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S7b. Why can a bound state of massless quarks be heavy?
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A system has a well-defined mass if it is in an eigenstate of p^2,
where p is the total momentum operator (whatever this is;
relativistically, bound states are very poorly understood).
So to understand, view it from a nonrelativistic perspective.
Because of E=mc^2, the mass shows up as energy, i.e., as eigenstate
of the Hamiltonian.
Now a bound state at rest defines the rest energy, and by giving
it uniform motion one can increase the energy by an arbitrary amount
of kinetic energy. The rest energy (and hence the rest mass), on the
other hand, is determined by the discrete spectrum of the Hamiltonian
in reduced coordinates, i.e., with center of mass motion separated out.
For forces that decay with distance, a bound state necessarily has
a mass that is less than the sum of the masses of the constituents.
For particles involving quarks, this does not apply since the strong
force increases with distance. Hence the rest mass of a bound state of
quarks could be anything.