Separation of muons in the giant air showers by the geomagnetic field

Abstract The observation of giant air showers with energies above ∼10 20  eV is extremely interesting for elementary particle physics and astrophysics. The giant air shower is a cascade of secondary particles (mainly electrons and muons) generated in the atmosphere by an ultrahigh energy (>10 19  eV) primary cosmic ray particle. The density of electrons and muons at a fixed distance from the shower axis (primary particle direction of motion) is usually used as shower energy estimator. The shower arrival direction is estimated with the help of the shower time front of the muons detected. Deflections of muons by the geomagnetic field are noticeable. These deflections perturb not only the energy estimator but also the time delays of the muons detected. Billions of muons diverging from the shower axis are deflected by the geomagnetic field. Because muons are produced at different depths in the atmosphere and with various energies and directions of motion it is a problem to simulate their trajectories. Calculations were carried out in terms of the quark–gluon string model for primary protons and an observation level of 1020 g/cm 2 for inclined showers. Interactions of neutral pions with nuclei in the atmosphere at ultrahigh energies were taken into account. The interactions of the primary particle with the nuclei in the atmosphere were simulated by the Monte Carlo method. The passing of secondary hadrons was treated with the help of the cascade equations. Muons were grouped into blocks with some differences in depth production, zenith and azimuth angles and energy. For every “block” of muons a relativistic equation of motion with ionization losses taken into account was solved as for a single muon with average energy, height production and zenith and azimuth angles in each bin (a method of “group” particle). The calculated lateral distribution of muons displays noticeable asymmetry at all distances from the shower axis and particularly the energy estimator changes by a factor of 1.5. Due to deflection in the geomagnetic field the arrival time of the detected muons increases by tens of ns disturbing the shower time front. Thus it is important to treat experimental data on giant air showers taking into account the geomagnetic field.