LHC data and cosmic ray coplanarity at superhigh energies

A new phenomenological model FANSY 2.0 is designed, which makes it possible to simulate hadron interactions via traditional and coplanar generation of most energetic particles as well as to reproduce a lot of LHC (ALICE, ATLAS, CMS, TOTEM, LHCf) data. Features of the model are compared with LHC data. Problems of coplanarity are considered and a testing experiment is proposed.


Introduction
A number of models of hadron interactions with nuclei is concurrently applied in cosmic-ray experiments as none of them can explain the entire experimental data set of EAS features. Besides, a number of phenomena observed in mountain-based and stratospheric X-rayemulsion chamber (XREC) experiments are not yet explained. One of these interesting phenomena is the so-called coplanarity of the most energetic cores of γ -ray-hadron families, i.e., groups of high-energy (E n · 1 TeV) particles in relatively young EAS cores initiated by protons and nuclei of the primary cosmic radiation (PCR) (see Sect. 3).
The phenomenological model FANSY 1.0 was designed a few years ago, which helped to understand general features of coplanar events [1]. FANSY 1.0 gives reasonable results as compared with experimental data on intensity of γ -ray families, energy dependence of the muon and hadron spectra and so on [1].
However, FANSY 1.0 cannot properly reproduce LHCf data on high-X F γ -rays e.g. [2], and neutrons, which are really important for cosmic ray experiments, as well as the transversal size of γ -ray families, e.g. [3].
To improve this situation, a new phenomenological model FANSY 2.0 is designed, which simulates traditional and coplanar particle generation and reproduce experimental data with a higher accuracy as compared with FANSY 1.0. FANSY 2.0 reproduces a number of ALICE, ATLAS, CMS, TOTEM data on charged, strange and charmed stable and resonance particle generation, LHCf data on high-X F gamma-rays and neutrons. This paper is devoted to pp interactions simulated at superhigh energies ( √ s = 900 GeV −13 TeV). Compatibility of FANSY 2.0 and LHC data will be discussed in more detail in another work [4].
This paper is organized as follows. Section 2 presents comparison of LHC data and simulated results. Coplanarity problem is briefly considered in Sect. 3

Charmed particles
Among different aims, FANSY 2.0 is designed to study the "forward-physics" aspects of the generation of charmed      particles. So these particles are considered below in more detail as compared with light-quark hadrons. Figure 5 shows LHCb dσ/dy distribution of D ± s mesons with 1.0 < p t < 8.0 GeV/c at √ s = 7 TeV in pp interactions (lower triangles). Figure 6 shows FANSY 2.0 and ATLAS dσ/d|η| distributions of D ± (left) and D* ± (right) mesons with p t > 3.5 GeV/c in pp interactions at √ s = 7 TeV [13]. Figure 7 shows ALICE dσ/dp t distributions of D + (top,left), D 0 (top,right) mesons as well as strange D + s (bottom,left), vector D * + (bottom,right) mesons at |y| < 0.5 and √ s = 7 TeV in pp interactions [14]. Experimental systematic uncertainties are approximately equal to statistical ones. Figure 8 shows LHCb data on d 2 σ/dp t dy distributions of D + mesons in five rapidity regions,    namely, at 2.0 − 2.5, 2.5 − 3.0, 3.0 − 3.5, 3.5 − 4.0, and 4.0 − 4.5 at √ s = 7 TeV (top) and √ s = 13 TeV (bottom) with diamonds, squares, circles, triangles, and crosses, respectively [15,16]. Spectra are multiplied by 10 m , where m = 4, 3, 2, 1, 0 for the above-mentioned rapidity ranges, respectively. Figures 9 and 10 show LHCb d 2 σ/dp t dy distributions of D * + and D + s mesons, respectively [15,16]. All the notations are the same as in Fig. 8. Figure 11 shows data of the ALICE experiment on d 2 σ/dydp t of ω 0 (squares) and φ mesons (triangles) at 2.5 < y < 4.5 [17]. Comparison of cross sections of generation of these mesons gives information on the suppression of strange quark generation. Figure 12 shows experimental dσ/dp t spectra of D ± (left) and D * ± (right) mesons at |η| < 2.1 by the ATLAS experiment at √ s = 7 TeV. Table 1 shows ALICE and FANSY 2.0 cross sections of D 0 , D + and D * + charmed-meson generation at |η| < 0.5 in wide p t ranges. Table 2 shows ALICE and FANSY 2.0 ratios of yields of charmed mesons, D + s /D + and D + s /D 0 , as well as a ratio of prompt vector mesons to prompt vector+pseudoscalar mesons, P V = D * /(D * + + D + ), at |η| < 0.5.

General view
A tendency to a coplanarity of the most energetic cores of γ -ray-hadron families observed was first found by the Pamir Collaboration [19][20][21][22][23] and confirmed later in [24][25][26][27]. The probability W f luct tot for the total set of these experimental results to be produced by cascade fluctuations is much lower than 10 −10 [1,28]. This result illustrates that strong "forward-physics" interactions at superhigh energies are not well-described with the quarkgluon string model (QGSM) concept.
The phenomenon is related to hadron-nucleus interactions at E 0 10 16 eV ( √ s 4 TeV) [29], characterized by a large cross section (comparable with σ pp inel ) and was initially interpreted as a manifestation of large transverse momenta of the most energetic fragmentationrange particles (X Lab = E/E 0 0.1) [28]. Figure 13. CMS+TOTEM and FANSY 2.0's dn ch /dη data for events selected at √ s = 8 TeV under the following requirements. "NSD-enhanced" data: n ch ≥ 1 in the ranges −6.5 < η < −5.3 and 5.3 < η < 6.5 (a); "more-forward" data: n ch ≥ 1 in the ranges −6.5 < η < −5.3 or 5.3 < η < 6.5 (b); "SD-enhanced" data (lower triangles): n ch ≥ 1 only in the ranges −6.5 < η < −5.3 or only 5.3 < η < 6.5 (c); "more-forward" data (upper squares) derived with displaced interaction points: n ch ≥ 1 in the ranges −7.0 < η < −6.0 or 3.7 < η < 4.8 (d).   This phenomenon could be reproduced in the framework of two concepts as a result of a) conservation of the angular momentum of a relativistic fast-rotating quark-gluon string (QGS) stretched between colliding hadrons [31]; b) semihard double diffraction (SHDID) dissociation and appearance of coplanarity as a result of QGS tension inside the diffraction cluster between a semihardly scattered constituent quark and other spectator quarks of the projectile hadron and its following rupture [32] with a lower multiplicity and higher average energy of particles; c) the most extraordinary explanation assumes that this phenomenon could be described within the recently proposed hypothesis of "crystal world", with latticed and anisotropic spatial dimensions and decrease of dimension number with increasing energy [33].

ISVHECRI 2016
In this work, only the first approach is considered.  To study this problem, FANSY 2.0 QGSCPG version is designed [34], which simulates both traditional and coplanar particle generation. More details of comparison of LHC data with results of simulation with the abovedescribed basic FANSY 2.0 QGSJ version are given in [34].

Coplanarity concepts
Simulation using tentative FANSY 2.0 QGSCPG versions demonstrated the following fundamental problem.
The originally exploited concept qualitatively explains the observed coplanarity of momenta of most energetic particles with assuming their high transverse momenta in a coplanarity plane. However, in this case a significant p t growth suppresses dσ/dy and dσ/dη distributions of hadrons at highest |y| and |η| values and creates robust peaks at 2 |η| 4 which are contrary to LHC data (Fig. 17). This was an unsolvable problem for all the QGSCPG versions based on the primary coplanarity concept. However, the coplanarity is observed in cosmicray experiments. Is it possible to reconcile this result with the LHC data?
Simulation has shown that a general agreement of LHC data and idea of coplanar generation becomes real Figure 19. Qualitative dependence of the traditional, intermediate and coplanarity ranges on rapidity.
only using a new concept of coplanarity origin, namely, some decrease of particle's transverse momenta directed normally to the coplanarity plane takes place so that the absolute p t values do no change. Figure 18 shows three examples of tracks of particles, generated in the same imaginary interaction, on a target plane, placed at some distance from the interaction point, in the cases of traditional QGSM-like interaction (left), primary-concept coplanar interaction with increased p t (middle), and new-concept coplanar interaction with traditional p t (right). Most energetic particles are shown with large black circles. The geometric scale is given in arbitrary units.

Coplanarity simulation
All simulated interaction characteristics (excluding azimuthal ones) simulated with FANSY 2.0 QGSJ and QGSCPG versions, are similar. The QGSJ and QGSCPG versions merge smoothly at √ s 2 TeV. In the QGSCPG version all characteristics of particles are primarily simulated with the traditional way. If the summary energy of secondary particles is higher than a fixed value, transversal momenta of high-rapidity particles in the coplanarity range (|y| > y copl ), the algorithm turns − → p t of each such particles towards the coplanarity plane. This plane is determined by the momenta of the interacting hadrons and − → p t of leaders surviving after the collision. The trend of turning of transverse momenta of secondary particles to this plane is weakening at y int < |y| < y copl (in the intermediate range) and disappears at |y| < y int ( the traditional range). Here |y max | = √ s/2/m, y copl ≈ y max − y ≈ 5 − 6, y int ≈ 2 − 3, y = 3 − 5, m is particle mass. Figure 19 shows a qualitative dependence of the traditional, intermediate and coplanarity ranges on rapidity.

On the search for coplanarity at the LHC
The CASTOR experiment seems to be promising in studying coplanarity (at least, in the framework of FANSY 2.0). Figure 20 shows a simplified CASTOR's cross section scheme and an example of detection of one coplanar interaction. The detector consists of 16 segments and is divided in the middle by a vertical slit. Particles are considered to be detected if their pseudorapidity values are in the range of 5.3 < η < 6.5 and they do not fall into the vertical slit. Black circles in Fig. 20 show tracks of  particles. The larger the circle size, the higher the energy of the particle. High-energy particles show a tendency to some coplanarity. Low-energy particles form a more or less azimuthally symmetric halo. To analyze events, energy values "measured" in each of the segments, E i (E i ≥ 100 GeV, i is the number of a segment), are used. Events with total energy E i ≥ 1 TeV "measured" in two or more segments are only analyzed. The first number is assigned to a segment with a maximum release of energy, E max . Here and below, E 1 = E max , E cop = E 1 + E 9 ; E tr = E 5 + E 13 , i.e., it is the energy measured in 9th and 13th segments, perpendicular to the first segment. A simple parameter is applied, namely, ε cop = E cop /(E cop + E tr ), which characterizes the event coplanarity degree. If ε cop = 1, the degree of event coplanarity is maximum. Figure 21 shows ε cop distributions for FANSY 2.0 QGSJ and QGSCPG versions at √ s = 7 TeV. Difference between model predictions becomes very large at ε cop → 1.

Conclusion
The FANSY 2.0 Monte Carlo code is designed to study superhigh-energy cosmic-ray "forward physics" interactions and includes traditional QGSJ QGSM-based version as well as a QGSCPG one which realizes a coplanar particle generation (CPG).
CPG process simulated with FANSY 2.0 QGSCPG does not contradict LHC data and could be tested in the CASTOR experiments. To reconcile experimental and simulated data, it is necessary to replace the primary concept of growth of transverse momenta of most energetic particles in the coplanarity plane with a new concept of reduction of transverse momenta directed normally to the coplanarity plane.
A version of the appearance of CPG processes in double-diffraction interactions only requires a separate consideration, as in this case the energy spectrum of secondary particles is more hard which is important in cosmic-ray experiments.