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On the analytic computation of massless propagators in dimensional regularization
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abstract
We comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation. Explicitly, we give results for all three-loop propagators with arbitrary insertions including order $\varepsilon^4$ and show examples at four and more loops. Further we prove that all coefficients of the $\varepsilon$-expansion of these integrals are rational linear combinations of multiple zeta values and in some cases possibly also alternating Euler sums.
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Transcendental structure of multiloop massless correlators and anomalous dimensions
A hatted representation of transcendental constants, fixed from four-loop integrals, predicts the pi-dependent terms in seven- and eight-loop beta functions and anomalous dimensions.
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