122 research outputs found

### Amplitudes for massive vector and scalar bosons in spontaneously-broken gauge theory from the CHY representation

In the formulation of Cachazo, He, and Yuan, tree-level amplitudes for
massless particles in gauge theory and gravity can be expressed as rational
functions of the Lorentz invariants $k_a \cdot k_b$, $\epsilon_a \cdot k_b$,
and $\epsilon_a \cdot \epsilon_b$, valid in any number of spacetime dimensions.
We use dimensional reduction of higher-dimensional amplitudes of particles with
internal momentum $\kappa$ to obtain amplitudes for massive particles in lower
dimensions. In the case of gauge theory, we argue that these massive amplitudes
belong to a theory in which the gauge symmetry is spontaneously broken by an
adjoint Higgs field. Consequently, we show that tree-level $n$-point amplitudes
containing massive vector and scalar bosons in this theory can be obtained by
simply replacing $k_a \cdot k_b$ with $k_a \cdot k_b - \kappa_a \kappa_b$ in
the corresponding massless amplitudes, where the masses of the particles are
given by $|\kappa_a|$.Comment: 7 pages, no figures; v2: added paragraph, published versio

### Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles

We generalize the scattering equations to include both massless and massive
particles. We construct an expression for the tree-level n-point amplitude with
n-2 gluons or gravitons and a pair of massive scalars in arbitrary spacetime
dimension as a sum over the (n-3)! solutions of the scattering equations, a la
Cachazo, He, and Yuan. We derive the BCJ relations obeyed by these massive
amplitudes.Comment: 22 pages. v2: clarification of eqs. (5.5) and (5.6

### Scattering equations and virtuous kinematic numerators and dual-trace functions

Inspired by recent developments on scattering equations, we present a
constructive procedure for computing symmetric, amplitude-encoded, BCJ
numerators for n-point gauge-theory amplitudes, thus satisfying the three
virtues identified by Broedel and Carrasco. We also develop a constructive
procedure for computing symmetric, amplitude-encoded dual-trace functions (tau)
for n-point amplitudes. These can be used to obtain symmetric kinematic
numerators that automatically satisfy color-kinematic duality. The S_n symmetry
of n-point gravity amplitudes formed from these symmetric dual-trace functions
is completely manifest. Explicit expressions for four- and five-point
amplitudes are presented.Comment: 24 pages; v2: minor sign corrections, added references; v3: minor
corrections, published versio

### IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM Theory

We derive a compact all-loop-order expression for the IR-divergent part of
the N=4 SYM four-gluon amplitude, which includes both planar and all
subleading-color contributions, based on the assumption that the higher-loop
soft anomalous dimension matrices are proportional to the one-loop soft
anomalous dimension matrix, as has been recently conjectured.
We also consider the Regge limit of the four-gluon amplitude, and we present
evidence that the leading logarithmic growth of the subleading-color amplitudes
is less severe than that of the planar amplitudes. We examine possible 1/N^2
corrections to the gluon Regge trajectory, previously obtained in the planar
limit from the BDS ansatz. The double-trace amplitudes have Regge behavior as
well, with a nonsense-choosing Regge trajectory and a Regge cut which first
emerges at three loops.Comment: 29 pages; v2: corrections to sections 5.1 and 5.2, references added;
v3: clarification in introduction, references added; v4: published versio

### Quantum Corrections to Deep Bags

Nontopological solitons, or ``bags,'' can arise when fermions acquire their
mass through a Yukawa coupling to some scalar field. Bags have played an
important role in models of baryons, nuclei, and more recently, in the idea
that a Higgs condensate may form around a very heavy top quark. It has been
claimed that deep bags, which correspond to tightly-bound states of fermions,
will form when the Yukawa coupling is strong. Quantum corrections, however, are
significant in this regime. We examine the effects of these quantum corrections
on the formation of nontopological solitons in an exactly solvable large-$N$
model. We find that quantum bags differ dramatically from those of the
classical theory. In particular, for large Yukawa coupling, the bags remain
shallow and the fermions weakly bound.Comment: Talk given at the XXVI Int. Conf. on High Energy Physics, August,
1992 LATEX file, 7 pages + 2 figures available upon request, JHU-TIPAC-92002

### KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry

Color-factor symmetry is used to derive a KLT-type relation for tree-level
QCD amplitudes containing gluons and an arbitrary number of massive or massless
quark-antiquark pairs, generalizing the expression for Yang-Mills amplitudes
originally postulated by Bern, De Freitas, and Wong. An explicit expression is
given for all amplitudes with two or fewer quark-antiquark pairs in terms of
the (modified) momentum kernel.
We also introduce the bicolor scalar theory, the "zeroth copy" of QCD,
containing massless biadjoint scalars and massive bifundamental scalars,
generalizing the biadjoint scalar theory of Cachazo, He, and Yuan. We derive
KLT-type relations for tree-level amplitudes of biadjoint and bicolor theories
using the color-factor symmetry possessed by these theories.Comment: 24 pages, 2 figures; v2: added referenc

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