2,356 research outputs found
Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
In this work we show how a double-cover (DC) extension of the Cachazo, He and
Yuan formalism (CHY) can be used to provide a new realization for the
factorization of the amplitudes involving gluons and scalar fields. First, we
propose a graphic representation for a color-ordered Yang-Mills (YM) and
special Yang-Mills-Scalar (YMS) amplitudes within the scattering equation
formalism. Using the DC prescription, we are able to obtain an algorithm
(integration-rules) which decomposes amplitudes in terms of three-point
building-blocks. It is important to remark that the pole structure of this
method is totally different to ordinary factorization (which is a consequence
of the scattering equations). Finally, as a byproduct, we show that the soft
limit in the CHY approach, at leading order, becomes trivial by using the
technology described in this paper.Comment: 50+7 pages and typos fixed. Some modifications were made to improve
the tex
Computation of Contour Integrals on
Contour integrals of rational functions over , the moduli
space of -punctured spheres, have recently appeared at the core of the
tree-level S-matrix of massless particles in arbitrary dimensions. The contour
is determined by the critical points of a certain Morse function on . The integrand is a general rational function of the puncture
locations with poles of arbitrary order as two punctures coincide. In this note
we provide an algorithm for the analytic computation of any such integral. The
algorithm uses three ingredients: an operation we call general KLT, Petersen's
theorem applied to the existence of a 2-factor in any 4-regular graph and
Hamiltonian decompositions of certain 4-regular graphs. The procedure is
iterative and reduces the computation of a general integral to that of simple
building blocks. These are integrals which compute double-color-ordered partial
amplitudes in a bi-adjoint cubic scalar theory.Comment: 36+11 p
Scattering Equations and Factorization of Amplitudes II: Effective Field Theories
We continue the program of extending the scattering equation framework by
Cachazo, He and Yuan to a double-cover prescription. We discuss how to apply
the double-cover formalism to effective field theories, with a special focus on
the non-linear sigma model. A defining characteristic of the double-cover
formulation is the emergence of new factorization relations. We present several
factorization relations, along with a novel recursion relation. Using the
recursion relation and a new prescription for the integrand, any non-linear
sigma model amplitude can be expressed in terms of off-shell three-point
amplitudes. The resulting expression is purely algebraic, and we do not have to
solve any scattering equation. We also discuss soft limits, boundary terms in
BCFW recursion, and application of the double-cover prescription to other
effective field theories, like the special Galileon theory.Comment: 39+14 page
N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
We give a proof by direct computation that at tree level, the twistor-like
superstring theory in the pure spinor formalism proposed very recently by
Berkovits describes ten-dimensional N=1 super Yang-Mills in its heterotic
version, and type II supergravity in its type II version. The Yang-Mills case
agrees with the result obtained by Mafra, Schlotterer, Stieberger and Tsimpis.
When restricting to gluon and graviton scattering, this new theory gives rise
to Cachazo-He-Yuan formula.Comment: two footnotes added; version submitted to JHE
The closed-string 3-loop amplitude and S-duality
The low-energy limit of the four-point 3-loop amplitude (including its
overall coefficient) is computed in both type IIA and IIB superstring theories
using the pure spinor formalism. The result is shown to agree with the
prediction of the coefficient for the type IIB interaction made by
Green and Vanhove based on S-duality considerations.Comment: 26 pages, harvmac. v3: factor of 3 in section 3.3 corrected, updated
abstract and dropped Z_3-symmetry argumen
One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
In this paper we reconsider the Cachazo-He-Yuan construction (CHY) of the so
called scattering amplitudes at one-loop, in order to obtain quadratic
propagators. In theories with colour ordering the key ingredient is the
redefinition of the Parke-Taylor factors. After classifying all the possible
one-loop CHY-integrands we conjecture a new one-loop amplitude for the massless
Bi-adjoint theory. The prescription directly reproduces the quadratic
propagators from of the traditional Feynman approach.Comment: 43 pages, new appendix added, few typos corrected. Accepted for
publication in JHE
Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
In this work we have studied the Kleiss-Kuijf relations for the recently
introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce
quadratic Feynman propagators. By doing this, we were able to identify the
non-planar one-loop Parke-Taylor factors. In order to check that, in fact,
these new factors can describe non-planar amplitudes, we applied them to the
bi-adjoint theory. As a byproduct, we found a new type of graphs that
we called the non-planar CHY-graphs. These graphs encode all the information
for the subleading order at one-loop, and there is not an equivalent of these
in the Feynman formalism.Comment: 35 pages, typos corrected, references adde
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