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arXiv · 1510.05626

Two-loop Integrand Decomposition into Master Integrals and Surface Terms

Harald Ita
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Abstract

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 products with universal numerator-tensors. Such a decomposition is an important input for the numerical unitarity approach, which constructs integrand coefficients from on-shell tree amplitudes. We present a new method to organise multi-loop integrands into a direct sum of terms that integrate to zero (surface terms) and remaining master integrands. This decomposition facilitates a general, numerical unitarity approach for multi-loop amplitudes circumventing analytic integral reduction. Vanishing integrals are well known as integration-by-parts identities. Our construction can be viewed as an explicit construction of a complete set of integration-by-parts identities excluding doubled propagators. Interestingly, a class of 'horizontal' identities is singled out which hold as well for altered propagator powers.

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Harald Ita. 2015-10-19. Two-loop Integrand Decomposition into Master Integrals and Surface Terms. https://doi.org/10.1103/physrevd.94.116015

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