48 research outputs found
On Tree Amplitudes in Gauge Theory and Gravity
The BCFW recursion relations provide a powerful way to compute tree
amplitudes in gauge theories and gravity, but only hold if some amplitudes
vanish when two of the momenta are taken to infinity in a particular complex
direction. This is a very surprising property, since individual Feynman
diagrams all diverge at infinite momentum. In this paper we give a simple
physical understanding of amplitudes in this limit, which corresponds to a hard
particle with (complex) light-like momentum moving in a soft background, and
can be conveniently studied using the background field method exploiting
background light-cone gauge. An important role is played by enhanced spin
symmetries at infinite momentum--a single copy of a "Lorentz" group for gauge
theory and two copies for gravity--which together with Ward identities give a
systematic expansion for amplitudes at large momentum. We use this to study
tree amplitudes in a wide variety of theories, and in particular demonstrate
that certain pure gauge and gravity amplitudes do vanish at infinity. Thus the
BCFW recursion relations can be used to compute completely general gluon and
graviton tree amplitudes in any number of dimensions. We briefly comment on the
implications of these results for computing massive 4D amplitudes by KK
reduction, as well understanding the unexpected cancelations that have recently
been found in loop-level gravity amplitudes.Comment: 22 pages, 3 figure
Constructing the Tree-Level Yang-Mills S-Matrix Using Complex Factorization
A remarkable connection between BCFW recursion relations and constraints on
the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that
mutual consistency of different BCFW constructions of four-particle amplitudes
generates non-trivial (but familiar) constraints on three-particle coupling
constants --- these include gauge invariance, the equivalence principle, and
the lack of non-trivial couplings for spins >2. These constraints can also be
derived with weaker assumptions, by demanding the existence of four-point
amplitudes that factorize properly in all unitarity limits with complex
momenta. From this starting point, we show that the BCFW prescription can be
interpreted as an algorithm for fully constructing a tree-level S-matrix, and
that complex factorization of general BCFW amplitudes follows from the
factorization of four-particle amplitudes. The allowed set of BCFW deformations
is identified, formulated entirely as a statement on the three-particle sector,
and using only complex factorization as a guide. Consequently, our analysis
based on the physical consistency of the S-matrix is entirely independent of
field theory. We analyze the case of pure Yang-Mills, and outline a proof for
gravity. For Yang-Mills, we also show that the well-known scaling behavior of
BCFW-deformed amplitudes at large z is a simple consequence of factorization.
For gravity, factorization in certain channels requires asymptotic behavior
~1/z^2.Comment: 35 pages, 6 figure
Note on graviton MHV amplitudes
Two new formulas which express n-graviton MHV tree amplitudes in terms of
sums of squares of n-gluon amplitudes are discussed. The first formula is
derived from recursion relations. The second formula, simpler because it
involves fewer permutations, is obtained from the variant of the Berends,
Giele, Kuijf formula given in Arxiv:0707.1035.Comment: 10 page
Effective action for Einstein-Maxwell theory at order RF**4
We use a recently derived integral representation of the one-loop effective
action in Einstein-Maxwell theory for an explicit calculation of the part of
the effective action containing the information on the low energy limit of the
five-point amplitudes involving one graviton, four photons and either a scalar
or spinor loop. All available identities are used to get the result into a
relatively compact form.Comment: 13 pages, no figure
Amplitudes and Spinor-Helicity in Six Dimensions
The spinor-helicity formalism has become an invaluable tool for understanding
the S-matrix of massless particles in four dimensions. In this paper we
construct a spinor-helicity formalism in six dimensions, and apply it to derive
compact expressions for the three, four and five point tree amplitudes of
Yang-Mills theory. Using the KLT relations, it is a straightforward process to
obtain amplitudes in linearized gravity from these Yang-Mills amplitudes; we
demonstrate this by writing down the gravitational three and four point
amplitudes. Because there is no conserved helicity in six dimensions, these
amplitudes describe the scattering of all possible polarization states (as well
as Kaluza-Klein excitations) in four dimensions upon dimensional reduction. We
also briefly discuss a convenient formulation of the BCFW recursion relations
in higher dimensions.Comment: 26 pages, 2 figures. Minor improvements of the discussio
On-shell recursion relations for all Born QCD amplitudes
We consider on-shell recursion relations for all Born QCD amplitudes. This
includes amplitudes with several pairs of quarks and massive quarks. We give a
detailed description on how to shift the external particles in spinor space and
clarify the allowed helicities of the shifted legs. We proof that the
corresponding meromorphic functions vanish at z --> infinity. As an application
we obtain compact expressions for helicity amplitudes including a pair of
massive quarks, one negative helicity gluon and an arbitrary number of positive
helicity gluons.Comment: 30 pages, minor change
On-Shell Recursion Relations for Generic Theories
We show that on-shell recursion relations hold for tree amplitudes in generic
two derivative theories of multiple particle species and diverse spins. For
example, in a gauge theory coupled to scalars and fermions, any amplitude with
at least one gluon obeys a recursion relation. In (super)gravity coupled to
scalars and fermions, the same holds for any amplitude with at least one
graviton. This result pertains to a broad class of theories, including QCD, N=4
SYM, and N=8 supergravity.Comment: 19 pages, 3 figure
Tree-Level Formalism
We review two novel techniques used to calculate tree-level scattering
amplitudes efficiently: MHV diagrams, and on-shell recursion relations. For the
MHV diagrams, we consider applications to tree-level amplitudes and focus in
particular on the N=4 supersymmetric formulation. We also briefly describe the
derivation of loop amplitudes using MHV diagrams. For the recursion relations,
after presenting their general proof, we discuss several applications to
massless theories with and without supersymmetry, to theories with massive
particles, and to graviton amplitudes in General Relativity. This article is an
invited review for a special issue of Journal of Physics A devoted to
"Scattering Amplitudes in Gauge Theories".Comment: 40 pages, 8 figures, invited review for a special issue of Journal of
Physics A devoted to "Scattering Amplitudes in Gauge Theories", R.
Roiban(ed), M. Spradlin(ed), A. Volovich(ed); v2: minor corrections,
references adde
Boundary Contributions Using Fermion Pair Deformation
Continuing the study of boundary BCFW recursion relation of tree level
amplitudes initiated in \cite{Feng:2009ei}, we consider boundary contributions
coming from fermion pair deformation. We present the general strategy for these
boundary contributions and demonstrate calculations using two examples, i.e,
the standard QCD and deformed QCD with anomalous magnetic momentum coupling. As
a by-product, we have extended BCFW recursion relation to off-shell gluon
current, where because off-shell gluon current is not gauge invariant, a new
feature must be cooperated.Comment: 26 pages, 4 figure
Tree amplitudes of noncommutative U(N) Yang-Mills Theory
Following the spirit of S-matrix program, we proposed a modified
Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of
noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes,
one can use this modified BCFW recursion relation to compute or analyze
color-ordered tree amplitudes without relying on any detail information of
noncommutative Yang-Mills theory. After clarifying the color structure of
noncommutative tree amplitudes, we wrote down the noncommutative analogies of
U(1)-decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations for
color-ordered tree amplitudes, and proved them using the modified BCFW
recursion relation.Comment: 24 pages, 3 figures. v2 References added. v3 some typos correcte