Investigation of angular distributions in the interaction of cosmic-ray particles with a dense target and comparison with data of the Large Hadron Collider.

[1] N.A Dobtoyin, A brief history of the first period of field work of cosmic rays at the Physics Institute of the USSR, FIAN, Moscow 1998 [2]. G.T. Zacepin, Nuclear cascade process and its role in the development of broad atmosfer showers // DAN USSR, 1949, T. 67, P. 993 [3] Sadykov T.Kh., Determining the height of the interaction of hadrons to install Hadron-44" // AGU Abay. 2003, No1 (7), P. 200-201. [4] S. Towers, Kernel probability density estimation methods, State University of New York at Stony Brook. [5] Observation of Long-Range, Near-Side Angular Correlations in Proton-Proton Collisions at the LHC. The CMS Collaboration_ . arXiv:1009.4122v1 [hep-ex] 21 Sep 2010 Studies of interactions of cosmic ray particles with a dense target using X-ray emulsion chambers (REC) have been carried out on the high altitude research station of cosmic rays, located at an altitude of 3340 m in the Tien-Shan mountains. [1,2]. REC method is based on X-ray emulsion detectors that enable to collect statistics for determined time period. The main object of study is a group of genetically related particles (gamma rays and hadrons) with sufficiently high energy, which result from interaction with solid target or with air nuclei of primary high-energy particles. These groups of particles called families. To determine azimuthal anisotropy in interaction of cosmic-ray particles two-particle correlations were used, which is a powerful tool for studying the formation mechanism of particles in high-energy collisions of hadrons and nuclei. These studies provide important information characterizing quantum chromodynamics (QCD) in the power mode, especially hadronization mechanism and possible collective effects due to the particles high density, which can be achieved in such collisions. From a consideration of the distribution presented it is evident that it is divided into three families, separated from each other. The left side corresponds to small EPC heights, the central part grouped around target events and the right side with the families of atmospheric interactions. Thus, using information from ionization calorimeter and application of above criteria enable to select 2657 gamma rays families from 10,199 recorded events. Further, 462 events were selected at gamma rays families with n≥4. Two-dimensional correlation functions as Δη-Δφ were studied for these events. Where Δη – difference by pseudorapidity (η = -ln (tan (θ / 2)) with the polar angle, measured as the deviation from beam axis, Δφ is the difference between azimuth angles of two particles. To find two-dimensional correlation function in plane of Δη-Δφ Gaussian kernel PDE can be application in Monte-Carlo generation with N events generated in a k-dimensional parameter space. These events are distributed by some unknown PDF, f(x). Gaussian kernel method carry out an assessment the value of the PDF at x point by the summary of Gaussains that centered at the Monte Carlo generated points, {yi, i=1, N} [4]: