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The importance of off-shell contributions is discussed for $H\to VV^{(*)}$with $V\in\{Z,W\}$ for large invariant masses $m_{VV}$ involving a standardmodel (SM)-like Higgs boson with $m_H=125$GeV at a linear collider (LC). Bothdominant production processes $e^+e^-\to ZH\to ZVV^{(*)}$ and$e^+e^-\to\nu\bar\nu H\to\nu\bar\nu VV^{(*)}$ are taken into account, and thesignal processes are compared with background yielding the same final state.The relative size of the off-shell contributions is strongly dependent on thecentre-of-mass energy. These contributions can have an important impact on thedetermination of cross sections and branching ratios. However, the combinationof on- and off-shell contributions can also be utilised to lift degeneraciesallowing to test higher-dimensional operators, unitarity and light and heavyHiggs interferences in extended Higgs sectors. The latter is demonstrated inthe context of a 2-Higgs-Doublet model. We also discuss the impact of theseaspects for the Large Hadron Collider (LHC) where they are relevant. Theimportance of a precise measurement of the Higgs mass for on-shellcontributions in $H\to VV^{(*)}$ is emphasized. A particular focus is put onmethods for extracting the Higgs width at a LC. Off-shell contributions areshown to have a negligible impact on the width determination at low $\sqrt{s}$when applying the $Z$ recoil method to extract branching ratios in combinationwith an appropriate determination of a partial width. On the other hand,off-shell contributions can be exploited to constrain the Higgs width in asimilar fashion as in recent analyses at the LHC. It is demonstrated that thisapproach, besides relying heavily on theoretical assumptions, is affected bythe negative interference of Higgs and background contributions that may limitthe sensitivity that is achievable with the highest foreseeable statistics atthe LHC and a LC.

Off-shell effects in Higgs processes at a linear collider and implications for the LHC