= R-xi gauge
{c}
{title2=$R_\xi$ gauge}
= Renormalizable gauge for a Higgsed vector field
{synonym}
For the Abelian <Higgs mechanism> with scalar phase $\chi$ and vector mass $m$, take $\mathcal L_{\rm gf}=-(\partial\cdot A+\xi m\chi)^2/(2\xi)$ when the scalar kinetic mixing is $-mA_\mu\partial^\mu\chi$. The cross term cancels this mixing after integration by parts. The resulting vector <propagator> is
$$
D_{\mu\nu}(k)=\frac{-i}{k^2-m^2+i0}\left(g_{\mu\nu}-(1-\xi)\frac{k_\mu k_\nu}{k^2-\xi m^2+i0}\right).
$$
At fixed finite $\xi$ it decays as $1/k^2$. Would-be <Goldstone bosons> and the required <Faddeev-Popov ghosts> remain in intermediate calculations; <BRST symmetry> identifies the physical states and ensures cancellation of unphysical modes. The limit $\xi\to\infty$ gives the <unitary gauge> propagator and is not uniform in ultraviolet momentum.
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