Lorentz Violating Backgrounds from Quadratic, Shift-Symmetric, Ultralight Dark Matter

We consider an effective theory for a shift-symmetric, quadratically-coupled,ultralight spin-0 field. The leading CP-conserving interactions with StandardModel fields in the effective theory arise at dimension 8. We discuss therenormalization group evolution and positivity bounds on these operators, aswell as their possible UV origins. Assuming that the spin-0 field is associatedwith an ultralight dark matter candidate, we discuss the effects of thedimension-8 operators on experiments searching for the oscillation offundamental constants and Lorentz violation. We find that the direct bounds onthese two effects are of similar strength but rather weak, corresponding to aUV cutoff scale of keV order, as they are mediated by dimension-8 operators.