Bootstrapping two-loop Feynman integrals for planar $ \mathcal{N}=4 $ sYM

Henn, Johannes; Herrmann, Enrico; Parra-Martinez, Julio

doi:10.1007/jhep10(2018)059

Title: Bootstrapping two-loop Feynman integrals for planar $$ \mathcal{N}=4 $$ sYM

Journal Article · Tue Oct 09 00:00:00 EDT 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep10(2018)059· OSTI ID:1490625

Henn, Johannes ^[1];

^[2];

^[3]

Johannes Gutenberg University, Mainz (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, Munchen (Germany)
SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States)
Univ. of California, Los Angeles, CA (United States)

We derive analytic results for the symbol of certain two-loop Feynman integrals relevant for seven- and eight-point two-loop scattering amplitudes in planar $$ \mathcal{N}=4 $$ super-Yang-Mills theory. We use a bootstrap inspired strategy, combined with a set of second-order 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 one-fold 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 42-letter 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 four-mass box square-root singularities. We point out that these algebraic letters are relevant at the amplitude level directly starting with N2MHV amplitudes even at one loop.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1490625

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 10; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 25 works

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Gravity On-shell Diagrams Herrmann, Enrico; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1604.03479	text	January 2016
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Cited By (1)

Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron arXiv https://doi.org/10.48550/arxiv.1909.09131	text	January 2019

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Table 1(p. 13)

Table 2(p. 14)

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