Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory

Abstract

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

18 pages, 3 figures; v2: minor typos corrected

References in corpus (5)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Bootstrapping an NMHV amplitude through three loops
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
• Simple loop integrals and amplitudes in N=4 SYM

Cited by in corpus (32)

• Heptagons from the Steinmann Cluster Bootstrap
• Bootstrapping pentagon functions
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• Cuts from residues: the one-loop case
• Crossing Symmetry in the Planar Limit
• Implications of the Landau Equations for Iterated Integrals
• Landau Singularities from the Amplituhedron
• Bootstrapping two-loop Feynman integrals for planar N=4 sYM
• All-loop singularities of scattering amplitudes in massless planar theories
• What is the $i\epsilon$ for the S-matrix?
• The elliptic double box and symbology beyond polylogarithms
• Principal Landau Determinants
• Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
• Symbol Alphabets from the Landau Singular Locus
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Analytic results for planar three-loop integrals for massive form factors
• All-Helicity Symbol Alphabets from Unwound Amplituhedra
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Schubert Problems, Positivity and Symbol Letters
• A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry
• A Note on Letters of Yangian Invariants
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• Intersection theory rules symbology
• Symbol Alphabets from Plabic Graphs II: Rational Letters
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves
• Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar{t}+$jet production at leading colour
• Natural Boundaries for Scattering Amplitudes
• Emergent unitarity from the amplituhedron
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• Generalized unitarity method for unstable particles
• Peaks and cusps: anomalous thresholds and LHC physics