The DZERO collaboration has just produced an update of their analysis of the dimuon charge asymmetry using 9.0 inverse femtobarns of proton-antiproton collisions. The new result confirms the previously reported effect, raising the discrepancy with the Standard Model prediction to over four standard deviations.

I feel this result is important to comment here, so I will do it regardless of the fact that another authoritative source has already discussed it in detail for the blogosphere (and this time, much more timely than I did). I however suggest that if you are interested in this topic you also read Jester's piece.


DZERO is a subnuclear physics experiment operating at the Fermilab Tevatron collider near the city of Batavia, in the Illinois prairie. Together with their colleagues/competitors operating the CDF experiment 120 degrees away along the collider ring, the DZERO physicists are mining the large amounts of proton-antiproton collisions collected since 2002. The Tevatron will soon stop operations (in September 2011), so the time for a big discovery is now: with over 10 inverse femtobarns of collisions already collected, a new physics effect is either observable in the data currently analyzable, or will never be.

[I should explain that after the data of energetic collisions is collected by the detector,  a significant amount of time is spent calibrating the output of the detector components and applying small corrections, then reconstructing the complex information. The process takes several weeks at the Tevatron, so the most advanced analyses are now capable of producing results based on data collected until a few months ago. That is the case of the present study.]

So, is DZERO on the verge of a big discovery ? Maybe. But what is it all about ?

Right and Left Shoes

The measurement is quite simple to explain, but its real meaning is much harder to clarify. Let me try to do a little of both here. First of all, what is measured is a quantity called "dimuon charge asymmetry", and it is computed by accounting how many pairs of muons are observed both with positive electric charge, subtracted by the number of pairs observed both with negative charge. The difference is then divided by the sum of the two numbers, in order to obtain a "fractional difference" which is independent on the size of the total collected data.

So far so good, right ? This is not so different from checking whether a one-legged thief is stealing in your shoe store by counting how many right shoes are there, subtracting the number of left shoes, and dividing by the total. A percentage significantly different from zero (given a certain rate of mistakes on your part as you tried to classify as right or left some particularly featureless kinds of sandals, say) will tell you that your suspects are well-founded.

In fact, the DZERO analysis is surprisingly simple because it is employing what we call an "inclusive" strategy: rather than trying to sort out a subset of events which are very well understood and attributable to a specific subnuclear process, and focusing then only on the characteristics of those events, DZERO shoots in the bulk. The advantage is clear: they get the highest possible statistical power, in exchange for a rather complicated task ahead -the one of determining how much they can trust their understanding of the detector. In the shoe store analogy, it is the tradeoff between globally counting left and right shoes and  trying to focus instead on the brand that the suspect had been seen wearing the other day. In the first case, the shoe seller may detect easily a global deficit, but he or she will have some trouble demonstrating that they were stolen; in the latter, even a smaller deficit might be a stronger proof, but the seller risks to be concentrating on the wrong brand.

Ok, enough with shoes. Let me tell you instead what could be the cause of an observed charge asymmetry. Muon pairs are produced by several processes, but the most common is the simultaneous decay to muons of a bottom and an anti-bottom quark, produced together in the proton-antiproton collision. Now, the mechanism by which muons are produced in the disintegration of bottom quarks is the following: bottom quarks have Q=-1/3 charge, and they usually decay into a charm quark by emitting a negative W boson. The negative W will in turn create a negatively-charged muon, together with a unobservable neutrino. The anti-bottom quark, instead, has Q=+1/3 charge, and it emits a positive W when turning into an anti-charm quark. This results in a positive muon.

It goes without saying that a b-antib pair thus produces muons of opposite charge. But there is a mechanism, called B oscillation, whereby the hadron containing the b quark may oscillate into a hadron containing an anti-b-quark! If one of the two b does this trick, the end result may be that one gets two bottoms, or two anti-bottoms; and thus two muons of the same charge (while of course, if both bottom and anti-bottom oscillate into their antiparticles, the end result is null).

The Result

Now, imagine that there were a new physics process which malignantly affected the probability that a bottom quark oscillates into its antibody: suppose, for instance, that this new physics process makes the probability of the oscillation b -> anti-b different from the probability of the opposite anti b -> b transition. One could then detect such a asymmetric behaviour by observing that more positive-positive muon pairs are emitted, globally, with respect to negative-negative pairs!

That is exactly what DZERO was after. And this is what they find: they measure the asymmetry as

Note that this result involves quite some cooking: the asymmetry due to different background processes needs to be factored in, and the observed asymmetry in events collected with a different selection (events with only one muon) enters as a correction factor. The DZERO article, in fact, is not a lightweight publication, and it will take the better part of your next weekend if you venture into a careful reading. However, neglecting these details, we may just note that the observed value is inconsistent with the Standard Model prediction (which is -0.009+-0.002%) by 4.2 standard deviations.

So what do these 4.2 sigma point to ? The explanation of such asymmetry could be a new process producing an abnormally large amount of CP violation in the semileptonic decay of b quarks. If proven correct, this result would thus cause a significant breach in the picture we have so tidily drawn of electroweak interactions of heavy quarks. It is interesting to read the last lines of the new DZERO paper:

Our results are consistent with the hypothesis that the anomalous like-sign dimuon charge asymmetry arises from semi-leptonic b-hadron decays. The significance of
the difference of this measurement with the SM prediction is not sufficient to claim observation of physics beyond the standard model, but it has grown compared to our previous measurement with a smaller data sample.
In other words, DZERO cannot claim that their observed effect is due to new physics yet. This looks like a understatement: they are just reporting that the deviation from the SM has grown in significance from their previous analysis (which employed two thirds of the data, and a slightly simpler technique). Since these 4.2 standard deviations will be unlikely to grow past five with the addition of just 20% more data (what DZERO will likely end up having after the Tevatron shuts down for good), the conclusion is not rosy: they might be seeing the effect of new physics, but they will not be able to claim its definitive observation. Unless CDF ends up finding a similar effect and decides to combine the datasets, of course...

This article would not be complete without the graph above, showing the result on the plane of two variables: the measured semileptonic charge asymmetry of B_d mesons (on the horizontal axis) and the asymmetry of to B_s mesons (on the vertical axis). The two kinds of hadrons behave differently -in particular, their oscillation frequency of the latter is much higher- so it makes sense to draw the functional form of their relative contributions to the observed asymmetry (in purple, with yellow boundary showing the 95% coverage). This allows to compare this measurement to other ones -in particular, ones derived from pure samples of B_d (the vertical band, measured in B factories that only produce B_d mesons) or B_s mesons (horizontal band, an exclusive measurement formerly produced by DZERO, sort of measuring just the deficit of right blue sandals in the shoe store metaphor). Note that the SM prediction (the black point on the upper right) is quite far from the DZERO measurement, while it is compatible with both previous results.