Ultralight Scalar Dark Matter with Off-Diagonal Flavor Couplings

Ultralight dark matter can behave as a coherent background field and induce time-dependent modifications of Standard Model parameters. We study a scenario in which a real ultralight scalar $\phi$ couples off-diagonally to down-type quarks, linking ultralight dark sectors to flavor physics. Working within an effective field theory, we diagonalize the quark mass matrix in a coherent $\phi$ background and derive analytic expressions for oscillatory shifts in down-type quark masses and CKM parameters. These effects lead to signatures in both the classical regime, where $\phi$ acts as a background field, and the quantum (particle) regime, where it contributes through on-shell production or off-shell mediation. Using precision flavor measurements, nuclear $\beta$ decays, atomic clocks, pulsar timing, and meson observables, we derive constraints on the flavor-violating couplings $\lambda_{ij}$ for $m_\phi \sim 10^{-24}$--$10^{-12}\,\mathrm{eV}$, highlighting the complementarity of time-domain and flavor probes of ultralight dark sectors.