Two-loop integrand decomposition into master integrals and surface terms

By H. Ita. 2015

198 citations recorded by the source corpus.

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.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/396843be8cad96db170d78e623e92fe6574606da

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In Computational Mathematics

In Computational Theory and Mathematics

In Nuclear and High Energy Physics

Citations in the corpus

Integral reduction with Kira 2.0 and finite field methods (2020, unknown): “In the last few years, new techniques have been explored and applied to integral reduction problems, employing syzygy equations [7–12], algebraic geometry [13–15], intersection numbers [16–20], finite field and interpolation techniques [21–26], or special integral representations [27–30].”
Cuts of Feynman Integrals in Baikov representation (2017, background): “In the recent years, progress has been made also towards the extension of these reduction methods for two-loop amplitudes at the integral [17, 18, 19, 20, 21, 22, 23, 24, 25, 26] as well as the integrand [27, 28, 29, 30, 31, 32] level.”
Collider physics at the precision frontier (2020, unknown): “Numerical unitarity has been extremely successful to calculate massless two-loop amplitudes [429, 448, 502, 503], including the first computation of the two-loop 4-gluon amplitude based on numerical unitarity [448] as well as progress towards two-loop five-point processes with one massive external l”