The decay of the standard model Higgs boson into four leptons via a virtual $W$- or $Z$-boson pair is one of the most important decay modes in the Higgs-boson search at the Large Hadron Collider. We present the complete electroweak radiative corrections of $\mathcal{O}(\alpha )$ to these processes, including improvements beyond $\mathcal{O}(\alpha )$ 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 percent and increase with growing Higgs mass $M_H$, reaching about 8% at $M_H\sim 500\mathrm{GeV}$. For not too large Higgs masses ($M_H\lesssim 400\mathrm{GeV}$) the corrections to the partial decay widths can be reproduced within $\lesssim 2\%$ 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 percent depending on the treatment of photon radiation. The discussed corrections have been implemented in a Monte Carlo event generator called Prophecy4f.

• Received 4 April 2006

DOI:https://doi.org/10.1103/PhysRevD.74.013004