Now the difference 0 . 0005 corresponds to 0 . 7 σ . The discrepancy of R$_{b}$ is 0 . 3%, but the difference in A b FB is about 4 . 4% - which is more than ten times larger than that of R$_{b}$ . Any new physics responsible for the deviation of A b FB should preserve the branching ratio of Z → b ¯ b with a high precision. If g b L and g b R were comparable in size, the total sum could be preserved by modifying g b L and g b R at a percent level with the opposite direction. However, in reality, the tree level value is where the left-handed contribution is about 27 times larger. In general it is possible for a left- handed coupling to obtain a percent level correction from a loop but to keep the branching ratio to be the same, we need about 25 percent correction to right-handed coupling g b $_{R}$. Without significant modification of the right-handed coupling, the loop correction to the left-handed coupling is typically negative (from charged Higgs) and make it impossible to keep R$_{b}$ as it is. If the charged Higgs is very light (lighter than 100 GeV) and tan β is close to 1, the (B)MSSM correction to Z → b ¯ b can be sizable such that R SM b can be reduced by 0.5%, 1% or 1.5% [25]. Light supersymmetric particles can cancel the charged Higgs loop. Fig. 4 shows R BMSSM b which also includes light stop. For tan β = 1 . 5, the predicted R BMSSM b = 0 . 2150 which is about 0 . 7 % smaller than the measured value. The correction appears in g$_{L}$ and it is impossible to make a sizable correction to g$_{R}$ (27 times larger one compared to g$_{L}$ ) from loop corrections to keep R$_{b}$ as it is. Such modification of g$_{L}$ , g$_{R}$ is not required if there are new processes which gives fake Z → b ¯ b signals. In light Higgs scenario of BMSSM, Z → hA → 2 b +(2 τ or c ¯ c ) can be counted as Z → 2 b + gluons events when tau jets are soft, because it is hard to distinguish soft tau jets from QCD backgrounds. In this case, measured R$_{b}$ value should be compared to R BMSSM total b = R BMSSM b + R fake b 12 g b L = − 1 2 + 1 3 sin $^{2}$θ$_{W}$ ≃ − 0 . 42 , (11) g b R = 1 3 sin $^{2}$θ$_{W}$ ≃ 0 . 08 , (12)