30,083 research outputs found
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.Comment: 31 page
Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
We present the building blocks that can be combined to produce tree-level
S-matrix elements of a variety of theories with various spins mixed in
arbitrary dimensions. The new formulas for the scattering of massless
particles are given by integrals over the positions of points on a sphere
restricted to satisfy the scattering equations. As applications, we obtain all
single-trace amplitudes in Einstein--Yang--Mills (EYM) theory, and
generalizations to include scalars. Also in EYM but extended by a B-field and a
dilaton, we present all double-trace gluon amplitudes. The building blocks are
made of Pfaffians and Parke--Taylor-like factors of subsets of particle labels.Comment: 18 pages. References and a new section on double-trace gluon
amplitudes added in v
- …