Higgs Experiment for new particle (decay widths)

[Jem]

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

Question:
An experiment is proposed to directly measure the width (Γ) and mass (m_H) of the Higgs boson via the reaction: muon+ + muon- > H.

Sketch a graph of the expected cross section as a function of centre of mass collision energy. Indicate on the graph Γ and m_Hc^2.

It is postulated that the Higgs boson could decay to as yet undiscovered particles that would not be detected by a usual particle physics detector. Explain how the above experiment would be able to test this hypothesis.

Answer:
I have drawn a Lorentzian graph of N(E) against E to show the width at Full Width Half Maximum and the graph is centred on x=E=m_Hc^2. I need help in explaining how this experiment would be able to test the hypothesis.
Would the centre of the graph shift if the mass of the products now includes a new unknown particle not just the Higgs?
Thanks!

 

[mfb]

Would the centre of the graph shift if the mass of the products now includes a new unknown particle not just the Higgs?

The question asks about Higgs decays. In the same way as the Higgs can decay e.g. to two quarks it might be possible that the Higgs can decay to a pair of undiscovered particles. You didn't consider all the known decay modes for the mass, why would you do this for an unknown decay mode?

What is the relation between width and lifetime, and between lifetime and decay modes?