Z-Boson reasonance and the number of neutrino varieties

Ngineer

I've read that the experimental results of Z-Boson resonance confirm the theoretical expectations that there are 3-types of Neutrinos, not 2 or 4.

How are these theoretical expectations calculated? I.e. how does the number of neutrino varieties affect Z-boson resonance?

Thank you

Vanadium 50

Does http://en.wikipedia.org/wiki/Neutrino#Types answer your question? If not, can you be more specific as to what you are looking for?

jkp

At the LEP experiment Z bosons were produced through colliding electrons and positrons. This was a very clean experiment, unlike the LHC, allowing the properties of the Z boson to be studied to high precision. The presence of the Z boson shows up as a peak in the total cross-section as a function of center of mass energy with the peak located at ~91 GeV corresponding to the mass of the Z boson (there is a nice plot of this on p711 fig.20.5 of Peskin & Schroeder). By measuring the Z peak very carefully they can determine the total width (##\Gamma_{tot}##) and the cross-section at the peak (##\sigma_{peak}##).

The total Z width ##\Gamma_{tot}## is actually made up of two parts. The first is the visible part ##\Gamma_{vis}## made up of decays to charged leptons and hadrons and this is related to the observed peak cross-section ##\sigma_{peak}##. The second is the invisible part ##\Gamma_{inv}## made up of decays to neutrinos which are not observed in the experiment. This second part can be determined by taking ##\Gamma_{tot}-\Gamma_{vis}=\Gamma_{inv}=N_\nu\Gamma(Z\to \nu\overline{\nu})## where ##N_\nu## is the number of active neutrinos. Notice it is "active" neutrinos that matter not the number of neutrinos as there might be "sterile" neutrinos which the Z doesn't decay to. Putting it all together we can get ##N_\nu## from
$$N_\nu = (\Gamma_{tot}-\Gamma_{vis})/\Gamma(Z\to \nu\overline{\nu})$$
and the result is very close to ##N_\nu=3##.

You can try to look at chapter 20 of Peskin & schroeder and in particular do the problems 20.2 and 20.3 on p 728 which will give you a good understanding of the Z resonance and how it relates to the number of active neutrinos.

Ngineer

This does help a lot. Thanks Vanadium and jkp.