Reduction of general two-loop self-energies to standard scalar integrals

Abstract

We present a method for reducing general two-loop self-energies to standard scalar integrals in massive gauge theories with special emphasis on the electroweak Standard Model. It includes the tensor integral reduction for all two-loop integrals appearing in self-energy calculations. The results are valid for arbitrary values of the invariant momentum $p^2$, all particle masses, the space-time dimension $D$ and the gauge parameters $\xi _i \; (i = \gamma , Z, W)$. The algebraic structure of the results clearly displays the gauge dependence of the considered quantities and allows to perform very stringent checks. We explicitly verify Slavnov-Taylor identities by calculating several thousand Feynman-diagrams and adding them up algebraically. As an application we calculate the light fermion contributions to the two-loop gauge boson self-energies of the electroweak SM. We study their gauge dependence and discuss the occurring standard integrals.Comment: LaTex, 32 pages, (+ 7 figures available from the authors as ps-files), to appear in Nuclear Physics

Precise prediction forMWin the MSSM

“…Technically, the calculation was done with support of the Mathematica packages FeynArts [46,47], OneCalc [48], and FormCalc [49]. A peculiarity among the box diagrams is the graph with a virtual photon, see diagram (4) in Fig.…”

Two-loop tensor integrals in quantum field theory

“…The original derivation is due to Weiglein, Scharf and Bohm [7]; for completeness we review here the necessary technology and refer the reader to Appendix B for the full list of results.…”

“…Apparently we meet an irreducible numerator, but we can generalize the procedure considering an intermediate reduction with respect to sub-loops, a technique originally introduced in [7]. In the following subsection we briefly illustrate this technique.…”

“…In this Section we give a full list of results following the method of Weiglein, Scharf and Bohm [7] as derived in Section 5. Scalar two-loop two-point functions are defined by…”

“…The complexity of handling two-loop tensor integrals is reflected in the following simple consideration: the complete treatment of one-loop tensor integrals was confined to the appendices of [6], while the reduction of general two-loop self-energies to standard scalar integrals already required a considerable fraction of [7]; the inclusion of two-loop vertices requires the whole content of this paper. Past experience in the field has shown the convenience of gathering a complete collection of results needed for a broad spectrum of applications in one place.…”