Precise predictions for the Higgs-boson decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>H</mml:mi><mml:mo>→</mml:mo><mml:mi>W</mml:mi><mml:mi>W</mml:mi><mml:mo>/</mml:mo><mml:mi>Z</mml:mi><mml:mi>Z</mml:mi><mml:mo>→</mml:mo><mml:mn>4</mml:mn></mml:math>leptons

The decay of the Standard Model Higgs boson into four leptons via a virtual W-boson or Z-boson pair is one of the most important decay modes in the Higgs-boson search at the LHC. We present the complete electroweak radiative corrections of O(\alpha) to these processes, including improvements beyond O(\alpha) originating from heavy-Higgs effects and final-state radiation. The intermediate W- and Z-boson resonances are described (without any expansion or on-shell approximation) by consistently employing complex mass parameters for the gauge bosons (complex-mass scheme). The corrections to partial decay widths typically amount to some per cent and increase with growing Higgs mass M_H, reaching about 8% at M_H \sim 500 GeV. For not too large Higgs masses (M_H <\sim 400 GeV) the corrections to the partial decay widths can be reproduced within <\sim 2% by simple approximations. For angular distributions the corrections are somewhat larger and distort the shapes. For invariant-mass distributions of fermion pairs they can reach several tens of per cent depending on the treatment of photon radiation. The discussed corrections have been implemented in a Monte Carlo event generator called PROPHECY4F.