Massive two--loop integrals in renormalizable theories

Abstract

We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy numerical integration, similar to a method proposed previously for treating diagrams without numerators. We reduce all possible tensor structures to a small set of scalar integrals, for which we provide integral representations in terms of four basic functions. The algebraic part is suitable for implementing in a computer program for the automatic generation and evaluation of Feynman graphs. The numerical part is essentially the same as in the case of Feynman diagrams without numerators.

to appear in Nucl. Phys. B

Cited by in corpus (29)

• $\pi \pi$ Scattering in Three Flavour ChPT
• Pion and Kaon Electromagnetic Form Factors
• Chiral Perturbation Theory Beyond One Loop
• TSIL: a program for the calculation of two-loop self-energy integrals
• On the Quantitative Impact of the Schechter-Valle Theorem
• Evaluation of two-loop self-energy basis integrals using differential equations
• Two-loop scalar self-energies in a general renormalizable theory at leading order in gauge couplings
• Strong and Yukawa two-loop contributions to Higgs scalar boson self-energies and pole masses in supersymmetry
• $K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering
• An Approach Toward the Numerical Evaluation of Multi-Loop Feynman Diagrams
• Two-loop QCD corrections to the MSSM Higgs masses beyond the effective-potential approximation
• Single mass scale diagrams: construction of a basis for the $\epsilon$-expansion
• Algebraic-Numerical Evaluation of Feynman Diagrams: Two-Loop Self-Energies
• Axial-vector Form Factors for $K_{\ell 2\gamma }$ and ${\pi }_{\ell 2\gamma }$ at $O(p^6)$ in Chiral Perturbation Theory
• Low Energy Constants from Kl4 Form-Factors
• Scalar Form Factors in SU(3) Chiral Perturbation Theory
• Effect of m_c on b quark chromomagnetic interaction and on-shell two-loop integrals with two masses
• On $C_J$ and $C_T$ in the Gross-Neveu and $O(N)$ Models
• Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations
• Numerical multi-loop integrals and applications
• The expansion by regions in pi K scattering
• Reduction and evaluation of two-loop graphs with arbitrary masses
• On the two-loop contributions to the pion mass
• One-loop integrals with XLOOPS-GiNaC
• Two-loop representations of low-energy pion form factors and pi-pi scattering phases in the presence of isospin breaking
• Exact O(g^2 alpha_s) top decay width from general massive two-loop integrals
• Exact non-factorizable O(alpha_s g^2) two-loop contribution to Z -> b bbar
• Momentum expansion of massive two-loop Feynman graphs around a finite value
• Evaluating massive planar two-loop tensor vertex integrals