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Proton e goes to zero, smaller g, , vacuum color polarization. 
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#1
Dec3013, 05:24 PM

P: 1,375

Suppose we consider a proton where we set the electric charge of the three quarks towards zero. At this point I assume we still would have the three quarks bound together?
Now reduce the strength of the strong force by say ten times. I was told in posts that the radius of the proton depends on the strong coupling constant like, r ≈ exp(c/g) or r ≈ exp(c/g^2) Can we assume the mass of the proton is dependent on the strength of the strong force? Quarks polarize the vacuum by two countering effects, virtual quark and virtual gluon production? As the strength of the color force is reduced is the reduction in the polarization of the vacuum proportional between virtual quark and virtual gluon polarizations? Is there some type of scale invariance here, do they both go to zero at the same rate? Thanks for any help! 


#2
Dec3113, 02:38 PM

P: 877

[tex]\beta(g) = \left(11  \frac{2}{3}N_f \right) \frac{g^3}{16 \pi^2}[/tex] The ##11## comes from the vacuum polarization by gluons. The ##\frac{2}{3}N_f## comes from the vacuum polarization by quarks##N_f## is the number of quark flavors. You can see that both terms are proportional to ##g^3/16 \pi^2## and so both go to zero as ##g \to 0##, and the ratio between these terms stays constant as ##g \to 0##. 


#3
Jan114, 09:30 AM

P: 390




#4
Jan114, 07:36 PM

P: 1,375

Proton e goes to zero, smaller g, , vacuum color polarization.
Thank you for your help! Looks like I will have to give up on dipole gluon radiation ? Maybe I just need a space of higher dimensions? Do we still have quark confinement in higher dimensions? Thanks again! 


#5
Jan114, 07:38 PM

P: 1,375




#6
Jan214, 02:00 AM

P: 390




#7
Jan214, 04:00 PM

P: 877




#8
Jan214, 04:51 PM

P: 390

For example suppose that there are in fact 18 flavours of quarks, of which 5 are nearly massless (the known quarks up to beauty), the sixth is 173 GeV (truth)  and the there are 12 more (6 more generations) of quarks, all of which have masses above the observed 173 GeV of truth. But not much more  say, all the 12 quarks have masses between 173 and 200 GeV. How would large numbers of massive quark flavours affect quark confinement? What is the currently observed minimum mass of seventh quark? 


#9
Jan214, 06:14 PM

P: 1,375

Thanks for your help! 


#10
Jan214, 06:27 PM

Mentor
P: 12,037

There is confinement for abelian theories in 2 and 3 dimensions according to this, cited at Wikipedia. 


#11
Jan214, 07:22 PM

P: 877

[Deleted since I wrote some stuff I now think is wrong]



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