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 $W$- 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 $\mathcal{O}(\ensuremath{\alpha})$ to these processes, including improvements beyond $\mathcal{O}(\ensuremath{\alpha})$ 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 ${M}_{H}\ensuremath{\sim}500\text{ }\text{ }\mathrm{GeV}$. For not too large Higgs masses (${M}_{H}\ensuremath{\lesssim}400\text{ }\text{ }\mathrm{GeV}$) the corrections to the partial decay widths can be reproduced within $\ensuremath{\lesssim}2%$ 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.

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