Standard and epsilon-finite Master Integrals for the rho-Parameter

Abstract

We have constructed an epsilon-finite basis of master integrals for all new types of one-scale tadpoles which appear in the calculation of the four-loop QCD corrections to the electroweak rho-parameter. Using transformation rules from the epsilon-finite basis to the standard minimal-number-of-lines basis, we obtain as a by-product analytical expressions for few leading terms of the epsilon-expansion of all members of the standard basis. The new master integrals have been computed with the help of the Pade method and by use of difference equations independently.

26 pages

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Cited by in corpus (13)

• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
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• Moments of Heavy Quark Current Correlators at Four-Loop Order in Perturbative QCD
• Bilinear quark operators in the RI/SMOM scheme at three loops
• The QCD improved electroweak parameter $\rho$
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• $(Z\alpha {)}^4$ order of the polarization operator in Coulomb field at low energy
• Hypergeometric functions with rational arguments
• A new analysis of the pQCD contributions to the electroweak parameter $\rho$ using the single-scale approach of principle of maximum conformality
• Evaluation of three-loop self-energy master integrals with four or five propagators
• Low-energy moments of non-diagonal quark current correlators at four loops
• Relation between pole and running masses of heavy quarks using the principle of maximum conformality