# Q & A: Measuring particle masses

Q:
How do scientists decide whether an element particle has mass or not? How do they measure the mass and with what kind of equipment do they achieve that?
- Bo (age 19)
Raffles Junior College, Singapore
A:
That's a great question!

Particle masses are measured in a great variety of ways. If they are big and heavy enough, you can put them on a scale. Subatomic particles have to be measured much more carefully than that.

Typically, subatomic particle masses are determined by the relationship between their energy and their momentum. If a particle is not moving, its total energy is E=mc^2. If it is moving, then E^2=(mc^2)^2+(pc)^2, where p is the momentum and c is the speed of light.

One way to measure the mass, say, of a proton, is to put it in a mass spectrometer. Accelerating it in a known electric field gives it an amount of kinetic energy proportional to its charge. Causing the proton to move in a circular path in a uniform, well-calibrated magnetic field allows the momentum to be measured quite precisely.

Another way of measuring the proton mass is to get a very pure sample of hydrogen molecules with a known number of protons in it, weigh it, and subtract off the masses of the electrons and also the binding energies of the electrons in their molecular orbits.

Some subatomic particles are heavy and unstable. You can measure their masses by computing the total energy and momentum of their decay products, if you happen to know the masses of their decay products and can measure their momentum (a typical situation in a high-energy experiment -- we usually have a big magnet and a detector inside which can measure particle's paths. The curvature of the paths tells what the momentum is).

Other particles are very light and do not decay. The photon is one of them. Models of electricity and magnetism which include a small mass for the photon predict that the electromagnetic interaction should have a finite range, kind of like the weak nuclear force, which is mediated by particles which are kind of like the photon, but are very massive. No evidence has been observed that the electromagnetic force has any range limitation, and upper limits have been set on the photon mass that are extremely stringent.

We used to think that neutrinos were massless. The more skeptical among us pointed out that there was no proof, experimental or theoretical that neutrinos couldn't have a mass, and so a series of experiments was constructed in Japan, Canada, the U. S. and Switzerland to see if neutrinos had mass. This one's tricky because they don't decay and interact only very seldom with matter at all. It turns out that there are three kinds of neutrinos that we know of, one corresponding to each kind of lepton -- the electron neutrino, the muon neutrino, and the tau neutrino. It turns out that if (at least some of) their masses are not zero, and some parameters called mixing angles are not zero, then neutrinos can change spontaneously from one type to another, and back. We call this "flavor oscillation". The rate of flavor oscillation, which can be measured experimentally, is proportional to the difference in the squares of the masses of the neutrinos undergoing oscillation. We don't yet have measurements of the masses of the neutrinos themselves, but know something about the differences in the squares of their masses.

Similar elegant oscillation techniques can determine with tremendous accuracy the mass difference between similar particles, for example, in the pair of neutral kaons.

Tom

(published on 10/22/2007)