A minimal approach to the scattering of physical massless bosons

Abstract

Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected onto a minimal basis of kinematic factors through linear algebra, by employing four dimensional spinor helicity methods or at its most general using projection techniques. The linear algebra analysis is closely related to amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton amplitudes. Projection techniques are known to reduce the computation of loop amplitudes with spinning particles to scalar integrals. Unitarity, locality and integration-by-parts identities can then be used to fix complete tree and loop amplitudes efficiently. The loop amplitudes follow algorithmically from the trees. A range of proof-of-concept examples is presented. These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons. Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes. Effective field theories are naturally and efficiently included into the framework. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, iterated unitarity cuts of four point amplitudes for non-supersymmetric gauge and gravity theories can be computed by matrix multiplication, generalising the so-called rung-rule of maximally supersymmetric theories. The philosophy of the approach to kinematics also leads to a technique to control color quantum numbers of scattering amplitudes with matter.

65 pages, exposition improved, typos corrected

References in corpus (12)

• New Relations for Gauge-Theory Amplitudes
• FIRE5: a C++ implementation of Feynman Integral REduction
• Minimal Basis for Gauge Theory Amplitudes
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Amplitudes and Spinor-Helicity in Six Dimensions
• New Relations for Einstein-Yang-Mills Amplitudes
• Expansion of All Multitrace Tree Level EYM Amplitudes
• Analytic Structure of Three-Mass Triangle Coefficients
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Graviton and gluon scattering from first principles

Cited by in corpus (19)

• Bounds on Amplitudes in Effective Theories with Massive Spinning Particles
• Constructing massive on-shell contact terms
• A prescription for projectors to compute helicity amplitudes in D dimensions
• Geometry in Scattering Amplitudes
• Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle
• The gluon Regge trajectory at three loops from planar Yang-Mills theory
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• 2-, 3- and 4-Body Decays in the Constructive Standard Model
• Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
• Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD
• Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering
• The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red
• A graphic approach to gauge invariance induced identity
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Gluonic evanescent operators: two-loop anomalous dimensions
• The origin of the KLT relations and nonlinear relations for Yang-Mills amplitudes