Euclidean asymptotic expansions of Green functions of quantum fields (II) Combinatorics of the asymptotic operation

Abstract

The results of part I (hep-ph/9612284) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-scheme in the regimes when some of the masses and external momenta are large with respect to the others. The large momenta are Euclidean, and the expanded diagrams are regarded as distributions with respect to them. The small masses may be equal to zero. The asymptotic operation for integrals is defined and a simple combinatorial techniques is developed to study its exponentiation. The asymptotic operation is used to obtain the corresponding expansions of arbitrary Green functions. Such expansions generalize and improve upon the well-known short-distance operator-product expansions, the decoupling theorem etc.; e.g. the low-energy effective Lagrangians are obtained to all orders of the inverse heavy mass. The obtained expansions possess the property of perfect factorization of large and small parameters, which is essential for meaningful applications to phenomenology. As an auxiliary tool, the inversion of the R-operation is constructed. The results are valid for arbitrary QFT models.

one .sty + one .tex (LaTeX 2.09) + one .ps (GSview) = 46 pp. Many fewer misprints than the journal version

Cited by in corpus (20)

• Neutral Higgs-Boson Pair Production at Hadron Colliders: QCD Corrections
• On the Precise Determination of the Fermi Coupling Constant from the Muon Lifetime
• Pole masses of quarks in dimensional reduction
• An Approach Toward the Numerical Evaluation of Multi-Loop Feynman Diagrams
• Automatic Computation of Feynman Diagrams
• Two-loop heavy top corrections to the Z boson partial widths
• Next-To-Leading-Order Matching for the Magnetic Photon-Penguin Operator in the $B\to X_s\gamma$ Decay
• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• Euclidean asymptotic expansions of Green functions of quantum fields (I) Expansions of products of singular functions
• Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
• Calculating four-loop tadpoles with one non-zero mass
• Combinatorics of renormalization as matrix calculus
• Pole mass determination in presence of heavy particles
• Towards Automatic Analytic Evaluation of Diagrams with Masses
• Towards systematic near-threshold calculations in perturbative QFT
• Radiation pions in two-nucleon effective field theory
• Top-quark loops and the muon anomalous magnetic moment
• Three-Loop Calculation of the Higgs Boson Mass in Supersymmetry
• Unregulated Divergences of Feynman Integrals
• Finite Z-less integral expressions for $\beta$-functions in the MS4 scheme