Abstract
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 standard model (SM)-like Higgs boson with $m_H=125$GeV at a linear collider (LC). Both dominant 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 the signal processes are compared with background yielding the same final state. The relative size of the off-shell contributions is strongly dependent on the centre-of-mass energy. These contributions can have an important impact on the determination of cross sections and branching ratios. However, the combination of on- and off-shell contributions can also be utilised to lift degeneracies allowing to test higher-dimensional operators, unitarity and light and heavy Higgs interferences in extended Higgs sectors. The latter is demonstrated in the context of a 2-Higgs-Doublet model. We also discuss the impact of these aspects for the Large Hadron Collider (LHC) where they are relevant. The importance of a precise measurement of the Higgs mass for on-shell contributions in $H\to VV^{(*)}$ is emphasized. A particular focus is put on methods for extracting the Higgs width at a LC. Off-shell contributions are shown to have a negligible impact on the width determination at low $\sqrt{s}$ when applying the $Z$ recoil method to extract branching ratios in combination with an appropriate determination of a partial width. On the other hand, off-shell contributions can be exploited to constrain the Higgs width in a similar fashion as in recent analyses at the LHC. It is demonstrated that this approach, besides relying heavily on theoretical assumptions, is affected by the negative interference of Higgs and background contributions that may limit the sensitivity that is achievable with the highest foreseeable statistics at the LHC and a LC.
Highlights
A particular contributions focus is put on methods for extracting the are shown to have a negligible impact on the
In extended Higgs sectors light and heavy Higgs contributions can interfere over a large range of mV V ΓH→V V (mV V), which we demonstrate in the context of a 2-Higgs-Doublet model (2HDM)
According to our discussion off-shell effects in Higgs boson decays manifest themselves in the differential cross section dσ/dmR, which we demonstrate in figure 8 for the Higgsstrahlung production process
Summary
Before we start our discussion of off-shell effects in H → V V (∗) in the subsequent section, we shortly elaborate on the relation between the mass and total width of the Higgs boson and the complex pole of the propagator. The peak in the on-shell region mZZ ≈ mH is mainly induced by contributions with the correct assignment of the two gauge bosons to the Higgs boson and the averaging over the three invariant mass combinations approximately corresponds to a division of the cross section obtained by eq (3.3) by a factor of 3. The resulting combination with differential cross sections H → ZZ(∗) for different dσ/dmZ√Z for energies s = Both 250, production processes in 350, 500 GeV and 1 TeV and a fixed polarisation of the initial state Pol(e+, e−) = (0.3, −0.8) are shown in figure 3. For the case of H → ZZ(∗) followed by decays of the two gauge bosons into leptons or quarks, i.e. Z → l±l∓/qq, on-shell and off-shell contributions can be discriminated by the invariant mass of the four leptons/quarks We conclude that within the “on-shell region” the ZWA is a valid approximation with an accuracy at the (sub-)permil level.
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