Attractive strong force, isospin and hypercharges

In summary, the electromagnetic interaction is characterized by opposite electric charges attracting each other. In the strong nuclear force, the proton p(uud) is attracted to the neutron n(udd) and the proton p(uud), and the neutron n(udd) is attracted to both the proton p(uud) and the neutron n(udd). Both protons and neutrons have a hypercharge Y=+1 and a 3rd component of isospin I3=-1/2 and +1/2 respectively. There are also many more heavy baryons (Σ,Δ,Λ) with different I3 and Y, both positive and negative. Regardless of their quantum numbers Y and I3, all bary
  • #1
Maximilien Kitutu
In the electromagnetic interaction, opposite electric charges q attract each other.

In the strong nuclear force,
  • the proton p(uud) is attracted to p(uud) and the neutron n(udd), and
  • n(udd) is attracted to p(uud) and n(udd).
Both neutrons and protons have
  • a hypercharge Y=+1, and
  • 3rd component of the isospin I3=-1/2 and + 1/2 respectively.
There are many more heavy baryons (Σ,Δ,Λ) with different I3 (3rd component of isospin) and Y (hypercharge) , positive as well as negative.
  • Are all the baryons attracted to each other, regardless of their 2 quantum numbers Y and I3 (assuming strong interaction acts within their lifetime)?
  • How the sign of the 3rd component of the isospin (I3) and the sign of the hypercharge (Y) are related to this attraction between quarks and between baryons ?
 
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  • #2
Isospin and hypercharge have nothing to do with the strong interactions.
 
  • #3
Maximilien Kitutu said:
Are all the baryons attracted to each other, regardless of their 2 quantum numbers Y and I3 (assuming strong interaction acts within their lifetime)?
Yes. A better electromagnetic equivalent would be uncharged molecules interacting via the van der Waals force.
 
  • #4
Orodruin said:
Isospin and hypercharge have nothing to do with the strong interactions.
This is a bit misleading. What you probably have in mind is weak isospin and hypercharge.

On the other hand there's a very important approximate "accidental symmetry" of QCD, the socalled chiral symmetry in the light-quark sector. The reason is that the light quarks have pretty small masses (small compared to the typical hadronic scale of around ##1 \;\text{GeV}##). Thus, neglecting the u- and d-quark masses, leads to a chiral symmetry of the strong interaction with symmetry group ##\mathrm{SU}(2)_{\text{L}} \times \mathrm{SU}(2)_{\text{R}}##.

This symmetry is, however, spontaneously broken due to strong attraction in the quark-antiquark channel, leading to the formation of a quark condensate, i.e., ##\langle \bar{\psi} \psi \rangle \neq 0##, which makes the chiral symmetry broken to the vector part, ##\mathrm{SU}(2)_{\text{V}}##, leading to three massless pseudoscalar Goldstone bosons, identified with the pions.

Now the pions are not massless, because also the quarks are not strictly massless, and that's why chiral symmetry is also explicitly broken, but that explicit symmetry breaking is small and can be treated as a perturbation, leading to chiral perturbation theory, which is the most important way to build effective low-energy hadronic models based on fundamental symmetries of QCD.

The ##\mathrm{SU}_{\text{V}}## symmetry stays intact even if the quarks are massive, but u- and d-quarks should have the same mass then, which is not the case in nature. Thus you have isospin symmetry on the same level of accuracy as chiral symmetry, and that's why isospin symmetry of the strong interactions has been discovered very early by Heisenberg, who grouped proton and neutron to an isospin doublet.

You can also extent the idea of chiral symmetry to strange quarks, which are however a bit heavier than the u and d quarks. This leads to a modern understanding of Gell-Mann's and Zweig's "eightfold way", which has been discovered as a mathematical pattern to bring order into the zoo of light+strange hadrons and lead to the discovery of quarks and finally QCD as the modern description of the strong interaction.

For some more details on chiral symmetry on a pretty elementary level, see my transparencies from a recent Lecture Week (Lecture I):

http://th.physik.uni-frankfurt.de/~hees/hgs-hire-lectweek17/

A very nice introduction (on which also my transparencies are mostly based) can be found here:

https://arxiv.org/abs/nucl-th/9706075
 
  • #5
I'm not sure this is an A level thread, because

Maximilien Kitutu said:
the proton p(uud) is attracted to p(uud) and the neutron n(udd), and

is not entirely right. The n-p force is negligible at large distances, attractive at short distances, and repulsive at even shorter distances. So there isn't a single "sign of the force". (And isospin does play a role here, although weak isospin does not)
 

1. What is the attractive strong force?

The attractive strong force is one of the four fundamental forces of nature, responsible for holding together the particles that make up the nucleus of an atom. It is the strongest force known to exist, but it only operates over very short distances.

2. What is isospin?

Isospin is a quantum number used to describe the strong interaction between subatomic particles. It is similar to the concept of electric charge, but it applies to particles that experience the strong force, such as protons and neutrons. Isospin can have values of 1/2 or -1/2, and it helps explain the phenomenon of nuclear spin.

3. What are hypercharges?

Hypercharge is a quantum number that describes the symmetry of subatomic particles in the strong interaction. It is related to the number of quarks in a particle, with up and down quarks having a hypercharge of 1/3 and strange quarks having a hypercharge of -2/3. Hypercharge is conserved in strong interactions.

4. How do attractive strong force, isospin, and hypercharges relate to each other?

The attractive strong force is mediated by particles called gluons, which carry a type of isospin known as color charge. This isospin is responsible for the strong force's ability to "glue" particles together. Hypercharge is related to the strong interaction through the concept of flavor symmetry, which helps explain the similarities between different types of particles, such as protons and neutrons.

5. What are the practical applications of understanding attractive strong force, isospin, and hypercharges?

Understanding these concepts is crucial for understanding the structure of matter at a fundamental level, as well as for developing theories and models in particle physics. This understanding has also led to practical applications, such as nuclear energy and medical imaging techniques like PET scans, which rely on the strong force to produce images of the body's internal structures.

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