Landau-Khalatnikov-Fradkin transformation and the mystery of even ζ-values in Euclidean massless correlators

The Landau-Khalatnikov-Fradkin transformation is a powerful and elegant transformation allowing us to study the gauge dependence of the propagator of charged particles interacting with gauge fields. With the help of this transformation, we derive a nonperturbative identity between massless propagators in two different gauges. From this identity, we find that the corresponding perturbative series can be exactly expressed in terms of a hatted transcendental basis that eliminates all even zeta-values. This explains the mystery of even zeta-values observed in multiloop calculations of Euclidean massless correlators for almost three decades now. Our construction further allows us to derive an exact formula relating hatted and standard zeta-values to all orders of perturbation theory.