The paper constructs a locally finite two-loop amplitude integrand for photoproduction in quark annihilation, using momentum-flow symmetrization and an antisymmetric counterterm vertex to remove transient collinear singularities.
Direct numerical integration for multi-loop integrals
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abstract
We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be performed directly in loop momentum space without the introduction of Feynman or Schwinger parameters. The method can be applied to finite multi-loop integrals and to divergent multi-loop integrals with suitable subtraction terms. The algorithm extends techniques from the one-loop case to the multi-loop case. Examples at two and three loops are discussed explicitly.
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General finite two-loop amplitude integrand for photoproduction in quark annihilation
The paper constructs a locally finite two-loop amplitude integrand for photoproduction in quark annihilation, using momentum-flow symmetrization and an antisymmetric counterterm vertex to remove transient collinear singularities.