Upper Limits on a Possible Gluon Mass

We analyze upper limits on a possible gluon mass, $m_g$. We first discuss various ways to modify quantum chromodynamics to include $m_g\mathrm{\ne }0$, including a bare mass, a Higgs mechanism, and dynamical breaking of color SU(3)${}_c$. From an examination of experimental data, we infer an upper limit $m_g<O(1)$ MeV. We discuss subtleties in interpreting gluon mass limits in view of the fact that at scales below ${\mathrm{\Lambda }}_{QCD}$, quantum chromodynamics is strongly coupled, perturbation theory is not reliable, and the physics is not accurately described in terms of the Lagrangian degrees of freedom, including gluons. We also point out a fundamental difference in the behavior of quantum chromodynamics with a nonzero gluon mass and a weakly coupled gauge theory with a gauge boson mass.