High-energy $ππ$ scattering without and with photon radiation
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| Format: | Preprint |
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2021
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| author | Lebiedowicz, Piotr Nachtmann, Otto Szczurek, Antoni |
| author_facet | Lebiedowicz, Piotr Nachtmann, Otto Szczurek, Antoni |
| contents | We discuss the processes $ππ\to ππ$ and $ππ\to ππγ$ from a general quantum field theory (QFT) point of view. We study the soft-photon limit where the photon energy $ω\to 0$ and where we have the theorems due to F.E. Low and S. Weinberg. We consider for the radiative amplitude the Laurent expansion in $ω$ and calculate the terms of order $ω^{-1}$ and $ω^{0}$. The pole term $\propto ω^{-1}$ is given by Weinberg's soft-photon theorem. Then we calculate the amplitudes for the above reactions for high center-of-mass energies and small momentum transfers, that is, in the soft-diffraction regime using the tensor-pomeron model. We identify places where "anomalous" soft photons could come from. Three soft-photon approximations (SPAs) are introduced. The corresponding SPA results are compared to those obtained from the full tensor-pomeron model for center-of-mass energies $\sqrt{s} = 10$ GeV and 100 GeV. The kinematic regions where the SPAs are a good representation of the full amplitude are determined. Finally we make some remarks on the type of fundamental information one could obtain from high-energy exclusive hadronic reactions without and with soft photon radiation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2107_10829 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | High-energy $ππ$ scattering without and with photon radiation Lebiedowicz, Piotr Nachtmann, Otto Szczurek, Antoni High Energy Physics - Phenomenology High Energy Physics - Experiment We discuss the processes $ππ\to ππ$ and $ππ\to ππγ$ from a general quantum field theory (QFT) point of view. We study the soft-photon limit where the photon energy $ω\to 0$ and where we have the theorems due to F.E. Low and S. Weinberg. We consider for the radiative amplitude the Laurent expansion in $ω$ and calculate the terms of order $ω^{-1}$ and $ω^{0}$. The pole term $\propto ω^{-1}$ is given by Weinberg's soft-photon theorem. Then we calculate the amplitudes for the above reactions for high center-of-mass energies and small momentum transfers, that is, in the soft-diffraction regime using the tensor-pomeron model. We identify places where "anomalous" soft photons could come from. Three soft-photon approximations (SPAs) are introduced. The corresponding SPA results are compared to those obtained from the full tensor-pomeron model for center-of-mass energies $\sqrt{s} = 10$ GeV and 100 GeV. The kinematic regions where the SPAs are a good representation of the full amplitude are determined. Finally we make some remarks on the type of fundamental information one could obtain from high-energy exclusive hadronic reactions without and with soft photon radiation. |
| title | High-energy $ππ$ scattering without and with photon radiation |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2107.10829 |