Why must the mediator of the strong force be heavy?

[Phys12]

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

 

[mfb]

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.

 

[haushofer]

Look at the (negative!) exponential in the yukawa potential. It surpresses the potential if the mass of the mediator gets larger.

 

[Orodruin]

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.

 

[Vanadium 50]

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.