The East-West method: an exposure-independent method to search for large scale anisotropies of cosmic rays

The measurement of large scale anisotropies in cosmic ray arrival directions at energies above 10^13 eV is performed through the detection of Extensive Air Showers produced by cosmic ray interactions in the atmosphere. The observed anisotropies are small, so accurate measurements require small statistical uncertainties, i.e. large datasets. These can be obtained by employing ground detector arrays with large extensions (from 10^4 to 10^9 m^2) and long operation time (up to 20 years). The control of such arrays is challenging and spurious variations in the counting rate due to instrumental effects (e.g. data taking interruptions or changes in the acceptance) and atmospheric effects (e.g. air temperature and pressure effects on EAS development) are usually present. These modulations must be corrected very precisely before performing standard anisotropy analyses, i.e. harmonic analysis of the counting rate versus local sidereal time. In this paper we discuss an alternative method to measure large scale anisotropies, the "East-West method", originally proposed by Nagashima in 1989. It is a differential method, as it is based on the analysis of the difference of the counting rates in the East and West directions. Besides explaining the principle, we present here its mathematical derivation, showing that the method is largely independent of experimental effects, that is, it does not require corrections for acceptance and/or for atmospheric effects. We explain the use of the method to derive the amplitude and phase of the anisotropy and we demonstrate its power under different conditions of detector operation.