I'm not clear on whether the coupling constant for strange to antidown is modified in the same way as for strange to down, i.e. multiplied by ##\sin(\theta_C)##. And are the coupling constants of interactions mediated by Z also dependent on the Cabibbo angle? And what happens if you have say a charm and down quark interact via weak to produce an up quark and antistrange quark? The coupling constant is modified at both vertices, multiplied by ##\sin(\theta_C)## in both cases. Decay width is proportional to the coupling constant squared, so does that mean it would then depend on ##sin^4(\theta_C)##? I've read a textbook (Griffiths Intro to Elementary Particle Physics) which made me ask these questions rather than helping to answer them!