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Atomic Parity Violation (APV) is usually quantified in terms of the weaknuclear charge $Q_W$ of a nucleus, which depends on the coupling strengthbetween the atomic electrons and quarks. In this work, we review the importanceof APV to probing new physics using effective field theory. Furthermore, using$SU(2)$ invariance, we correlate our findings with those from neutrino-nucleuscoherent scattering. Moreover, we investigate signs of parity violation inpolarized electron scattering and show how precise measurements on the Weinbergangle, $\sin \theta_W$, will give rise to competitive bounds on light mediatorsover a wide range of masses and interactions strength. Lastly, apply our boundsto several models namely, Dark Z, Two Higgs Doublet Model-$U(1)_X$ and 3-3-1,considering both light and heavy mediator regimes.

New Physics Probes: Atomic Parity Violation, Polarized Electron Scattering and Neutrino-Nucleus Coherent Scattering