Sequential discontinuities of Feynman integrals and the monodromy group

Jacob Bourjaily (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen Ø, DK-2100, Denmark; Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, PA, 16892, USA) ; Holmfridur Hannesdottir (Department of Physics, Harvard University, Cambridge, MA, 02138, USA) ; Andrew McLeod (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen Ø, DK-2100, Denmark) ; Matthew Schwartz (Department of Physics, Harvard University, Cambridge, MA, 02138, USA) ; Cristian Vergu (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen Ø, DK-2100, Denmark)

We generalize the relation between discontinuities of scattering amplitudes and cut diagrams to cover sequential discontinuities (discontinuities of discontinuities) in arbitrary momentum channels. The new relations are derived using time-ordered perturbation theory, and hold at phase-space points where all cut momentum channels are simultaneously accessible. As part of this analysis, we explain how to compute sequential discontinuities as monodromies and explore the use of the monodromy group in characterizing the analytic properties of Feynman integrals. We carry out a number of cross-checks of our new formulas in polylogarithmic examples, in some cases to all loop orders.

{
  "_oai": {
    "updated": "2021-05-27T10:20:04Z", 
    "id": "oai:repo.scoap3.org:59767", 
    "sets": [
      "JHEP"
    ]
  }, 
  "authors": [
    {
      "affiliations": [
        {
          "country": "Denmark", 
          "value": "Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen \u00d8, DK-2100, Denmark", 
          "organization": "University of Copenhagen"
        }, 
        {
          "country": "USA", 
          "value": "Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, PA, 16892, USA", 
          "organization": "Pennsylvania State University"
        }
      ], 
      "surname": "Bourjaily", 
      "email": "bourjaily@psu.edu", 
      "full_name": "Bourjaily, Jacob", 
      "given_names": "Jacob"
    }, 
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "Department of Physics, Harvard University, Cambridge, MA, 02138, USA", 
          "organization": "Harvard University"
        }
      ], 
      "surname": "Hannesdottir", 
      "email": "holmfridur_hannesdottir@g.harvard.edu", 
      "full_name": "Hannesdottir, Holmfridur", 
      "given_names": "Holmfridur"
    }, 
    {
      "affiliations": [
        {
          "country": "Denmark", 
          "value": "Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen \u00d8, DK-2100, Denmark", 
          "organization": "University of Copenhagen"
        }
      ], 
      "surname": "McLeod", 
      "email": "amcleod@nbi.ku.dk", 
      "full_name": "McLeod, Andrew", 
      "given_names": "Andrew"
    }, 
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "Department of Physics, Harvard University, Cambridge, MA, 02138, USA", 
          "organization": "Harvard University"
        }
      ], 
      "surname": "Schwartz", 
      "email": "schwartz@g.harvard.edu", 
      "full_name": "Schwartz, Matthew", 
      "given_names": "Matthew"
    }, 
    {
      "affiliations": [
        {
          "country": "Denmark", 
          "value": "Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen \u00d8, DK-2100, Denmark", 
          "organization": "University of Copenhagen"
        }
      ], 
      "surname": "Vergu", 
      "email": "c.vergu@nbi.ku.dk", 
      "full_name": "Vergu, Cristian", 
      "given_names": "Cristian"
    }
  ], 
  "titles": [
    {
      "source": "Springer", 
      "title": "Sequential discontinuities of Feynman integrals and the monodromy group"
    }
  ], 
  "dois": [
    {
      "value": "10.1007/JHEP01(2021)205"
    }
  ], 
  "publication_info": [
    {
      "page_end": "95", 
      "journal_title": "Journal of High Energy Physics", 
      "material": "article", 
      "journal_volume": "2021", 
      "artid": "JHEP01(2021)205", 
      "year": 2021, 
      "page_start": "1", 
      "journal_issue": "1"
    }
  ], 
  "$schema": "http://repo.scoap3.org/schemas/hep.json", 
  "acquisition_source": {
    "date": "2021-05-27T09:43:39.623789", 
    "source": "Springer", 
    "method": "Springer", 
    "submission_number": "fcd98c30becf11eb92440a580a640a05"
  }, 
  "page_nr": [
    95
  ], 
  "license": [
    {
      "url": "https://creativecommons.org/licenses//by/4.0", 
      "license": "CC-BY-4.0"
    }
  ], 
  "copyright": [
    {
      "holder": "The Author(s)", 
      "year": "2021"
    }
  ], 
  "control_number": "59767", 
  "record_creation_date": "2021-01-29T16:30:16.154415", 
  "_files": [
    {
      "checksum": "md5:1ceb921b7b8e5337edf9de6ec5cb20b1", 
      "filetype": "xml", 
      "bucket": "407a7853-c321-43e5-a77d-5f53ab6e241e", 
      "version_id": "d5f1f577-9248-4d80-b18b-554427e722f0", 
      "key": "10.1007/JHEP01(2021)205.xml", 
      "size": 13004
    }, 
    {
      "checksum": "md5:8055f9a59975627de0713f684c1d8e35", 
      "filetype": "pdf/a", 
      "bucket": "407a7853-c321-43e5-a77d-5f53ab6e241e", 
      "version_id": "e16cdc61-f6a5-4176-8d4d-e3a6dc3678e8", 
      "key": "10.1007/JHEP01(2021)205_a.pdf", 
      "size": 2314578
    }
  ], 
  "collections": [
    {
      "primary": "Journal of High Energy Physics"
    }
  ], 
  "arxiv_eprints": [
    {
      "categories": [
        "hep-th", 
        "hep-ph"
      ], 
      "value": "2007.13747"
    }
  ], 
  "abstracts": [
    {
      "source": "Springer", 
      "value": "We generalize the relation between discontinuities of scattering amplitudes and cut diagrams to cover sequential discontinuities (discontinuities of discontinuities) in arbitrary momentum channels. The new relations are derived using time-ordered perturbation theory, and hold at phase-space points where all cut momentum channels are simultaneously accessible. As part of this analysis, we explain how to compute sequential discontinuities as monodromies and explore the use of the monodromy group in characterizing the analytic properties of Feynman integrals. We carry out a number of cross-checks of our new formulas in polylogarithmic examples, in some cases to all loop orders."
    }
  ], 
  "imprints": [
    {
      "date": "2021-01-29", 
      "publisher": "Springer"
    }
  ]
}
Published on:
29 January 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 1
Pages 1-95
DOI:
https://doi.org/10.1007/JHEP01(2021)205
arXiv:
2007.13747
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: