{"arxiv_id":"1509.07167","incoming":{"papers":25,"sentences":41,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":6,"sentences":7,"quotes":[{"arxiv_id":"1609.02454","title":"NLO cross sections in 4 dimensions without DREG","url":"/paper/1609.02454","section":"Introduction","sentence":"In this document, we will describe a new method based on the Loop-Tree Duality (LTD) theorem [ref] ; we will present the general algorithm for the mapping between real and virtual variables so the cancelation of singularities is achieved at integrand level, meaning that integrals can be done in $d=4$ dimensions; finally, we will present a realisation of the method in the $γ^* →qq̅(g)$ process at NLO in QCD.","intent_p":0.93,"contests_p":null},{"arxiv_id":"1506.04617","title":"Towards gauge theories in four dimensions","url":"/paper/1506.04617","section":"Introduction","sentence":"In this paper, we describe an alternative approach which is based on the loop-tree duality (LTD) theorem [ref] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"1709.07802","title":"QED and QCD self-energy corrections through the loop-tree duality","url":"/paper/1709.07802","section":"Introduction","sentence":"With the purpose of building renormalized quantities, we work the renormalization constants with the application of the LTD [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1907.12450","title":"Four-dimensional representation of scattering amplitudes and physical observables through the application of the Loop-Tree Duality theorem","url":"/paper/1907.12450","section":"Massive scalar decay rate from the four-dimensional unsubtraction","sentence":"This singularity is integrable and can be treated numerically by contour deformation [ref] , but for the toy scalar model that we are considering – and later in this chapter, the physical examples – there is a simpler solution.","intent_p":0.81,"contests_p":null},{"arxiv_id":"1608.01584","title":"Four-dimensional unsubtraction with massive particles","url":"/paper/1608.01584","section":"Massive scalar decay rate from four-dimensional unsubstraction","sentence":"This singularity is integrable and can be treated numerically by contour deformation [ref] .","intent_p":0.92,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2006.13818","title":"Universal opening of four-loop scattering amplitudes to trees","url":"/paper/2006.13818","section":"Introduction","sentence":"For instance, the number of integration variables in numerical implementations is independent of the number of external legs [ref] .","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":5,"sentences":5,"quotes":[{"arxiv_id":"2005.02119","title":"Asymptotic expansions through the loop-tree duality","url":"/paper/2005.02119","section":"Introduction","sentence":"In recent years an alternative regularization method based on the loop-tree duality (LTD) has been developed and applied both at one loop and beyond [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"2201.04381","title":"From Causal Representation of Multiloop Scattering Amplitudes to Quantum Computing","url":"/paper/2201.04381","section":"Introduction","sentence":"This methodology has been deeply studied [ref] and many applications have been developed [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"2109.14476","title":"Geometry and causal flux in multi-loop Feynman diagrams","url":"/paper/2109.14476","section":"A brief introduction to Loop-Tree Duality","sentence":"Besides that, LTD turns out to be particularly useful for exploring simplifications in asymptotic expansions at integrand level [ref] , connections with the color-kinematics duality [ref] and efficient numerical integration strategies [ref] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"2112.05584","title":"Four-loop scattering amplitudes through the loop-tree duality","url":"/paper/2112.05584","section":"Introduction","sentence":"Since the introduction of this formalism, a great effort has been dedicated to understand it in depth, and many interesting features have been found [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1608.01800","title":"Applications of the loop-tree duality","url":"/paper/1608.01800","section":"Conclusions and outlook","sentence":"The numerical treatment of threshold singularities by contour deformation has also been investigated recently in Refs. 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Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1509.07167"}}