Two-loop Integrand Decomposition into Master Integrals and Surface Terms

Oct 19, 2015
26 pages
Published in:
  • Phys.Rev.D 94 (2016) 11, 116015
  • Published: Dec 23, 2016
e-Print:
Report number:
  • FR-PHENO-2015-011

Citations per year

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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