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### Where is that new physics hiding?

We are all very busy at the moment analysing our one inverse femtobarn of data in preparation for the winter conference season, so I don’t have any new results to tell you all about. Instead, I thought I’d try to explain one of our more complicated results from last summer, namely the $$B \rightarrow K^* + \mu^+ + \mu^-$$ decay.

I’m warning you all now that when I say complicated, I mean complicated. In fact, I’m going to even preface it with a comic from xkcd:

Sorry, I just wanted an excuse to use the image. But seriously, try to bear with me as I try to explain the intricacies of the physics.

Okay, let’s start with the decay, $$B \rightarrow K^* + \mu^+ + \mu^-$$. What exactly are we looking for here? We are looking for a $$B$$ meson (made of a $$b$$ and a $$u$$ quark) decaying into an excited $$K$$ meson (made of a $$s$$ and a $$u$$ quark) and two muons [*]. On the right is a Feynman diagram of the process, which I have taken from here. This type of Feynman diagram is called an electroweak penguin [**], where the heavy particles in the loop (the $$Z$$ and $$W$$ bosons as well as the $$t$$ quark) mean that it is very rare.

So why is this particular rare decay interesting? It turns out that an asymmetry in the direction in which the positively charged muon is emitted with respect to the $$K^*$$ meson is an excellent probe of new physics. If the positively charged muon is emitted in the same direction as the the $$K^*$$ meson, this is designated as a forward decay, if it is emitted in the opposite direction, this is called a backward decay.

This asymmetry can be quantified by a parameter, $$A_{FB}$$, which is a measure of the relative number of forward decays and backward decays. If all positively charged leptons are emitted in the forward direction, the value of $$A_{FB}$$ would be +1. If they are all emitted in the backward direction, it is -1. If the number of forwards and backwards decays are exactly the same, then $$A_{FB}$$ would be 0.

Everybody with me so far? I hope so, because there’s just one more thing I need to explain before I can show you some results. If you look closely at the Feynman diagram above, you might notice that it says Z boson or photon. Below, I’ve explicitly shown the Feynmann diagrams for each process.

Why is this seemingly minor fact important? Due to the two interfering processes, $$A_{FB}$$ is not simply -1, 0 or 1, but actually depends on a parameter called $$q^2$$, which corresponds to the invariant mass of the dimuon pair. In the Standard Model, $$A_{FB}$$ should be negative for small $$q^2$$, and positive for the larger $$q^2$$.

So now that you understand the physics, to set the stage, I present the results from BaBar (upper left, 2009), Belle (lower left, 2009) and CDF (right, 2010).

Each of these graphs shows $$A_{FB}$$ as a function of $$q^2$$, with the experimental results (points) and predictions from the Standard Model (solid lines) and various new physics models (dotted lines). It may not be obvious from first glance, but if you look closely at the small $$q^2$$ regions of each graph, it can be seen that all of the experiments report a positive value of $$A_{FB}$$ while the Standard Model predicts a negative value. Could this be an indication of new physics?

Cue dramatic music…

Enter LHCb…

Here is our result from the past summer compared with the Standard Model prediction and the results of the other experiments.

It is a very impressive result, using almost all of the available data at the time, which a lot of people worked very hard to achieve, as the analysis is quite complicated. However, as impressive as it is, the result is somewhat disappointing as it matches the theory so well.

So to answer my own question from the title of this post… no new physics here…

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[*] For all you experts out there, I have simplified the final state here, since the $$K^*$$ meson in the decay is the $$K^*(892)^0$$ meson which decays into a $$K^+$$ meson and a $$\pi^-$$ meson.

[**] The use of the word penguin to describe a type of Feynman diagram was the result of a bet (which is very nicely described in the Wikipedia article) and it has since been the source of some amusing nomenclature such as penguin pollution and cute images in talks and blog entries, like the one on the right.

For those who are wondering why I choose this particular image; in the Standard Model, the $$B \rightarrow K^* + \mu^+ + \mu^-$$ decay can proceed via a penguin box process as well as the electroweak penguin process I show earlier. The interference of this box process has to be taken into account when performing the analysis.

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