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 $π^+ π^-\to π^+ π^-$ reactions
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| Format: | Preprint |
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2023
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| _version_ | 1866929295815868416 |
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| author | Abreu, Luciano M. Song, Jing Brandão, Pedro C. S. Oset, Eulogio |
| author_facet | Abreu, Luciano M. Song, Jing Brandão, Pedro C. S. Oset, Eulogio |
| contents | In this note we study the tensor and vector exchange contributions to the elastic reactions involving the pseudoscalars mesons $π^+ π^-$, $K^{+}K^{-}$ 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 $ρ$ 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 $ππ$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_14015 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 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 $π^+ π^-\to π^+ π^-$ reactions Abreu, Luciano M. Song, Jing Brandão, Pedro C. S. Oset, Eulogio High Energy Physics - Phenomenology In this note we study the tensor and vector exchange contributions to the elastic reactions involving the pseudoscalars mesons $π^+ π^-$, $K^{+}K^{-}$ 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 $ρ$ 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 $ππ$ 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. |
| title | 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 $π^+ π^-\to π^+ π^-$ reactions |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2310.14015 |