Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering of Massless Particles: Scalars, Gluons and Gravitons   In a recent note we presented a compact formula for the complete tree-level
S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime
dimension. In this paper we show that a natural formulation also exists for a
massless colored cubic scalar theory. In Yang-Mills, the formula is an integral
over the space of n marked points on a sphere and has as integrand two factors.
The first factor is a combination of Parke-Taylor-like terms dressed with U(N)
color structures while the second is a Pfaffian. The S-matrix of a U(N)xU(N')
cubic scalar theory is obtained by simply replacing the Pfaffian with a U(N')
version of the previous U(N) factor. Given that gravity amplitudes are obtained
by replacing the U(N) factor in Yang-Mills by a second Pfaffian, we are led to
a natural color-kinematics correspondence. An expansion of the integrand of the
scalar theory leads to sums over trivalent graphs and are directly related to
the KLT matrix. We find a connection to the BCJ color-kinematics duality as
well as a new proof of the BCJ doubling property that gives rise to gravity
amplitudes. We end by considering a special kinematic point where the partial
amplitude simply counts the number of color-ordered planar trivalent trees,
which equals a Catalan number. The scattering equations simplify dramatically
and are equivalent to a special Y-system with solutions related to roots of
Chebyshev polynomials.

21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat