## Predictions for SUSY particle masses! September 2, 2008

Posted by dorigo in cosmology, news, science.
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Dear reader, if you are not a particle physicist you might find this post rather obscure. I apologize to you in that case, and I rather prefer to direct you to some easier discussion of Supersymmetry than attempting to shed light for you on the highly technical information discussed below:

• For an introduction, see here.
• For dark matter searches at colliders, see a three-part post here and here and here.
• Other dark matter searches and their implications for SUSY are discussed here.
• For a discussion of the status of Higgs searches and the implications of SUSY see here and here.
• For a discussion of the implications for supersymmetry of the g-2 measurement, see here;
• A more detailed discussion can be found in a report of a seminar by Massimo Passera on the topic, here and here.
• For $B \to \mu \mu$ searches and their impact on SUSY parameter space, see here.
• For other details on the subject, see this search result.
• And for past rumors on MSSM Higgs signals found at the Tevatron, have a look at these links.

If you have some background in particle physics, instead, you should definitely give a look at this new paper, appeared on August 29th in the arxiv. Like previous studies, it uses a wealth of experimental input coming from precision Standard Model electroweak observables, B physics measurements, and cosmological constraints to determine the allowed range of parameters within two constrained models of Supersymmetry -namely, the CMSSM and the NUHM1. However, the new study does much more than just turning a crank for you. Here is what you get in the package:

1. direct -and more up-to-date- assessments of the amount of data which LHC will need to wipe these models off the board, if they are incorrect;
2. a credible spectrum of the SUSY particle masses, for the parameters which provide the best agreement between experimental data and the two models considered;
3. a description of how much will be known about these models as soon as a few discoveries are made (if they are), such as the observation of an edge in the dilepton mass distribution extracted by CMS and ATLAS data;
4. a sizing up of the two models, CMSSM and NUHM1 -which are just special cases of the generic minimal supersymmetric extension of the standard model. Their relative merit in accommodating the current value of SM parameters is compared;
5. most crucially, a highly informative plot showing just how much we are going to learn on the allowed space of SUSY parameters from future improvements in a few important observables.

So, if you want to know what is currently the best estimate of the gluino mass: it is very high, above 700 GeV in the CMSSM and a bit below 600 for the NUHM1. The lightest Higgs boson, instead, is -perhaps unsurprisingly- lying very close to the lower LEP II limit, in the 115 GeV ballpark (actually, even a bit lower than that, but that is a detail – read the paper if you want to know more about that). The LSP is instead firmly in the 100 GeV range. For instance, check the figure below, showing the best fit for the CMSSM (which, by the way, implies $M_0 = 60 GeV$, $M_{1/2}=310 GeV$, $A_0 = 240 GeV$, and $\tan \beta =11$).

The best plots are however the two I attach below: they represent a commendable effort to make things simpler for us. Really a highly distilled result of the gazillions of CPU-intensive computations which went into the determination of the area of parameter space that current particle physics measurements are allowing. In them, you can read out the relative merit of future improvements in a few of the most crucial measurements in electroweak physics, B physics, and cosmology, as far as our knowledge of MSSM parameters are concerned. The allowed area in the space of two parameters -$m_0 \div m_{1/2}$ as well as $m_0 \div \tan \beta$, at 95% confidence level, is studied as a function of the variation in the total uncertainty on five quantities: the error on the gyromagnetic ratio of the muon, $\Delta (g-2)_\mu$, the uncertainty in the radiative decay $b \to s \gamma$, the uncertainty in cold dark matter $\Omega h^2$, the branching fraction of $B \to \tau \nu$ decays, and the W boson mass $M_W$.

Extremely interesting stuff! one learns that future improvements in the measurement of the dark matter fraction will yield NO improvement in the constraints of the MSSM parameter space. In a way, dark matter does point to a sparticle candidate, but WMAP has already measured it too well!

Another point to make from the graphs above is that of the observables listed the W boson mass is the one whose uncertainty is going to be reduced sizably very soon -that is where we expect to be improving matters most in the near future, of course if LHC does not see SUSY before! Instead, the $b \to s \gamma$ branching fraction uncertainty might actually turn out to need larger uncertainties than those assumed in the paper, making the allowed MSSM parameter space larger rather than smaller. As for the muon $g-2$, things can go in both directions there as well, as more detailed estimates of the current uncertainties are revised. These issues are discussed in detail in the paper, so I have better direct you to it rather than inserting my own misunderstandings.

Finally, the current fits slightly favor the NUHM1 scenario (the single-parameter Non-Universal Higgs Model) over the CMSSM. The NUHM1 scenario includes one further parameter, governing the difference between the soft SUSY-breaking contribution to $M_H^2$ and to squark and sleptons masses. The overall best-fit $\chi^2$ is better, and this implies that the additional parameter is used successfully by the fitter. The lightest Higgs boson mass also comes up at a “non-excluded” value of 118 GeV, higher than for the best fit point of the CMSSM.

1. Luboš Motl - September 2, 2008
2. Yuri Danoyan - September 2, 2008
3. Anonymous coward - September 2, 2008

As far as I understand, CMSSM is not SUSY, it is susy plus some (quite unmotivated and drastic) assumptions on the soft breaking parameters. As such, any falsification will not falsify SUSY, but the assumptions. And any experiment would test mainly these assumptions. Beware.

4. anomalous cowherd - September 2, 2008

Anonymous coward writes:

“…CMSSM is not SUSY, it is susy plus some (quite unmotivated and drastic) assumptions on the soft breaking parameters.”

The CMSSM is a simple susy model that passes all experimental tests, and which is used to allow people to fit data for limits, and for experimentalists to tune their Monte-Carlos. In the cases of both phenomenologists and experimentalists, it allows them to get a
general idea of how well they’re doing in their exploration of susy…

…now as to “(quite unmotivated and drastic) assumptions”, I don’t wish to question what you consider motivating, but I personally think that, for example, it’s interesting how much the F-theory constructions considered by Ibanez et al. in arXiv:0805.2943, resemble the CMSSM or NUHM1 models considered in this paper arXiv:0808.4128.
So perhaps you should add the disclaimer that it is you, personally, who don’t feel the motivation, rather than projecting your feelings on the models in question…

5. Kea - September 2, 2008

Unfortunately, the fact that they are willing to falsify sparticles doesn’t mean that the community as a whole is willing to falsify them. And the empirical confinement of parameters is hardly a ‘prediction’ in the same class of a clear theoretical derivation.

6. Ben Allanach - September 3, 2008

I have to say: check http://arxiv.org/abs/0705.0487 which does basically the same fit. There are big differences depending upon whether you plot minimum chi^2 or a Bayesian probability density (we did both). The minimum chi^2 (or “profile likelihood”, see fig 6a) does look a little different in our paper, and it is not immediately clear to me why, since the fits are basically similar….

7. dorigo - September 3, 2008

Hi Ben,

thank you for pointing out your paper. I usually do not comment on phenomenological publications, but I sometimes make an exception, as in this case.

Cheers,
T.

8. maireadmeagher - September 3, 2008

super post, most informative…Cormac O Raifeartaigh (logged in as a colleague)

9. cecil kirksey - September 3, 2008

Hi Tommaso:
Can you for us illerates define the minimum mass relative to say a proton of ANY WIMP? I am trying to understand the term “massive”. Also any comments on the PAMELA results? Exactly how does a WIMP annililate? The SUSY WIMP is suppose to be stable right.

Also I read that the axion of QCD was invented to solve the CP violation problem of QCD. It is also a candidate for a WIMP. But if someother particle is the WIMP and missing dark matter what happens to the CP problem? The axion may just have a very small mass?

BTW really enjoy your blog. Nice to get a perspective of physics outside the US.

10. Haelfix - September 3, 2008

This paper and several like it are what we call in the biz benchmark papers. They are not really completely sharp predictions perse b/c you can finagle things around, but they do sort of give an expectancy of where we ought to be looking. One has to appreciate the amount of effort and work it takes to produce plots like the above.

Essentially if you had an infinite amount of universes similar to ours with the same known current experimental constraints and they all possessed fairly ‘natural’ MSSM spectrums, you would roughly expect to see something like a gaussian around values like this.

One thing to be aware off (having worked on similar sorts of plots in years past). These sorts of analysis’s have in the past been quite off for SuSy with predicted values that have since been falsified, leading some to wonder why it just so coincidentally happens that nature chooses to hide SuSY and the Higgs just barely out of current particle accelerator reach.

Otoh since the MSSM is extremely desirable from both a theoretical and phenomenological point of view, we keep at it.

11. dorigo - September 3, 2008

Welcome, Lubos.

Thank you, Cormac.

Cecil, massive may mean anything, provided M>0. However, as far as the lightest stable SUSY particle goes, massive means “in the 100 GeV range”, which is about 107 proton masses.

No, I refrain from commenting the very suggestive data that have been published without permission around… I pass on that one.

The SUSY WIMP to be the LSP candidate has to be stable, and it is so by invoking a R-parity, which is a number conserved in decays: the lightest particle with R=1 cannot decay because there is nothing with R=1 lighter than it.

The axion, if I remember correctly, can be very light. In principle there can be more particles which make up the missing mass. And in fact there are. At least there are the neutrinos.

BTW Thanks for the support.

Haelfix, yes, I remember SUSY predictions pointing at much lighter particles 15 years ago… That is one of the reason of my skepticism in fact.

Cheers all,
T.

12. Luboš Motl - September 4, 2008

Dear Tommaso,

15 years ago, some people also thought that the top quark might have been lighter – and the increase of the believed superpartner masses is not too different from the increase of the believed top quark mass. See e.g. one of the most cited 1993 papers with “supersymmetry” in the title

http://arxiv.org/abs/hep-ph/9312272

Also, people arguably wanted to make their research and predictions closer to everyday life and doable experiments, including LEP, so they were picking unnaturally low superpartner masses. If they had avoided this bias, there would be almost no change between 1993 and 2008. In other words, your skepticism is largely based on well-understood sociology, not on non-trivial scientific arguments.

Best
Lubos

13. Sven Heinemeyer - September 4, 2008

I would like to stress that the analysis Tommaso featured in his blog does not make any assumptions on the SUSY masses. It uses purely experimental
data. The rest is simply the result of the analysis. Thus the “predicted” SUSY
masses are not biased by any “human prejudice”.
If fact, the featured paper states explicitly that with about 1 fb^-1 of well understood LHC data the model under consideration, i.e. the CMSSM or the
NUHM1, can be ruled out.

14. Luboš Motl - September 4, 2008

Dear Sven,

I completely agree – what you write is, in fact, completely equivalent to what I am writing.

These calculated superpartner masses are just objective results of calculations, the values are reasonable – every opinion that it is not reasonable is unreasonable – and they are just more accurate and objective than any other previous estimates.

I wrote that if someone expected gluino to be 40 GeV or something like that 15 years go, it was an unsubstantiated prejudice because it wasn’t supported by anything similar to the high-precision data in your paper. I just wanted to make sure that the “prejudice” was certainly not my label for your paper, quite on the contrary.

Best
Lubos

15. Animalous cow hard (was anonymous coward) - September 6, 2008

Yes, serious analyses like this take time and should be respected – if nothing else – for this. Just – just – I remark that these are not predictions for susy masses, but for cmssm masses.

About ‘F-theory’ constructions, personally I would leave them in the realm of (well-paid) human amusement activities, far from being complete and useful as phenomenological theories. But – but – if you insist in the connection, it seems to me that a similar set of assumptions is present in those models, as is in the CMSSM.

So again, I just warn that while it is useful to restrict to minimal or natural parameters, sometimes necessary and certainly informative, it does not lead to predictions. It is like searching only where you can make light, and not everywhere.

Early or non- predictions are politically and scientifically veeery dangerous. This already happened before: proton decay (there is no real prediction from GUT), string constructions (there is no unique vacuum as gepner would have liked), leptogenesis (no real bound on m_nuR), susy FV, etc…

Then, I would be contempt with a title like

Predictions for CMSSM particle masses!

16. Luboš Motl - September 6, 2008

Dear anonymous cow hard,
well, yes and no.

“Predictions for SUSY masses” is the same thing as “predictions of CMSSM masses” if the world is (essentially) CMSSM, and it is the same thing as “Vafa et al. predictions for F-theory MSSM masses” if Vafa’s construction is correct.

Both CMSSM predictions and F-theory predictions for superpartner masses are predictions for superpartner masses. They’re not “all” predictions that have been made about superpartner masses but both groups belong to the category of predictions of superpartner masses. ;-)

I agree that CMSSM and F-theory are, from this viewpoint, on equal footing. And they predict significantly different numbers. Well, predictions are dangerous, but without this danger, it is hard to make progress because this risk is in inherent part of the scientific process. An unreliable or not-quite-justified prediction is often a precursor to a better or even completely successful prediction (that can even be verified).

The CMSSM masses have surely more substance behind these predictions than Gepner’s dreams about the uniqueness. But from a broader perspective, these are all predictions, and whether they’re right or wrong are good questions and the answers are bound to be interesting, too.

Best wishes
Lubos

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