Abstract
Abstract
A method for reducing Feynman integrals, depending on several kinematic variables and masses, to a combination of integrals with fewer variables is proposed. The method is based on iterative application of functional equations proposed by the author. The reduction of the one-loop scalar triangle and box integrals with massless internal propagators to simpler integrals is described in detail. The triangle integral depending on three variables is represented as a sum over three integrals depending on two variables. By solving the dimensional recurrence relations for these integrals, an analytic expression in terms of the 2
F
1 Gauss hypergeometric function and the logarithmic function was derived.
By using the functional equations, the one-loop box integral with massless internal propagators, which depends on six kinematic variables, was expressed as a sum of 12 terms. These terms are proportional to the same integral depending only on three variables different for each term. For this integral with three variables, an analytic result in terms of the F
1 Appell and 2
F
1 Gauss hypergeometric functions was derived by solving the recurrence relation with respect to the spacetime dimension d. The reduction equations for the box integral with some kinematic variables equal to zero are considered.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference61 articles.
1. ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett.
B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
2. CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett.
B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
3. M. Mangano et al., Future Circular Collider, CERN-ACC-2018-0056 [INSPIRE].
4. D.I. Kazakov, Multiloop Calculations: Method of Uniqueness and Functional Equations, Theor. Math. Phys.
62 (1985) 84 [INSPIRE].
5. S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys.
A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
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