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Massless on-shell box integral with arbitrary powers of propagators. (English) Zbl 1396.81096

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 \(\varepsilon = (4 - d)/2\) expansion of the result are given.

MSC:

81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T18 Feynman diagrams
33C20 Generalized hypergeometric series, \({}_pF_q\)

Software:

NumExp; Hypexp
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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