101,972 research outputs found
Reduction to master integrals via intersection numbers and polynomial expansions
No full textIntersection numbers are rational scalar products among functions that admit
suitable integral representations, such as Feynman integrals. Using these
scalar products, the decomposition of Feynman integrals into a basis of
linearly independent master integrals is reduced to a projection. We present a
new method for computing intersection numbers that only uses rational
operations and does not require any integral transformation or change of basis.
We achieve this by systematically employing the polynomial series expansion,
namely the expansion of functions in powers of a polynomial. We also introduce
a new prescription for choosing dual integrals, de facto removing the explicit
dependence on additional analytic regulators in the computation of intersection
numbers. We describe a proof-of-concept implementation of the algorithm over
finite fields and its application to the decomposition of Feynman integrals at
one and two loops.Comment: 36 pages, 5 figures, published versio
On monomial generalized almost perfect nonlinear functions
No full textGeneralized almost perfect nonlinear (GAPN) functions are a generalization of APN functions to finite fields of odd characteristic p introduced in 2017 by Kuroda and Tsujie. In this paper we deal with GAPN functions of monomial type. To this aim, we connect the GAPN property for a monomial function over Fpjavax.xml.bind.JAXBElement@7f2e9ed8 to the existence of suitable rational points of an algebraic curve defined over Fpjavax.xml.bind.JAXBElement@425705. We give necessary conditions for a monomial function to be GAPN, providing the converse of recent results by Özbudak and Sălăgean and by Zha, Hu and Zhang
Local integrands for two-loop all-plus Yang-Mills amplitudes
No full textWe express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4 − 2ε dimensions
Reduction to master integrals and transverse integration identities
No full textThe reduction of Feynman integrals to a basis of linearly independent master integrals is a pivotal step in loop calculations, but also one of the main bottlenecks. In this paper, we assess the impact of using transverse integration identities for the reduction to master integrals. Given an integral family, some of its sectors correspond to diagrams with fewer external legs or to diagrams that can be factorized as products of lower-loop integrals. Using transverse integration identities, i.e. a tensor decomposition in the subspace that is transverse to the external momenta of the diagrams, one can map integrals belonging to such sectors and their subsectors to (products of) integrals belonging to new and simpler integral families, characterized by either fewer generalized denominators, fewer external invariants, fewer loops or combinations thereof. Integral reduction is thus drastically simpler for these new families. We describe a proof-of-concept implementation of the application of transverse integration identities in the context of integral reduction. We include some applications to cutting-edge integral families, showing significant improvements over traditional algorithms
Two-loop QCD corrections to the V → qq ̄ g helicity amplitudes with axial-vector couplings
No full textWe compute the two-loop corrections to the helicity amplitudes for the coupling of a massive vector boson to a massless quark-antiquark pair and a gluon, accounting for vector and axial-vector couplings of the vector boson and distinguishing isospin non-singlet and singlet contributions. A new four-dimensional basis for the decomposition of the amplitudes into 12 invariant tensor structures is introduced. The associated form factors are then computed up to two loops in QCD using dimensional regularization. After performing renormalization and infrared subtraction, the finite parts of the renormalized non-singlet vector and axial-vector form factors are shown agree with each other, and to reproduce the previously known two-loop amplitudes. The singlet axial-vector amplitude receives a contribution from the axial anomaly from two loops onwards. This amplitude is computed for massless and massive internal quarks. Our results provide the last missing two-loop amplitudes entering the NNLO QCD corrections of vector-boson-plus-jet production at hadron colliders
Multiloop integrand reduction for dimensionally regulated amplitudes
No full textWe present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary dimensionally regulated loop integrals with any number of loops and external legs, which can be used to obtain the decomposition of any integrand analytically with a finite number of algebraic operations. The general results are illustrated by applications to two-loop Feynman diagrams in QED and QCD, showing that the proposed reduction algorithm can also be seamlessly applied to integrands with denominators appearing with arbitrary powers
Next-to-Leading-Order QCD Corrections to Higgs Boson Production in Association with a Top Quark Pair and a Jet
No full textMulti-leg one-loop massive amplitudes from integrand reduction via Laurent expansion
No full textWe present the application of a novel reduction technique for one-loop scattering amplitudes based on the combination of the integrand reduction and Laurent expansion. We describe the general features of its implementation in the computer code Ninja, and its interface to GoSam. We apply the new reduction to a series of selected processes involving massive particles, from six to eight legs
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