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## Weak force

I encountered an argument that says that the weak mediators must be massive because the weak force is short range, by the uncertainty principle. But isn't the uncertainty principle relates the uncertainty in mass, $$\delta m$$ and $$\delta t$$ and not the absolute value of the mass?

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The uncertainty principle is a weak reed for this case. The range of an interaction, from Fourier transform of the scattering amplitude, is proportional to the inverse of the intermediate boson mass.

They are very massive because they can only last a short amount of time, in the it's early stages of theory Fermi just gave them infinite mass.  It also helps when you think that the Electromagnetic force, which acts infinitely far is mediated by the photon which has no mass.

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## Weak force

Maybe a little mathier way to look at it is that they are massive because their symmetry is broken. The color symmetry of QCD is not broken so the gluons are massless, and the u(1) symmetry of electric charge in EM is not broken so the photon is massless, but the su(2)Xu(1) symmetry of isospin and hypercharge is broken so the W+, W-, Z_0 get a mass.

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Quote by touqra 					 				 				I encountered an argument that says that the weak mediators must be massive because the weak force is short range
That argument is backwards anyway. It confuses cause and effect. The weak force is short range because its mediators are heavy. But other mechanisms - e.g. charge screening - can also shorten range.

Quote by touqra 					 				 				I encountered an argument that says that the weak mediators must be massive because the weak force is short range, by the uncertainty principle. But isn't the uncertainty principle relates the uncertainty in mass, $$\delta m$$ and $$\delta t$$ and not the absolute value of the mass?

There is only a spread on time ! The energy is set equal to the rest energy of the particle ! Because :
1) we just wanna find out the range of a massive particle.
2) suppose you know the rest energy (which is detected by experiment), one can use that value to plug into the deltaE !

In the end, we just wanna find out that having mass means having finite range and we wanna have like an estimation of that range, not an exact value !

Check out : http://hyperphysics.phy-astr.gsu.edu.../exchg.html#c2

Quote by Vanadium 50 					 				 				That argument is backwards anyway.  It confuses cause and effect.  The weak force is short range because its mediators are heavy.  But other mechanisms - e.g. charge screening - can also shorten range.
Doesn't have to be he case. One can also state that the opposite. Look at the "rage-formula" in the website above

marlon

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Quote by marlon

Quote by Vanadium 50 					 				 				That argument is backwards anyway. It confuses cause and effect. The weak force is short range because its mediators are heavy. But other mechanisms - e.g. charge screening - can also shorten range.
Doesn't have to be he case. One can also state that the opposite. Look at the "rage-formula" in the website above
One can state whatever one wants, I suppose. That doesn't make it correct.

Massive implies short range.
Short range does not imply massive.

The force carried by the gluon is short range, but that's because of confinement, not because the gluon is massive. In fact, it's massless.

Quote by Vanadium 50 					 				 				One can state whatever one wants, I suppose.  That doesn't make it correct.
True, but what i stated is backed up by a formula which is in accordance with experimental results, so....

Massive implies short range. Short range does not imply massive.
I never stated that short range implies massive. Besides, i never used the word "implication" here because we are dealing with an "equality", which is identical "in both directions", NOT an equivalence !

So, i would say this is a semantics issue.

marlon

"Check out : http://hyperphysics.phy-astr.gsu.edu.../exchg.html#c2  Look at the "rage-formula" in the website above"  When something is determined on dimensional grounds, almost any derivation, no matter how wrong, will give the correct answer. The QM concept of range is usually discussed in the context of the Yukawa force, mediated by the exchange of a pion of mass m, which is the only dimensional object that can appear in the potential.  The only reasonable modification of the Coulomb potential is the dimensionless factor exp(-mr).  Thus ANY dervation will give the range as 1/m.

Quote by pam 					 				 				"Check out : http://hyperphysics.phy-astr.gsu.edu.../exchg.html#c2  Look at the "rage-formula" in the website above"  When something is determined on dimensional grounds, almost any derivation, no matter how wrong, will give the correct answer. The QM concept of range is usually discussed in the context of the Yukawa force, mediated by the exchange of a pion of mass m, which is the only dimensional object that can appear in the potential.  The only reasonable modification of the Coulomb potential is the dimensionless factor exp(-mr).  Thus ANY dervation will give the range as 1/m.
Is it me or is this link not working ?
Besides, i cannot find the text that pam quoted.

marlon

I tried to just copy the website you gave in post #6.  Maybe something got left out.

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