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!
Tags: LHCb
Hey Anna, as a BaBarian and a B-physics enthusiast I just want to say that this in amazing result! To see a branching fraction that is of the order of 10^-8 means that LHCb is well and truly past the reach of the B factories. I can’t wait to see what else LHCb has to offer.
Neat. But why does the intermediate quark have to be a top or a charm? Why not up?
Yes, you are right, the intermediate quark can also be an up quark. However, this transition is just as unlikely as the other two.
Is the rate of that decay compatible with the SM prediction?
Hi,
Thanks for taking an interest! Yes, the measured branching ratio [(2.4 ± 0.6 (stat) ± 0.2 (syst))×10−8] is compatible with the Standard Model prediction [(1.96 ± 0.21)×10−8]. I would have made a point of it if it wasn’t!
Cheers,
Anna
Hi Anna,
With regard to the B+ decay, should not the B+ consist of an UP quark and an anti B quark to give a charge of + 1. I enjoy your Blog.
Thanks
Hi,
Thanks for noticing that the Feynman diagram didn’t match the text. I’ve changed everything to be B-.
Cheers,
Anna