# In typical decay experiments what range of energies do electron neutrinos and muon neutrinos exhibit?

in experiments over decay of particles, what are the typical range of energies of electron neutrinos and muon neutrinos? I would guess I need to specify in the inertial frame of a lab here on earth? Does the range differ much between differnt types of experiments? For instance in a muon decay (Michel decay) the muon decays into an electron, an electron anti neutrino and a muon neutrino, what typical range of energies do the electron anti neutrinos have and what energy do the muon neutrinos have? Are there other types of decay where the range of energies of the neutrinos have a much different range? Can you specify what types of decays produce the biggest differences in ranges of energy?

Many thanks

• We can find neutrinos from the keV to the TeV range and particle physicists have built detectors for low energy solar neutrinos as well as high energy cosmic neutrinos. There is no obvious reason why the neutrino spectrum should have a high energy cutoff, the higher energies are simply harder to detect because the spectrum falls off with something like $E^{-2.x}$, which is just barely offset by an increase in cross section that goes with $E^2$. The remaining difficulty is then given by the very long track length of TeV muons in water-Cherenkov detectors, requiring $km^3$ sized detectors. – CuriousOne Dec 21 '15 at 18:08

## 2 Answers

Because of the large mass difference between the muon and the heaviest decay product (the electron) we can reasonable approximate the decay as symmetric with respect to the selection of which product you ask about.

Ergo, the neutrinos in the decay $$\mu^- \longrightarrow e^- + \bar{\nu}_e + \nu_\mu \,,$$ have an energy spectrum much like that of the electron meaning a cut-off around $50\,\mathrm{MeV}$, a peak near $30\,\mathrm{MeV}$ and a tail down to zero.

For types of decay other than muon, there is pion or K meson decay $$\pi^- (K^-) \to \mu^-+\overline \nu_\mu$$ As it is a two body decay, the energies are fixed in the decaying particle frame. In the pion case the neutrino energy is $29.80$ MeV and (using the same formula with $M_x=493.66$ the neutrino energy is $152$ MeV

The $Z$ boson decays about $20\%$ of the time into a neutrino/antineutrino pair. Each carries half the $Z$ mass, or $45.6$ GeV. The $W$ bosons decay to lepton/(anti)neutrino pairs about $30\%$ of the time, producing neutrinos of just about this energy.

Very high energy neutrinos can be seen in the lab when the decaying particle has high energy in the lab