Building on the open-loop algorithm we introduce a new method for the automated construction of one-loop amplitudes and their reduction to scalar integrals. The key idea is that the factorisation of one-loop integrands in a product of loop segments makes it possible to perform various operations on-the-fly while constructing the integrand. Reducing the integrand on-the-fly, after each segment multiplication, the construction of loop diagrams and their reduction are unified in a single numerical recursion. In this way we entirely avoid objects with high tensor rank, thereby reducing the complexity of the calculations in a drastic way. Thanks to the on-the-fly approach, which is applied also to helicity summation and for the merging of different diagrams, the speed of the original open-loop algorithm can be further augmented in a very significant way. Moreover, addressing spurious singularities of the employed reduction identities by means of simple expansions in rank-two Gram determinants, we achieve a remarkably high level of numerical stability. These features of the new algorithm, which will be made publicly available in a forthcoming release of the OpenLoops program, are particularly attractive for NLO multi-leg and NNLO real-virtual calculations.


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    Title :

    On-the-fly reduction of open loops


    Contributors:

    Publication date :

    2018-01-01


    Remarks:

    Buccioni, Federico; Pozzorini, Stefano; Zoller, Max (2018). On-the-fly reduction of open loops. European Physical Journal C - Particles and Fields, 78:70.



    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Classification :

    DDC:    629




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