Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
By P. Baikov, K. Chetyrkin. 2010
190 citations recorded by the source corpus.
The old “glue-and-cut” symmetry of massless propagators, first established in Ref. [1] (Chetyrkin and Tkachov, 1981), leads — after reduction to master integrals is performed — to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas (ζ2n) in the Adler function and other similar functions essentially reducible to massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicitly performing the corresponding five-loop master integrals.
Subfields: Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/b8c1c22834b4e1b4e322e51fe641dcc039bd1d4b
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In Geometry and Topology
In Nuclear and High Energy Physics
Citations in the corpus
- Minimally subtracted six loop renormalization of $O(n)$-symmetric $\phi^4$ theory and critical exponents (2017, methodology): “iv[4]) (13) gives the group factor for vacuum (i.”
- Feynman integrals and hyperlogarithms (2015, background): “Similarly, the calculation [11] of all master integrals for four-loop massless propagators determines a finite number of coefficients for each graph (with all ae = 1), just sufficient for four-loop computations.”