Two-loop Integrand Decomposition into Master Integrals and Surface Terms - INSPIRE

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Two-loop Integrand Decomposition into Master Integrals and Surface Terms

Harald Ita
(
- Freiburg U.
)

Oct 19, 2015

26 pages

Published in:

Phys.Rev.D 94 (2016) 11, 116015

Published: Dec 23, 2016

e-Print:

1510.05626 [hep-th]

DOI:

10.1103/PhysRevD.94.116015

Report number:

FR-PHENO-2015-011

View in:

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Abstract: (APS)

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 organize multiloop 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 multiloop 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.

Note:

58 pages, 3 figures

master integral
loop integral
scattering amplitude: on-shell
tree approximation
unitarity
surface

References(87)

Figures(3)

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