Are Standard-Model particles bound states?

In summary, the conversation discusses the compositeness hierarchy, which includes atoms, nuclei, and hadrons as bound states of smaller particles. The discussion also touches on the possibility of Standard-Model particles being bound states of other particles, with lower limits of a few TeV for interactions and excited leptons. The concept of relative binding energy is also mentioned, with a need for extreme fine-tuning for an electron to be a bound state. The conversation ends with a question about whether any model builder has come up with a way for this to happen.
  • #1
lpetrich
988
178
So far, we've discovered this compositeness hierarchy:
Atoms - bound states of electrons, nuclei, photons
Nuclei - bound states of nucleons and other hadrons
Hadrons - bound states of quarks and gluons

So are any Standard-Model particles bound states of any other particles?

The compositeness searches described in the Particle Data Group's pages yield lower limits of a few TeV for 4-elementary-fermion interactions and lower limits from 100 GeV to a few TeV for excited leptons. More generally, work like [hep-ex/0001023] Standard Model Physics at LEP describes very good agreement up to about 100 GeV per particle for electron-positron collisions.

This is about 200,000 times an electron's rest mass, and if electrons are bound states, one must somehow get cancellation at least as good as that. That is rather difficult to picture. For atoms, one gets relative binding energies around 10^(-8) - 10^(-5), for nuclei, around 0.01, and for hadrons, around 1. So for an electron to be a bound state, its relative binding energy must be at least 200,000. Has any model builder come up with a way for that to happen?
 
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  • #2
The sum of particle masses plus (negative) binding energy must be 511 keV. As particle masses are usually arbitrary in theory and the coupling strength can be arbitrary, too, I would expect that this is possible somehow. It looks a bit like fine-tuning, however.
 
  • #3
Rather extreme fine tuning - less than 1 part in 200,000.

Binding energy = (energy of free particles) - (energy of bound state)

If (mass of bound state) << (mass of free particles), then one gets the extreme cancellation that I'd mentioned.
 
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1. What are Standard-Model particles?

The Standard Model of particle physics is a theory that describes the fundamental particles and their interactions that make up the universe. These particles include quarks, leptons, and gauge bosons.

2. What is a bound state?

A bound state is a system composed of two or more particles that are held together by a strong force, such as the strong nuclear force. In this state, the particles are confined to a specific energy level and cannot escape each other's influence.

3. Are Standard-Model particles bound states?

No, Standard-Model particles are not bound states. They are fundamental particles and do not consist of smaller, bound particles. However, they can form bound states with other particles through interactions.

4. How are bound states formed?

Bound states are formed when two or more particles interact and their energy levels align, creating a stable system. This can occur through attractive forces, such as the strong nuclear force, or through repulsive forces, such as the electromagnetic force.

5. What is the significance of bound states in particle physics?

Bound states play a crucial role in understanding the behavior and interactions of particles. They help explain the stability and structure of matter and provide insights into the forces that govern the universe at a microscopic level.

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