In case you hadn’t heard, the past few days have been big days for B physics, i.e. particle physics involving a b quark. On the 18th and 19th, there were three results released in particular, two by LHCb and one by CMS. Specifically, on the 18th LHCb released their analysis of \( B_{(s)}\to\mu\mu\) using the full 3 fb\(^{-1}\) dataset, corresponding to 1 fb\(^{-1}\) of 2011 data at 7 TeVand 2 fb\(^{-1}\) of 2012 data at 8 TeV. Additionally, CMS also released their result using 5 fb\(^{-1}\) of 7 TeV and 30 fb\(^{-1}\) of 8 TeV data.
The decay \(B_{(s)}\to\mu\mu\) cannot decay via tree-level processes, and must proceed by higher level processes ( shown below)
These analyses have huge implications for SUSY. The decay \( B_{(s)}\to\mu\mu\) cannot proceed via tree-level processes, as they would involve flavor changing neutral currents which are not seen in the Standard Model (picture to the right). Therefore, the process must proceed at a higher order than tree level. In the language of Feynman Diagrams, the decay must proceed by either loop or penguin diagrams, show in the diagrams below. However, the corresponding decay rates are then extremely small, about \(3\times10^{-9}\). Any deviation from this extremely small rate, however, could therefore be New Physics, and many SUSY models are strongly constrained by these branching fractions.
The results reported are:
| Experiment | \(\mathcal{B}(B_{s}\to\mu\mu)\) | Significance | \(\mathcal{B}(B\to\mu\mu)\) |
| LHCb | \( 2.9^{+1.1}_{-1.0} \times 10^{-9}\) | 4.0\(\sigma\) | \(<7.4\times 10^{-10}(95\% CL) \) |
| CMS | \(3.0^{+1.0}_{-0.9}\times 10^{-9}\) | 4.3 \(\sigma\) | \(< 1.1\times 10^{-9} (95\% CL)\) |
Higher order diagrams
Both experiments saw an excess of events events for the \(B_{s}\to\mu\mu)\) channel, corresponding to \(4.o\sigma\) for LHCb (updated from \(3.5 \sigma\) of last year), and \(4.3\sigma\) for CMS. The combined results will, no doubt, be out very soon. Regardless, as tends to happen with standard model results, SUSY parameter space has continued to be squeezed. Just to get a feel of what’s happening, I’ve made a cartoon of the new results overlaid onto an older picture from D. Straub to see what the effect of the new result would be. SUSY parameter space is not necessarily looking so huge. The dashed line in the figure represents the old result. Anything shaded in was therefore excluded. By adding the largest error on the branching fraction of \(B_s\to\mu\mu\), I get the purple boundary, which moves in quite a bit. Additionally, I overlay the new boundary for \(B\to\mu\mu\) from CMS in orange and from LHCb in green. An interesting observation is that if you take the lower error for LHCb, the result almost hugs the SM result. I won’t go into speculation, but it is interesting.
Cartoon of Updated Limits on SUSY from \(B\to\mu\mu\) and \(B_s\to\mu\mu\). Orange Represents the CMS results and green represents LHCb results for \(B_s\to\mu\mu\) . Purple is the shared observed upper limit on \(B\to\mu\mu\). Dashed line is the old limit. Everything outside the box on the bottom left is excluded. Updated from D. Straub (http://arxiv.org/pdf/1205.6094v1.pdf)
Additionally, for a bit more perspective, see Ken Bloom’s Quantum Diaries post.
As for the third result, stay tuned and I’ll write about that this weekend!
Tags: B to mu mu, Bs to mu mu, CMS, LHCb, susy
