If small corrections of order (m_f/M_Z)²are neglected, the partial width for Z⁰†’ ffÌ… arising from the lowest-order diagrams of Figure 10.12 are given by

where q_f is the electric charge of the fermion in units of e, θw is the weak mixing angle and where the plus sign applies for f = „“^ˆ’, d, s, b and the minus sign applies for f = ν_„“, u, c, t. Assuming that sin² θ_W = 0.25, calculate the branching ratios for Z⁰ †’ ccÌ… and Z⁰ †’ bbÌ…, and the decay widths to charged lepton pairs and to hadrons. Compare the latter two to the experimental values (10.29a) and (10.29b) and comment on any significant discrepancy.

Figure 10.12

Transcribed Image Text:

GFM [1 Гу Зл у2 +qj sin? Ow + 2q3 sin Ow z° (a) (b) z°. (c)