Energy and angular distributions of atmospheric muons at the Earth

A fair knowledge of the atmospheric muon distributions at Earth is a prerequisite for the simulations of cosmic ray setups and rare event search detectors. A modified power law is proposed for atmospheric muon energy distribution which gives a good description of the cosmic muon data in low as well as high energy regime. Using this distribution, analytical forms for zenith angle (theta) distribution are obtained. Assuming a flat Earth, it leads to the cos theta(n-1) theta form where it is shown that the parameter n is nothing but the power of the energy distribution. Exact analytical function is obtained for inclined trajectory of muon. A new closed form for zenith angle distribution is obtained without assuming a flat Earth and which gives an improved description of the data at all angles even above 70 degrees. These distributions are tested with the available atmospheric muon data of energy and angular distributions. The parameters of these distributions can be used to characterize the cosmic muon data as a function of energy, angle and altitude.