𝜋+⁢𝜋−Coulomb interaction study and its use in data processing

In this work, the Coulomb effects (Coulomb correlations) in 𝜋+⁢𝜋− pairs produced in p+Ni collisions at 24  GeV/𝑐, are studied using experimental 𝜋+⁢𝜋− pair distributions in 𝑄, the relative momentum in the pair center-of-mass system (c.m.s.), and its projections 𝑄𝐿 (longitudinal component) and 𝑄𝑡 (transverse component) relative to the pair direction in the laboratory system (LS). The major part of the pion pairs (“Coulomb pairs”) is produced in the decay of 𝜌, 𝜔 and Δ resonances and other short-lived sources. In these pairs, the significant Coulomb interaction occurs at small 𝑄, dominating the 𝜋+⁢𝜋− interaction in the final state. The minor part of the pairs (“non-Coulomb pairs”) is produced if one or both pions arose from long-lived sources like 𝜂,𝜂′ or from different interactions. In this case, the final state interaction is practically absent. The 𝑄, 𝑄𝐿, and 𝑄𝑡 distributions of the Coulomb pairs in the c.m.s. have been simulated assuming they are described by the phase space modified by the known point-like Coulomb correlation function 𝐴𝐶⁡(𝑄), corrected for small effects due to the nonpointlike pair production and the strong two-pion interaction. The same distributions of non-Coulomb pairs have been simulated according to the phase space, but without 𝐴𝐶⁡(𝑄). In all 𝑄𝑡 intervals, the experimental 𝑄𝐿 spectrum shows a peak around 𝑄𝐿=0 caused by the Coulomb final state interaction. The full width at half maximum increases with 𝑄𝑡 from 3  MeV/𝑐 for 0<𝑄𝑡<0.25  MeV/𝑐 to 11  MeV/𝑐 for 4.0<𝑄𝑡<5.0  MeV/𝑐. The experimental 𝑄𝐿 distributions have been fitted with two free parameters: the fraction of Coulomb pairs and the normalization constant. The precision of the description of these distributions is better than 2% in 𝑄𝑡 intervals 2–3, 3–4, and 4–5  MeV/𝑐 and better than 0.5% in the total 𝑄𝑡 interval 0–5  MeV/𝑐. It is shown that the number of Coulomb pairs in all 𝑄𝑡 intervals, including the small 𝑄𝑡 (small opening angles 𝜃 in the LS) is calculated with theoretical precision better than 2%. The comparison of the simulated and experimental numbers of Coulomb pairs at small 𝑄𝑡 allows us to check and correct the detection efficiency for the pairs with small 𝜃 (0.06 mrad and smaller). It is shown that Coulomb pairs can be used as a new physical tool to check and correct the quality of the simulated events. The special property of the Coulomb pairs is the possibility of checking and correcting the detection efficiency, especially for the pairs with small opening angles.