Finite width effects in Higgs decays as a means of measuring massive particle widths

We calculate decays of a Standard Model Higgs boson to a virtual massive particle and discuss how this depends on the massive particle total width. If the partial width of Higgs to a virtual massive particle can be measured this gives a measurement of that massive particle's width. We discuss how one would go about measuring these partial widths of a Higgs experimentally, and how this could lead to a measurement of the $W$ boson and $t$ quark width. For the latter extreme dependence on the Higgs mass and the small $H\to tt^*$ branching ratios mean that little can be learnt about the $t$ quark width. For the former there is also large dependence on the Higgs mass; however this can be removed by taking the ratio of $H\to WW^*$ decays to $H\to ZZ^*$ decays. This ratio also has the advantage of being fairly insensitive to physics beyond the Standard Model. Unfortunately, for Higgs masses of interest the $H\to ZZ^*$ branching ratio is small enough that we require many 1000's of tagged Higgs decays before an accurate measurement of the $W$ width can be made. This is likely to be hard experimentally.