# Energy-mass equiliance and mass defect

Hi!
According to E=mc^2, we have the phenomena mass defect. For example, when we put a proton and neutron together, that particle has a slightly lower mass than the sum of mass of the free particles due to the binding energy between the nucleons. OK, I'm fine with that - a lower energy results in a lower mass.

Now I hear that the binding energy between quarks is responsible for the major part of a proton's (and all particles made of quarks) mass. But shouldn't binding energy *lower* the mass of the quarks in the same manner as the above stated example? Where does my reasoning fail?

/Nick

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Bill_K
The QCD potential is like a harmonic oscillator: it starts at zero and rises to infinity at large distances. So a state can have positive binding energy and still be bound.

But does the QCD potential in a system of baryons (e.g a proton and a neutron) have the opposite sign (negative) compared to the quark system? I mean, why does the mass decrease when we put together a neutron and a proton, but increase in a quark system?

mfb
Mentor
The nucleon-nucleon interaction can be described similar to the electromagnetic interaction, but with a massive particle (pion) as force carrier. This gives an attracting potential (Yukawa potential), and negative binding energy (compared to a large separation) for stable nuclei.

This is not possible inside the nucleus, where you "see" net color charges of quarks. This leads to a different potential shape, and a positive binding energy. Unlike for nucleons, those quarks cannot escape - the potential does not go to zero for large distances.

Ah, these answers together solved my quandary. Thanks Bill_K and mfb!