Coulomb interacting Bose–Einstein correlations in Fourier space

In high-energy heavy-ion physics experiments, a state of matter is created that existed in the early Universe: the quark-gluon plasma. This strongly interacting matter exists in today’s experiments only within a range of a few femtometers and for a duration of a few femtometers per speed of light, making its resolution with optical tools impossible. However, there is a method that allows for a closer look into the structure of the quark-gluon plasma: femtoscopy. Initially used in astronomy, femtoscopy is based on the quantum mechanical indistinguishability of identical particles, which causes them to arrive at detectors in a correlated manner. The measurable correlation is related to the space–time structure of the particle-emitting source, which in heavy-ion physics is the quark-gluon plasma created in collisions. For free particles, a relatively simple relationship exists between the source and the correlation (essentially a Fourier transform). However, this relationship becomes complex when accurately accounting for the repulsive Coulomb interaction between final-state electrically charged particles. Our paper presents a new method that is more precise than previously used ones, yet less computationally demanding, especially for the exotic source function shapes. Mathematically, the method is interesting because it exactly handles many emerging integrals and limits. Practically, it is ready for use in experimental analyses.