# Two Questions: Yukawa Potential and Weak Force

by ChaseRLewis73
Tags: force, potential, weak, yukawa
 P: 24 1. Yukawa Potential So reading about the yukawa potential I notice that the constant k is related to the inverse of the effective distance of the force from what I've been reading. Thing is everything I read about the strong force states it has infinite range but simply has a maximum potential at ~ 10k Newtons. My question than is for the strong force is k related to ∞ or related to the point it levels out? The yukawa potential seems to be an equation that uses the coupling constant to relate different forces or that's what I keep reading. So for the fine structure constant and r = ∞ it illustrates Coulomb's Law. Does this extend to all forces such as gravity and weak as well? 2. The weak force I'm reading about is the result of exchanging bosons that results in quark transmutation. (up,charm,top) -> (down,strange,bottom). I can understand how this would result in destabilization in large atoms. However, what are the stimuli that cause the generation of these bosons in a nucleus? I mean 90 GeV type energies don't come from nowhere. A whole proton is just slight of 1 GeV in energy so I find it difficult to imagine where it comes.
 P: 9 1) The Yukawa potential is an effective description of the remnant strong force between hadrons (bound states of quarks and gluons), not of the fundamental strong force between quarks and gluons. As this effective strong force is mediated by massive hadrons itself, it has a finite range. In contrast to this, the electromagnetic force is mediated by the massless photon, so you get it by m=0 and g=Q. 2) No real W is produced in a weak decay of a nucleus. There are just virtual W's and that is the reason why these processes are relatively slow even if the coupling is large.
Mentor
P: 10,501
 Quote by ChaseRLewis73 Thing is everything I read about the strong force states it has infinite range but simply has a maximum potential at ~ 10k Newtons.
Newton is a unit of force, not potential. That force occurs between objects with color charge, and is unrelated to the Yukawa potential.

P: 31

## Two Questions: Yukawa Potential and Weak Force

https://en.wikipedia.org/wiki/Yukawa_potential.

Can be used for for all types potentials/fields. Just reduces to Coulomb potential if m =0 (photons). g, another coupling constant, can not be charge: units don't fit. Would be depending on ε0 and μ0. For Coulomb field, the value of mentioned k coupling constant in e-kmr is of no importance.

'Inside' the charge carrier, electron or proton, its mass(density) does matter so k does have a value. k should be dimensionless and the fine structure constant is a good candidate. The fine structure constant does fit the description it commonly has http://en.wikipedia.org/wiki/Fine-structure_constant.

The mass density is quite high, given common radius of 2.8e-15 [m], with almost 1e13 kg/m3, a minimal movement inside will give rise to a potential depending on r of order from 4 to 7. Very short range potential. No wonder one needs to blast particles onto each other with energies in the 10 ths GeV range to get into reacting range of the quarks.
 P: 2 The color force is mediated by massless gluons, the representations of an UNBROKEN SU(3) group(three squared minus one=8 gluons). However,...,being non-abelian, it was discovered by the late Sidney Coleman's graduate students at Harvard, that a property of "asymptotic freedom" is manifest with this unbroken SU(3) color gauge field. Read the Nobel lectures of Gross,Politzer and Wilczek in, for example,Reviews Of Modern Physics, Volume 77, July 2005.

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