Explicit solutions of the 3-loop vacuum integral recurrence relations
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Explicit formulas for the solutions of the recurrence relations for 3-loop vacuum integrals are suggested in this paper, which can also be used for direct calculations and demonstrate a high efficiency.About:
This article is published in Physics Letters B.The article was published on 1996-09-26 and is currently open access. It has received 161 citations till now. The article focuses on the topics: Vacuum polarization & Recurrence relation.read more
Citations
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High-precision calculation of multiloop feynman integrals by difference equations
TL;DR: Algorithms for the construction of the systems using integration-by-parts identities and methods of solutions by means of expansions in factorial series and Laplace transformation and procedures for generating and solving systems of differential equations in masses and momenta for master integrals are shown.
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Algorithm FIRE—Feynman Integral REduction
TL;DR: The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-Bases and integrating explicitly over loop momenta when possible.
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Black Hole Binary Dynamics from the Double Copy and Effective Theory
TL;DR: In this article, a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory is described, combining methods for integration and matching adapted from effective field theories, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions.
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Quark and Gluon Form Factors to Three Loops
P.A. Baikov,K.G. Chetyrkin,K.G. Chetyrkin,Alexander V. Smirnov,Alexander V. Smirnov,Vladimir A. Smirnov,Vladimir A. Smirnov,Matthias Steinhauser +7 more
TL;DR: This is the first calculation of complete three-loop vertex corrections within massless perturbative quantum chromodynamics and provides building blocks for many third-order cross sections.
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Three-loop polarization function and O(αs2) corrections to the production of heavy quarks
TL;DR: In this paper, the three-loop vacuum polarization function induced by a massive quark is calculated and a comprehensive description of the method is presented. But this method is not suitable for the case of large numbers of quarks.
References
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Integration by parts: The algorithm to calculate β-functions in 4 loops
K.G. Chetyrkin,F.V. Tkachov +1 more
TL;DR: In this paper, it was proved that the counterterm for an arbitrary 4-loop Feynman diagram in an arbitrary model is calculable within the minimal subtraction scheme in terms of rational numbers and the Riemann ζ-function in a finite number of steps via a systematic "algebraic" procedure involving neither integration of elementary, special, or any other functions, nor expansions in and summation of infinite series of any kind.
Journal ArticleDOI
A theorem on analytical calculability of 4-loop renormalization group functions
TL;DR: In this article, a method of evaluating massless propagator-type Feynman integrals is presented, which guarantees that the counterterm of an arbitrary 4-loop diagram can be calculated analytically within the minimal substraction scheme.
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Corrections of order O(GFMt2αs2) to the ϱ parameter
TL;DR: In this article, the three-loop QCD corrections to the ϱ parameter from top and bottom quark loops are calculated and the result differs from the one recently calculated by Avdeev et al.
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$0(\alpha \alpha_s^2)$ correction to the electroweak $\rho$ parameter
TL;DR: In this article, the three-loop QCD contributions to the vacuum polarization functions of the Z and W bosons at zero momentum were calculated in the framework of dimensional regularization as well as regularization by dimensional reduction.
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Two-loop gluon-condensate contributions to heavy-quark current correlators: exact results and approximations
David J. Broadhurst,P.A. Baikov,V. A. Ilyin,Jochem Fleischer,O.V. Tarasov,Vladimir A. Smirnov +5 more
TL;DR: In this paper, the coefficient functions of the gluon condensate in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of z = q 2 4m 2.
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