Ananthanarayan, B and Bera, S and Pathak, T (2023) AlgRel.wl: Algebraic relations for the product of propagators in Feynman integrals. In: Nuclear Physics B, 995 .

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Abstract
Motivated by the foundational work of Tarasov, who pointed out that the algebraic relations of the type considered here can lead to functional reduction of Feynman integrals, we suitably modify the original method to be able to implement and automatize it and present a MATHEMATICA package AlgRel.wl. The purpose of this package is to help derive the algebraic relations with arbitrary kinematic quantities, for the product of propagators. Under specific choices of the arbitrary parameters that appear in these relations, we can write the original integral with all massive propagators in general, as a sum of integrals which have fewer massive propagators. The resulting integrals are of reduced complexity for computational purposes. For the oneloop cases, with all different and nonzero masses, this would result in integrals with one massive propagator. We also devise a strategy so that the method can also be applied to higherloop integrals. We demonstrate the procedure and the results obtained using the package for various oneloop and higherloop examples. Due to the fact that the Feynman integrals are intimately related to the hypergeometric functions, a useful consequence of these algebraic relations is in deriving the sets of nontrivial reduction formulae. We present various such reduction formulae and further discuss how, more such formulae can be obtained apart from the ones described here. The AlgRel.wl package and an example notebook Examples.nb can be found at GitHub. Â© 2023 The Author(s)
Item Type:  Journal Article 

Publication:  Nuclear Physics B 
Publisher:  Elsevier B.V. 
Additional Information:  The copyright for this article belongs to the Authors. 
Department/Centre:  Division of Physical & Mathematical Sciences > Centre for High Energy Physics 
Date Deposited:  22 Nov 2023 03:26 
Last Modified:  22 Nov 2023 03:26 
URI:  https://eprints.iisc.ac.in/id/eprint/83192 
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