Solutions to the R_b, R_c and alpha_s puzzles by Vector Fermions
  We propose two minimal extensions of Standard Model, both of which can easily accommodate the recent puzzling observations about the excess in $R_b$, the deficit in $R_c$ and the discrepancy in the low energy and high energy determinations of $\alpha_{s}$. Each model requires three additional heavy vectorial fermions in order to resolve the puzzles. The current phenomenological constraints and the new potential phenomena are also discussed. 
Chia-Hung V. Chang, Darwin Chang, Wai-Yee Keung