Bootstrapping twoloop Feynman integrals for planar $$ \mathcal{N}=4 $$ sYM
Abstract
We derive analytic results for the symbol of certain twoloop Feynman integrals relevant for seven and eightpoint twoloop scattering amplitudes in planar $$ \mathcal{N}=4 $$ superYangMills theory. We use a bootstrap inspired strategy, combined with a set of secondorder partial differential equations that provide powerful constraints on the symbol ansatz. When the complete symbol alphabet is not available, we adopt a hybrid approach. Instead of the full function, we bootstrap a certain discontinuity for which the alphabet is known. Then we write a onefold dispersion integral to recover the complete result. At six and seven points, we find that the individual Feynman integrals live in the same space of functions as the amplitude, which is described by the 9 and 42letter cluster alphabets respectively. Starting at eight points however, the symbol alphabet of the MHV amplitude is insufficient for individual integrals. In particular, some of the integrals require algebraic letters involving fourmass box squareroot singularities. We point out that these algebraic letters are relevant at the amplitude level directly starting with N2MHV amplitudes even at one loop.
 Authors:

 Johannes Gutenberg University, Mainz (Germany); MaxPlanckInstitut für Physik, WernerHeisenbergInstitut, Munchen (Germany)
 SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States)
 Univ. of California, Los Angeles, CA (United States)
 Publication Date:
 Research Org.:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1490625
 Grant/Contract Number:
 AC0276SF00515
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Volume: 2018; Journal Issue: 10; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 1/N Expansion; Scattering Amplitudes; Supersymmetric Gauge Theory
Citation Formats
Henn, Johannes, Herrmann, Enrico, and ParraMartinez, Julio. Bootstrapping twoloop Feynman integrals for planar $ \mathcal{N}=4 $ sYM. United States: N. p., 2018.
Web. doi:10.1007/jhep10(2018)059.
Henn, Johannes, Herrmann, Enrico, & ParraMartinez, Julio. Bootstrapping twoloop Feynman integrals for planar $ \mathcal{N}=4 $ sYM. United States. doi:10.1007/jhep10(2018)059.
Henn, Johannes, Herrmann, Enrico, and ParraMartinez, Julio. Tue .
"Bootstrapping twoloop Feynman integrals for planar $ \mathcal{N}=4 $ sYM". United States. doi:10.1007/jhep10(2018)059. https://www.osti.gov/servlets/purl/1490625.
@article{osti_1490625,
title = {Bootstrapping twoloop Feynman integrals for planar $ \mathcal{N}=4 $ sYM},
author = {Henn, Johannes and Herrmann, Enrico and ParraMartinez, Julio},
abstractNote = {We derive analytic results for the symbol of certain twoloop Feynman integrals relevant for seven and eightpoint twoloop scattering amplitudes in planar $ \mathcal{N}=4 $ superYangMills theory. We use a bootstrap inspired strategy, combined with a set of secondorder partial differential equations that provide powerful constraints on the symbol ansatz. When the complete symbol alphabet is not available, we adopt a hybrid approach. Instead of the full function, we bootstrap a certain discontinuity for which the alphabet is known. Then we write a onefold dispersion integral to recover the complete result. At six and seven points, we find that the individual Feynman integrals live in the same space of functions as the amplitude, which is described by the 9 and 42letter cluster alphabets respectively. Starting at eight points however, the symbol alphabet of the MHV amplitude is insufficient for individual integrals. In particular, some of the integrals require algebraic letters involving fourmass box squareroot singularities. We point out that these algebraic letters are relevant at the amplitude level directly starting with N2MHV amplitudes even at one loop.},
doi = {10.1007/jhep10(2018)059},
journal = {Journal of High Energy Physics (Online)},
issn = {10298479},
number = 10,
volume = 2018,
place = {United States},
year = {2018},
month = {10}
}
Web of Science