Uniqueness of two-loop master contours
By S. Caron-Huot, Kasper J. Larsen. Journal of High Energy Physics, 2012
207 citations recorded by the source corpus.
Generalized-unitarity calculations of two-loop amplitudes are performed by expanding the amplitude in a basis of master integrals and then determining the coefficients by taking a number of generalized cuts. In this paper, we present a complete classification of the solutions to the maximal cut of integrals with the double-box topology. The ideas presented here are expected to be relevant for all two-loop topologies as well. We find that these maximal-cut solutions are naturally associated with Riemann surfaces whose topology is determined by the number of states at the vertices of the double-box graph. In the case of four massless external momenta we find that, once the geometry of these Riemann surfaces is properly understood, there are uniquely defined master contours producing the coefficients of the double-box integrals in the basis decomposition of the two-loop amplitude. This is in perfect analogy with the situation in one-loop generalized unitarity. In addition, we point out that the chiral integrals recently introduced by Arkani-Hamed et al. can be used as master integrals for the double-box contributions to the two-loop amplitudes in any gauge theory. The infrared finiteness of these integrals allow for their coefficients as well as their integrated expressions to be evaluated in strictly four dimensions, providing significant technical simplification. We evaluate these integrals at four points and obtain remarkably compact results.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/e9d1d92b1e4320b6e64baa4bd764dab447906cfb
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Citations in the corpus
- Hexagon functions and the three-loop remainder function (2013, background): “For example, an elliptic integral, in which the kernel is not rational but contains a square root, enters the two-loop equal-mass sunrise graph [58, 59], and it has been shown that a very similar type of integral enters a particular N3MHV 10-point scattering amplitude in planar N = 4 super-Yang-Mill”
- Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence (2016, background): “This means that the integrand has two genuine branch cuts that cannot be removed by any change of variables, yielding an elliptic function upon integration [59, 93].”
- 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.”
- The elliptic dilogarithm for the sunset graph (2013, methodology): “The sunset integral arises as the two-loop self-energy diagram in the evaluation of higher-order correction in QED, QCD or electroweak theory precision calculations [4], or as a sub-topology of higher-order computation [5].”
- Two-loop integrand decomposition into master integrals and surface terms (2015, methodology): “This approach does not require integration over multi-dimensional phase spaces and thus differs from the direct extraction of integral coefficients [46] or possible extensions using the duality between master integrals and homology cycles of the phase spaces [47, 48, 52].”
- Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph (2017, unknown): “05 46”
- Feynman integrals and hyperlogarithms (2015, background): “Also in massless integrals, counterexamples to polylogarithmic results have been identified [61, 63], even in supersymmetric theories [67, 133].”