Anomaly of Zb b-bar coupling revisited in MSSM and NMSSM

The Zb b-bar coupling determined from the Z-pole measurements at LEP/SLD shows an about 3σ deviation from the SM prediction, which would signal the presence of new physics in association with the Zb b-bar coupling. In this work we give a comprehensive study for the full one-loop supersymmetric effects on the Zb b-bar coupling in both the MSSM and the NMSSM by considering all current constraints which are from the precision electroweak measurements, the direct search for sparticles and Higgs bosons, the stability of Higgs potential, the dark matter relic density, and the muon g-2 measurement. We analyze the characters of each type of the corrections and search for the SUSY parameter regions where the corrections could be sizable. We find that the sizable corrections may come from the Higgs sector with light mA and large tan β, which can reach -2% and -6% for ρb and sin 2θeffb, respectively. However, such sizable negative corrections are just opposite to what needed to solve the anomaly. We also scan over the allowed parameter space and investigate to what extent supersymmetry can narrow the discrepancy. We find that under all current constraints, the supersymmetric effects are quite restrained and cannot significantly ameliorate the anomaly of Zb b-bar coupling. Compared with χ2/dof = 9.62/2 in the SM, the MSSM and NMSSM can only improve it to χ2/dof = 8.77/2 in the allowed parameter space. Therefore, if the anomaly of Zb b-bar coupling is not a statistical or systematic problem, it would suggest new physics beyond the MSSM or NMSSM.