# Fundamental particles and mass quantization

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## Main Question or Discussion Point

We know that the energy levels for electrons surrounding nucleus are quantized , only coming in discrete levels.
When I see the standard model of elementary particles table I notice specific masses for each of the particles whether they be quarks or leptons or bosons like the higgs.
I know that particle masses are not quantized the same way electron energy levels are, but my questions would be

1) Would it be fair to say that each particle only comes with a discrete mass
2) The mass given for each particle is corresponding to the energy at which it was found during say proton-proton collisions in LHC for example?

3) Besides the fact that these elementary particles seem discrete in terms of their energy at which they are created , it also seems to me that there are also a given (fixed?) number of composite particles into which these elementary particles can arrange in? (Or should I say fixed number of bound states that quarks can create?)

4) Lastly, here wiki lists a table of both known and proposed baryons for example https://en.wikipedia.org/wiki/List_of_baryons
do all the proposed yet never observed baryons are proposed mainly because mathematically they seem possible and so are considered?

And is there a reason why only few baryons like protons, neutrons are stable while most of the baryons are not stable and decay in extremely short lifetimes?

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mathman
And is there a reason why only few baryons like protons, neutrons are stable while most of the baryons are not stable and decay in extremely short lifetimes?
Free neutrons are not stable - half life ~ 10 minutes.

mfb
Mentor
1) Would it be fair to say that each particle only comes with a discrete mass
Yes.
2) The mass given for each particle is corresponding to the energy at which it was found during say proton-proton collisions in LHC for example?
No, the mass corresponds to the energy the particle has at rest. In other frames that energy can be much higher.
3) Besides the fact that these elementary particles seem discrete in terms of their energy at which they are created , it also seems to me that there are also a given (fixed?) number of composite particles into which these elementary particles can arrange in? (Or should I say fixed number of bound states that quarks can create?)
For composite particles made out of quarks we call them hadrons, yes.
do all the proposed yet never observed baryons are proposed mainly because mathematically they seem possible and so are considered?
Yes. Based on patterns in the observed baryons they should exist, but they might be too difficult to observe so far. Or these patterns might not be valid everywhere, we don't know.
And is there a reason why only few baryons like protons, neutrons are stable while most of the baryons are not stable and decay in extremely short lifetimes?
If a decay is possible it will happen eventually, and "eventually" usually means very fast on human timescales. Only a few particles cannot decay because they are the lightest baryon (like the proton), lightest charged particle in general (like the electron) or because some other conserved quantity makes decays impossible. Free neutrons are unstable, but in nuclei their low energy levels can make the nucleus stable.

berkeman
Ok, @mfb so how do they get the energy each particle has at rest? I presume it's not just a mathematical construct but is arrived at from the energies that were present during the collisions that made the particle?
I remember the LHC working at their upper limits where the higgs was eventually found after many collisions, so what is the relation to this energy put into he pp collision and rest mass of a newly created particle?

ps. I guess I will have to look up neutron traps, seems like they can trap a neutron long enough to see it decay into a proton.

While we are at it , the weak force is called weak not because it's weak but because it's strength falls off with distance much faster than that of the strong force or electric field ?

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mfb
Mentor
Typically one of these:
Measure the mass of a particle, then multiply by the speed of light squared (works well for long-living particles)
Measure the energy needed to produce the particles (especially in electron/positron collisions)
Measure the energies of decay products (the typical approach for short-living particles)

The total collision energy in the LHC is way above the mass of the Higgs boson (factor ~100), but higher energies make the production much more likely. It's still a very rare process - once every few billion collisions. The Higgs mass was measured by studying its decay products.
While we are at it , the weak force is called weak not because it's weak but because it's strength falls off with distance much faster than that of the strong force or electric field ?
It's always weak.

So the method where you simply measure the mass of a particle can only be applied to stable particles with charge as they are the easiest to control ? Like a proton going through a mass spectrometer and then one can calculate the energy required to deflect it and arrive at a mass for the particle, where one subtracts the kinetic energy etc and arrives at the rest mass ?

So in a LHC collision at say a certain energy input one creates multiple new particles, so in order to know the energy of each one , one must take the total energy that went in to create them and subtract the energies of the other particles made in order to know the energy of the specific one in question?

Did they used the decay products of the higgs because the higgs itself was very short lived and so they couldn't arrive at a specific energy for it?

I guess the same question could be asked about the W+- and Z bosons, they seem to be extremely short lived so were they observed as real physical phenomena in a detector or were they arrived at by secondary means like the neutrino interaction with the electron in the "Gargamelle bubble chamber " where they only saw the effects on the electron and so deduced the rest?

in the "discovery" section for the W and Z bosons in wiki it only says "unambiguous signals of W bosons were seen " this in of itself doesn't tell much to me.

mfb
Mentor
So the method where you simply measure the mass of a particle can only be applied to stable particles with charge as they are the easiest to control ? Like a proton going through a mass spectrometer and then one can calculate the energy required to deflect it and arrive at a mass for the particle, where one subtracts the kinetic energy etc and arrives at the rest mass ?
That's the easiest approach but it only works for long-living particles, yes.
So in a LHC collision at say a certain energy input one creates multiple new particles, so in order to know the energy of each one , one must take the total energy that went in to create them and subtract the energies of the other particles made in order to know the energy of the specific one in question?
That doesn't work at hadron colliders like the LHC. Electron-positron colliders can do this.
Did they used the decay products of the higgs because the higgs itself was very short lived and so they couldn't arrive at a specific energy for it?
Measuring the decay products is the easiest approach and leads to the most accurate measurement.
There are some indirect measurements as the mass of the Higgs boson influences some other properties slightly.

W/Z live to short to fly through a detector but we can measure their decay products or use a couple of indirect measurements to determine their mass.

@mfb ok i'm going to guess here.
What is the exact reason why for hadrons one can't simple take the energy in vs energy out/divided by particles?

In an electron positron collider this works because the annihilation of the pair converts 100% of their mass into the newly created particles?
ps. I assume the total energy that has to be conserved in an electron positron pair is the rest mass of each of the particle + the kinetic energy at the moment of annihilation?

As for the W/Z bosons since you confirm their timespan is too short to "observe" them directly , are they then known to exist solely based on the interactions they produce? Would it be right to compare them to virtual photons in this regard?

vanhees71
mfb
Mentor
Hadron collisions at high energy are messy and you never find every collision product. Too many particles fly close to the beam axis and don't make it into the detectors.
Electron/positron collisions are much cleaner and you can find every particle. If the collision product is a single particle then the combined energy must match its mass. ϒ(4s) is a common target for these collisions. It decays to a pair of B mesons. It's not the only option. You also get things like ##e^- e^+ \to D^+ D^-## and many more, where the produced particles carry significant kinetic energy. How much depends on their mass because the total energy is always conserved.
As for the W/Z bosons since you confirm their timespan is too short to "observe" them directly , are they then known to exist solely based on the interactions they produce?
The interactions, and their decays. At high energies we can produce them as real particles. Just very short-living ones.

vanhees71
@mfb , so your saying that at high energies the W/Z bosons are produced as real particles , so then what are they at low energies? Not real?
Or is it that at higher energies they "stay around" long enough to be caught in the detector vs at low energies being registered only from secondary properties or influence seen in the detector on other particles?

mfb
Mentor
so your saying that at high energies the W/Z bosons are produced as real particles
Sure.
so then what are they at low energies? Not real?
They are not produced, but you can still learn something about them via their fields - the fields still participate in interactions. If you write that down as Feynman diagrams you get W/Z as virtual particles, not as real particles.

Multiply the lifetime of W and Z by the speed of light and consider how close detectors could realistically be.

Typically one of these:
Measure the mass of a particle, then multiply by the speed of light squared (works well for long-living particles)
Measure the energy needed to produce the particles (especially in electron/positron collisions)
Measure the energies of decay products (the typical approach for short-living particles)

The total collision energy in the LHC is way above the mass of the Higgs boson (factor ~100), but higher energies make the production much more likely. It's still a very rare process - once every few billion collisions. The Higgs mass was measured by studying its decay products.It's always weak.
The weak interaction is not always weak . The strength of interactions varies depending on what energy we study them.The top quark first decays to its products before interacting through electromagnetism or through the strong interaction so the weak interaction can be considered to be stronger.

@mfb so the W/Z lifetime until decay is so fast that the "detector" would have to be within the nucleus itself in order to "catch them" as real particles, otherwise we only see the decay products of them aka other particles?

Does this lifetime of the W/Z is the same for all their energies? aka both low and high?

mfb
Mentor
Well, you can't build a detector smaller than an atom. Yes, we only see decay products.
Does this lifetime of the W/Z is the same for all their energies? aka both low and high?
There is time dilation, of course, but it's not enough to matter. You can calculate that as well. Aim at ~20 micrometers flight length, that's cutting-edge vertex reconstruction.

vanhees71