We study the impact of a leptophobic $Z^{\prime }$ gauge boson on the $C_{1q}$ and $C_{2q}$ parameters that describe the low-energy, parity-violating electron-quark neutral current interaction. We complement previous work by including the penguin-like vertex corrections, thereby completing the analysis of one-loop calculation up to $\mathcal{O}(m_{q^{\prime }}^2/M_{Z^{\prime }}^2)$ terms. We analyze the sensitivity of these probes to the different couplings $Z^{\prime }\overline{u}q$ ($q=u$, $c$, $t$) and $Z^{\prime }\overline{d}q$ ($q=d$, $s$, $b$) in a model-independent way that can be applied to any specific $Z^{\prime }$ scenario. We show that constraints from neutral kaon and heavy flavor studies preclude significant contributions from flavor nondiagonal couplings except for those involving top quarks. We apply our results to a light $Z^{\prime }$ with flavor diagonal couplings to up or down quarks, a scenario proposed in the literature to explain the CDF $W$ plus dijet anomaly. We find that such a particle would not affect the $C_{1q}$ coefficients, but it would have a sizable impact on $C_{2q}$ couplings that can be probed by future measurements of parity-violating deep inelastic scattering of polarized electrons off of deuterium.

• Received 25 December 2012

DOI:https://doi.org/10.1103/PhysRevD.87.055013