HEM 2016: Four-dimensional unsubtraction from the loop-tree duality


Four-dimensional unsubtraction from the loop-tree duality

We present a new algorithm to construct a purely four dimensional representation of higher-order perturbative corrections to physical cross-sections at next-to-leading order (NLO). The algorithm is based on the loop-tree duality (LTD), and it is implemented by introducing a suitable mapping between the external and loop momenta of the virtual scattering amplitudes with the external momenta of the real emission corrections. In this way, the sum over degenerate infrared states is performed at the integrand level and the cancellation of infrared divergences occurs locally without introducing subtraction counter-terms to deal with soft and final-state collinear singularities. The dual representation of ultraviolet counter-terms is also discussed in detail, in particular for self-energy contributions. The method is first illustrated with the scalar three-point function, before proceeding with the calculation of the physical cross-section for γqq¯(g), at its generalisation to multi-leg processes. The extension to next-to-next-to-leading order (NNLO) is briefly commented.

Comments: 38 pages, 7 figures
Subjects: High Energy Physics – Phenomenology (hep-ph); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)
Report number: IFIC/15-73
Cite as: arXiv:1604.06699 [hep-ph]
(or arXiv:1604.06699v1 [hep-ph] for this version)


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