71 research outputs found
The Kinematic Algebras from the Scattering Equations
We study kinematic algebras associated to the recently proposed scattering
equations, which arise in the description of the scattering of massless
particles. In particular, we describe the role that these algebras play in the
BCJ duality between colour and kinematics in gauge theory, and its relation to
gravity. We find that the scattering equations are a consistency condition for
a self-dual-type vertex which is associated to each solution of those
equations. We also identify an extension of the anti-self-dual vertex, such
that the two vertices are not conjugate in general. Both vertices correspond to
the structure constants of Lie algebras. We give a prescription for the use of
the generators of these Lie algebras in trivalent graphs that leads to a
natural set of BCJ numerators. In particular, we write BCJ numerators for each
contribution to the amplitude associated to a solution of the scattering
equations. This leads to a decomposition of the determinant of a certain
kinematic matrix, which appears naturally in the amplitudes, in terms of
trivalent graphs. We also present the kinematic analogues of colour traces,
according to these algebras, and the associated decomposition of that
determinant.Comment: 23 pages, 4 figure
BCFW Recursion Relations and String Theory
We demonstrate that all tree-level string theory amplitudes can be computed
using the BCFW recursion relations. Our proof utilizes the pomeron vertex
operator introduced by Brower, Polchinski, Strassler, and Tan. Surprisingly, we
find that in a particular large complex momentum limit, the asymptotic
expansion of massless string amplitudes is identical in form to that of the
corresponding field theory amplitudes. This observation makes manifest the fact
that field-theoretic Yang-Mills and graviton amplitudes obey KLT-like
relations. Moreover, we conjecture that in this large momentum limit certain
string theory and field theory amplitudes are identical, and provide evidence
for this conjecture. Additionally, we find a new recursion relation which
relates tachyon amplitudes to lower-point tachyon amplitudes.Comment: 36 pages, JHEP3; reference and note added, improved discussion in
section
The Lee-Wick Standard Model
We construct a modification of the standard model which stabilizes the Higgs
mass against quadratically divergent radiative corrections, using ideas
originally discussed by Lee and Wick in the context of a finite theory of
quantum electrodynamics. The Lagrangian includes new higher derivative
operators. We show that the higher derivative terms can be eliminated by
introducing a set of auxiliary fields; this allows for convenient computation
and makes the physical interpretation more transparent. Although the theory is
unitary, it does not satisfy the usual analyticity conditions.Comment: 20 pages, 4 figures. Improved discussion and reference added. Contour
prescription clarifie
Black holes and the double copy
Recently, a perturbative duality between gauge and gravity theories (the
double copy) has been discovered, that is believed to hold to all loop orders.
In this paper, we examine the relationship between classical solutions of
non-Abelian gauge theory and gravity. We propose a general class of gauge
theory solutions that double copy to gravity, namely those involving stationary
Kerr-Schild metrics. The Schwarzschild and Kerr black holes (plus their
higher-dimensional equivalents) emerge as special cases. We also discuss plane
wave solutions. Furthermore, a recently examined double copy between the
self-dual sectors of Yang-Mills theory and gravity can be reinterpreted using a
momentum-space generalisation of the Kerr-Schild framework.Comment: 22 pages; typos corrected and references adde
Constraints on New Physics from Baryogenesis and Large Hadron Collider Data
We demonstrate the power of constraining theories of new physics by insisting
that they lead to electroweak baryogenesis, while agreeing with current data
from the Large Hadron Collider. The general approach is illustrated with a
singlet scalar extension of the Standard Model. Stringent bounds can already be
obtained, which reduce the viable parameter space to a small island.Comment: 4 pages, 2 figures. References added, figures updated. Version to
appear in PR
Mixed Action Effective Field Theory: an Addendum
We correct a mistake in the literature regarding the additive lattice spacing
corrections to the mixed valence-sea meson mass and discuss the consequences
for mixed action extrapolation formulae.Comment: 4 pages, version published in PR
Colour-Kinematics Duality for One-Loop Rational Amplitudes
Colour-kinematics duality is the conjecture of a group theory-like structure
for the kinematic dependence of scattering amplitudes in gauge theory and
gravity. This structure has been verified at tree level in various ways, but
similar progress has been lacking at loop level, where the power of the duality
would be most significant. Here we explore colour-kinematics duality at one
loop using the self-dual sector as a starting point. The duality is shown to
exist in pure Yang-Mills theory for two infinite classes of amplitudes:
amplitudes with any number of particles either all of the same helicity or with
one particle helicity opposite the rest. We provide a simple Lagrangian-based
argument in favour of the double copy relation between gauge theory and gravity
amplitudes in these classes, and provide some explicit examples. We further
discuss aspects of the duality which persist after integration, leading to
relations among partial amplitudes. Finally, we describe form factors in the
self-dual theory at tree level which also satisfy the duality.Comment: 36 pages, 5 figures; v2: published versio
The Radial Action from Probe Amplitudes to All Orders
We extract the relativistic classical radial action from scattering
amplitudes, to all orders in perturbation theory, in the probe limit. Our
sources include point charges and monopoles, as well as the Schwarzschild and
pure-NUT gravitational backgrounds. A characteristic relativistic effect, that
scattering trajectories may wind around these sources any number of times, can
be recovered when all-order amplitudes are available. We show that the
amplitude for scattering a probe off a pure NUT is given by the solution of a
transcendental equation involving continued fractions, and explain how to solve
this equation to any desired loop order
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