While flavor physics often offers a multitude of witty jokes (read as bad puns), I think I’ll skip one just this time and let the analysis speak for itself. Just recently, at the Lake Louise Winter Institute, a new result was released for the analysis looking for \( b\to s\gamma\) transitions. Now this is a flavor changing neutral current, which cannot occur at tree level in the standard model. Therefore, the the lowest order diagram which this decay can proceed by is the one loop penguin shown below to the right.

From quantum mechanics, photons can have either left handed or right handed circular polarization. In the standard model, the photon in the decay \(b\to s\gamma\) is primarily left handed, due to spin and angular momentum conservation. However, models beyond the standard model, including some minimally super symmetric models (MSSM) predict a larger than standard model right handed component to the photon polarization. So even though the decay rates observed for \(b\to s\gamma\) agree with those predicted by the standard model, the photon polarization itself is sensitive to new physics scenarios.

As it turns out, the decays \(B^\pm \to K^\pm \pi^\mp \pi^\pm \gamma \) are well suited to explore photon polarizations after playing a few tricks. In order to understand why, the easies way is to consider a picture.

In the picture to the left, we consider the rest frame of a possible resonance which decays into \(K^\pm \pi^\mp \pi^\pm\). It is then possible to form the triple product of \(p_\gamma\cdot(p_{\pi,slow}\times p_{\pi,fast})\). Effectively, this defines the angle \(\theta\) defined in the picture to the left.

Now for the trick: Photon polarization is odd under parity transformation, and so is the triple product defined above. Defining the decay rate as a function of this angle, we find:

\(\frac{d\Gamma}{d \cos(\theta)}\propto \sum_{i=0,2,4}a_i cos^i\theta + \lambda_i\sum_{j=1,3} a_j \cos^j \theta\)

This is an expansion in Legendre Polynomials up to the 4th order. The odd moments are those which would contribute to photon polarization effects. The lambda is the photon polarization. Therefore, by looking at the decay rate as a function of this angle, we can directly access the photon polarization. However, another way to access the same information is by taking the asymmetry between the decay rate for events where theta is above the plane and those where theta is below the plane. This is then proportional to the photon polarization as well and allows for direct statistical calculation. We will call this the up-down asymmetry, or \(A_{ud}\). For more information, a useful theory paper is found here.

Enter LHCb. With the 3 fb\(^{-1}\) collected over 2011 and 2012 containing ~14,000 signal events, the up-down asymmetry was measured.

In bins of invariant mass of the \(K \pi \pi\) system, we see the asymmetry is clearly non-zero, and varies across the mass range given. As seen in the note posted to the arXiv, the shapes of the fit of the Legendre moments are not the same in differing mass bins, either. This corresponds to a 5.2\(\sigma\) observation of photon polarization in this channel. What this means for new physics models, however, is not interpreted, though I’m sure that the arXiv will be full of explanations given about a week.