Study of High-Altitude Coplanarity Phenomena in Super-High-Energy EAS Cores with a Thick Calorimeter

Abstract

A number of phenomena were observed in experiments on the study of cosmic rays at mountain altitudes and in the stratosphere at ultra-high energies; in particular, the coplanarity of the most energetic particles and local subcascades in the so-called families of γ-rays and hadrons in the cores of extensive air showers at E₀ ≳ 2·10¹⁵ eV (√s ≳ 2 TeV). These effects are not described by theoretical models. To explain this phenomenon, it may be necessary to introduce a new process of generating the most energetic particles in the interactions of hadrons with the nuclei of atmospheric atoms. A new experimental array of cosmic ray detectors, including the ADRON-55 ionization calorimeter, has been created to study processes in EAS cores at ultra-high energies. The possibility of using it to study the coplanarity effect is being considered.

1. Introduction

At present, a number of models of hadron–nucleus interactions and the development of so-called extensive air showers (EASs) in the atmosphere are used in experiments investigating super- and ultra-high-energy cosmic rays. Nevertheless, all the models used are not able to describe well enough the complete set of all observed experimental characteristics of air showers. In addition, some results obtained in experiments with X-ray emulsion chambers (XRECs) in mountains and stratosphere have not yet been explained.

One of the interesting phenomena observed in XREC experiments carried out at high altitudes (on mountains and in the stratosphere) is the tendency for the most energetic (E ≈ 10 TeV) γ-rays, electrons/positrons, and hadrons in the central core of a single shower to arrive at the detector in a single plane. As a result, the particle tracks on the detector surface tend towards a straight line. Such groups of high-energy particles are commonly referred to as γ-ray-hadron (γ-h) families. It is important that the above-mentioned phenomena of coplanarity arise and are observed at the initial stage of EAS development. It follows from this that the characteristics of the observed events are somehow related to the characteristics of first interactions of primary cosmic-radiation (PCR) particles in the atmosphere.

Due to high energy thresholds for single particles, γ-ray–hadron families are mainly generated by PCR protons at super-high energies, E₀ ≳ 10¹⁵ eV.

There are five independent sets of experimental data [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16].

First of all, these are high-altitude data obtained by the Pamir Collaboration with the so-called carbon (C) and lead (Pb) XRECs, in γ-ray families with measured energies ΣE_γ > 700 TeV [1,2,3,4,5], and Fe-XRECs (ΣE_γ > 500 TeV) of the Mt. Canbala Collaboration [6,7].

The first data on the phenomenon of coplanarity were obtained by the Pamir Collaboration in high-altitude REC experiments to observe gamma-ray families with measured energies of >700 TeV [1,2,3,4,5], and later by the Mt. Canbala Collaboration [6,7].

The most interesting are two superfamilies (“Strana” [8,9] and “JF2AF2” [10,11,12,13,14,15]) with energies above 1 PeV isolated in the detectors. These events were recorded in experiments carried out, respectively, on a stratospheric balloon and a supersonic Concorde aircraft at very high altitudes. The emulsion technique was used in both experiments. The degree of coplanarity of the most energetic particles in the gamma–hadron families “Strana” and “JF2AF2” is close to the maximum possible value.

In these experiments, the thickness of the atmospheric layer above the detectors is much less than in high-altitude experiments. Accordingly, in this case, the possible nontrivial features of high-energy events associated with a change in the characteristics of the interaction of a PCR particle should be more noticeable. As the thickness of the atmosphere above the detector increases, the characteristics of events observed in high-altitude experiments are distorted by secondary interactions of cascade hadrons in the atmosphere.

It has been concluded that the probability of observing this set of experimental data as a result of fluctuations in the development of EAS is very low [16]. In addition, it has been concluded that the phenomenon is associated with some process of coplanar particle generation (CPG) of the most energetic particles (x_Lab = E/E₀ ≳ 0.01–0.05) at the initial stage of the EAS development initiated mainly by primary protons at E₀ ≳ 2·10¹⁵ eV (√s ≳ 2 TeV).

The ideas proposed to explain the appearance of the CPG at super-high energies are divided into two fundamentally different groups:

(1)

Nuclear-physical mechanisms of hadron interactions, implying large transverse momenta in the coplanar plane, and linking the effect with (a) the angular momentum of the quark-gluon string [17] and (b) the formation of specific leading systems [18,19,20];

(2)

An evolution of the space dimensionality on small scales from three to two dimensions (3D ↔ 2D) with increasing energy [21,22].

Note that the ideas [18,19,20] inevitably include the formation of a coplanar plane by large (compared to the commonly used values) transverse momenta. At the same time, the components of transverse momenta that are directed normally to the plane of coplanarity are characterized by traditional values. A special hypothesis [21,22] is that at very high energies of strong interaction, a decrease in the dimensionality of space can occur, from three dimensions to two dimensions (the so-called three-dimensional ↔ two-dimensional evolution). As a result, localization of transverse momenta of the produced hadrons will take place in a certain plane. The components of transverse momenta directed perpendicular to this coplanarity plane will completely disappear.

The phenomenon of coplanarity of the most energetic particles is observed in the central areas of shower cores. Naturally, it must be associated with the most energetic particles generated in hadron interactions at super-high energies [16]. These experimental data can show that we do not understand some features of hadron interactions. Unfortunately, these phenomena cannot be studied in experiments at the LHC due to the specific collider design [23], which allows only low-energy particles to be registered in the central kinematic region. As a result, the coplanarity effect, as well as its existence, remains unexplored to the end.

Currently, the only experiment that has the potential to investigate the generation of the most energetic particles in hadron interactions of cosmic rays at super-high energies is the ADRON-55 experiment [24].

The ionization calorimeter ADRON-55 is a part of the Hadron–M complex with an effective area of 45,000 m², which also includes scintillation detectors. The complex is located at an altitude of 3340 m a.s.l. and designed to study the shape of the spectrum of primary cosmic radiation (PCR) and its mass composition at energies above 10¹⁵ eV. At present, this energy range has not been studied at all in direct experiments in space. Due to the low intensity of PCR particles, satellite experiments (at least in the energy range of 10¹⁵ eV–10¹⁶ eV) require very large (on the order of several tens of meters) and heavy (weighting several tens of tons) detectors. This is impossible with the current level of development of space technologies. The complex is unique in its location at a high altitude and its ability to register hadrons in EAS cores. These two circumstances significantly increase the information content of EAS investigations. No other installation in the world has such capabilities.

This article presents an analysis of the calorimeter’s capabilities to answer questions related to the above-mentioned coplanarity phenomenon.

2. Cascade Simulation

2.1. Model of Hadron Interactions

To simulate the experimentally observed coplanarity effects, the phenomenological model FANSY 2.0 was developed, including both traditional QGSJ (quark–gluon–string and jets) version and coplanar-particle generation version [25]. In the FANSY 2.0 model, the maximum coplanarity is associated with the most energetic hadrons. With decreasing the absolute value of rapidity, $\left|y\right|$, the coplanarity weakens and completely disappears in the central kinematic region at $\left|y\right|\lesssim y_{thr}\approx 2-3$. In interaction simulation, the “coplanarization” process is applied after the interaction has been played out in the traditional FANSY 2.0 QGSJ version. In this case, the transverse momenta of the particles are turned towards a randomly chosen coplanarity plane [25,26,27].

The development of a nuclear-electromagnetic cascade in the atmosphere after the first interaction of a PCR particle is simulated within the framework of the scheme originally used for the FANSY 1.0 model [28]. Since all the proposed theoretical models associate the coplanarity phenomenon with proton interactions, vertical EASs from PCR protons with an energy of $E_0$ ≥ 2 PeV were simulated at the first stage. The energy threshold for registering EAS particles was taken to be $E_{thr}$ = 200 GeV. When simulating cascades in the atmosphere, events were recorded in which the total energy of all particles of the electromagnetic and hadronic components arriving at the calorimeter surface exceeded 500 TeV.

It should be emphasized that FANSY 2.0 is an ad hoc model, i.e., purely phenomenological, since its physical foundations remain unclear. If we remain within the framework of generally accepted concepts, then theoretical models [17,18,19,20] almost inevitably require large values of the transverse momentum to describe coplanarity (which contradicts the LHC data); otherwise, we would have to assume a decrease in the transverse momentum components directed perpendicular to the coplanarity plane (which does not fit into the framework of modern concepts). Therefore, from a phenomenological point of view, the most suitable physical process is the 3D ↔ 2D evolution [21,22] (hereinafter, for brevity, the 2D hypothesis), reproduced by the FANSY 2.0 2D version.

2.2. On the Lateral Resolution of ADRON-55

Simulation of the detector response is a complex task that requires a lot of computer time. In addition, it is difficult to expect fundamental changes in the results even after a very detailed examination of the detector response. Therefore, at the first stage of the research, the goal of our simulations is to calculate the distribution of the energy fluxes of the electromagnetic and hadronic components arriving at the upper surface of the ADRON-55 detector, within the FANSY 2.0’s QGSJ and 2D versions.

The lateral resolution of the ADRON-55 detector is primarily determined by the resolution of the ionization chambers (ICs), which in each layer are located perpendicular to the ICs in the adjacent layers. The effective width of each IC, Δ_IC, is about 11 cm. For the calculations, Δ_IC = 10 cm was chosen. To simplify the modeling, it was assumed that the upper surface of the detector consists of cells of 10 × 10 cm² in size. Obviously, in such a detector, it is possible to determine the coordinates of only a few of the most powerful energy fluxes entering individual cells, and not individual particles. This, in itself, is a very difficult problem, which can be solved by improving the registration system. However, this paper does not address detector response issues. We want to understand whether any differences between EAS subcore characteristics obtained within different models persist at the ADRON-55 calorimeter location level. In particular, the objective of the present modeling was to study the azimuthal characteristics of the most powerful energy flows of the electromagnetic and hadronic components falling on individual cells.

2.3. The “Decascading” Procedure

In order to isolate the energy flows of the EAS subcores falling on individual cells and to combine individual energy flows initiated by genetically related EAS particles, generated in the interactions of more energetic shower particles, into more powerful conventional objects (hereinafter conventionally called “particles”), the work presented in this article uses the so-called “decascading” procedure (see e.g., Ref. [29]) described below.

The so-called decascading parameter Z_C is determined. All the “particles” of the event are arranged in order of decreasing energy. We select the “particle” with the lowest energy (this will be, for example, the i-th “particle”). After that, we go through all the paired combinations of the i-th “particle” with other “particles” (with the k-th, l-th, m-th… “particles”). For each pair of “particles” (for the i-th and k-th, for example), the parameter Z_ik = R_ik·(1/E_i + 1/E_k)⁻¹ is calculated. Here, R_ik is the distance between the “particles”, E_i and E_k are their energies. If Z_ik < Z_C, and this value is the smallest of all the combinations considered, then the i-th and k-th “particles” are combined into a certain virtual “particle” with energy E* = E_i + E_k and coordinates x* = (x_i·E_i + x_k·E_k)/E* and y* = (y_i·E_i + y_k·E_k)/E*, considered further as a single whole. After this, the procedure is repeated, i.e., all the “particles” of the event under consideration (including the new virtual “particle”) are again lined up in order of decreasing energy, after which the “particle” with the lowest energy is selected, for which all paired combinations with other particles are sorted out, and so on.

The physical meaning of this procedure is as follows. At the small Z_C, decascading combines electromagnetic particles (e^±, γ) into some virtual objects that arose as a result of the development of the EM cascades initiated by individual γ- rays that arose during the decays of π⁰ mesons. With an increase in Z_C by several times, we combine into one object the e^± and γ-rays that arose as a result of the development of EM cascades from both γ-rays that arose during the decay of a π⁰ meson. With a further increase in Z_C, e^± and γ-rays that arose as a result of the development of EM cascades from γ- rays that arose during the decay of several π⁰ mesons that were born in one hadron interaction are combined into one object. Decascading at even higher values of Z_C combines electromagnetic particles and hadrons into one object. In very simplified terms, as the Z_C value increases, we move from the observation level to the beginning of the cascade, i.e., to the first interaction of the PCR particle. The actual effective Z_C values depend on the experimental conditions (observation height, registration thresholds, etc.).

For further analysis, three types of events are selected, containing (a) only the electromagnetic component; (b) only the hadronic component; (c) “all”, i.e., the sum of the electromagnetic and hadronic components. These events must satisfy the conditions as follows: (a) ΣE_EM ≥ 500 TeV, (b) ΣE_h ≥ 500 TeV, (c) ΣE_All ≥ 500 TeV, respectively, with initial multiplicity n₀ (Zc = 0) ≥ 4. The initial number of selected events is denoted by M₀.

It should be recalled that the number of particles in the γ-ray-hadron family, n₀ (Zc = 0), is limited. The number of virtual “particles” of the event, n′(Zc), that can potentially be used to calculate the parameter λ_N decreases as the value of the parameter Zc increases. At some values of Zc, n′(Zc) becomes less than N. In this case, this event can no longer be used to calculate the parameter λ_N. Accordingly, in this case, the total number of events selected for consideration, Msel (Zc), also gradually decreases as Zc increases.

2.4. Determining the Coplanarity of an Event

To analyze the alignment of N objects on a detector surface, the parameter ${\lambda }_N={\Sigma }_{i \ne j \ne k}^N Cos 2{\phi }_{ij}^k/\left[N\left(N-1\left)\right(N-2)\right.\right]$ is used (see [1,4] e.g.,). It decreases from unity (in a case of N objects located on a perfectly direct line) t o λ_N ≈ −1/(N − 1) (in cases close to isotropic). Here, ${\phi }_{ij}^k$ is the angle determined by vectors directed from the k-th object to the i-th object and j-th one.

Therefore, the variable N determines the number of the most powerful coplanar energy fluxes entering the detector cells, which are subject to further consideration.

Events are considered as “coplanar” if the condition λ_N ≥ λ_copl is satisfied for the N most energetic objects of these events. We use the values N = 4 and 6 with λ_copl = 0.80, 0.90, and 0.95.

3. Results

As a result of the analysis of γ-ray-hadron families, Z_C dependences of the W (Z_C, λ_N ≥ λ_copl) probability of observing coplanar events with N most energetic objects were obtained. Here, W (Z_C, λ_N ≥ λ_copl) = M_copl (Z_C, λ_N ≥ λ_copl)/M_sel (Z_C) shows the probability that when using the decascading parameter Z_C, M_sel (Z_C) events are selected for further analysis, of which M_copl (Z_C, λ_N ≥ λ_copl) events satisfy the coplanarity requirement λ_N ≥ λ_copl.

Figure 1 shows the dependence on Z_C of the probability of selection (using the λ₄ criterion) of the four most powerful coplanar energy flows arriving at the detector cells, W (Z_C, λ₄ ≥ 0.80), W (Z_C, λ₄ ≥ 0.90), W (Z_C, λ₄ ≥ 0.95) (from top to bottom) for the QGSJ (left) and 2D (right) versions of the FANSY 2.0 model for the electromagnetic (“EM”) component, the hadronic (“hadrons”) component, and energy flows that can include particles of both the electromagnetic and hadronic components (“All”) arriving at the same cell.

The errors shown in the figure are statistical. Their growth is due to the decrease in M_copl (Z_C, λ_N ≥ λ_copl) and M_sel (Z_C) with the growth of the Z_C parameter.

A small but stable difference in values of the W (λ₄ ≥ 0.80) probability distributions given by QGSJ and 2D versions can be seen. The difference in the W (λ₄ ≥ 0.90) distributions in QGSJ and 2D versions is already more noticeable (although it is still small). A more noticeable difference is demonstrated by the W (λ₄ ≥ 0.95) distributions. It is significant that the observed excess in the 2D version predictions compared to the QGSJ version predictions occurs only for the hadronic component.

We draw attention to the fact that in both models, the values of the W (Z_C, λ₄ ≥ λ_copl) probability distributions are very small. The experimental values of W (λ₄ ≥ λ_copl) in XREC experiments [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] are considered in the range of ~0.2–0.99. However, the values of W (Z_C, λ₄ ≥ λ_copl) probability distributions, shown in Figure 1, do not exceed 0.01 even for λ_copl = 0.80, whereas for λ_copl = 0.90 and 0.95, the simulated probabilities are even lower.

The fact that the values of the W (Z_C, λ₄ ≥ λ_copl) probabilities, predicted by both the models, do not differ too much, indicates a very important role of fluctuations in the EAS development and their significant influence on the occurrence of background-aligned events at the altitude of the ADRON-55 calorimeter. In addition, the above results show that the sizes of the detector cells (Δ_x,y = 10 cm) and the corresponding lateral resolution, within which it is necessary to separate the energy flows, are not effective enough to carry out such experiments. The reason is that the higher the energies of the particles (and the subcascades initiated by them), the closer their trajectories are to the shower axis.

The reason is that the higher the energies of the particles (and subcascades initiated by them), the closer to the shower axis the trajectories of these particles are located. In a large part of the events arriving at ADRON-55, the most powerful energy flows with a high probability fall into one cell. For comparison, we recall that in experiments with high-altitude and stratospheric XRECs, the values of the corresponding lateral resolution are much better, namely, Δ_x,y ~ 1 mm.

Figure 2 shows the dependence on Z_C of the probability of separation of events with the six most powerful coplanar energy flows arriving at the detector cells, W (λ₆ ≥ 0.8). According to the QGSJ (left) and 2D (right) models for the EM component, the hadronic component and energy flows that can include particles of both components arrive at the same cell (“All”).

One can see a small difference in the W (λ₆ ≥ 0.8) probability distributions for the hadronic component in the QGSJ and 2D versions. However, the statistical significance of the results is too low to discuss these results.

With further tightening of the selection conditions (increasing the number of powerful coplanar energy flows under consideration and the values of λ_copl), the number of selected events rapidly decreases. In particular, the dependence on Z_C of the probability of detecting eight aligned most powerful energy flows arriving at the detector cells was considered, i.e., W (λ₈ ≥ 0.8), W (λ₈ ≥ 0.9), W (λ₈ ≥ 0.95). However, no statistically significant results have been obtained within the framework of both the models, QGSJ and 2D.

Thus, we can hope that we will be able to understand whether coplanar generation of the most energetic particles in the interactions of PCR particles actually exists, if we manage to isolate four or five most powerful energy flows of the hadron component in the EAS cores. Calculations show that with the existing design of the ADRON-55 detector, it is not easy to isolate the effects associated with real coplanar generation of particles (QGP) (regardless of the nature of the physical processes leading to the appearance of QGP). At a minimum, a very large experimental database is required.

4. Conclusions

The obtained preliminary results are intermediate. However, we can draw some preliminary cautious conclusions.

It is necessary to additionally implement a large amount of simulation; in particular, it is necessary to consider the response of the ADRON-55 calorimeter to the passage of EAS particles through it.

The ADRON-55 ionization calorimeter can potentially be used to study the coplanar generation of the most energetic particles in EAS initiated by ultra-high-energy PCR particles.

It will be necessary to accumulate large statistics of experimental data and simulated events.

The hadron component is the most informative EAS component.