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.

中文翻译：

---

π+π−库仑相互作用研究及其在数据处理中的应用


在这项工作中，使用 Q 中的实验 π+π− 对分布在 Q 中、对质心系统 （cms） 中的相对动量及其投影 QL（纵向分量）和 Qt 来研究 π+π− 对中产生的库仑效应（库仑相关性）（横向分量）相对于实验室系统 （LS） 中的对方向。π 对（“库仑对”）的主要部分是在 ρ、ω 和 Δ 共振以及其他短期源的衰变中产生的。在这些对中，显著的库仑相互作用发生在小 Q 处，在最终状态下主导 π+π− 相互作用。如果一个或两个 pions 产生自 η，η′ 等长寿命来源或来自不同的相互作用，则会产生对的次要部分（“非库仑对”）。在这种情况下，最终的 state 交互实际上是不存在的。c.m.s. 中库仑对的 Q、QL 和 Qt 分布已经被模拟，假设它们是由已知的点状库仑相关函数 AC（Q） 修改的相空间描述的，并针对由于非点状对产生和强双 pion 相互作用而产生的小效应进行了校正。根据相空间模拟了非库仑对的相同分布，但没有 AC（Q）。 在所有 Qt 区间中，实验 QL 谱图都显示由 Coulomb 最终状态相互作用引起的 QL=0 附近的峰值。半峰全宽随 Qt 的增加而增加，从 0<Qt<0.25 MeV/c 的 3 MeV/c 增加到 4.0<Qt<5.0 MeV/c 的 11 MeV/c。实验 QL 分布拟合了两个自由参数：库仑对的分数和归一化常数。这些分布的描述精度在 Qt 区间 2-3、3-4 和 4-5 MeV/c 中优于 2%，在总 Qt 区间 0-5 MeV/c 中优于 0.5%。结果表明，所有 Qt 区间中的库仑对数，包括小 Qt（LS 中的小张开角 θ）的计算精度优于 2%。通过比较小 Qt 处库仑对的模拟数和实验数，我们可以检查和校正 θ 小（0.06 mrad 及更小）的库仑对的检测效率。结果表明，库仑对可以用作检查和校正模拟事件质量的新物理工具。库仑对的特殊特性是可以检查和校正检测效率，特别是对于张开角度较小的对。