## Guest post: Ben Allanach, “Predictions for SUSY Particle Masses”September 4, 2008

Posted by dorigo in cosmology, news, physics, science.
Tags: , ,

Ben Allanach is a reader in theoretical physics at the University of Cambridge. Before that he was a post-doc at LAPP (Annecy, France), CERN (Geneva, Switzerland), Cambridge (UK) and the Rutherford Appleton Laboratory (UK). He likes drawing and playing guitar in dodgy rock bands. He is currently interested in beyond the standard model collider phenomenology, and is the author of SOFTSUSY, a computer program that calculates the SUSY particle spectrum. He also tries to do a bit of outreach from time to time. I invited him to discuss the results of his studies here after I discussed the paper by Buchmuller et al. two days ago, since I was interested in understanding the subtle differences between today’s different SUSY forecasts.

In a paper last year “Natural Priors, CMSSM Fits and LHC Weather Forecasts “, we (Kyle Cranmer, Chris Lester, Arne Weber and myself) performed a global fit to a simple supersymmetric model (the CMSSM). Data included were:

• relic density of dark matter
• Top mass, strong coupling constant, bottom mass and fine structure
constant data
• Electroweak data: W mass and the weak mixing angle
• Anomalous magnetic moment of the muon
• B physics: $B_s \rightarrow \mu\mu$ branching ratio,
$b \rightarrow s \gamma$ branching ratio, and
$B \rightarrow K^* \gamma$ isospin asymmetry
• All direct search limits, including higgs limits from LEP2

and used to make predictions for supersymmetric particle masses and cross sections. We showed two characterisations of the data: Bayesian (with various prior probability measures) and the more familiar frequentist one, which I’ll discuss here.

We vary all parameters in order to produce a profile likelihood plot of the LHC cross-sections for producing either strongly interacting SUSY particles, weak gaugino SUSY particles or sleptons directly. This is equivalently a plot of $latex e^{-\chi^2)/2}$:

The good news is that the LHC has great prospects for producing SUSY particles in large numbers assuming the CMSSM: for 1 $fb^{-1}$ of data, we expect the production of over 2000 of them to 95% confidence level (shown by the downward facing arrows). Of these, some fraction will escape detection, but the message is very positive. The CMSSM prefers a light higgs, as shown by this plot:

The different curves correspond to different assumptions about the priors (the green one labelled profile shows the usual $\chi^2$ interpretation), but as the figure shows, these aren’t so important. Arrows show the 95% confidence level upper bounds: 118 GeV for the lightest neutral higgs $h$.

### Comparison of results from two papers

The results are quite similar to the recent ones of the Buchmueller et al crowd (who use recent updated data and more observables) lightish SUSY is preferred, primarily because the anomalous magnetic moment of the muon prefers a non-zero SUSY contribution. Also, the W boson mass and weak mixing angle show a slight preference for light SUSY. Because the LHC has enough energy to produce these particles, detection should be quite easy.

The central results of each paper can be expressed in the parameter plane $m_0$ vs $M_{1/2}$ (scalar supersymmetric particle masses vs gaugino supersymmetric particle mass). Here, I show the result of our fit on the left and theirs on the right:

To compare the two figures, you must convert their axes of the right-hand figure to the one on the left (note the different scales, although I tried to re-size them to make the scales comparable – apologies to Buchmueller et al for flipping their axes to aid comparison). The comparison should be between the solid line of the right-hand diagram, and the outer solid line on the left (both 95% confidence level contours), but the Buchmueller et al gang get lighter scalars than us, by a factor
of about 2 or so.

### Why should the two results differ?

The top mass has changed in the last year from $m_t=170.9 \pm 1.8$ GeV to $m_t=172.4 \pm 1.2$ GeV. Also, Buchmueller et al include additional observables: other electroweak, B and K-physics ones. My understanding is that none of these is very sensitive to the SUSY particle masses, given the constraints from direct searches though. Perhaps most of these extra observables very slightly prefer light SUSY, so that they disfavour $m_0=1000-2000$ GeV range? Buchmueller et al should be able to tell us by examining their data.

Thanks to Tommaso for inviting this guest post.