相关论文: Integration-by-parts reductions from unitarity cut…

Integration-by-parts reductions play a central role in perturbative QFT calculations. They allow the set of Feynman integrals contributing to a given observable to be reduced to a small set of basis integrals, and they moreover facilitate…

We show that for a class of two-loop diagrams, the on-shell part of the integration-by-parts (IBP) relations correspond to exact meromorphic one-forms on algebraic curves. Since it is easy to find such exact meromorphic one-forms from…

Generalized-unitarity calculations of two-loop amplitudes are performed by expanding the amplitude in a basis of master integrals and then determining the coefficients by taking a number of generalized cuts. In this paper, we present a…

We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general…

We introduce an algebro-geometrically motived integration-by-parts (IBP) reduction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines…

We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…

We present an alternative reduction to master integrals for one-loop amplitudes using a unitarity cut method in arbitrary dimensions. We carry out the reduction in two steps. The first step is a pure four-dimensional cut-integration of tree…

Generalized unitarity cut of a Feynman diagram generates an algebraic system of polynomial equations. At high-loop levels, these equations may define a complex curve or a (hyper-)surface with complicated topology. We study the curve cases,…

Integration by parts is used to reduce scalar Feynman integrals to master integrals.

We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully…

Scattering amplitudes at loop level can be reduced to a basis of linearly independent Feynman integrals. The integral coefficients are extracted from generalized unitarity cuts which define algebraic varieties. The topology of an algebraic…

We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…

Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…

The techniques of integration by parts and differential reduction differ in the counting of master integrals. This is illustrated using as an example the two-loop sunset diagram with on-shell kinematics. A new algebraic relation between the…

We extend the notion of generalized unitarity cuts to accommodate loop integrals with higher powers of propagators. Such integrals frequently arise in for example integration-by-parts identities, Schwinger parametrizations and Mellin-Barnes…

The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…

Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on…

In this paper, we generalize the unitarity method to two-loop diagrams and use it to discuss the integral bases of reduction. To test out method, we focus on the four-point double-box diagram as well as its related daughter diagrams, i.e.,…

We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…