$Z'$ near the $Z$-pole

Abstract

We present a fit to precision electroweak data in the standard model (SM) extended by an additional vector boson, $Z′$, with suppressed couplings to the electron compared to the $Z$ boson, with couplings to the b-quark, and with mass close to the mass of the $Z$ boson. This scenario provides an excellent fit to forward-backward asymmetry of the $b$-quark measured on the $Z$-pole and ±2 GeV off the $Z$-pole, and to lepton asymmetry, $A_e$, obtained from the measurement of left-right asymmetry for hadronic final states, and thus it removes the tension in the determination of the weak mixing angle from these two measurements. It also leads to a significant improvement in the total hadronic cross-section on the $Z$-pole and $R_b$ measured at energies above the $Z$-pole. We explore in detail properties of the $Z'$ needed to explain the data and present a model for $Z′$ with required couplings. The model preserves standard model Yukawa couplings; it is anomaly-free and can be embedded into grand unified theories. It allows a choice of parameters that does not generate any flavor violating couplings of the $Z′$ to standard model fermions. Out of standard model couplings, it only negligibly modifies the left-handed bottom quark coupling to the $Z$ boson and the third column of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix. Modifications of standard model couplings in the charged lepton sector are also negligible. It predicts an additional down-type quark, $D$, with mass in the few hundred GeV range, and an extra lepton doublet, $L$, possibly much heavier than the $D$-quark. We discuss signatures of the $Z′$ at the Large Hadron Collider and calculate the $Z′b$ production cross-section, which is the dominant production mechanism for the $Z′$.