Why must the mediator of the strong force be heavy?

In summary, when Yukawa proposed his theory of the strong force, it was an indication that the mediator of that force must be a heavy particle since the force is a short ranged force. This is because a massless mediator would result in a long range Coulomb potential, while a massive mediator leads to a Yukawa potential with a negative exponential that decreases the potential as the mass of the mediator increases. Additionally, the residual strong force, mediated by pions, is different from the strong force itself, which is mediated by massless gluons. The reason for this difference is confinement, where only colorless states exist at lower energies. This is further explained in problem 1.2, as mentioned by Griffiths.
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I'm reading Griffith's Introduction to Elementary Particles and it says that when Yukawa proposed his theory of the strong force, it was an indication that the meadiator of that force must be a heavy particle since the force is a short ranged force. Why is that the case? I cannot get the intuition behind it
 
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A massless mediator leads to a Coulomb potential - it has a long range. A massive mediator leads to a Yukawa potential, where larger masses lead to shorter ranges.
 
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Look at the (negative!) exponential in the yukawa potential. It surpresses the potential if the mass of the mediator gets larger.
 
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Also note that this is the residual strong force mediated by pions. The strong force itself is mediated by massless gluons. The reason that this does not lead to a Coulomb potential is confinement, i.e., that only colourless states exist at lower energies.
 
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Phys12 said:
Why is that the case?

You know how right after he writes that, Griffiths says "See Problem 1.2"? You should see problem 1.2.
 

Related to Why must the mediator of the strong force be heavy?

Question 1:

Why is the mediator of the strong force heavy?

The mediator of the strong force, also known as the gluon, is heavy because it carries a large amount of energy due to its role in binding quarks together. This energy is known as the strong nuclear force and is responsible for holding atomic nuclei together.

Question 2:

What is the relationship between the mass of the mediator and the strength of the strong force?

The mass of the mediator directly affects the strength of the strong force. The heavier the mediator, the stronger the force. This is because the gluon's mass is directly related to the energy it carries, which in turn determines the strength of the force it mediates.

Question 3:

Why can't the mediator of the strong force be massless like the photon?

The mediator of the strong force cannot be massless like the photon because the strong force is a short-range force and requires a massive mediator to carry enough energy to bind quarks together. Additionally, a massless mediator would result in an infinite range for the strong force, which is not observed in nature.

Question 4:

How does the heavy mediator of the strong force contribute to the stability of matter?

The heavy mediator of the strong force plays a crucial role in the stability of matter. Without it, quarks would not be bound together and would fly apart. The strong force is responsible for holding protons and neutrons together in the nucleus of an atom, allowing for the stability of matter as we know it.

Question 5:

Are there any theories that suggest a lighter mediator for the strong force?

Some theories, such as supersymmetry, suggest the existence of a lighter mediator for the strong force called the gluino. However, this is still a hypothetical particle and has not been observed in experiments. The overwhelming evidence currently supports the existence of a heavy mediator, the gluon, for the strong force.

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