A Quantum Diaries Survivor

I am preparing the slides for the PPC08 conference, which will be held in Albuquerque next week, and I thought I would post here two slides that show how present Tevatron data is increasingly wiping off the board one Supersymmetric model after another - yes, I regard a choice of parameters as a single “model”, since the phenomenological implications of varying the >100 SUSY parameters are just too varied to call it a single model: instead, SUSY is a framework, and points in the parameter space are models.

The models we kill today belong to a version of the minimal supersymmetric extension of the Standard Model which has “minimal SO(10) soft-SUSY breaking boundary conditions“. No, I am not going to tell you what this is: you will have to read it on hep-ph/0506233 if you really must. Instead, I will show the present limit that CDF has obtained on a particular decay of the meson, which is heavily suppressed in the standard model, but which could be enhanced by up to three orders of magnitude in SUSY models. Because of this enhancement, and because we could be sensitive to it, the matter is intriguing: by measuring the decay, one would instantly achieve two things: 1) prove the SM is wrong; 2) favor some SUSY models among the various possible interpretations of the effect.

mesons are hadrons composed of a b and a s quark. They are electrically neutral, and have a long lifetime because the b-quark is unwilling to turn into a 2nd generation charm quark (decays across generations are suppressed). But they do, in about a picosecond. Blitzing fast for our senses, but quite slow for 5 GeV unstable subatomic bodies. What happens is that the b-quark emits a W boson, changing into the charm quark. The W boson is virtual, because it has a mass way below its nominal one of 80.4 GeV, and it immediately turns into a pair of light quarks or a lepton-neutrino pair.

What is described above is the rule, but there are exceptions. In an exceedingly rare combination of circumstances, the standard model predicts that a meson will instead decay by emitting two W bosons, with a box diagram (see below, top) or a penguin diagram (bottom) whose end product may be a pair of charged muons: a striking signature of the decay! This, however, is calculated to happen only four times in a billion decays. That means we have to study several billion decays to observe it!

Searching in 2 inverse femtobarns of data, CDF has seen no signal, and a limit on the fraction of these rare decays has been set at 5.8E-8: no more than 58 in a billion. The search was done by looking for pairs of muons with an invariant mass compatible with that of the meson, and by training a neural network on the dimuon kinematics and purity to distinguish true decays from other backgrounds.

In the slide below you can see the neural network discriminator output for signal and backgrounds, in the top right graph. The scatterplot in the lower right instead shows the NN output versus the reconstructed dimuon mass: the two small boxes are the regions where the signal for and mesons were sought.

The result on the branching fraction has implications on the models of SUSY with SO(10) soft susy breaking, as was said at the beginning. In the slide below you can see that indeed, for a particular choice of the parameters describing the space of these theories, the area not yet painted with any color - indicating it was still not disproven by searches of Higgs bosons, charginos, or other constraints - has been fully excluded by the CDF limit.

In the graph, the green band is the one most favoured by cosmological bounds on the relic density of dark matter. The full black line is the lower limit on charginos found by LEP. That bound has also been updated by CDF, and from 104 GeV the lower limit has been brought up to 140 GeV.

As Veltman puts it, “SUSY is hiding just around the corner… It has been hiding there for a while” (I am quoting by heart… but the meaning is unaltered). So, as we continue turning corners and finding nothing but good-old standard model physics, one starts to wonder whether we are fooling ourselves.