38 research outputs found
A covariant representation of the Ball-Chiu vertex
In nonabelian gauge theory the three-gluon vertex function contains important
structural information, in particular on infrared divergences, and is also an
essential ingredient in the Schwinger-Dyson equations. Much effort has gone
into analyzing its general structure, and at the one-loop level also a number
of explicit computations have been done, using various approaches. Here we use
the string-inspired formalism to unify the calculations of the scalar, spinor
and gluon loop contributions to the one-loop vertex, leading to an extremely
compact representation in all cases. The vertex is computed fully off-shell and
in dimensionally continued form, so that it can be used as a building block for
higher-loop calculations. We find that the Bern-Kosower loop replacement rules,
originally derived for the on-shell case, hold off-shell as well. We explain
the relation of the structure of this representation to the low-energy
effective action, and establish the precise connection with the standard
Ball-Chiu decomposition of the vertex. This allows us also to predict that the
vanishing of the completely antisymmetric coefficient function S of this
decomposition is not a one-loop accident, but persists at higher loop orders.
The sum rule found by Binger and Brodsky, which leads to the vanishing of the
one-loop vertex in N=4 SYM theory, in the present approach relates to worldline
supersymmetry.Comment: 32 pages, 1 figure, final revised version (calculation of the
two-point functions included, minor corrections, references added
Dressed scalar propagator in a non-abelian background from the worldline formalism
We study the propagator of a colored scalar particle in the background of a
non-abelian gauge field using the worldline formalism. It is obtained by
considering the open worldline of a scalar particle with extra degrees of
freedom needed to take into account the color charge of the particle, which we
choose to be in the fundamental representation of the gauge group. Specializing
the external gauge field to be given by a sum of plane waves, i.e. a sum of
external gluons, we produce a master formula for the scalar propagator with an
arbitrary number of gluons directly attached to the scalar line, akin to
similar formulas derived in the literature for the case of the scalar particle
performing a loop. Our worldline description produces at the same time the
situation in which the particle has a color charge given by an arbitrarily
chosen symmetric or antisymmetric tensor product of the fundamental.Comment: 21 pages, 1 figure; title modified, discussion improved, references
added, main results unchanged. Matches version published in PR
Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
In this work we have studied the Kleiss-Kuijf relations for the recently
introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce
quadratic Feynman propagators. By doing this, we were able to identify the
non-planar one-loop Parke-Taylor factors. In order to check that, in fact,
these new factors can describe non-planar amplitudes, we applied them to the
bi-adjoint theory. As a byproduct, we found a new type of graphs that
we called the non-planar CHY-graphs. These graphs encode all the information
for the subleading order at one-loop, and there is not an equivalent of these
in the Feynman formalism.Comment: 35 pages, typos corrected, references adde
Assisted neutrino pair production in combined external fields
Neutrino--antineutrino () pair production is one of the main
processes responsible for the energy loss of stars. Apart from the collision of
two () or three ()
real photons, photon decay and photon collisions in the presence of nuclear
Coulomb fields or external magnetic fields have been considered previously.
Here, we study the low-energy photon decay into a pair of neutrino and
antineutrino in the presence of a combined homogeneous magnetic field and the
Coulomb field of a nucleus with charge number .Comment: 6 pages, 2 figure
Master formulas for the dressed scalar propagator in a constant field
The worldline formalism has previously been used for deriving compact master
formulas for the one-loop N-photon amplitudes in both scalar and spinor QED,
and in the vacuum as well as in a constant external field. For scalar QED,
there is also an analogous master formula for the propagator dressed with N
photons in the vacuum. Here, we extend this master formula to include a
constant field. The two-photon case is worked out explicitly, yielding an
integral representation for the Compton scattering cross section in the field
suitable for numerical integration in the full range of electric and magnetic
field strengths.Comment: minor typos corrected in eqs. (7) and (41), matches version published
in NP