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Dynamical gluon mass generation has been traditionally plagued with seagull divergences, and all regularization procedures proposed over the years yield finite but scheme-dependent gluon masses.
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The demonstration of the existence of a bound state, and in particular a zero-mass bound state, in realistic field theories is a difficult dynamical problem, usually studied by means of integral equations known as Bethe-Salpeter equations (see, e.g., E. C. Poggio, E. Tomboulis and S. H. Tye, Phys. Rev. D 11
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