Why Proton & Neutron Contain 3 Quarks - Not 2 or 4?

[mathman]

TL;DR

Some plausible combination do not exist. Why?

Proton and neutron are made up of three quarks (uud and udd). Why aren't there particles uuu or ddd?

 

[nrqed]

Summary:: Some plausible combination do not exist. Why?

Proton and neutron are made up of three quarks (uud and udd). Why aren't there particles uuu or ddd?

There are! See for example https://en.wikipedia.org/wiki/List_of_baryons.

 

[mathman]

Thank you. Why are the lifetimes so short?

 

[nrqed]

Thank you. Why are the lifetimes so short?

Because the decay proceed through the strong interaction. And there is a fair amount of phase space available (in other words, they are quite a bit more massive than the sum of the rest masses of the decay products).

 

[nrqed]

Thank you. Why are the lifetimes so short?

To add to my previous post: if you look at the decays of the $\Delta^{++}$ and $\Delta^-$, a quark-antiquar pair was created, which came from a gluon. This is a strong decay.

If you look below in the table, the lifetime of the $\Omega^-$ is much much longer. If you look at the quark content, you will see that the the decay occurred through the weak interaction.

 

[Orodruin]

Because the decay proceed through the strong interaction. And there is a fair amount of phase space available (in other words, they are quite a bit more massive than the sum of the rest masses of the decay products).

This of course begs the question ”why are they more massive?” That boils down to the proton-neutron forming an isospin doublet unlike the deltas, which are an isospin quadruplet. In essence, because of the difference in symmetries of those states, the spatial wave functions of the deltas have a higher energy ground state.

 

[PeroK]

Summary:: Some plausible combination do not exist. Why?

Proton and neutron are made up of three quarks (uud and udd). Why aren't there particles uuu or ddd?

Try this!

https://www.physicsforums.com/insights/a-beginners-guide-to-baryons/

 

[snorkack]

Look around the baryon decuplet:
Δ are 1232 MeV (imprecise because resonances)
Σ^* are 1383 to 1387 MeV, say average 1385 MeV
Ξ^* are 1532 to 1535 MeV say average 1533 MeV
Ω is 1672,4 MeV.
Differences are thus: Δ to Σ 153 MeV, Σ to Ξ 148 MeV, Ξ to Ω 139 MeV. A narrow range.
The octuplet is lower in spin and energy.
N at average 939 MeV
Σ from 1189 to 1197 MeV, say average 1193 MeV. But uds is split to Σ⁰ at 1193 MeV, among the other Σ, and Λ at 1116 MeV.
Ξ from 1315 to 1322 MeV, say 1318 MeV.
The splits are then: N to Σ 254 MeV, Σ to Ξ 125 MeV, N to Λ 177 MeV, Λ to Ξ 202 MeV.

Note how N is 293 MeV below Δ. Σ 192 MeV below Σ^* and Ξ 215 MeV below Ξ^*

And now look at mesons.
π are 135 and 140 MeV.
K are 494 and 498 MeV.
The difference π to K is about 358 MeV. Compare to the 139 to 154 MeV differences of baryon decuplet.

uuu and ddd are unstable because π mass is so low. All decuplet baryons can deexcite by emitting π... except Ω, because the difference Ω to Ξ is still about 354 MeV, and K is far too heavy.

Why is the mass difference K-π so different from the baryon mass differences?