Two-loop Integrand Decomposition into Master Integrals and Surface Terms
Oct 19, 201526 pages
Published in:
- Phys.Rev.D 94 (2016) 11, 116015
- Published: Dec 23, 2016
e-Print:
- 1510.05626 [hep-th]
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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- [5]
- [5]
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- [6]
- [6]
- [7]
- [8]
- [9]
- [10]
- [11]
- [12]
- [13]
- [13]
- [14]
- [15]
- [16]
- [17]
- [18]
- [19]
- [20]