  New-physics (NP) constraints on first-generation quark-lepton interactions
are particularly interesting given the large number of complementary processes
and observables that have been measured. Recently, first hints for such NP
effects have been observed as an apparent deficit in first-row CKM unitarity,
known as the Cabibbo angle anomaly, and the CMS excess in $q\bar q\to e^+e^-$.
Since the same NP would inevitably enter in searches for low-energy parity
violation, such as atomic parity violation, parity-violating electron
scattering, and coherent neutrino-nucleus scattering, as well as electroweak
precision observables, a combined analysis is required to assess the viability
of potential NP interpretations. In this article we investigate the interplay
between LHC searches, the Cabibbo angle anomaly, electroweak precision
observables, and low-energy parity violation by studying all simplified models
that give rise to tree-level effects related to interactions between
first-generation quarks and leptons. Matching these models onto Standard Model
effective field theory, we derive master formulae in terms of the respective
Wilson coefficients, perform a complete phenomenological analysis of all
available constraints, point out how parity violation can in the future be used
to disentangle different NP scenarios, and project the constraints achievable
with forthcoming experiments.
