accuracy of the energy determination of the observed showers is estimated to be about 20%, and the location of the starting point can be made with the accuracy of 1 r.l. The minimum energy of showers to be detected in the X-ray films is about 2 TeV for one year exposure at Mt. Kanbala. Then, family events are divided into two classes, i.e. “gamma families” and “hadron families”. The former is composed of only gamma-rays and the latter of both gamma-rays and hadrons. The

number of gamma-ray showers in a family is expressed as Ng and their energy sum is

expressed as

!

3. – Monte Carlo simulation

To confirm the validity of our clustering method, we first generated many pseudo-family events by a Monte Carlo method. By the application of our new method to these events, we then examined how well this clustering method can reproduce the structures of these family events. Since we are interested in the reproducibility of the events, the results will not depend strongly on the details of hadronic interactions to generate family events. The latest accelerator data show that the pseudorapidity

h

(

(

)

)

described by a multicluster model in which each cluster decays isotropically in its rest system [8]. On the other hand, the particles observed in the emulsion chamber experiment have high threshold energy, so that almost all of them are produced in the very forward region. Thus a few clusters produced in the forward region would contribute to a family formation. Based on these facts, we adopted a simple fireball model for the particle production. That is:

1) Primary particles are assumed to be protons with a fixed energy of 4000 TeV. They collide with air nuclei in the atmosphere and produce secondary particles.

Interaction mean free path of protons in the air is taken to be 80 g/cm2_{. In this}

simulation, however, the successive interactions of primary particles are neglected. 2) The production height of family events is sampled in several places ranging from 500 m to 3000 m over the chamber in the atmosphere. The observation height was fixed to be 5500 m above the sea-level (Mt. Kanbala height).

3) Secondary particles are generated through decay of a single fireball (or cluster). This moves relatively to the center-of-mass system with the Lorentz factor gf, and decays into pions in its rest system. Here, the value of gfis estimated to be 45 using the accelerator data shown in fig. 1.

4) The average number of pions from a fireball is assumed to be 15 (2_{). The}

energy spectrum of pions in the forward regions derived using this multiplicity and the

(1_{) In emulsion chamber experiments, a cascade unit (c.u.) is sometimes used instead of radiation} length.

(2_{) According to the accelerator results, total number of secondary particles produced at} E0= 4000 TeV is estimated to be about 70. However, almost all these are produced near the central region so that they do not contribute to a family formation.

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Fig. 1. – Relation between the energy (S1 O2_{) (energy (E}

lab) in laboratory system) in the center-of-mass system and the Lorentz factor gf of fireball. Secondary particles are isotropically

produced in its rest system.jdenote the accelerator results, whereas{denotes the value of gf

used for our simulation.

the Lorentz factor gf= 45 is shown to be almost consistent with that obtained by more

exact treatments [8, 9]. The momentum distribution of these secondary pions is given as follows:

f (Pf) d Pf4 Pf2exp [2

k

(1)

where E0= 130 MeV.

Gamma-rays decayed from p0_{mesons cause electromagnetic cascade showers in the}

atmosphere. Behavior of the gamma-family events in the atmosphere is considerably affected by fluctuation of the development of electromagnetic cascades in the atmosphere, so that cascade processes induced by the produced gamma-rays were calculated by a full Monte Carlo method under the approximation A [10].

4. – Method of cluster analysis

As discussed in sect. 1, family events observed with emulsion chambers are the products of a large number of interactions occurring at various atmospheric depths. That is, in general gamma-ray showers constituting a family are a mixture of those produced at different depths through cascade processes in the atmosphere. When the main interaction height is low, however, it is expected that almost all gamma-rays produced can reach the observation level without significant influence of cascades. In

such a case, we can get direct information about particle production through the analysis of gamma-family events. We briefly discuss the influence of cascades on the

family observation. Spread of gamma-rays in a family is mostly determined by Ptg of

gamma-rays produced by a collision, the decay angle of p0

K 2 g, and the size of the spread by cascades. When the spread by cascades at the observation point is smaller than the spreads of the former two, it is possible to separate individual gamma-rays generated by multiple production, with the help of clustering as discussed later. First, we discuss the effect of transverse momentum of produced gamma-rays. Let the energy of a gamma-ray generated by multiple production be E and its transverse

momentum Ptg. When the production height is H, the spread by Ptg is expressed as

R APtgOE 3 H. On the other hand, the spread by cascading rcas is written as

rcasA EsO(E exp [2HOX0] ) 3X0, where Es= 21 MeV is a scattering constant, X0 the radiation length of air. Then, a height giving almost same spread is obtained by solving

the equation _HOX0exp [2HOX0] AEsOPtg. By substituting Ptg= 100–200 MeV/c

(Ptg-value produced in the forward region is in the order of 100 MeV [11]), we obtain

H A (2–3) X0or 2000–3000 m.

That is to say, if H is lower than about 2000 m, then individual gamma-rays produced by a collision can be distinguished from those generated by cascade processes. In other words, the effect of cascades is very small.

The influence of the decay angle of p0 _{is as follows. Two gamma-rays with an}

opening angle u2 g at the height H are separated by the distance R2 gA H Q u2 g at the observation level. The opening angle u2 gis given by u2 g4 mp0c2_O

k

and Eg2are the energies of two gamma-rays, respectively, and mp0is the rest mass of a

pion. If R2 gO2 D rcas (this means the spread by cascading), then two gamma-rays can

also be distinguished on the X-ray films. We calculated the values of rcasaccording to a Monte Carlo method by changing the energy of pions and the production height. The

results for the case of Eg14 Eg2 are shown in fig. 2, comparing with R2 g. From this

figure, it is seen that the separable production height of two gamma-rays is around 2000 m when the energy of gamma-rays is as high as 200 TeV. Thus, the results are almost the same as those by Ptg.

4.1. Clustering method. – Since cascade particles with energy E spread as wide as

EsOE , a group of gamma-rays close to one another with such a separation can be

regarded as a cluster, each of members having the same origin. It has been verified that an application of this method to the family analysis is effective for the study of the average behavior of family events [6]. It is, however, a fact that some extra showers coalesce into a cluster when the production height of the family is low, though some showers are missing when it is high. Since our aim is to estimate the production height of individual family events, another approach will be required. To compensate the defects seen in the previous methods, we have developed a new clustering method as follows.

Here, we explain our method using a family event obtained by our Monte Carlo simulation. In this family, we arbitrarily choose a shower particle among the showers and compute its distance R to another shower of energy E. All the combinations of the chosen shower with every other shower in the event are taken into account. The scatter plot of R vs. E is shown in fig. 3. It is seen that there are two shower groups, i.e. one with smaller R and the other with larger R. Then a shower group in the side where R is small can be treated as a cluster. We examined this analysis using many Monte Carlo

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Fig. 2. – Comparison of the lateral spread of gamma-rays (R2 g(E) O2) caused by the decay of p0

K 2 g with that caused by cascades (rcas(E)). E denotes the energy of gamma-rays decayed from p0_meson.

identify showers forming a cluster, as shown in fig. 3. Based on this result, we

introduce a distance Wj

(i)

between two showers i and j in a family, which is defined as

Wj

(i)

4 (Ei1 a) Q RijQ

k

(2)

where the values of a , b are determined experimentally, so division of the showers into two groups will be done more efficiently. Using the Monte Carlo data, the numerical

values of a = 3 TeV and b = 15 (TeV1 O2) were obtained, while depending weakly on the

height of observation. For convenience, we further introduce the quantity Lj

(i)

, defined below, so that this quantity takes a value between 0 and 1

Lj (i) 4 1 2 exp [2Wj (i) ] . (3)

Figure 4 shows the same sample as fig. 3, which is plotted using this variable. More clear separation is doubtless possible. In order to express the energy density of shower particles with the variable Lj

(i)

, we introduce another variable Dj

(i) which is defined as Dj (i) 4 3

k

where three showers are used to smooth out the variable D(i)_{. Then the position L}

Fig. 3. – Correlation between lateral spread R and energy E of showers in a family. The distance R is measured from a certain shower which is arbitrarily chosen from the family members.jis the same cluster member as a certain shower, others are denoted bym. A straight line RkE = const is also shown together with the lines of ER = const and R = const.

where the value D(i)_{becomes a minimum, is taken as a boundary of the cluster. Using}

this value, we can pick up showers as members of a cluster. The actual procedure for clustering is as follows.

1) All the showers (labeled as 1 , 2 , 3 , R , i , R , N) in a family are arranged in decreasing order of energy, since a high-energy shower is considered to be closer to the center of a cluster. The first shower particle with the highest energy is regarded as the representative of a cluster, and we call this one the first cluster.

2) We calculate the value of Lj

(1) and Dj

(1)

for the j-th shower ( j42, 3, R , N22) to find the position of Lc( 1 ). All the showers satisfying the conditions of EjE E1 and

Lj

( 1 )

E Lc( 1 )are regarded as members of the first cluster.

3) Then we look for the next shower with the highest energy among the remaining showers. This shower (k-th shower) is regarded as a representative of the next cluster. In this step, all the showers except the representative of the cluster are treated as candidates for membership of this cluster, even if the showers are involved in the other cluster in the previous step.

4) For the k-th cluster, we calculate the values of Lj(k), Dj(k)and Lc(k), and then get the members of k-th cluster, as in step 2.

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Fig. 4. – Correlation between energy E and parameter L. For details, see text.

the values of EjRkj and EjRlj. If EjRkjE EjRlj, then this shower is included in the

k-th cluster.

6) The above steps (from 3 to 5) are repeated until showers belonging to none of the clusters disappear. Finally, we count the number of clusters in a family as Nc.

We applied these procedures to the Monte Carlo events and our results were compared with those obtained by the conventional method [6], as shown in figs. 5. Figures 5.1 and 5.2 represent the family events produced at the height 500 m and 5000 m, respectively. In these figures, all the boldface lines denote the showers to be truly incorporated, whereas lightfaced lines denote those by clustering. From these results it is found that the conventional method has a tendency to cause amalgamation of extra showers to the clusters for family events produced at low altitude, while some showers are left behind in the clustering of those produced at high altitude. However, it has been confirmed that our method makes clustering possible with a considerable correctness, almost independent of the production height of family events.

4.2. Energy estimation of parent particles of individual clusters. – When the

production height of family is not high, it is possible to find a relation among the energy

E0cof parent gamma-ray of each cluster, the cluster energy

!

arb. So, a relation between

!

gOE0c and arb was examined using Monte Carlo events.

The observation point is fixed on Mt. Kanbala. The results are shown in fig. 6. From

this figure, we can then find the following relation to estimate the energy Ec

Fig. 5.1. – Target diagram of showers in a family produced at the height 500 m above the chamber. a) Example of the clusterization according to the conventional method. b) Same as a), but by our method. The boldface line indicates a cluster to be truly amalgamated, whereas the lightfaced line is a cluster by the two methods.

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Fig. 5.2. – Target diagram of showers in a family produced at the height 5000 m. a) and b) are the same as those in fig. 5.1.

gamma-ray of each cluster in the family

Ec

0(

!

!

(

)

Ec

0(

!

!

(5b)

We use this relation in the following discussion, but we must take care when this is used for the family events produced at high altitude.

4.3. Estimation of the production height of family. – Since p0 _{mesons immediately}

decay into two gamma-rays (t A10216_{s), the production point of p}0_{mesons and g-rays}

is the same. These gamma-rays initiate electromagnetic cascades with the mean free path of 9/7 r.l. in the atmosphere, forming clusters. The lateral spread of clusters is mostly determined by the starting point of cascades, which fluctuate considerably. Based on the cascade theory [12], however, it is expected that there is a relation between the lateral spread of cluster and its production height when the cascade is in the early stage of its development, or, in other words, its production height is low in the atmosphere. For such events, clusters are well separated from each other since their

lateral spreads due to cascades are smaller than those by Ptg as discussed above. In

order to find out this relation, Monte Carlo simulation was done for various values of

the primary energy Ec

0 and the production height T (r.l.). Figure 7 shows correlation

between the production height T(r.l.) and the lateral spread of cluster arb for various

values of the cluster energy

!

g. This figure reveals that the production height of

clusters can be approximately expressed as a function of the spread arb and its energy

sum

!

!

!

Fig. 6. – Correlation between

!

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Fig. 7. – Relation between the height T (r.l.) and mean spread of clusters aRb for various cluster energies.

The actual value of T obtained from the above expression markedly fluctuates

according to the size of the dispersion of arb and

!

estimation of the production height of family events with

!

such fluctuations can be diminished by taking the average of many clusters in the family. As discussed later, Monte Carlo results show that the estimation of the production height of family events produced at low altitude can be made with a considerable degree of accuracy.

5. – Check of the analysis

In this section, we examine to what extent the physical quantities characterizing the features of family events can be reproduced through our analysis, using the Monte Carlo events. Hereafter, the physical quantities directly obtained from the simulation are expressed by attaching a subscript “simu.”, whereas those estimated by our method are expressed by attaching a subscript “recas.”

5.1. Energy of parent gamma-rays of clusters. – First of all, let us consider the

parent gamma-ray energy Ec

0 of clusters. For this purpose, we simulated 100

superfamily events by protons. For these events, clustering processing was executed in accordance with the method discussed above. In the following, the clusters consisting

of a single shower ns4 1 , are also included in the analysis, where ns means

Fig. 8.1. – Reproducibility of parent gamma-ray energy of clusters in a family produced at 1000 m.

Fig. 8.2. – Reproducibility of parent gamma-ray energy of clusters in a family produced at 2000 m.

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clusters in the family events produced at the height 1000 m, in comparison with that estimated by our method. It is seen that our method can well reproduce the cluster energies for these family events. When the production height is high, however, the number of clusters consisting of a single shower or isolated clusters increases because of the influence of cascades in the atmosphere and the energy distribution of clusters is shifted to lower energy (fig. 8.2). It is however concluded that for the family events with production heights lower than about 2 km our clustering method works well so that the energy of the parent gamma rays of clusters can be well estimated, in other words, electromagnetic cascades give only minor deformation to the original features of the family events.

5.2. Lateral spread. – As discussed above, when the production height is not high,

almost all gamma-rays produced by a collision can reach the observation point without serious influence of cascades in the atmosphere, so that original features of the family events would be maintained. The lateral spreads of gamma-rays in the family events are generally obtained by use of the distance of each shower measured from the energy-weighted center of showers in the family, since we do not know the direction of incident primary particles. Figure 9 shows the distribution of the lateral spread, R, of each cluster in the family, thus obtained. We compare this with that of the parent gamma-ray in the family at the observation point, where the distance R is measured from the axis of incident primary particles. No obvious differences are found between them as far as we do not assume extremely asymmetrical particle production in the azimuthal direction in our Monte Carlo simulation.

Fig. 10. – Scatterplots of parent gamma-ray energy of clusters and its spread in a family produced at 2000 m. a) Results given by simulation. b) Results obtained by our method.

5.3. E-R correlation. – Figure 10 shows scatterplots of the energy of parent

gamma-rays of clusters and the lateral spread in the family. The results of the simulation and those estimated by our clustering method are compared in this figure. Since the transverse momentum of particles produced in the multiple production is almost constant, data are expected to distribute around the straight line E Q R 4const,

which corresponds to a value of H 3Pt. It is, however, shown that the correlations

become worse with increasing of the production height due to cascading effects. Thus, such a correlation can be used to select the family events produced low in the atmosphere preferentially.

5.4. Production height. – The considerable fluctuations of family phenomena we

observe are attributed mostly to large fluctuations of the interaction height of primary cosmic rays with air nuclei. This means that, if we knew the height of interaction, these fluctuations would considerably be diminished. According to a Monte Carlo simulation [2], the production height of family events on average distributes around the height of several kilometers with a large fluctuation above the observation point. Thus, there will be a chance to observe family events produced low in the atmosphere, and these will provide direct information about the hadronic interactions at very high energies. We examine to what extent the production height of family events can be estimated by our clustering method. For this purpose, we simulated family events induced by protons at various atmospheric depth. Our clustering method was then applied to these super-family events with observed energies higher than 1000 TeV. In this analysis clusters consisting of a single shower are neglected, since most of these are surviving showers of cascading. The production height H(m) of each cluster in the family was estimated by means of eq. (6) shown in subsect. 4.3.

In fig. 11, the ratio of the difference between the estimated height and the true one to the true height is shown. From the figure, it is seen that for the families whose production height is relatively low, ranging from 1000 m to 2000 m, the mean value of

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Fig. 11. – Reproducibility of the production height. The abscissa denotes the true height (m), whereas the ordinate denotes the ratio of the difference between the estimated height and the true one to the true height. j represents the mean value, whereas the solid line denotes one standard deviation.

the height shows fairly satisfactory consistency with the given height. There is a tendency, however, for the mean value to become slightly higher for the events produced at lower altitude, and vice versa. From this study, it may be concluded that for the family events produced low in the atmosphere, say lower than about 2000 m, our clustering method can provide a reliable estimate of the production height.

5.5. Transverse momentum. – Knowledge of the production height of families will

provide detailed information on the features of particle interactions generating family events, such as the transverse momentum and pseudorapidity distributions of

produced particles. The Ptg value of the parent gamma-ray of cluster is estimated by

use of the relation Ptg4 E0c( MeV ) Q R( m ) OH( m ), where R( m ) is the lateral spread of cluster in a family and Ec

0( MeV ) the energy of parent gamma-ray of cluster estimated

by use of eq. (5) given in subsect. 4.2. Figure 12 shows an example of the distribution of

Ptg of parent gamma-rays thus obtained, comparing with those obtained by the

simulation. It is also found that the estimated Pt-distribution is almost consistent with the given one, when the production height is lower than about 2000 m above the chamber. For such events, the deviation from the real value is estimated to be within A 14 % , almost independent of the height.

6. – Analysis of the family events observed at Mt. Kanbala

We applied our clustering method to the super-family events observed in the emulsion chambers at Mt. Kanbala [2]. The family events actually observed are in

Fig. 12. – Pt distribution of clusters with nsF 2. The estimated values are compared with those given by simulation. Height 4 2000 m.

general superposition of nuclear interactions ranging for several generations. Also, for primary particles concerned, not only proton but also various types of nuclei such as helium, carbon, etc. are contained. However since the energy of the individual showers in the family events observed with emulsion chambers is very high, more than 70% of the family events detected are induced by protons [2]. According to Monte Carlo simulation, the family events occurred by an almost single interaction at relatively low altitude can be selected by examining the following: 1) the lateral spread of constituent gamma-rays is rather small and 2) the ER-distribution of gamma-rays is close to an

exponential-type function, that is, this distribution more or less reflects the Pt

distribution of produced gamma-rays. It is, however, known that this distribution approaches a power-law type during the development of cascades. Shown in fig. 13 is an example of the correlation between E and R for a Monte Carlo family observed under the same conditions as the experiment at Mt. Kanbala. This family event was obtained by a full Monte Carlo calculation based on the reliable nuclear interactions which can explain the cosmic-ray data well [2]. Here, we introduce a variable rc(3) to express the distance from each cluster to a straight line expressing ER = const in this figure. This

(3_{) r}

c4 c

!

n the number of clusters. c is estimated to be 5 by use of the Monte Carlo data. According to the Monte Carlo simulation, the value of rcthat can be regarded as ER = const is estimated to be 12.

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Fig. 13. – Examples of the correlation between E and R of clusters in the Monte Carlo events with

!

based on a reliable interaction model [2]. a) Event with multiple nuclear interactions. No correlation is found between E and R (rc= 14.2). b) Single interaction event produced at low altitude of H 41200 m (rc4 6.7).

will give a measure of the degree of concentration of the clusters onto a straight line

whose value of ER is assumed to be constant. Taking the value of rcinto consideration,

we apply our clustering method to the experimental data. Our analysis was focused on

the super-family events whose energy sum (

!

number of the constituent clusters is more than 20. The features of these events obtained from this analysis are summarized in table I.

Here, some more detailed investigation is given to the family event K2F528 with the highest observed energy.

TABLE I. – List of the super-family events with

!

Kanbala.

Name

!

interaction (yOn ) s (h) aPtb (MeV/c) K2F528F 8143.5(4) 485 72 1822 y 0.92 273 K2P244A 2187.9(2) 145 52 2073 y 1.02 311 K1017F 2037.6(2) 174 46 1357 n K1020F 2036.4(2) 152 34 2015 y 0.73 184 K7P667 1959.7(2) 98 20 1521 y 0.71 184 K4F123F 1289.8(4) 82 33 1452 n K6P944F 1285.4(2) 97 33 2524 y 0.22 136 K80B028 1279.0(2) 145 34 1977 n K4P777F 1276.8(2) 89 22 2682 y 0.84 194

Event K2F528

Figure 14a) shows a target diagram of showers in this event

(

and

!

separated fairly well in spite of their high observed energy and also a relatively symmetric distribution of showers is seen in the target diagram. The total number of

clusters obtained is 254, among which the number of the clusters with nsF 2, is 72

Fig. 14. – a) Target diagram of the event K2F528. b) E vs. R distribution of clusters with nsF 2. A straight line of large Ptg (= 260 MeV/c) at the height 2000 m is also shown. c) Clusterization of showers in the central part of the family. d) H distribution of clusters estimated by our method.

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Fig. 14. – (Continued) e) Ptdistribution.

(Nc4 72 ). Figure 14b) shows the scatter plot of energy Ec and spread R of clusters

with nsF 2. It is seen that there is a fairly strong correlation between them, which

distribute around a straight line of ER = const (rc4 10 ). Shown in fig. 14c) is the

clusterization of showers in the central part of this event. The clusters not enclosed by solid lines are the ones regarded as single shower events.

Based on the method discussed in the previous section, we estimated the production height of each cluster with nsF 2 in the family and its distribution is shown in fig. 14d). We then estimate that the main production height of this family is 1822 m. The angular distribution, expressed with pseudo-rapidity h, of the parent particles of clusters shows a Gaussian type with a dispersion s A 0.92. This value is consistent with the assumption that these particles are generated from a fireball which decays isotropically in its rest system. The transverse-momentum distribution of clusters (parent gamma-rays) can also be obtained as shown in fig. 14e). Its mean value is calculated to be A 273 MeV/c. The straight line in fig. 14b) is equivalent to the case of H = 2000 m and

aPtgb = 260 MeV/c. The mean Ptgvalue of gamma-rays produced in the forward region

at accelerator energy region is about 100 MeV/c [11], so that this event seems to

suggest particle production with a large Pt. Further observation of such an event will

make clear the mechanism of particle production at extremely high energies.

7. – Summary

A new method to analyze the family events observed with mountain emulsion chambers has been developed on the basis of a cluster analysis. This method was examined by the use of a Monte Carlo simulation and was shown to have the following advantages.

1) Using the mean lateral spread and the energy sum of clusters in the family, it is possible to estimate the energy of parent particles of clusters and also their production height. These enable us to estimate the main interaction height of super-family events which are produced low in the atmosphere.

2) Based on the result 1), we can obtain a direct information about hadronic interactions through the analysis of family events with energy higher than 1000 TeV.

That is, some important quantities such as angular distribution and Ptdistribution of

secondary particles produced at a collision can be estimated.

Our clustering method was actually applied to the super-family events observed in

the emulsion chambers at Mt. Kanbala. We examined 9 events with

!

Some of these events are estimated to be produced at low altitude, say less than 2000 m. Among the events shown in table I, two events, K2F528 and K2P244, seem to suggest

particle production with a large Ptin the very forward region. Further observation of

such events is very important to get information about hadronic interactions at

energies over 1016eV and our clustering method will be very powerful for the analysis

of such events.

* * *

The author is grateful to Prof. H. NANJO for his encouragement and valuable

discussion. He is deeply indebted to Prof. T. YUDA for his valuable suggestions and

helpful comments. He also wishes to thank all the members of the Japan-China Emulsion Chamber Collaboration for allowing him to use the experimental data and for their kind support. Data analysis and Monte Carlo calculation were made with the computer ACOS 3000 of General Information Processing Center, Hirosaki University.

R E F E R E N C E S

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