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Hadron mass equal quark mass? 
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#1
Aug214, 02:43 AM

P: 231

How is the mass of hadrons calculated from constituent quarks?
It seems classically it should come from three parts: (p^{2}+m^{2})^{1/2} for each constituent quark with rest mass m, plus interactions between the quarks, which would be electromagnetic Coloumb 1/R potential between any two of the three quarks, and the linear R potential between any two quarks which is responsible for confinement at strong coupling. Quantum mechanically, if you could measure the size of the hadron, and assume the quarks are confined to a box of that size, then you would only need to add the rest mass of the quarks to the particlesinabox energies to get the energy of the hadron, and wouldn't have to know the momentum p of each constituent quark or the coefficient of the string potential R. Is this right? I seem to recall that the u and d quarks are taken to have almost zero rest mass. So is all the energy of hadrons made from those quarks due to E&M and confinement? What about hadrons involving heavier quarks? 


#3
Aug214, 03:34 PM

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P: 12,113

Those potentials are effective models, describing the complex QCD interactions. "2 quarks"/"3 quarks" are a bad model for mesons/baryons. Those are the valence quarks, and their high expectation values for the kinetic energy are an important contribution to the total energy, but you also have sea quarks and gluons with significant energy.



#4
Aug214, 09:07 PM

PF Gold
P: 2,938

Hadron mass equal quark mass?
Still, there is an intriguing coincidence in the Standard Model: that the QCD mass is not far of the yukawianhiggs mass. Nothing in the standard model requires it. But you have then the mass of the proton nicely between the mass of, say, muon and tau. There is not a SU(3) horizontal of flavour, but still a triad of electron tau and muon should have a mass not counting electromagnetism" exactly the double of a QCR triad (a proton, say).



#5
Aug314, 05:44 AM

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Well, (maybe apart from neutrinos) all known particle masses and all energy scales are close together if you consider a log scale from the electron to the planck scale. That just means the planck scale is far away.



#6
Aug314, 06:02 AM

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#7
Aug314, 06:16 AM

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What is a "a SU(3) horizontal of flavour", what do you mean with "[not] counting electromagnetism", why "should" the sum of the masses of electron+muon+tau be exactly the double of something made out of quarks? (It is not) Given enough numbers (and we have tons of hadrons), you can always find things that are close together. That does not need any special reason. 


#8
Aug314, 06:27 AM

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#9
Aug314, 04:52 PM

P: 231

I've been trying to follow the discussion on scales, but I lack basic knowledge.
It's my understanding that the only dimensionful parameter in the Standard Model is the coefficient of the quadratic term in the Higgs (and possibly a mass term of a sterile neutrino). That would seem to imply there is only one scale (let's ignore the existence of the sterile neutrino scale which hasn't been proven) and as a consequence, all dimensionful parameters should either blow up or go to zero when the Higgs symmetry is restored at high temperature (although doesn't the temperature at which that happens provide a scale?). Beyond the Standard Model there seems to be one more scale, the Planck scale. So really there are only three scales, the EW scale, the Planck scale, and a sterile neutrino mass. So what's the QCD scale? Also, would pure QED have a scale? In pure QED you no longer have the EW scale because you're only considering E&M. You would have the mass terms of your charged particles, so would the pure QED scale(s) be the mass(es) of your charges particles? 


#10
Aug314, 07:26 PM

P: 370

You're right though that this scale is not present in the classical Lagrangian. It essentially appears during renormalisation. As for QED, well, it does have a Landau pole at some high energy, which I guess is kind of similar. The QED coupling constant does blow up there, but I think this is considered a problem with perturbation theory rather than something physically important like the confinement scale. 


#11
Aug314, 09:57 PM

P: 231

So there should be a lot of scales? 


#12
Aug314, 11:36 PM

P: 370




#13
Aug414, 07:15 PM

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#14
Aug614, 07:14 PM

PF Gold
P: 2,938

And yes still we could be looking for random coincidences with QCD but you really know that it is not the case, do you? Remenber that here in this same forum we were not looking for qcd when we added electrón muon and tau and divided by 6. We were calculating the mass MO in Koide formula for leptons, and it happened to be 313 Mev, the same mass that a consituent quark. And years later, I used Koide to calculate charm mass from bottom and top not my idea, but Rodejohann and Zhong and then charm and bottom to calculate strange. And it happened that the M0 of the triplet of s c and b was ,940 MeV, three times the one of leptons. if you call this random, you have a peculiar concept of randomness. Is this remark ontopic? I think yes, because the OP asked how quark and hadron mass are related. The obvious answer, vía the chiral expansión, involves constants which come from QCD, and the same happens with lattice calculations. So it is on topic to remark that the QCD scale itself could be related to quark "yukawahiggs" masses. 


#15
Aug714, 04:26 PM

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P: 12,113

Why do you claim those masses "should" have a relation in post #4? And you still did not explain what a "a SU(3) horizontal of flavour" is. It has exactly 1 google hit: your post. 


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