# Particle Mass

1. Mar 8, 2009

### Phrak

Would anyone notice (unless they were looking for it) that the mass of a particle species had a span, rather than a fixed mass?

Say there were an as-yet-undiscoved particle with a range of mass. Would you notice it in collider run data if it's mass were not fixed?

If the mass of a neutrino ranged, could you tell?

Last edited: Mar 8, 2009
2. Mar 8, 2009

### Buzzy^

I suppose that would just follow from momentum conservation... unless of course there happen to be more than one of those kind of fields involved in a single interaction.

3. Mar 8, 2009

Staff Emeritus
All particle with a lifetime have a range of masses, given by a Breit-Wigner distribution, characterized by a width.

4. Mar 8, 2009

### xepma

Like stated above, particles which decay show an uncertainty in their mass spectrum. You can interpret it (naively) to a Heisenberg uncertainty relation:

$\Delta E \Delta t \geq \frac{h}{4\pi}$

then

$\Delta m c^2 \Delta t \geq \frac{h}{4\pi}$

so

$\Delta m \geq \frac{1}{c^2\Delta t}\frac{h}{4\pi}$

where you should interpret the "uncertainty in time" as some quantification of the lifetime of the particle, while the uncertainty in the mass reflects the width of the spectrum you get when you measure the particle's mass. I don't know a more solid derivation of this relation.. Is it the Breit-Wigner distribution?

In fact, I think the relation is even used the other way around. By measuring the width of a mass spectrum for some decaying particle, one can quantify the lifetime the particle.

5. Mar 8, 2009

### Phrak

I don't know what to make of this, except that a particle would be detected as a resonance, with a resonant bandwidth where the particle shows up as a peak, right? But if the signal were equally distributed over all frequencies would the usual methods of searching for particles miss it?

I'd thought that all known particles had an idealized mass, such as what you would read of a chart of elementry particles. Do some particles not have this sort of idealized mass?

Last edited: Mar 8, 2009
6. Mar 8, 2009

Apart from the uncertainty mentioned above there is the experimental uncertainty of the measurements,these alone prevent us from pinning anything down to an exact value.

7. Mar 9, 2009

### blechman

the width in the Breit-Wigner distribution is related to the uncertainty principle, as mentioned above.

This width corresponds to the inverse lifetime.

So, if the width of the particle becomes very large, the lifetime of the particle is very short, and we would never see it! If it were distributed over ALL frequencies, its lifetime would be ZERO and it wouldn't exist!

All masses are always quoted with widths (or lifetimes, which is the same thing). That implicitly tells us the probability distribution of seeing a particle of that type with a given mass. Electrons and protons, which to our knowledge are perfectly stable, have very well-defined masses. Particles like the top quark, on the other hand, do not.

The mass that is quoted is well defined, and the AVERAGE mass that is measured (the peak of the Breit-Wigner).

8. Mar 10, 2009

### Bob S

All of the stable particles (electron, proton, deuteron, alpha) have exact masses because the Heisenberg uncertainty principle does not apply. The quoted uncertainty in their masses is experimental measurement uncertainty. Neutrons and tritium both have long half lives, and therefore narrow mass width distributions.

Last edited: Mar 11, 2009
9. Mar 11, 2009

### Phrak

If it were distributed over ALL frequencies, its lifetime would be ZERO and it wouldn't exist!

Thanks, blechman. That's what I needed to hear. Although the question still might be interesting in it's own right, such as zero mass particles, off-shell, particles...