Gauge bosons associated with unbroken gauge symmetries, under which all standard model fields are singlets, may interact with ordinary matter via higher-dimensional operators. A complete set of dimension-six operators involving a massless $U(1)$ field, ${\gamma }^{\prime }$, and standard model fields is presented. The $\mu \to e{\gamma }^{\prime }$ decay, primordial nucleosynthesis, star cooling, and other phenomena set lower limits on the scale of chirality-flip operators in the 1–15 TeV range if the operators have coefficients given by the corresponding Yukawa couplings. Simple renormalizable models induce ${\gamma }^{\prime }$ interactions with leptons or quarks at two loops, and may provide a cold dark matter candidate.

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