# Decay Amplitudes Notation

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?

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What does the state $|B_p\rangle$ represent? Is that a baryon state? – David Z Dec 19 '11 at 0:56
@DavidZaslavsky Yes It may be $B^- (b\bar{u}) ,B^0(b\bar{d})$ etc. $B_p$ means a b quark with a u/d quark – yayu Dec 19 '11 at 1:19
Oh, B mesons. Got it. – David Z Dec 19 '11 at 2:46
Any chance you could provide a reference to where you saw this? I've been thinking about it and there does appear to be something missing. – David Z Dec 19 '11 at 6:59