Soft theorems for two-scalar sigma models
Abstract In this paper, we study the scattering amplitudes and soft theorems for the sigma models with two scalars. We show that if the particles are Goldstone bosons, then you necessarily get Adler zero with no possibility for non-trivial soft theorems. For non-Goldstone bosons, the soft behavior i...
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| Format: | Article |
| Language: | English |
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2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)009 |
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| author | Karol Kampf Jiri Novotny Mikhail Shifman Jaroslav Trnka |
| author_facet | Karol Kampf Jiri Novotny Mikhail Shifman Jaroslav Trnka |
| author_sort | Karol Kampf |
| collection | DOAJ |
| description | Abstract In this paper, we study the scattering amplitudes and soft theorems for the sigma models with two scalars. We show that if the particles are Goldstone bosons, then you necessarily get Adler zero with no possibility for non-trivial soft theorems. For non-Goldstone bosons, the soft behavior is generically captured by the geometric soft theorem studied by Cheung et al., and the right-hand side contains derivatives of lower-point amplitudes. Inspired by the recent work on the 2D sigma models, we study one special two-scalar sigma model, where the presence of symmetries in the target space translates into a special but non-trivial soft theorem without derivatives. We further generalize the construction to two larger classes of such models and derive certain soft theorem sum rules, again avoiding the derivatives of amplitudes. Our analysis provides an interesting hierarchy of two-scalar sigma models and soft theorems, ranging from Goldstone boson case to a generic target space, and showing that there are interesting theories in between. |
| format | Article |
| id | doaj-art-7bd6b6299e58419e973007a648452c0f |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-7bd6b6299e58419e973007a648452c0f2025-01-19T12:07:15ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025114010.1007/JHEP01(2025)009Soft theorems for two-scalar sigma modelsKarol Kampf0Jiri Novotny1Mikhail Shifman2Jaroslav Trnka3Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles UniversityInstitute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles UniversityWilliam I. Fine Theoretical Physics Institute, University of MinnesotaInstitute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles UniversityAbstract In this paper, we study the scattering amplitudes and soft theorems for the sigma models with two scalars. We show that if the particles are Goldstone bosons, then you necessarily get Adler zero with no possibility for non-trivial soft theorems. For non-Goldstone bosons, the soft behavior is generically captured by the geometric soft theorem studied by Cheung et al., and the right-hand side contains derivatives of lower-point amplitudes. Inspired by the recent work on the 2D sigma models, we study one special two-scalar sigma model, where the presence of symmetries in the target space translates into a special but non-trivial soft theorem without derivatives. We further generalize the construction to two larger classes of such models and derive certain soft theorem sum rules, again avoiding the derivatives of amplitudes. Our analysis provides an interesting hierarchy of two-scalar sigma models and soft theorems, ranging from Goldstone boson case to a generic target space, and showing that there are interesting theories in between.https://doi.org/10.1007/JHEP01(2025)009Effective Field TheoriesScattering AmplitudesSigma ModelsNonperturbative Effects |
| spellingShingle | Karol Kampf Jiri Novotny Mikhail Shifman Jaroslav Trnka Soft theorems for two-scalar sigma models Journal of High Energy Physics Effective Field Theories Scattering Amplitudes Sigma Models Nonperturbative Effects |
| title | Soft theorems for two-scalar sigma models |
| title_full | Soft theorems for two-scalar sigma models |
| title_fullStr | Soft theorems for two-scalar sigma models |
| title_full_unstemmed | Soft theorems for two-scalar sigma models |
| title_short | Soft theorems for two-scalar sigma models |
| title_sort | soft theorems for two scalar sigma models |
| topic | Effective Field Theories Scattering Amplitudes Sigma Models Nonperturbative Effects |
| url | https://doi.org/10.1007/JHEP01(2025)009 |
| work_keys_str_mv | AT karolkampf softtheoremsfortwoscalarsigmamodels AT jirinovotny softtheoremsfortwoscalarsigmamodels AT mikhailshifman softtheoremsfortwoscalarsigmamodels AT jaroslavtrnka softtheoremsfortwoscalarsigmamodels |