Landau Singularities from Whitney Stratifications
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914689252851712 |
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| author | Helmer, Martin Papathanasiou, Georgios Tellander, Felix |
| author_facet | Helmer, Martin Papathanasiou, Georgios Tellander, Felix |
| contents | We demonstrate that the complete and non-redundant set of Landau singularities of Feynman integrals may be explicitly obtained from the Whitney stratification of an algebraic map. As a proof of concept, we leverage recent theoretical and algorithmic advances in their computation, as well as their software implementation, in order to determine this set for several nontrivial examples of two-loop integrals. Interestingly, different strata of the Whitney stratification describe not only the singularities of a given integral, but also those of integrals obtained from kinematic limits, e.g.~by setting some of its masses or momenta to zero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_14787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Landau Singularities from Whitney Stratifications Helmer, Martin Papathanasiou, Georgios Tellander, Felix High Energy Physics - Theory Mathematical Physics Algebraic Geometry We demonstrate that the complete and non-redundant set of Landau singularities of Feynman integrals may be explicitly obtained from the Whitney stratification of an algebraic map. As a proof of concept, we leverage recent theoretical and algorithmic advances in their computation, as well as their software implementation, in order to determine this set for several nontrivial examples of two-loop integrals. Interestingly, different strata of the Whitney stratification describe not only the singularities of a given integral, but also those of integrals obtained from kinematic limits, e.g.~by setting some of its masses or momenta to zero. |
| title | Landau Singularities from Whitney Stratifications |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2402.14787 |