What does ⟨Bₚ|b†b|Bₚ⟩ mean in B meson decay?

[liealgebra]

This question is mostly about how to interpret notation used in Particle Physics. At lowest order the rate of $b\rightarrow s\gamma$ is proportional to

$\langle B_p|b^\dagger b|B_p\rangle$ where p is either u or d labels and b, b+ are creation annhilation operators. However, I am unable to understand this notation. For some initial state transforming to a final state isn't the amplitude given by $\langle \mbox{final}|\hat{O}|\mbox{initial}\rangle$. Shouldn't the amplitude be in this case $\langle s\gamma|b^\dagger b|b\rangle$ or something?

So what does the provided matrix element mean, exactly?

 

[petergreat]

Where did you read this? It may be understandable if given the context, like how these variables are defined.