# Why do we have so few neutrinos to study?

According to Wikipedia most neutrinos passing through the Earth emanate from the Sun. About 65 billion (6.5^10) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun in the region of the Earth.

However the IceCube Neutrino Observatory or other neutrino detectors only detect a few neutrinos every year. Why?

It's not that the neutrino detectors don't have a chance of detecting a neutrino, but that the neutrinos do not interact with matter (well hardly ever).

If there are $6.5\times 10^{10}$ neutrinos per second per $cm^2$ and if the detector has an area of $10^{6} cm^2$, and it detects 1 neutrino per year, then 1 out of $2.05\times 10^{24}$ neutrinos interacts with the detector. $2.05\times 10^{24}$ pass through the detector unnoticed.

It is because the neutrinos cross section is very small.

Roughly, the cross section is a measure of the interaction probability (for a given force) of the given particle with your target.

Since the probability for interaction depends upon the strength and range of the interaction, the cross-sections for neutrino interactions are very small since they interact only by the weak interaction.

Hence, it is not that we receive few neutrinos, rather it is our (in)ability to detect them, due to our current knowledge of their intrinsic nature, which prevent us from measuring high fluxes of neutrinos.

For this very reason, neutrinos detectors are made of huge volume targets, in order to maximize the detection probability.

• The cross section is so small that I doubt whether it is useful to put neutrino detectors in mines. How to know neutrinos are from a particular source, say, our sun? – questionhang Jan 30 '15 at 16:49
• Underground detectors are built in such a way in order to minimize background. Neutrinos are known coming from a given source because of the direction of their products (they are indirectly inferred), according to the models we have that produce that given neutrinos flux (we expect a given amount of a certain neutrino flavor from, say, the sun). See the GALLEX experiment But this would deserve a different question (and answer). – Py-ser Jan 30 '15 at 16:54