# How are particle masses measured?

1. Oct 27, 2007

### Moth

Masses of quarks, leptons and bosons are often given as a range of values. How are the masses measured experimentally, why are they so inaccurate and how are they being made more accurate?

2. Oct 28, 2007

### malawi_glenn

if they are charged you often measure their masses by defelection in magnetic field, the radius is proportional to their masses (Lorentz force), in order to use that method you need the momentum of the particle.

3. Oct 28, 2007

### meopemuk

Most elementary particles have very short lifetimes, so direct measurements of their masses are impossible. These unstable particles are usually created in collisions of other (stable) particles, and their presence is reflected in resonances (bumps) of scattering cross-sections as functions of energy. Knowing energetic positions of these resonances one can figure out the masses of the unstable particles. The resonances have finite widths, so the exact values of masses cannot be established. It follows from laws of quantum mechanics that the uncertainty of mass is inversely proportional to the particle's lifetime. This fundamental uncertainty is the major factor of mass "inaccuracies" in particle tables.

Eugene

4. Oct 28, 2007

### arivero

are inferred from models, except for the top quark.
the electron and muon and known since old. For the neutrinos, mass differences are inferred from experiment, assuming three neutrinos
bosons that suffer strong decay have short lifetimes, so it is not only difficult to measure directly, but indirectly the Breit Wigner width is very wide and it is not easy to locate the peak.

5. Oct 28, 2007

### Meir Achuz

The three classes you mention are quite different.
Quarks have never been produced, so there masses can only be inferred using some theory, and comparing with experimental results that depend on the quark mass. Different theories can give different values for the quark mass.
The mass of the charged electron and muon leptons are found by measuring their energy and momentum, and using M^2=E^2-p^2. These masses can also be measured by the binding energy of hydrogen, which depends on the lepton mass.
For the short lived tau lepton, E and p of its decay products are used to measure its mass. Some charged bosons live long enough the E and p can be measured directly.
For short lived nosons, E and p of the decay products are measured.
In any case, the mass is found by M^2=E^2-p^2.

6. Oct 28, 2007

### Moth

I understand how it is possible to measure mass by deflection in a magnetic field or from resonances due to collisions. But estimating the mass of quarks by theory must be quite challenging. Also the Higgs boson, which not been seen, has been given an estimated mass of 120GeV, I assume is due to a theory.

What kind of experiment would test a quark mass theory? For example I am currently using a program called calcHEP, which allows me to compute particle decay or collision properties. Do any of these experiments involve decays or collisions?

7. Oct 29, 2007

### blechman

The problem with the mass of the quarks (as has been alluded to but never explicitly stated) is that quarks are not "free particles" - they are always living in bound states. As you might know, the "mass" of a bound state particle is always lower than that of a free particle, since binding energy decreases it (the mass of positronium is LESS than $2m_e$). Therefore, you can never isolate a quark to study its mass, since when we say that a quark decays, we really mean that the hadron the quark lives in decayed. The top quark is an exception to this because it decays before it has a chance to hadronize, and therefore there is a hope of doing a resonance analysis. The other "heavy quarks" (b,c) are heavy enough that you might hope to dis-entangle the QCD crap from the quark itself (remember, QCD is strong at low energies/masses); but this is a VERY dangerous game, wrought with theoretical difficulties ("renormalon ambiguities", for example). However, the "light quarks" (u,d,s) can never be separated from the QCD muck, and talking about their masses doesn't really make sense. For example: one book says $m_u=3$ GeV, another says $m_u=300$ GeV - since they're talking about different definitions of "quark mass"!

As to your other point about the Higgs: that comes from 2 places: (1) We haven't seen the Higgs boson yet, so it must be heavier than what we've been able to see (114 GeV), and precision electroweak measurements (higher order corrections in the perturbation theory) have been tested and suggest that the higgs cannot be much heavier than roughly 150 GeV. I should mention that BOTH of these constraints can be avoided, actually, and as I'm sure you know, the Higgs is still proving very elusive.

I think you misunderstood the phrase "quark mass theory". Like I said, you can NEVER truly measure the quark mass, except for the top quark.

8. Oct 30, 2007

### Moth

Sorry, I didn't mean "quark mass theory", but simply a theory that infers the quark mass.

And which experiments have been done traditionally to test these theories. So that I might research them in more detail.

9. Oct 30, 2007

### blechman

Off the top of my head: deep inelastic scattering; Drell-Yan production; Z/W->2jets; top/bottom production and decay; e+e- ->hadrons; all test quark models and QCD. But let me re-emphasize: they are testing QCD, and that's not a model. Every model is wrong in some sense! It is, by definition, only modeling the real world. What HEP people really want to do is test QCD.
(Actually, what most hep people *really* want to do is test electroweak, but we can't do that until we understand how to get through the QCD!)

As I said before: except for the top quark, you can't properly talk about a quark mass.