Automatic computation of Feynman diagrams

Harlander, Robert V.; Steinhauser, Matthias

doi:10.1016/s0146-6410(99)00095-2

Cited by 64 publications

(76 citation statements)

References 196 publications

(221 reference statements)

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“…For a general overview concerning the automation of Feynman diagram computation we refer to [116]. The large number of diagrams which occurs in particular if one considers higher loop orders makes it necessary to generate the diagrams automatically.…”

Section: A3 Automation Of Feynman Diagram Computationmentioning

confidence: 99%

Results and techniques of multi-loop calculations

Steinhauser

2002

Physics Reports

100

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In this review some recent multi-loop results obtained in the framework of perturbative Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore the connection to observables involving a scalar Higgs boson is worked out in detail. An all-order low energy theorem is derived which establishes a relation between the coefficient functions in the hadronic Higgs decay and the decoupling constants. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order α 4 s and α 3 s , respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Padé approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass-dependence. In particular, we concentrate on the evaluation of the total cross section for the production of hadrons in e + e − annihilation. The knowledge of the complete mass dependence at order α 2 s has triggered a bunch of theory-driven analyses of the hadronic contribution to the electromagnetic coupling evaluated at high energy scales. The status is summarized in this review. In a further application four-loop diagrams are considered which contribute to the order α 2 QED corrections to the µ decay. Its relevance for the determination of the Fermi constant G F is discussed. Finally the calculation of the three-loop relation between the MS and on-shell quark mass definitions is presented and physical applications are given. To complete the presentation, some technical details are presented in the Appendix, where also explicit analytical results are listed.

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Section: A3 Automation Of Feynman Diagram Computationmentioning

confidence: 99%

Results and techniques of multi-loop calculations

Steinhauser

2002

Physics Reports

100

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“…The occurring vacuum diagrams are passed to MATAD [22] and the massless propagator type diagrams are evaluated to MINCER [23]. More details on the automatic computation of Feynman diagrams can be found in [24].…”

Section: Spectral Function In Full Qcdmentioning

confidence: 99%

Heavy-light current correlators at order $\alpha_\mathrm{s}^2$ in QCD and HQET

2001

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The non-diagonal correlators of vector and scalar currents are considered at threeloop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries mass M . We exploit the decoupling relations between the full theory and the heavy quark effective theory (HQET) in order to obtain the logarithmic parts of the leading threshold terms. With the help of conformal mapping and Padé approximation numerical estimates for the nonlogarithmic terms are extracted which in turn lead to a prediction of the correlator in HQET at order α 2 s . As applications of the vector and scalar correlator we consider the single-top-quark production via the process qq → tb and the decay rate of a charged Higgs boson into hadrons, respectively. In both cases the computed NLO corrections are shown to be numerically much less important than the leading ones. On the contrary, the NLO order QCD corrections to the HQET sum rule for the leptonic decay rate of a heavy-light meson proves to be comparable to the leading one.

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“…Recently, some calculations have been done which would seem impossible only a few years ago. This is due to the high degree of automation of the process of generation, analyses and calculation of Feynman diagrams, which is achieved via extensive use of computer algebra (see [1] for review and references). All such calculations are performed in the framework of dimensional regularization [2], i.e.…”

Section: Introductionmentioning

confidence: 99%