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### There’s competition?

LHCb is in somewhat of a unique position in that it has no direct competition. No other experiment is currently able to perform all the physics measurements that are possible at LHCb with comparable precision. However, there are a few measurements where there is fierce competition, and one of these is the search for the decay of a $$B_s$$ meson into two muons, $$B_s \rightarrow \mu^+\mu^-$$.

This particular decay is extremely interesting as it is a flavour changing, helicity suppressed decay, meaning that it is very rare. In fact, in the Standard Model, the expected decay rate is $$(3.2 \pm 0.2) \times 10^{-9}$$, meaning that only 3 out of a billion $$B_s$$ mesons is expected to decay into two muons. Because the decay is so rare, it provides a powerful indirect way of discovering new physics. If we observe that the decay rate is higher than what is predicted, we have found something! Maybe even Flip’s supersymmetric penguin!

Unfortunately for the supersymmetric penguin, so far all searches for this rare decay have seen nothing. However this year, for the first time, experiments have the datasets to start detecting a signal, even if it’s as rare as the Standard Model predicts. Not only is LHCb sensitive to the decay, but so is ATLAS and CMS, as well as CDF and D0.

And in true competition, ATLAS, CDF, CMS and LHCb have all released new results in time for the winter results. Now, before you all get too excited, there hasn’t been an observation yet, so all experiments have set new upper limits:

• CDF: $$3.1\times10^{-8}$$ (10 inverse femtobarns of proton-antiproton collision data at 2 TeV)
• ATLAS: $$2.2\times10^{-8}$$ (2.4 inverse femtobarns of proton-proton collision data at 7 TeV)
• CMS: $$7.7\times10^{-9}$$ (4.9 inverse femtobarns of proton-proton collision data at 7 TeV)
• LHCb: $$4.5\times10^{-9}$$ (1 inverse femtobarns of proton-proton collision data at 7 TeV)

There are a few of interesting things to note about the results…

Firstly, all experiments are getting dangerously close to the Standard Model prediction. I say dangerously close, because the limits are so close to the prediction that there probably won’t be any new physics in this decay, which is quite disappointing. The plot below (a modified version from this paper) shows what types of new physics models increase the rate of this decay and how many have been excluded by the measured upper limits.

Secondly, the experiments have fairly similar sensitivities to the decay, despite the varying datasets used in the analyses. The reason for this is a little complicated, since the sensitivity of an experiment to a measurement of decay rate depends on many things. There is the production rate of $$B_s$$ mesons, which depends on the energy of the proton-(anti)proton collisions. This is why CDF needs 10 inverse femtobarns of data to be competitive with ATLAS, CMS and LHCb. There is then the efficiency and accuracy of detecting and measuring $$B_s$$ meson decay. This is why LHCb only needs a fraction of the ATLAS and CMS datasets to be competitive. Then there are the technical details of how the analyses are performed, which I’m not going to go through here, but they do vary from experiment to experiment as people try different methods to make the most of the data they have.

But of course, the most important point to take away is that LHCb produces the best limit! *winks* Here is an event display for a detected $$B_s \rightarrow \mu^+\mu^-$$ candidate. The muons are the pink lines which pass through the entire detector. A zoom in on the vertex region shows that they are displaced from the primary vertex, as would be expected if they decayed from a $$B_s$$ meson.

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