# Z-Boson reasonance and the number of neutrino varieties

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1. Jan 18, 2013

### 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

2. Jan 18, 2013

Staff Emeritus
3. Jan 21, 2013

### 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.

4. Jan 22, 2013

### Ngineer

This does help a lot. Thanks Vanadium and jkp.