6,261 research outputs found
Relations for Einstein-Yang-Mills amplitudes from the CHY representation
We show that a recently discovered relation, which expresses tree-level
single trace Einstein-Yang-Mills amplitudes with one graviton and gauge
bosons as a linear combination of pure Yang-Mills tree amplitudes with
gauge bosons, can be derived from the CHY representation. In addition we show
that there is a generalisation, which expresses tree-level single trace
Einstein-Yang-Mills amplitudes with gravitons and gauge bosons as a
linear combination of pure Yang-Mills tree amplitudes with gauge bosons. We
present a general formula for this case.Comment: 13 pages, version to be publishe
Properties of scattering forms and their relation to associahedra
We show that the half-integrands in the CHY representation of tree amplitudes
give rise to the definition of differential forms -- the scattering forms -- on
the moduli space of a Riemann sphere with marked points. These differential
forms have some remarkable properties. We show that all singularities are on
the divisor . Each
singularity is logarithmic and the residue factorises into two differential
forms of lower points. In order for this to work, we provide a threefold
generalisation of the CHY polarisation factor (also known as reduced Pfaffian)
towards off-shell momenta, unphysical polarisations and away from the solutions
of the scattering equations. We discuss explicitly the cases of bi-adjoint
scalar amplitudes, Yang-Mills amplitudes and gravity amplitudes.Comment: 40 pages, version to be publishe
Proof of the fundamental BCJ relations for QCD amplitudes
The fundamental BCJ-relation is a linear relation between primitive tree
amplitudes with different cyclic orderings. The cyclic orderings differ by the
insertion place of one gluon. The coefficients of the fundamental BCJ-relation
are linear in the Lorentz invariants . The BCJ-relations are well
established for pure gluonic amplitudes as well as for amplitudes in super-Yang-Mills theory. Recently, it has been conjectured that the
BCJ-relations hold also for QCD amplitudes. In this paper we give a proof of
this conjecture. The proof is valid for massless and massive quarks.Comment: 24 pages, version to be publishe
Asymptotic behavior of global entropy solutions for nonstrictly hyperbolic systems with linear damping
In this paper we investigate the large time behavior of the global weak
entropy solutions to the symmetric Keyftiz-Kranzer system with linear damping.
It is proved that as t tends to infinite the entropy solutions tend to zero in
the L p nor
Classical off-shell currents
We consider tree-level off-shell currents of two massive particles and
massless bosons in the classical limit, which can be fused into the classical
limit of scattering amplitudes. We show that dressing up the current with
coherent wave-functions associated with the massive particles leads to the
recently proposed Worldline Quantum Field Theory (WQFT) path integral. The
currents thus constructed encode solutions of classical equations of motion so
they can be applied to contexts where the classical limit is relevant,
including hard thermal loops. We give several examples of these currents in
scalar, gauge and gravitational theories.Comment: 28 pages, v2: clarifications in Sec.2, references added, typos fixed,
matches published versio
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