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Register a new userD0C : A code to calculate scalar one-loop four-point integrals with complex masses
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We present a new Fortran code to calculate the scalar one-loop four-point integral with complex internal masses, based on the method of t Hooft and Veltman. The code is applicable when the external momenta fulfill a certain physical condition. In particular it holds if one of the external momenta or a sum of them is timelike or lightlike and therefore covers all physical processes at colliders. All the special cases related to massless external particles are treated separately. Some technical issues related to numerical evaluation and Landau singularities are discussed.
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We present a program for the numerical evaluation of scalar integrals and tensor form factors entering the calculation of one-loop amplitudes which supports the use of complex masses in the loop integrals. The program is built on an earlier version of the golem95 library, which performs the reduction to a certain set of basis integrals using a formalism where inverse Gram determinants can be avoided. It can be used to calculate one-loop amplitudes with arbitrary masses in an algebraic approach as well as in the context of a unitarity-inspired numerical reconstruction of the integrand.
We present a program for the numerical evaluation of form factors entering the calculation of one-loop amplitudes with up to six external legs. The program is written in Fortran95 and performs the reduction to a certain set of basis integrals numerically, using a formalism where inverse Gram determinants can be avoided. It can be used to calculate one-loop amplitudes with massless internal particles in a fast and numerically stable way.
Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak Standard Model and many extensions thereof, one often encounters more mass scales of comparable magnitude. For this reason, a numerical approach for the evaluation of three-loop vacuum integrals with arbitrary mass pattern is proposed here. Concretely, one can identify a basic set of three master integral topologies. With the help of dispersion relations, each of these can be transformed into one-dimensional or, for the most complicated case, two-dimensional integrals in terms of elementary functions, which are suitable for efficient numerical integration.
We present a new approach for obtaining very precise integration results for infrared vertex and box diagrams, where the integration is carried out directly without performing any analytic integration of Feynman parameters. Using an appropriate numerical integration routine with an extrapolation method, together with a multi-precision library, we have obtained integration results which agree with the analytic results to 10 digits even for such a very small photon mass as $10^{-150}$ GeV in the infrared vertex diagram.
We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at leading color in QCD. We provide a set of pure integrals together with differential equations in canonical form. We obtain analytic differential equations efficiently from numerical samples over finite fields, fitting an ansatz built from symbol letters. The symbol alphabet itself is constructed from cut differential equations and we find that it can be written in a remarkably compact form. We comment on the analytic properties of the integrals and confirm the extended Steinmann relations, which govern the double discontinuities of Feynman integrals, to all orders in $epsilon$. We solve the differential equations in terms of generalized power series on single-parameter contours in the space of Mandelstam invariants. This form of the solution trivializes the analytic continuation and the integrals can be evaluated in all kinematic regions with arbitrary numerical precision.
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