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A minimal approach to the scattering of physical massless bosons

  • Rutger H. Boels
  • Hui Luo
Open Access
Regular Article - Theoretical Physics

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 number of proof-of-concept examples are 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. Dimensional regularisation is employed throughout; different regularisation schemes are worked out explicitly. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, in the introduced approach 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 colour quantum numbers of scattering amplitudes with matter, especially efficient in the adjoint and fundamental representations.

Keywords

Scattering Amplitudes Space-Time Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Supplementary material

13130_2018_8214_MOESM1_ESM.nb (2.1 mb)
ESM1 Results in different schemes (NB 2179 kb)
13130_2018_8214_MOESM2_ESM.txt (21 kb)
ESM2 Coefficient tables cij of ten gluon basis elements and master integrals (TXT 21 kb)
13130_2018_8214_MOESM3_ESM.txt (18 kb)
ESM3 Coefficient tables of eight independent graviton basis elements and three master integrals (TXT 18 kb)

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© The Author(s) 2018

Authors and Affiliations

  1. 1.II. Institut für Theoretische PhysikUniversität HamburgHamburgGermany

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