A new hypergeometric representation of one-loop scalar integrals in $d$ dimensions
Fleischer, Jochem
Jegerlehner, F
Tarasov, OV
A difference equation w.r.t. space-time dimension $d$ for $n$-point one-loopintegrals with arbitrary momenta and masses is introduced and a solutionpresented. The result can in general be written as multiple hypergeometricseries with ratios of different Gram determinants as expansion variables.Detailed considerations for $2-,3-$ and $4-$point functions are given. For the$2-$ point function we reproduce a known result in terms of the Gausshypergeometric function $_2F_1$. For the $3-$point function an expression interms of $_2F_1$ and the Appell hypergeometric function $F_1$ is given. For the$4-$point function a new representation in terms of $_2F_1$, $F_1$ and theLauricella-Saran functions $F_S$ is obtained. For arbitrary $d=4-2\epsilon$,momenta and masses the $2-,3-$ and $4-$point functions admit a simple one-foldintegral representation. This representation will be useful for the calculationof contributions from the $\epsilon-$ expansion needed in higher orders ofperturbation theory. Physically interesting examples of $3-$ and $4-$pointfunctions occurring in Bhabha scattering are investigated.
ELSEVIER SCIENCE BV
2003
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/1609642
Fleischer J, Jegerlehner F, Tarasov OV. A new hypergeometric representation of one-loop scalar integrals in $d$ dimensions. <em>NUCLEAR PHYSICS B</em>. 2003;672(1-2):303-328.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.nuclphysb.2003.09.004
info:eu-repo/semantics/altIdentifier/issn/0550-3213
info:eu-repo/semantics/altIdentifier/wos/000186583100013
info:eu-repo/semantics/altIdentifier/arxiv/hep-ph/0307113
info:eu-repo/semantics/closedAccess