Sensitivity to light weakly-coupled new physics at the precision frontier

Precision measurements of rare particle physics phenomena (flavor oscillations and decays, electric dipole moments, etc.) are often sensitive to the effects of new physics encoded in higher-dimensional operators with Wilson coefficients given by ${\rm C}/(\Lambda_{\rm NP})^n$, where C is dimensionless, $n\geq 1$, and $\Lambda_{\rm NP}$ is an energy scale. Many extensions of the Standard Model predict that $\Lambda_{\rm NP} $ should be at the electroweak scale or above, and the search for new short-distance physics is often stated as the primary goal of experiments at the precision frontier. In rather general terms, we investigate the alternative possibility: ${\rm C} \ll 1$, and $\Lambda_{\rm NP} \ll m_W$, to identify classes of precision measurements sensitive to light new physics (hidden sectors) that do not require an ultraviolet completion with additional states at or above the electroweak scale. We find that hadronic electric dipole moments, lepton number and flavor violation, non-universality, as well as lepton $g-2$ can be induced at interesting levels by hidden sectors with light degrees of freedom. In contrast, many hadronic flavor- and baryon number-violating observables, and precision probes of charged currents, typically require new physics with $\Lambda_{\rm NP} \gtrsim m_W$. Among the leptonic observables, we find that a non-zero electron electric dipole moment near the current level of sensitivity would point to the existence of new physics at or above the electroweak scale.