Nuclear vs Hadron Mass: Exploring the Paradox

[kashiark]

independently these two points make sense but when you put them together it seems as if they should be consistent: hadrons express the energy that holds them together as mass and the boson that expresses the force is massless; a portion of a nucleus's mass is expressed as energy - the energy that holds the nucleus together though the boson which transmits the force is massive; can anyone enlighten me?

 

[humanino]

The nuclei mass is less than the sum of the masses of the constituents (nucleons). This is just default of mass due to binding energy. The fact that hadrons are much more heavy than their constituents is known as the "mass-gap" and it is much more complicated. It is a unique situation in the realm of bound states in general that the constituents are confined.

 

[kashiark]

the nuclei makes sense but i don't understand the hadrons; I've seen some authors account the extra mass to the sea of virtual particles around it but because they're virtual they are unable to be detected including their mass or am i wrong? and if not all particles would appear to have more mass than they do (unless it has to do with confinement but i was under the impression that the only reason that the strong interaction is strong enough to enforce confinement was because of these virtual particles and the symmetry between the different color charges which results in the amplification of the force)

 

[humanino]

First I will not be able to give you a fully satisfactory answer, since the issue is not resolved. The mass-gap problem is a well-defined mathematical problem whose solution is worth $1M (Clay millennium problem).

Physically we have some hindsights. First, the vacuum inside hadrons is not the same as the vacuum outside. From this point you can understand why all this is related to confinement. Now in the vacuum inside hadron, you can picture valence quark propagating as constantly exchanging gluons between the other valence quarks. A gluon is pretty similar to, and willing to fluctuate into, a pair quark-antiquark. All those gluons and quark-antiquark pairs are virtual. So you may picture a naked valence quark with mass of a few MeV in the vacuum inside hadrons really as dressing into a constituent quark with mass around 300 MeV. This crazy claim is supported by more rigorous Dyson-Schwinger method to calculate the quark propagator (among other model calculations). I don't remember what chiral symmetry breaking has to say about "constituent mass" however.

 

[kashiark]

ahh ok that makes sense and tyvm for answering so quickly!