6 The parameter U plays a fairly unimportant role, all the neutral current and low energy observables depend only on S and T [48]. In addition U is often predicted to be very small. In most of the models U should differ from zero by only a percent of T . In the case of an extra family with the doublet ( t ′ b ′ ) , the contribution to T and S param- eters are given by [34] with Including QCD and QED corrections, the Z → b ¯ decay width can be written as [51] where and δ ’s are various corrections which are discussed below. In the decay of the Z → b ¯ , the top quark mass enters in the loop correction to the vertex mediated by the W gauge boson. Due to spontaneous symmetry breaking effects the top mass can not be neglected in the calculation. In fact there is a top mass dependence that grows like m 2 t m 2 Z as in many other one-loop weak processes such as K − ¯ K , B − ¯ B (Δ F = 2 mixings), b → sℓ $^{+}$ℓ − etc. The additional contribution to the Zb ¯ b vertex, due to nonzero value of the top quark mass can be written as: δ q QED gives small final-state QED corrections that depend on the charge of final fermion, δ q QED = 3 α 4 π Q 2 $_{q}$. (9) δ$_{b}$ ≈ 10 − 2 ( − m 2 t 2 m 2 Z + 0 . 5 ) | V$_{tb}$ | 2 + ( − m 2 t ′ 2 m 2 Z + 0 . 5 ) | V$_{t}$ ′ b | 2 ) . (8) Γ( Z → q ¯ q ) = N$_{c}$ 48 α s 2 $_{W}$c 2 W m$_{Z}$ ( | a$_{q}$ | 2 + | v$_{q}$ | $^{2}$) × ( 1 + δ (0) b )( 1 + δ q QED )( 1 + δ q QCD )( 1 + δ q µ )( 1 + δ q tQCD )( 1 + δ$_{q}$ ) , (6) v$_{q}$ = ( 2 I q 3 − 4 | Q$_{q}$ | s 2 W ) , a$_{q}$ = 2 I q $_{3}$, (7) δm$_{12}$ = 1 2 M 2 Z ( m 2 1 + m 2 − 2 m 2 $_{1}$m 2 m 2 1 − m 2 ln( m 2 $_{1}$/m 2 $_{2}$) ) . (5) T$_{4}$ = 1 8 πx$_{W}$ (1 − x$_{W}$ ) [ 3 ( | V$_{t}$ ′ b ′ | $^{2}$δm$_{t}$ ′ b ′ + | V$_{t}$ ′ b | $^{2}$δm$_{t}$ ′ b + | V$_{tb}$ ′ | $^{2}$δm$_{tb}$ ′ − | V$_{t}$ ′ b | $^{2}$δm$_{tb}$ (3) + | V$_{t}$ ′ s | $^{2}$δm$_{t}$ ′ s ) + δm$_{l}$$_{4}$$_{ν}$$_{4}$ ] , 2 S$_{4}$ = 3 6 π ( 1 − 1 3 ln m t ′ m 2 b ′ ) , (4) B. Vertex corrections to Z → b ¯