# Why not accurate masses of elementary particles?

In the standard model of particle accuracy in calculating mass is very low. And you can not predict the upper limit of Higgs particle mass accurately. Why not accurate masses of elementary particles?

## 1 Answer

Part of this is due to lifetime considerations. When you have an unstable particle, the lifetime is short, and there is an uncertainty in its energy which goes like the inverse lifetime. The ratio of inverse lifetime (in natural units) to rest-mass is called the width of the particle, because it is the width of the peak in the scattering amplitude you see when you make this particle.

The wider the particle, the more statistics you need to determine the parameters of mass and width accurately. You need to figure out the center of the rising and falling scattering distribution (in an idealized experiment) to determine the mass, and this is not doable without large statistics.

For the electron, the proton, and the neutron, we have acccurate masses. For the unstable muon, the lifetime is long enough that the width issues are negligible. For the W's and Z's, we have enormous statistics, so we know these particle masses well. For the tau, you have less accuracy.

The second problem with mass is when the particle is hardly interacting. For the neutrinos, we can hardly measure their mass at all. The uncertainty in neutrino mass is understandable, and hard to rectify.

For quarks, there is a second issue, which is that they are confined. So the definition of their mass is by the properties of quark propagation at short distances, since at long distances, they are confined. This parameter is hard to measure from the physics of the bound-states of quarks, the hadrons, you need to extrapolate it from light quarks using sums of the scatterings of many hadrons and mathematical tricks. For light quarks, there is a lot of uncertainty in the mass due to this confinement problem. This problem goes away for the heavier quarks, the charm and bottom, but for the top, you get a large width and statistics issues again limiting the accuracy.