In the old Yukawa model of nuclear forces, it was proposed that short-range interactions were mediated by exchanges using massive force carriers (originally, mesons were proposed for this).

If one considers a Yukawa potential with negative carrier mass, one is left with an effective confinement potential

Is there a reason to expect gluons to have effectively negative mass (at least while considering the long distances/IR limit)? Have negative mass carriers been proposed to model confinement?

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    $\begingroup$ What about virtual particles in in feynman diagrams? can go through negative masses as they are off mass shell. $\endgroup$ – anna v Mar 31 '20 at 6:09

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