Colour-Kinematics duality for one-loop rational amplitudes
By R. Boels, Reinke Sven Isermann, R. Monteiro, D. O’Connell. 2013
139 citations recorded by the source corpus.
A bstractColour-kinematics duality is the conjecture of a group theory-like structure for the kinematic dependence of scattering amplitudes in gauge theory and gravity. This structure has been verified at tree level in various ways, but similar progress to all multiplicity has been lacking at loop level, where the power of the duality would be most significant. Here we explore colour-kinematics duality at one loop using the self-dual sector as a starting point. The duality is shown to exist in pure Yang-Mills theory for two infinite classes of amplitudes: amplitudes with any number of particles either all of the same helicity or with one particle helicity opposite the rest. We provide a simple Lagrangian-based argument in favour of the double copy relation between gauge theory and gravity amplitudes in these classes, and provide some explicit examples. We further discuss aspects of the duality which persist after integration, leading to relations among partial amplitudes. Finally, we describe form factors in the self-dual theory at tree level which also satisfy the duality.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ed3649ad69d8c7b2f70f21bb15d29ce10b428b6b
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Citations in the corpus
- TASI Lectures on Scattering Amplitudes (2017, background): “ other theories. This construction generates a web of relations of the form “graviton = gluon2” and “Galileon = pion2”. BCJ duality is proven at tree-level [100] and vigorously checked at higher loop [101, 102, 103, 104, 105, 106, 107]. Remarkably, it is also a property of numerous QFTs. 6.1 Color S”
- The double copy: Bremsstrahlung and accelerating black holes (2016, background): “This extension remains conjectural, but it has been verified in highly nontrivial examples at multiloop level [4, 14–35].”
- One-loop amplitudes on the Riemann sphere (2015, methodology): “uge, because such { 27 { amplitudes correspond to the self-dual sector of the theory [60,61]. The rules for the vertices and external factors in all-plus amplitudes in gauge theory can be taken to be [44] (i+;j+;k ) = X i;jf a ia ja k; e(+) i = 1 hii2 ; (3.27) whereas in gravity they are (i ++;j ;k ”
- The classical double copy for Taub–NUT spacetime (2015, background): “[20,54] where, in the latter, the Yang-Mills action can be made manifestly cubic [55], and a full interpretation of BCJ duality obtained.”