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

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

### 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.

1. Luboš Motl - September 4, 2008

I understand that the papers are about similar topics but there are several reasons why I find the recent one more readable:

1) It actually tells us some “average” figures for the masses in the statistical distribution
2) It tells us something about the time needed to detect the preferred scenario(s) by the LHC

These might be superficial, easy things but in my optics, they increase the value of the recent paper significantly.

Given the similarity of the problems solved in the two papers, it is somewhat puzzling why a more direct comparison is not possible. Cannot each team, for example, rerun their algorithm with the same set of quantities (and the same values and error margins) that the other group used, to check their (two papers’) mutual compatibility?

To check that the differences are really because of a different set of high-precision observables and due to their different values and not, sorry for this heretical hypothesis, because of serious errors in at least one of the papers? 😉

Best
Lubos

2. dorigo - September 4, 2008

Hi Lubos,

these calculations are horribly CPU intensive. It usually requires a lot of babysitting, not a weekend job I would say. Of course I am just guessing, Ben probably will have something to say about this.

Cheers,
T.

3. Luboš Motl - September 4, 2008

Ciao Tommaso,

I would actually be very surprised if the Camgrid required more than a weekend to draw one of these 2D charts. At any rate, is science still supposed to be reproducible? 😉

Best
Lubos

4. Nicola - September 4, 2008

Hi,
What do you think of the surprising rise in CR e+ spectrum found by PAMELA satellite (and recently “stolen” by Italian theoreticians)?
It seems to be the most direct proof about the particle dark matter observed in CRs.

5. Haelfix - September 5, 2008

They could probably recompile with the additional updated top mass and electroweak constraints if they had computer time but including additional b and k physics could require some moderatedly long recoding and perhaps algorithm changes.

Either way they’re pretty darn close (and its purely academic since we will know anyway in a few months), but given the usual sensitivity to the top mass, I suspect they’d be very nearly equivalent with updated data.

6. Ben Allanach - September 5, 2008

“Cannot each team, for example, rerun their algorithm with the same set of quantities (and the same values and error margins) that the other group used, to check their (two papers’) mutual compatibility?”

This can be done of course – the problem is that it is a lot of work for my team. A lot less work would be for Buchmueller et al to just have a look at points they have already sampled to see the effect of their additional variables. I feel justified in asking them to do this, since theirs is the new paper, and readers may expect a comparison/explanation of differences with previous literature.
The hypothesis of an error in one of our calculations could of course be true, but there may hopefully be a more legitimate reason.

7. Ben Allanach - September 5, 2008

“What do you think of the surprising rise in CR e+ spectrum found by PAMELA satellite (and recently “stolen” by Italian theoreticians)?
It seems to be the most direct proof about the particle dark matter observed in CRs.”

I’d agree: it’s a fascinating result. Of course the “smoking gun”
would be if at higher energies, the positron fraction drops off rapidly and we see the background re-emerging. I understand that Pamela can increase their reach by about a factor of 2. I should think it’s worth a post by Tommaso: the only place I’ve seen a representation of the data is in a phenomenology paper.

8. Ben Allanach - September 5, 2008

Just a quick update on the difference: my research student Matt Dolan checked the Buchmueller et al best fit point through our machinery, and got a Higgs mass of 109 GeV, which would be quite disfavoured by LEP2. Since our calculation uses SOFTSUSY and the other group uses FeynHiggs, I wonder if the discrepancy lies within this observable?

9. Nicola - September 5, 2008

Hi Ben, look also this
http://arxiv.org/abs/0808.3867 (Cirelli, Strumia)
and this one
http://arxiv.org/abs/0808.3725 (Bergstrom et al.)
Despite their claim to explain the e+ excess in terms of SUSY particles annihilations, the so-called astrophysical “boost factor” is still needed to match the data… and other astrophisical contributions (eg e+ from pulsar) are poorly known.
So, without any drop in the spectrum, I would say that puzzle seems to be still unsolved…

10. Luboš Motl - September 5, 2008

Dear Ben,

I agree that their program is the more natural one to do the comparison, because 1) new papers should explain their relationship to the old ones that they should know, and because 2) it should be easier to modify a program they played with recently.

Concerning the “falsifications” by predicting too light a Higgs, pure Standard Model is even worse, with the optimum Higgs mass being near 85 GeV. In this sense, Nature seems to be even more supersymmetric than MSSM. 😉

Best
Lubos

11. Ben Allanach - September 6, 2008

Dear Nicola,

thanks for pointing these papers out. It does appear that the boost factors needed are really large (they’re quoting 10000 in the case of SUSY, and 100 for other models).

The thick plottens….
Best,
Ben

12. Sven Heinemeyer - September 8, 2008

Hi Ben,
this is of course not the place to have a detailed comparison between different analyses. Therefore just one comment: our best-fit point is accidentally very close to SPS1a. This point always had a Higgs mass of about 114 GeV (for a top quark mass of 175 GeV). We find a mass that is a bit lower, probably mostly due to the lower top mass of 172.4 GeV.

I do not think that the differences between your analysis (the one you did ‘our way’) and ours are that large. We show how different treatments of e.g. the errors of (g-2)_mu or BR(b -> s gamma) can influence the range in m_0 and m_1/2. This was actually one of the three main points in our paper.

Cheers, Sven

13. Ben Allanach - September 8, 2008

Hi Sven,

no I agree that it’s not that large – qualitatively, they are similar.
Still, a factor of 2 in m0 reach is quite a difference….
Best,
Ben

14. Ben Allanach - September 22, 2008

I should point out that the Bayesian fits in terms of the CMSSM parameters in arXiv:0705.2012 are very similar to the Bayesian results in our paper, despite the fact that most of the sub-programs used are different to ours (with the notable exception of
SOFTSUSY).
In Bayesian fits, one finds that the dark matter constraint makes the largest difference, above and beyond all other constraints, contrary to what happens in the frequentist interpretation in Buchmueller et al’s results.

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