Three-loop QCD corrections and b-quark decays -: art. no. 074016

We present three-loop next-to-next-to-next-to-leading order corrections to the heavy-to-heavy quark transitions in the limit of equal initial and final quark masses. In analogy with the previously found next-to-next-to-leading order corrections, the bulk of the result is due to the beta(0)(2)alpha(s)(3) corrections. The remaining genuine three-loop effects for the semileptonic b-->c decays are estimated to increase the decay amplitude by 0.2(2)%. The perturbative series for the heavy-heavy axial current converges very well.