Massless on-shell box integral with arbitrary powers of propagators

The massless one-loop box integral with arbitrary indices in arbitrary space-time dimension d is shown to reduce to a sum over three generalized hypergeometric functions. This result follows from the solution to the third order differential equation of hypergeometric type. The Gröbner basis techniqu...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 51; no. 27; pp. 275401 - 275412
Main Author Tarasov, O V
Format Journal Article
LanguageEnglish
Published IOP Publishing 06.07.2018
Subjects
differential equations
Feynman integrals
Gröbner basis
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Summary:The massless one-loop box integral with arbitrary indices in arbitrary space-time dimension d is shown to reduce to a sum over three generalized hypergeometric functions. This result follows from the solution to the third order differential equation of hypergeometric type. The Gröbner basis technique for integrals with noninteger powers of propagators is used to derive the differential equation. A short description of our algorithm for finding the Gröbner basis is given and a complete set of recurrence relations from the Gröbner basis is presented. The first several terms in the expansion of the result are given.
Bibliography:JPhysA-109664.R1
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aac57f