8,244 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
QED corrections to the Altarelli-Parisi splitting functions
We discuss the combined effect of QED and QCD corrections to the evolution of
parton distributions. We extend the available knowledge of the Altarelli-Parisi
splitting functions to one order higher in QED, and provide explicit
expressions for the splitting kernels up to . The results presented in this article allow to perform a
parton distribution function analysis reaching full NLO QCD-QED combined
precision.Comment: 11 pages, 1 figure. References added, improved discussion. Final
version published in EPJC. Typo corrected in Eq. (22
Two-loop QED corrections to the Altarelli-Parisi splitting functions
We compute the two-loop QED corrections to the Altarelli-Parisi (AP)
splitting functions by using a deconstructive algorithmic Abelianization of the
well-known NLO QCD corrections. We present explicit results for the full set of
splitting kernels in a basis that includes the leptonic distribution functions
that, starting from this order in the QED coupling, couple to the partonic
densities. Finally, we perform a phenomenological analysis of the impact of
these corrections in the splitting functions.Comment: 17 pages, 5 figures. Typos corrected, 1 figure added. Final version
published in JHEP. Comment added about Eq. (51
Towards gauge theories in four dimensions
The abundance of infrared singularities in gauge theories due to unresolved
emission of massless particles (soft and collinear) represents the main
difficulty in perturbative calculations. They are typically regularized in
dimensional regularization, and their subtraction is usually achieved
independently for virtual and real corrections. In this paper, we introduce a
new method based on the loop-tree duality (LTD) theorem to accomplish the
summation over degenerate infrared states directly at the integrand level such
that the cancellation of the infrared divergences is achieved simultaneously,
and apply it to reference examples as a proof of concept. Ultraviolet
divergences, which are the consequence of the point-like nature of the theory,
are also reinterpreted physically in this framework. The proposed method opens
the intriguing possibility of carrying out purely four-dimensional
implementations of higher-order perturbative calculations at next-to-leading
order (NLO) and beyond free of soft and final-state collinear subtractions.Comment: Final version to appear in JHE
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