One year ago, a paper by a distinguished group of theorists announced first evidence of new physics from measurements of the properties of B_s mesons performed at the Tevatron by the CDF and DZERO experiments. They had combined all the available information, obtaining a result which disagreed with the Standard Model (SM) prediction by more than three standard deviations.

The study was quickly criticized because of some of its inputs: the unavailability of some information on the Likelihood function used by DZERO in their experimental results was not a fault of the authors, but was enough to cast doubt on the results. Moreover, claiming evidence for new physics on the sole basis of a 3-sigma offset from the SM prediction appeared a bit too happy.

Soon after the publication of that paper, CDF and DZERO made a more rigorous combination of their data, arriving at a result which, while not in very good agreement with the SM prediction, was not too exciting either. Now, one year after those facts, the Tevatron experiments have updated their combination using their improved analyses, which use more collider data (2.8 inverse femtobarns of analyzed proton-antiproton collisions each). They obtain a result which disagrees with the Standard Model by 2.1 standard deviations. So, the new result does not confirm, nor kill, the suggestive effect seen one year ago.

Now, in order to explain the physics at the basis of the measurement in question, I would need to spend my whole afternoon on this article; this appears a rather silly thing to do, since I am currently on vacation in a very beautiful, secluded island south of Greece. All I can offer, given my poor knowledge of the details of B-meson physics, is the following summary.

CP violation -the non-conservation of a quantum symmetry of a physical system when combining the operations of charge-conjugation C with parity P- is enabled in the Standard Model by the presence of a complex phase in the Cabibbo-Kobayashi-Maskawa matrix (CKM), a 3x3 matrix describing the mixing of the three generations of quarks. Due to the particular value of the CKM parameters, the system of B_s mesons (neutral particles composed of a bottom and a anti-strange quark) is expected to display a tiny amount of CP violation if the Standard Model is valid. These bodies can only be studied in detail at the Tevatron collider these days, so it is clear that CDF and DZERO are investing a sizable effort in the investigation of their properties: they are really breaking new ground in this specialized sector of particle physics.

A significant amount of CP violation in the decay of B_s mesons would be a clear indication of new physics effects. Actually, one could turn the argument around, and say that it is difficult to conceive new physics beyond the SM which does not cause a deviation of the amount of CP violation observable in the system of B_s mesons. It is for this reason that theorists have explicitly invented "Minimal Flavor Violation" scenarios, which amount to new physics entering the fray in their tiptoes, leaving everything almost unmodified as far as the phenomenology of flavor violation is concerned. If you will, this sounds like yet another conspiracy theories, not different from the one of "split Supersymmetry", where one hypothesizes that Supersymmetric particles exist but some obscure mechanism casts them away from the region we can explore with today's technology.

Anyway, let me say in few words what CDF and DZERO measure. They identify B_s decays in a very striking final state, $B_s \to J/\psi \phi$. These decays can be recorded by selecting events with two muons, then finding two additional kaon tracks due to the decay of the phi meson, $\phi \to KK$. The signal is really clean because the mass of the two-body resonances is very well defined. Both experiments reconstruct the distribution of lifetime of the decayed B_s meson from the decay length -the distance from the collision point of the decay vertex; then, as a function of the measured lifetime, a study of the angular distributions of the J/psi and phi mesons yields information on the CP properties of the B_s meson at decay time.

From the observed kinematical properties and flavour information of the decayed B_s mesons, it is possible to derive a measurement of the difference in lifetime of the two mass eigenvalues of the B_s system, the parameter called $\Delta \Gamma_s$, as well as a determination of the phase between the mixing and decay amplitudes, the parameter labeled $\phi_s$ -or equivalently, a similar phase $\beta_s$. A proper definition of these quantities can be found in the DZERO summary paper.

Both CDF and DZERO perform fits to their data extracting two-dimensional Likelihood contours in the plane of $\Delta \Gamma_s$ versus $\beta_s$. A very accurate error analysis allows to take in account the true shape of the Likelihood functions, avoiding the assumption of Gaussian tails and combining the two results in a coherent way. The technique is summarized in the figure below, which shows how Likelihood values are "readjusted" to correspond to those expected for Gaussian errors for a given confidence level (the value on the vertical axis), before combining them.

On the horizontal axis you read off a difference between the Likelihood value at the maximum and the value in another point of the two-parameter plane; this difference would correspond to a smaller probability (a smaller vertical intercept with the red line) if a Gaussian approximation were used. Beware of non-Gaussian tails, thou seeker of new physics!

The final result is shown in the following figure. Here you can see 1-sigma (blue), 2-sigma (red), and 3-sigma (green) contours for the allowed range of the two studied parameters, once the likelihoods of the two experiments has been combined. The Standard Model prediction ($\Delta \Gamma_s = 0.096 ps^{-1}$, $\beta_s = 0.02$) is shown with a small vertical black bar (the vertical size is due to the uncertainty in the prediction for $\Delta \Gamma_s$), while the possible values corresponding to new physics models affecting the amount of CP violation in the B_s system are shown by the light green sinusoidal band.

The computed discrepancy of measurement and SM value is, as I noted above, equal to 2.1 standard deviations, equivalent to a p-value of 3.4%. That means that a similar result should be found by chance once every thirty times, in universes where the SM's view of B_s physics is valid. On the other hand, most of the values of $\Delta \Gamma_s$ and $\beta_s$ in the plane allowed by new physics theories score no better than the SM! As always, when you compare the SM with a universe of other theories, it is not hard to find an alternative which is "more probable" than the SM. This, to me, always sounds like the uneven fight of reality and fiction.

So, is the new combination of Tevatron measurements of $B_s \to J/\psi \phi$ decays an indication of the first fractures appearing in the SM ? It is apparently hard to judge, but one hint can be provided by observing that there are several (be this read as an euphemism) places where the SM could be broken in the physics of B mesons, and is instead showing better p-values than the one we are focusing on today. Thirty ? Maybe even more! Check the particle properties data book and you will find thousands of measurements, many of which could have arisen to the same degree our interest if they had shown a departure from predictions similar to the one we are discussing here.

In other words, this might be taken from the perspective of the "look elsewhere effect": if you search for an anomaly and you have N places to find it, you are quite likely to find one which has a probability of the order of 1/N of being a fluctuation. Am I a sceptical bastard? Of course! Does that mean you should not buy my arguments ? Judge by yourself.