A Quantum Diaries Survivor

Last week the D0 Collaboration released the first result I am aware of which uses two inverse femtobarns of Tevatron Run II data. It is a search for the rare decay of B_s mesons into pairs of muons , a process which in the Standard Model has a probability of only three parts in ten billions of happening.

It is of course quite pleasing to see such a large set of data finally milked out for precise results. But even more pleasing is to see that the accuracy of the result has increased by a whooping factor of five from the previous best limit on that super-rare decay.

The limit found by D0 is B(Bs->mu mu) < 9 x 10^-9 (at 95% C.L., see here for an explanation of the lingo). That is still about thirty times above the predicted SM rate, so one could well ask what is the relevance of the measurement in the current state of affairs.

Well, the relevance is that, one spoonful at a time, ground is being dug  for the grave of supersymmetric theories by results such as the one above. [Unfortunately, I fear I have to get into the details a bit more than I usually do, if I want to explain. My apologies to those of you who feel they are left in the dark... Please ask if you need more information.]

So, about the digging. Most supersymmetric theories imply the existence of particles which cannot be kept from contributing to hadronic decays via virtual loops in the decay diagrams. By assuming the particles are massive – more massive than current experimental limits, of course, or the theory would be dead – SUSY aficionados kill two birds with one stone: not only does the theory dodge the mass limits, but the virtual contributions to rare decays and CP-violating amplitudes are kept small.

Small, but not infinitesimal, that is: and a very small contribution can best be observed in processes which are predicted to have a very small rate in the standard model, such as the mentioned B_s decay to muon pairs.

Take the following prediction, which I found in  Hep-ph/0602056 (“Mixing Among the Neutral Higgs Bosons and Rare B Decays in the CP Violating MSSM“) : in minimal supersymmetric theories which include some CP violation, the rate of the Bs decays does receive indeed sizable contributions from virtual exchange of SUSY particles.

The plot is a busy one, quite typical of phenomenological papers. However, let me make some sense of it. On the x axis there is a CP-violating phase phi (in units of PI) due to the MSSM Lagrangian (that is, the effective contribution to CP violation from purely supersymmetric processes). Think of it as a free parameter and let’s move on. On the y axis, there is the probability of B_s decay to muon pairs, in 10^-9 units. The different curves depend on the origin of the CP phase and on the accuracy of the calculation (which includes one-loop virtual diagrams or two-loop diagrams too). Also, worth mentioning is that the plot is valid only for specific values of a few critical parameters, such as tan(beta). But you need not be concerned with it (or if you are, get the paper from the link I cited and find out by yourself what I cannot explain here).

What one should carry home from the objectively arcane discussion above is that MSSM theories with CP violation can start to be nipped in the bud by experimental limits such as that obtained by D0.

Of course, MSSM could well get away with no CP violation at all. And indeed, a few experimental results seem to imply that SUSY needs to carry little or no CP violation, if we want to keep it alive.

I guess the lesson is always the same: you can never totally kill a theory which has too many free parameters, because there will always be some unreachable tiny corner of phase space which you cannot reach. On the other hand, the question why Nature (the bitch, not the magazine) should hide in those corners the truth about itself is a legitimate one…

UPDATE: A reader from D0 (see in the comments section) points out that the limit is 9E-8, not 9E-9! This means there is still no real constraint to the MSSM with the choice of parameters used for the graph above. Apologies…