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### Needle in a haystack

We are back to discussing B physics today, with the observation of the rare decay: $$B^- \rightarrow \pi^- \mu^+ \mu^-$$. So what is this decay? It’s a $$B^-$$ meson (made of a b and an anti-u quark) decaying into a $$\pi^-$$ meson (made of a d and an anti-u quark) and two muons. And why is it so rare? Well, it’s a flavour changing neutral current decay. Which means that there’s a change in quark flavour in the decay, but not charge. This type of decay is forbidden at tree level in the Standard Model and so has to proceed via a loop, which can be seen in the centre of the Feynman diagram below.

If you look closer at the loop, you can see that for the decay to occur, a b quark needs to change flavour to a t or c quark, which then needs to change to a d quark. This is another reason why this decay is so rare. Transitions in quark flavour are governed by the CKM matrix, which I illustrate on the right, where the larger squares indicate more likely transitions. So while the transition from b to t is likely, the transition from t to d is very unlikely, and the b to c and c to d transitions are both fairly unlikely. This means, that whichever path is taken, the b to d quark transition is very very unlikely.

Okay, now to the LHCb result. Below I have a plot of the fitted invariant mass for selected $$\pi^-\mu^+ \mu^-$$ candidates, showing a clear peak for $$B-$$ decays (green long dashed line). Also shown are the backgrounds from partially reconstructed decays (red dotted line) and misidentified $$K^-\mu^+ \mu^-$$ decays (black dashed line). Candidates for which the $$\mu^+ \mu^-$$ pair is consistent with coming from a $$J/\psi$$ or $$\psi(2S)$$ are excluded.

We see around 25 $$B^- \rightarrow \pi^- \mu^+ \mu^-$$ events and measure a branching ratio of approximately 2 per 100 million decays. This result makes this decay the rarest $$B$$ decay ever observed!

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