Master integrals for bipartite cuts of three-loop photon self energy

Abstract

We calculate master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the $4m$ cut, reduce to Goncharov's polylogarithms. The master integrals for $4m$ cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for $4m$ cut.

arXiv comment17 pages

References in corpus (19)

• Multiloop integrals in dimensional regularization made simple
• Asymptotic expansion of Feynman integrals near threshold
• Differential Equations for Feynman Graph Amplitudes
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Connection between Feynman integrals having different values of the space-time dimension
• HPL, a Mathematica implementation of the harmonic polylogarithms
• FIESTA 4: optimized Feynman integral calculations with GPU support
• Numerical evaluation of multi-loop integrals by sector decomposition
• Reducing differential equations for multiloop master integrals
• Sector Decomposition
• Resolution of singularities for multi-loop integrals
• Numerical evaluation of phase space integrals by sector decomposition
• Extension of HPL to complex arguments
• Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen
• A geometric method of sector decomposition
• Accuracy of Calculations Involving ${\alpha }^3$ Vacuum-Polarization Diagrams: Muonic Hydrogen Lamb Shift and Muon $g-2$
• Blowing up Feynman integrals
• $\epsilon$-regular basis for non-polylogarithmic multiloop integrals and total cross section of the process $e^{+}{e}^{-}\to 2(Q\bar{Q})$

Cited by in corpus (4)

• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
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• Hadronic vacuum polarization to three loops in chiral perturbation theory