On the integrand-reduction method for two-loop scattering amplitudes
We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop momenta, and that the reduction of the amplitudes in terms...
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| Published in | The journal of high energy physics Vol. 2011; no. 11 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer-Verlag
01.11.2011
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1029-8479 1029-8479 |
| DOI | 10.1007/JHEP11(2011)014 |
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| Abstract | We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop momenta, and that the reduction of the amplitudes in terms of master integrals can be realized through polynomial fitting of the integrand, without any apriori knowledge of the integral basis. We discuss how the polynomial shapes of the residues determine the basis of master integrals appearing in the final result. We present a four-dimensional constructive algorithm that we apply to planar and non-planar contributions to the 4- and 5-point MHV amplitudes in
SYM. The technique hereby discussed extends the well-established analogous method holding for one-loop amplitudes, and can be considered a preliminary study towards the systematic reduction at the integrand-level of two-loop amplitudes in any gauge theory, suitable for their automated semianalytic evaluation. |
|---|---|
| AbstractList | We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop momenta, and that the reduction of the amplitudes in terms of master integrals can be realized through polynomial fitting of the integrand, without any apriori knowledge of the integral basis. We discuss how the polynomial shapes of the residues determine the basis of master integrals appearing in the final result. We present a four-dimensional constructive algorithm that we apply to planar and non-planar contributions to the 4- and 5-point MHV amplitudes in SYM. The technique hereby discussed extends the well-established analogous method holding for one-loop amplitudes, and can be considered a preliminary study towards the systematic reduction at the integrand-level of two-loop amplitudes in any gauge theory, suitable for their automated semianalytic evaluation. We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop momenta, and that the reduction of the amplitudes in terms of master integrals can be realized through polynomial fitting of the integrand, without any apriori knowledge of the integral basis. We discuss how the polynomial shapes of the residues determine the basis of master integrals appearing in the final result. We present a four-dimensional constructive algorithm that we apply to planar and non-planar contributions to the 4- and 5-point MHV amplitudes in SYM. The technique hereby discussed extends the well-established analogous method holding for one-loop amplitudes, and can be considered a preliminary study towards the systematic reduction at the integrand-level of two-loop amplitudes in any gauge theory, suitable for their automated semianalytic evaluation. |
| ArticleNumber | 14 |
| Author | Mastrolia, Pierpaolo Ossola, Giovanni |
| Author_xml | – sequence: 1 givenname: Pierpaolo surname: Mastrolia fullname: Mastrolia, Pierpaolo email: ppaolo@mppmu.mpg.de organization: Max-Planck Insitut für Physik, Departamento de Física Teórica, Universidad Autónoma de Madrid – sequence: 2 givenname: Giovanni surname: Ossola fullname: Ossola, Giovanni organization: Physics Department, New York City College of Technology, City University of New York, The Graduate School and University Center, The City University of New York |
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| Snippet | We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on... |
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| SubjectTerms | Algorithms Amplitudes Classical and Quantum Gravitation Elementary Particles Gauge theory High energy physics Integrals Physics Physics and Astronomy Polynomials Quantum Field Theories Quantum Field Theory Quantum Physics Reduction Relativity Theory Residues Scattering String Theory |
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| Title | On the integrand-reduction method for two-loop scattering amplitudes |
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