How fast do neutrinos travel if they have mass?

[Ishanmu]

The Nobel Prize in Physics 2015 was awarded jointly to Takaaki Kajita and Arthur B. McDonald "for the discovery of neutrino oscillations, which shows that neutrinos have mass" So I was wondering if they have mass how fast are they traveling?

 

[Orodruin]

As for anything with mass, this depends on their kinetic energy. In most cases, the neutrino mass is very small compared to the energy, which makes them ultra relativistic, i.e., they travel at speeds very close to the speed of light.

 

[mfb]

If I remember correctly, the neutrinos detected at OPERA (after ~700km of flight) are expected to be less than the diameter of a proton (10^-15m) behind light in vacuum.

 

[Orodruin]

If I remember correctly, the neutrinos detected at OPERA (after ~700km of flight) are expected to be less than the diameter of a proton (10^-15m) behind light in vacuum.

Easy to check. The average neutrino energy in OPERA is roughly 17 GeV, we also have that
$$
1-v = 1- \frac pE \simeq \frac{m^2}{2E^2}.
$$
With an upper mass bound of order 1 eV, this would mean a lag of roughly 700 km * (1.7 * 10^-21), which evaluates to something surprisingly close to 10^-15 m ...

 

[jtbell]

For a solar p-p neutrino with E = 400 keV and mc² = 1 eV, and a flight distance of 93 million miles (sun to earth), I get a lag of about 0.5 m.

 

[snorkack]

How much is the lag from neutrinos emitted by gamma ray bursts?