A note on the tensor and vector exchange contributions to \(K \bar K \to K \bar K, D \bar D \to D \bar D \) and \(\pi^+ \pi^-\to \pi^+ \pi^-\) reactions

• Published in: arXiv.org
• Main Authors: Abreu, Luciano M, Song, Jing, Brandão, Pedro C S, Oset, Eulogio
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 13.03.2024
• Subjects: Exchanging; Mathematical analysis; Mesons; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2310.14015

In this note we study the tensor and vector exchange contributions to the elastic reactions involving the pseudoscalars mesons \(\pi^+ \pi^-\), \(K^{+}K^{-}\) and \(D^{+}D^{-}\). In the case of the tensor-exchange contributions we assume that an intermediate tensor \(f_2(1270)\) is dynamically generated from the interaction of two virtual \(\rho\) mesons, with the use of a pole approximation. The calculation of the two-loop amplitude is facilitated since the triangle loops can be factorized and computed separately. The results show very small contributions coming from the tensor-exchange mechanisms when compared with those from the vector-exchange processes. We compare our results for \(\pi \pi\) and \(K\bar{K}\) scattering with those obtained in other works where the \(f_2(1270)\) is considered as an ordinary \(q\bar{q}\) meson. Our picture provides a smaller contribution but of similar order of magnitude for pion scattering and stabilizes the results in the case of \(K\bar{K}\), allowing us to make estimates for \(D\bar{D}\) scattering.