This question is mostly about how to interpret notation used in Particle Physics. I am given that 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 $b$, $b^\dagger$ 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?
