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Title: Logarithmic forms and differential equations for Feynman integrals

Abstract

We describe in detail how a d log representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized unitarity. For the examples we study, the alphabet of the differential equation is related to special points in kinematic space, described by certain cut equations which encode the geometry of the Feynman integral. At one loop, we reproduce the motivic formulae described by Goncharov [1] that reappeared in the context of Feynman integrals in [2–4]. The d log representation allows us to generalize the differential equations to higher loops and motivates the study of certain mixed-dimension integrals.

Authors:
ORCiD logo [1]; ORCiD logo [2]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. Univ. of California, Los Angeles, CA (United States). Mani L. Bhaumik Inst. for Theoretical Physics
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1608837
Grant/Contract Number:  
AC02-76SF00515; PHY-1607611
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Differential and Algebraic Geometry; Scattering Amplitudes

Citation Formats

Herrmann, Enrico, and Parra-Martinez, Julio. Logarithmic forms and differential equations for Feynman integrals. United States: N. p., 2020. Web. doi:10.1007/jhep02(2020)099.
Herrmann, Enrico, & Parra-Martinez, Julio. Logarithmic forms and differential equations for Feynman integrals. United States. doi:https://doi.org/10.1007/jhep02(2020)099
Herrmann, Enrico, and Parra-Martinez, Julio. Mon . "Logarithmic forms and differential equations for Feynman integrals". United States. doi:https://doi.org/10.1007/jhep02(2020)099. https://www.osti.gov/servlets/purl/1608837.
@article{osti_1608837,
title = {Logarithmic forms and differential equations for Feynman integrals},
author = {Herrmann, Enrico and Parra-Martinez, Julio},
abstractNote = {We describe in detail how a d log representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized unitarity. For the examples we study, the alphabet of the differential equation is related to special points in kinematic space, described by certain cut equations which encode the geometry of the Feynman integral. At one loop, we reproduce the motivic formulae described by Goncharov [1] that reappeared in the context of Feynman integrals in [2–4]. The d log representation allows us to generalize the differential equations to higher loops and motivates the study of certain mixed-dimension integrals.},
doi = {10.1007/jhep02(2020)099},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2020,
place = {United States},
year = {2020},
month = {2}
}

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