The Landau Bootstrap
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910705087676416 |
|---|---|
| author | Hannesdottir, Holmfridur McLeod, Andrew Schwartz, Matthew D. Vergu, Cristian |
| author_facet | Hannesdottir, Holmfridur McLeod, Andrew Schwartz, Matthew D. Vergu, Cristian |
| contents | We advocate a strategy of bootstrapping Feynman integrals from just knowledge of their singular behavior. This approach is complementary to other bootstrap programs, which exploit non-perturbative constraints such as unitarity, or amplitude-level constraints such as gauge invariance. We begin by studying where a Feynman integral can become singular, and the behavior it exhibits near these singularities. We then characterize the space of functions that we expect the integral to evaluate to, in order to formulate an appropriate ansatz. Finally, we derive constraints on where each singularity can appear in this ansatz, and use information about the expansion of the integral around singular points in order to determine the value of all remaining free coefficients. Throughout, we highlight how constraints that have previously only been derived for integrals with generic masses can be extended to integrals involving particles of equal or vanishing mass. We illustrate the effectiveness of this approach by bootstrapping a number of examples, including the four-point double box with a massive internal loop. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Landau Bootstrap Hannesdottir, Holmfridur McLeod, Andrew Schwartz, Matthew D. Vergu, Cristian High Energy Physics - Phenomenology High Energy Physics - Theory We advocate a strategy of bootstrapping Feynman integrals from just knowledge of their singular behavior. This approach is complementary to other bootstrap programs, which exploit non-perturbative constraints such as unitarity, or amplitude-level constraints such as gauge invariance. We begin by studying where a Feynman integral can become singular, and the behavior it exhibits near these singularities. We then characterize the space of functions that we expect the integral to evaluate to, in order to formulate an appropriate ansatz. Finally, we derive constraints on where each singularity can appear in this ansatz, and use information about the expansion of the integral around singular points in order to determine the value of all remaining free coefficients. Throughout, we highlight how constraints that have previously only been derived for integrals with generic masses can be extended to integrals involving particles of equal or vanishing mass. We illustrate the effectiveness of this approach by bootstrapping a number of examples, including the four-point double box with a massive internal loop. |
| title | The Landau Bootstrap |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.02424 |