Abstract
We present a first numerical implementation of the loop–tree duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and we present explicit results for scalar and tensor integrals with up to eight external legs (octagons). The LTD method features an excellent performance independently of the number of external legs.
Highlights
The recent discovery of the Higgs boson at the LHC represents a great success of the standard model (SM) of elementary particles
We present a first numerical implementation of the loop–tree duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals
The loop–tree duality (LTD) method [24,25,26,27,28,29,30,31,32,33,34,35,36,37] establishes that generic loop quantities in any relativistic, local and unitary field theory can be written as a sum of tree-level-like objects obtained after making all possible cuts to the internal lines of the corresponding Feynman diagrams, with one single cut per loop and integrated over a measure that closely resembles the phase space of the corresponding real corrections [24,25]
Summary
The recent discovery of the Higgs boson at the LHC represents a great success of the standard model (SM) of elementary particles. The loop–tree duality (LTD) method [24,25,26,27,28,29,30,31,32,33,34,35,36,37] establishes that generic loop quantities (loop integrals and scattering amplitudes) in any relativistic, local and unitary field theory can be written as a sum of tree-level-like objects obtained after making all possible cuts to the internal lines of the corresponding Feynman diagrams, with one single cut per loop and integrated over a measure that closely resembles the phase space of the corresponding real corrections [24,25].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
