Efficient and robust calculation of femtoscopic correlation functions in spherical harmonics directly from the raw pairs measured in heavy-ion collisions

We present the formalism for calculating the femtoscopic correlation function directly in spherical harmonics. The numerator and denominator are stored as a set of one-dimensional histograms representing the spherical harmonic decompositions of each. We present the formalism to calculate the correlation function from them directly, without going to any three-dimensional histogram. We discuss the practical implementation of the method and we provide an example of its use. We also discuss the stability of the method in the presence of angular holes in the underlying data (e.g., from experimental acceptance).