The DZERO collaboration just sent to the Cornell ArXiv a paper which presents their new precise cross-section limits for the rare decay of mesons into pairs of muons. This important new article hides a small controversy, at least to my untrained eye. And since I am a bitch who thrives in the mud of controversies (or, at least some would describe me that way), let me do precisely that here.

As usual, before I go to the heart of the matter, I wish to give some background for those of you who spent their life doing better things than studying the phenomenology of bottom-flavoured mesons, Supersymmetry, and the like. Let me see if I manage to keep you on board.

All You Need To Know About Mesons, And Wouldn't Dream Of Asking

mesons are fancy particles composed of a bottom quark and a strange quark. Both are heavier than the up- and down- quarks which make up ordinary matter, the protons and neutrons contained in any nucleus. Both are only produced in energetic collisions. And both decay quickly, if left alone, to lighter particles.

We know almost everything on mesons that there is to know: the particle data group's Review of Particle Properties, the particle physicist's bible, lists no less than 34 decay modes, along with dozens of determinations of the lifetime, the mass, and other properties. These are well-studied particles! And there is a reason why they have been studied in as much detail as possible: actually, two reasons.

On one side, the phenomenology of mesons allows us to study a property of weak interaction called CP asymmetry: the non-equality of behaviour of a particle with the mirror-image of its antiparticle analogue. Through a detailed understading of CP asymmetry we might disclose some of the deepest secrets of Nature -the bitch, not the magazine. But it is not on CP asymmetries that I wish to focus on today.

The second reason, more relevant here, is that some particular decays of mesons are heavily suppressed in the Standard Model: that means that they should happen at an exceedingly rare rate, if our current theory of the subatomic world is correct. Insted, and here's the gold mine, if Supersymmetric particles exist, these could affect the decay rates of mesons, making some of them less rare after all!

Here we have in our hands a powerful, indirect way of discovering new physics: if we observe that the rate of rare decays is much higher than what is predicted by the Standard Model (less than four times in a billion!), that is big news! Note that it is the intrinsic rarity of the Standard Model processes what makes these decays appealing. Measuring a small effect is much, much easier if it sits on top of something even smaller, much like a beetle is easier to spot if it is riding on top of an ant rather than if it is riding on top of an elephant.

The decay on which we concentrate our focus is one which our detectors should see very easily and reconstruct with accuracy: it involves the annihilation of the two quarks within the meson into a pair of muons.

Knowledgeable physicists here will raise their eyebrows, because the term "annihilation" is used improperly, but you need not bother with the detail. Instead, all what matters is that two energetic muons arise from the disintegration, and nothing else. By measuring the energy and momentum of the muons, the total mass of the originating decaying particle is measurable, providing a clear signature. The two diagrams on the left describe the two simplest Standard Model processes which turn a meson in two muons. A particle enters from the right, the two quarks which make it up merge and emit weak bosons, and the latter eventually turn into muons. Maybe not that simple, but as far as subatomic interactions go, this is what you get.

DZERO's Search

DZERO has amassed a huge amount of data from proton-antiproton collisions at 2 TeV energy provided by the Tevatron accelerator. This data (6.1 inverse femtobarns, which means about 500 trillion collisions ) have been scanned in search for events containing two muons of opposite charge, and with the characteristics expected from the decay of mesons.

The top panel in the graph below shows how DZERO reconstructs the invariant mass of the candidate particles. The black points are real data, while the red histogram shows the expected mass distribution that one would observe from meson decays, if their rate of production were 100 times larger than the one which is expected from Standard Model theory. It is clear that such a signal would be easily spotted, since it would stand over backgrounds quite clearly. This tells us that the DZERO limit will exclude rates exceeding by 100 times the Standard Model one, and even ones smaller than that.

So, instead of showing a peak at about 5.3 GeV (the mass of the particle), the data distributes orderly along the black line, which is the expected background, a sum of two different sources of muon pairs of opposite sign: sequential decays of B mesons ( followed by ), which peak at low mass, and decays of pairs of B mesons ( and ), the flatter distribution. If you do not understand these reactions, do not worry -there is no need to do it in order to understand this post. If you are curious, though, I will just say that D mesons are ones containing the charm quark, and these are the most frequent products of the decay of the bottom quark inside the . Instead, X stands for "anything else in addition"; X and X' must include at least a neutrino, since we have singled out a muon in the reactions above, and leptons (muons and muon neutrinos) can only be produced in pairs.

The bottom panel in the figure above shows another distribution which is useful to identify true decays: the output of a Neural Network classifier, which discriminates true decays from backgrounds based on the kinematics of the event and other characteristics. Again, the data follows the background-only expectations, up to the highest values of  (where the discrimination of the signal is highest, and signal-like events would peak).

In the end, from the absence of a signal, DZERO manages to put a upper limit on the rate of the process. Specifically, they limit the fraction of mesons that decay into a dimuon final state: a pure number, a probability if you want. It is a number which can be directly compared with theoretical predictions for both the Standard Model, and for different flavours of Supersymmetric models.

But wait -you might now ask, why could Supersymmetry influence the decay rate into dimuon pairs ? Hmmm, I have not yet explained that yet. Basically, if massive new particles exist, they may "mediate" the transition of the bottom-antistrange quark combination making up the meson into the pair of muons. To the two diagrams schematizing the process which you see in the first figure above, which MUST exist if the Standard Model is correct, others might be added if new Supersymmetic particles existed. And the addition of new diagrams might increase the decay rate in the wanted final state.

The World's Best Limit ?

Now let me come to the "controversy". DZERO writes in its preprint that:

Presently, the best experimental bound for the branching fraction of at the 95% C.L. is given by the CDF collaboration.

[Above, B(...) means the "branching ratio of...", id est the probability of a particular decay]. This would be true for anybody who had not checked the recent results of CDF, which are accessible here for instance.

In that web page you find the most recent CDF result on the search for decays, which results in the limit , at 95% confidence level. This is A 25% tighter -i.e, better- limit than the one quoted in the DZERO paper. The DZERO result is quoted later in the preprint:

The resulting combined limit is at the 95% (90%) C.L.

So at 95% confidence level they have B<51 billionths, while CDF has B<43 billionths. Whose is the best limit ? A sixth grader should be able to tell. In the DZERO paper, though, you read the final claim that

This result is more stringent than the previous results [16, 17] and the best limit to date.
Hmmm. I leave you seventh graders to sort this one out.

As for me, however, I may know what the confusion is due to. DZERO is choosing to only quote in its article results already appeared in printed scientific magazines. One might object that its article is not published yet, either...  But leaving aside that detail, you should note that each Collaboration chooses to update in print similar searches only once they become significantly more interesting, and only update their public results in their webpages and conference talks in the meantime. It would be silly to clog scientific magazines every second week, just because you added twenty percent more data to your analysis! The current CDF result on decays to dimuon pairs is veritably B<43 billionths, and it still is the best in the world on this search, even after the new DZERO analysis.

Or, as Groucho used to say, those are my opinions, and if you don't like them... Well, I have others!