# How are 'margin of error' and 'sigma' (standard deviation) combined in a particle physics experiment?

If a particular experiment is done to determine a particular value, say the charge radius of a particle, and they give a 'sigma' of two and a 'margin of error' of a femtometer, does that mean there is a 95% chance of the particle's true radius laying within a femtometer of the given number?

An example from Scientific American:

PHYSICS Missing Neutrons May Lead a Secret Life as Dark Matter. This may be the reason experiments can’t agree on the neutron lifetime, according to a new idea.

By Clara Moskowitz on January 29, 2018

Both classes of experiments find neutrons can last for only about 15 minutes outside of atoms. But bottle experiments measure an average of 879.6 seconds plus or minus 0.6 second, according to the Particle Data Group, an international statistics-keeping collaboration. Beam experiments get a value of 888.0 seconds plus or minus 2.0 seconds. The 8.4-second difference may not seem like much, but it is larger than either of the calculations’ margins of error—which are based on the experimenters’ understanding of all the sources of uncertainty in their measurements. The difference leaves the two figures with a statistically significant “4-sigma” deviation. Experimenters behind both methods have scoured their setups for overlooked problems and sources of uncertainty, with no luck so far.

• Can you quote the full sentence(s) for context? If the quote is something like "the radius is [given-number] with a 2-sigma margin-of-error is one femtometer", then I would agree with your reading. Commented Jun 29, 2021 at 2:46

I checked on google "margin of error elementary particles", and the statement is used like this:

"Brookhaven’s measurement overshot the prediction by nearly three times its supposed margin of error, known as a three-sigma deviation. "

So it is a term used in describing new results of particle physics experiments for wider audiences.

In the scientific papers, the errors are given in two parts, the statistical error, which is the standard deviation of gaussian statistics, i.e. how many events have been studied, and the systematic error due to the method of measurement. It is not useful to study huge statistics, if the systematic errors are large, they will dominate the result.

So "margin of error" is the handwaving way of describing for wider audiences the fact that there are two errors, statistical and systematic.

For example see this table of measurements with errors of the Higgs mass, the "total" is the combined statistical+systematic, which is not simple.

• Ah Anna, you have overtaken me!!! -Niels Commented Jun 30, 2021 at 18:59