6 research outputs found
Universal dual amplitudes and asymptotic expansions for and in four dimensions
Though the one-loop amplitudes of the Higgs boson to massless gauge bosons
are finite because there is no direct interaction at tree-level in the Standard
Model, a well-defined regularization scheme is still required for their correct
evaluation. We reanalyze these amplitudes in the framework of the
four-dimensional unsubtraction and the loop-tree duality (FDU/LTD), and show
how a local renormalization solves potential regularization ambiguities. The
Higgs boson interactions are also used to illustrate new additional advantages
of this formalism. We show that LTD naturally leads to very compact integrand
expressions in four space-time dimensions of the one-loop amplitude with
virtual electroweak gauge bosons. They exhibit the same functional form as the
amplitudes with top quarks and charged scalars, thus opening further
possibilities for simplifications in higher-order computations. Another
outstanding application is the straightforward implementation of asymptotic
expansions by using dual amplitudes. One of the main benefits of the LTD
representation is that it is supported in a Euclidean space. This
characteristic feature naturally leads to simpler asymptotic expansions.Comment: 11 pages, no figures. Minor modifications, discussion improved. Final
version published in EPJ
Recent developments from the loop-tree duality
In this talk, we review the most recent developments of the four-dimensional
unsubstraction (FDU) and loop-tree duality (LTD) methods. In particular, we
make emphasis on the advantages of the LTD formalism regarding asymptotic
expansions of loop integrands.Comment: 8 pages, 1 figure. Presented at 13th International Symposium on
Radiative Corrections RADCOR2017, 24-29 September 2017, St. Gilgen, Austri
On the interplay between the loop-tree duality and helicity amplitudes
The spinor-helicity formalism has proven to be very efficient in the
calculation of scattering amplitudes in quantum field theory, while the loop
tree duality (LTD) representation of multi-loop integrals exhibits appealing
and interesting advantages with respect to other approaches. In view of the
most recent developments in LTD, we exploit the synergies with the
spinor-helicity formalism to analyse illustrative one- and two-loop scattering
processes. We focus our discussion on the local UV renormalisation of IR and UV
finite amplitudes and present a fully automated numerical implementation that
provides efficient expressions which are integrable directly in four space-time
dimensions.Comment: 12 pages, 5 figures. In v2: discussion on the application of two-loop
local renormalisation added; references update
Open loop amplitudes and causality to all orders and powers from the loop-tree duality
Multiloop scattering amplitudes describing the quantum fluctuations at
high-energy scattering processes are the main bottleneck in perturbative
quantum field theory. The loop-tree duality is a novel method aimed at
overcoming this bottleneck by opening the loop amplitudes into trees and
combining them at integrand level with the real-emission matrix elements. In
this Letter, we generalize the loop-tree duality to all orders in the
perturbative expansion by using the complex Lorentz-covariant prescription of
the original one-loop formulation. We introduce a series of mutiloop topologies
with arbitrary internal configurations and derive very compact and factorizable
expressions of their open-to-trees representation in the loop-tree duality
formalism. Furthermore, these expressions are entirely independent at integrand
level of the initial assignments of momentum flows in the Feynman
representation and remarkably free of noncausal singularities. These
properties, that we conjecture to hold to other topologies at all orders,
provide integrand representations of scattering amplitudes that exhibit
manifest causal singular structures and better numerical stability than in
other representations.Comment: Final version to appear in Physical Review Letter
On the interplay between the loop-tree duality and helicity amplitudes
The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop-tree duality (LTD) representation of multiloop integrals exhibits appealing and interesting advantages with respect to other approaches. In view of the most recent developments in LTD, we exploit the synergies with the spinor-helicity formalism to analyze illustrative one- and two-loop scattering processes. We focus our discussion on the local UV renormalization of IR and UV finite helicity amplitudes and present a fully automated numerical implementation that provides efficient expressions, which are integrable directly in four space-time dimensions