High-precision ϵ-expansions of massive four-loop vacuum bubbles

In this Letter we calculate at high-precision the expansions in ϵ=(4−D)/2 of the master integrals of 4-loop vacuum bubble diagrams with equal masses, using a method based on the solution of systems of difference equations. We also show that the analytical expression of a related on-shell 3-loop self-mass master integral contains new transcendental constants made up of complete elliptic integrals of first and second kind.