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How interact makes mass ? 
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#1
Feb313, 04:48 PM

P: 83

Hello all .
We know about 95 percent to 98 percent of proton mass is not contributed by quark mass. In truth, most proton mass is derived from interaction energy between the quarks . MY question is how interact makes mass ? the mass means inertial mass or relative mass ? 


#2
Feb313, 06:33 PM

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It's standard rest mass; w/o using a particle collider or something like that you can't see that the mass is caused by interaction.
In quantum field theory you can in principle do the following: find an eigenstate E,p=0> of the Hamiltonian H and the momentum operator P such that HE,p> = EE,p> PE,p> = 0 b/c p=0, whenever E>0 this is due to interaction (kin. energy is zero) 


#3
Feb313, 11:57 PM

P: 229

Also I thought bound state energies are always negative, so if anything, shouldn't the proton mass be less than the sum of the quark masses? 


#4
Feb413, 12:18 AM

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P: 5,437

How interact makes mass ?
E<0 is not reasonable for a particle mass, but E=0 is.
The idea of bound states which are lighter as their constituents makes some implicit assumptions which are no longer valid in QCD  it means that one can identify a fixed, finite number of constituents (quarks, gluons)  it means that one can add rest masses to get the mass of the bound state ( mass defect i.e. binding energy)  it often starts with a potential and its energy levels In QCD  the number of constituents is not fixed; it has to be derived from the theory; and it turns out that it becomes scale dependent  the kinetic energy of quarks and gluons dominates the total mass; so the quarks and gluons are highly relativistic  there is no potential to start with So having relativistic quarks and gluons it becomes clear the the proton rest mass is due to the energy of it's 'constituents' 


#5
Feb413, 05:44 AM

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#6
Feb413, 09:22 AM

P: 229

Also, if the number of constituents is not fixed and depends on scale, but the mass of a proton is always the same, does this mean that the constituents always conspire to change their masses at each scale so that their total mass equals the proton mass? Also, can you find the mass of a bound state via the propagator? Take the photon propagator. Technically, shouldn't there be an isolated pole at the bound state of an electron and positron? I don't ever recall seeing this though in the photon propagator. 


#7
Feb413, 09:26 AM

P: 229

So the QCD potential is a harmonic oscillator at large distances. But at short distances, isn't it free (asymptotic freedom)? Is there a transition zone? 


#8
Feb413, 09:30 AM

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#9
Feb413, 09:54 AM

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#10
Feb413, 01:40 PM

P: 887

If you could somehow get a lone quark, it's mass would be something like infinite, so the proton does indeed have less mass. 


#11
Feb413, 05:59 PM

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P: 5,437

Please be careful; there is no potential U(x) in QCD!
The linear potential is a derived quantity, a result, and expectation value, not an input like in Standard QM. In QCD the interaction is due to a Coulomb gauge Hamiltonian (plus other terms); for a reference you may have a look at slide 4ff of http://www.ectstar.eu/meetings/Confs.../Reinhardt.pdf 


#13
Feb613, 01:06 AM

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And no one said it isn't; we should be clear about that



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