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Title: Six-Gluon amplitudes in planar N $$$$ \mathcal{N} $$$$ = 4 super-Yang-Mills theory at six and seven loops

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [4];  [5];  [6]
  1. McGill Univ., Montreal, QC (Canada). Dept of Physics
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Humboldt Univ. of Berlin (Germany). Inst. for Physics
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  4. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of Copenhagen (Denmark). The Niels Bohr Inst.
  5. SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of Copenhagen (Denmark). The Niels Bohr Inst.
  6. Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
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We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an application of the extended Steinmann relations and using the cosmic Galois coaction principle. Starting from a minimal space of functions constructed using these principles, we identify the amplitude by matching its symmetries and predicted behavior in various kinematic limits. Through five loops, the MHV and NMHV amplitudes are uniquely determined using only the multi-Regge and leading collinear limits. Beyond five loops, the MHV amplitude requires additional data from the kinematic expansion around the collinear limit, which we obtain from the Pentagon Operator Product Expansion, and in particular from its single-gluon bound state contribution. We study the MHV amplitude in the self-crossing limit, where its singular terms agree with previous predictions. Analyzing and plotting the amplitudes along various kinematical lines, we continue to find remarkable stability between loop orders.

Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC02-76SF00515
OSTI ID:
1562503
Report Number(s):
SLAC–PUB–17413; TRN: US2000738
Journal Information:
Journal of High Energy Physics (Online), Vol. 2019, Issue 8; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 95 works
Citation information provided by
Web of Science

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Cited By (15)

The Multi-Regge Limit from the Wilson Loop OPE text January 2019
All-order amplitudes at any multiplicity in the multi-Regge limit text January 2020
The Multi-Regge Limit from the Wilson Loop OPE text January 2020
Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills journal October 2019
Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory journal April 2020
n -point QCD two-loop amplitude journal April 2020
On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring journal November 2019
The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes text January 2019
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes text January 2019
All-order amplitudes at any multiplicity in the multi-Regge limit text January 2019
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit text January 2020
The Multi-Regge Limit from the Wilson Loop OPE text January 2019
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes text January 2019
On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring text January 2019
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops text January 2019

Figures / Tables (10)

Table 1(p. 23)table Table 1
Figure 1(p. 30)figure Figure 1
Figure 2(p. 31)figure Figure 2
Figure 3(p. 31)figure Figure 3
Figure 4(p. 32)figure Figure 4
Figure 5(p. 33)figure Figure 5
Figure 6(p. 33)figure Figure 6
Figure 7(p. 34)figure Figure 7
Figure 8(p. 35)figure Figure 8
Figure 9(p. 36)figure Figure 9

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Scattering Amplitudes
Supersymmetric Gauge Theory