Massive Feynman diagrams and inverse binomial sums

By A. I. Davydychev, M. Kalmykov. 2003

227 citations recorded by the source corpus.

Abstract When calculating higher terms of the ɛ -expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with respect to their parameters. Exploring this connection and using it together with an approach based on generating functions, we analytically calculate a number of such infinite sums, for an arbitrary value of the argument which corresponds to an arbitrary value of the off-shell external momentum. In such a way, we find a number of new results for physically important Feynman diagrams. Considered examples include two-loop two- and three-point diagrams, as well as three-loop vacuum diagrams with two different masses. The results are presented in terms of generalized polylogarithmic functions. As a physical example, higher-order terms of the ɛ -expansion of the polarization function of the neutral gauge bosons are constructed.

Subfields: Algebra and Number Theory, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b4e74963c235d2deb45666f7ab14ed5f9cccd0da

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In Algebra and Number Theory

In Nuclear and High Energy Physics

Citations in the corpus

Iterated Binomial Sums and their Associated Iterated Integrals (2014, unknown): “[59] in terms of LogSine-functions [97].”
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes (2012, background): “es it was realized however that for certain multi-loop integrals new classes of transcendental functions arise that can no longer be expressed in terms of the classical polylogarithm functions, e.g., [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,”
Higgs boson mass and new physics (2012, background): “6) in [99])”
pySecDec: A toolbox for the numerical evaluation of multi-scale integrals (2017, unknown): “ calculates a massless planar on-shell two-loop 7-propagator box in two different ways: 12 Table 1 Result for the two-loop triangle P126 at p2 3 = 9 and m2 = 1 compared to the analytic result of Ref. [33]. order pySecDec result 2 (-0.0379735 - i0.0747738) (0.000375449 + i0.000695892) 1 (0.2812615 ”
Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop (2006, methodology): “Integrals in the third and fourth line were calculated already in [18]1 and [22, 21, 19].”