Let me explain what's on this plot. It assumes the so-called mSUGRA scenario which is cherished by experimentalist because it parametrizes the multitude of the MSSM parameters in terms of just 5 variables, thus creating an illusion of order in the Universe. 2 of these variables, the A-term and tanβ, are fixed above to a specific value, the same as the one assumed by CMS and ATLAS in their theoretical interpretations. This leaves 3 variables: the universal scalar mass m_0, the universal gaugino mass M_1/2, and the μ-term (the first two are defined at the GUT scale and related to the physical masses of the SUSY particles by complicated differential equations; this is one of the curious idiosyncrasies of SUSY phenomenology). Quite generally, in the MSSM one can compute the weak scale, that is the Higgs vacuum expectation value, in terms of the parameters of the lagrangian. In the case at hand, to reproduce the correct weak scale or equivalently the correct Z boson mass, the 3 remaining variables need to satisfy the constraint of the form

This constraint divides the mSUGRA parameter space into 3 regions:

- If m_0 and M_1/2 are too small one cannot solve the above constraint for any μ. This corresponds to the "vev=0" region on the left-hand side of the plot.
- For large SUSY breaking parameters the Higgs potential may not have a stable minimum. This corresponds to the "vev = ∞" region on the right-hand side of the plot.
- In the remaining parameter space one can always choose μ such that the above constraint is satisfied. Nature could in principle choose one particular point in this region.

You may want to zoom in to fully appreciate the impact of the LHC searches:

Recall that blue is theoretically unavailable, light red is excluded by LEP, dark red is excluded by the LHC, and white is allowed. The breathtaking endeavor of the LHC for the next few years will be to further shrink the white stripe.

Of course, the way it is presented here is a bit tendentious, and in a larger picture things might look less bleak. For example, the plot refers to a very specific constrained SUSY scenario; in more favorable scenarios the unexcluded parameter space may be twice as large. Furthermore, the ATLAS and to some extent also the CMS search are not completely robust. Thus, one can easily design SUSY scenarios that are less constrained by the LHC, at least for another month until Moriond. For example, SUSY models without light charginos would be missed by the ATLAS search. As a last resort, one can always present the results such that the allowed parameter space is better visible:Here, the x-axis corresponds to a relative fine-tuning of a given point in the mSUGRA parameter space: small fine-tuning on the right (when SUSY parameters are or order the Z boson mass), big fine-tuning on the left. The allowed parameter space is the green chimney close to the left edge. The breathtaking endeavor of the LHC for the next few years will be to move the red region further up the chimney.

See also Alessandro's paper for more details. For more pedagogical and less malicious comments on LHC SUSY searches see this post on US/LHC Blog.

## 20 comments:

Congratulations to getting 1% closer to your $100. Don't you want to double our bet now? $200 vs $20,000? ;-)

Nope. It would be unethical.

First SUSY signals and you simply throw that plot to the paper basket. So, what's the point? Who believes in mSugra anyway?

Dear Jester, your ethical concerns are appreciated. ;-)

But (not only) your argument with the measures is deeply flawed. SUSY doesn't really predict that you must live in the center of some random graphs. It is actually very reasonable for the parameters to take such values so that solutions to some constraints "barely exist" (near the vev=0 region).

Good physics is actually full of such things. Nature is walking on a thin line of consistency. This comment may be in some tension with the naturalness but there's no straight contradiction here.

In other words, your argument is not a strictly valid naturalness arguments.

Moreover, comments that 99% of the mSUGRA or CMSSM or another restricted parameter space is excluded is exactly as relevant as the comment that 99.999999999999% of the mass interval for the Higgs mass in the Standard Model is excluded - because the a priori mass interval goes to the Planck scale while we seem to have excluded all Higgs masses above 200 GeV.

You just choose the 99% against SUSY argument to be more trustworthy than the similar argument for the SM, but this is just a prejudice.

Is it possible to determine how much of the parameter space of other SUSY models is excluded now?

All this plot really means is that LHC is closing in on a discovery of supersymmetry, which will likely occur this time next year.

Lubos doesn't accept anything else than a 5 sigma proof :)

But is sounds good he start to talk of other 'realities'.

"It is actually very reasonable for the parameters to take such values so that solutions to some constraints "barely exist" (near the vev=0 region)."

I guess it sounds better in his own ears when he himself say it:)

(sorry I screwed up something at the first attempt, I just wanted to point out a typo).

"small fine-tuning on the right (when SUSY parameters are or order the Z boson mass), big fine-tuning on the right."

You mean "big fine tuning on the LEFT"

While we are at it, I am curious about the details of your infamous bet with Motl. If I remember correctly, you'll pay 10k dollars if a claim that SUSY has been discovered stands up for one year. Now,

1) under which conditions will Motl pay 100 dollars to you?

2) what happens if a hypothetical claim for SUSY is revealed to be bogus after more than a year? Will you get the money back?

Left/right corrected, thx.

I don't remember the details very well now. On my side the condition was something like 5 sigma from both ATLAS and CMS, and the claim should survive 1 year, I think. So flukes will not be a worry, but indeed there may be a problem if the experimentalists call SUSY something that is not. But let's not worry about it now. On Lubos side there was some number of femtobarns at 14 TeV, so not very soon.

@Anon-6, as far as I know no analyses in the context of alternative SUSY scenarios have been published yet. There should be much more experimental data available after Moriond, and then theorists will have 6 months to graze on that.

Dear Ulla, 5 sigma is actually not enough with these sloppy arguments - otherwise the Standard Model would already be excluded. The probability that a random Higgs mass jumps to the 100-200 GeV, when it can uniformly go up to the Planck scale, is one part in trillion. Five sigma is just one part in a million or so.

Whoever closes a question with less than 5 sigma is playing a very dangerous game but even 5 sigma may fail to be enough.

Hi Lubos, I have a problem with your SM Higgs example. In fact the right way to look at it is from the top-down. If you consider as available the whole range of Higgs mass from 0 to Mpl (or quartic coupling basically from zero to infinity) AT the Planck scale, then this range gets focused at the electroweak scale to something quite narrow, more or les between 130 and 170 GeV (the famous perturbativity and stability bounds).

Sorry, Anonymous, I am not sure what you mean - "how" does the Higgs mass get "focused"? Are you denying the existence of the hierarchy problem - e.g. the fact that in a top-down theory defined at a high scale, it's overwhelmingly likely that the physical Higgs mass will end up comparable to the high scale?

The stability etc. are constraints only if one studies the physics from the bottom up.

Strictly speaking, Lubos' argument applies not to the Higgs boson mass, but to the Higgs vev, and is known as the hierarchy problem. (As Anon points out, once the Higgs vev is fixed the Higgs mass cannot be arbitrarily high but has to be 130-170 GeV if you assume the SM is valid up to the Planck scale, or 0 - 1 TeV if you're fine with a lower cutoff). The difference between SM and SUSY is that we know that the SM exists and we measured the Higgs vev to be 246 GeV (via W mass). Thus, the hierarchy problem is not an argument against the existence of the SM but rather a puzzle that we're trying to explain (by invoking supersymmetry, technicolor, extra dimensions, etc). Similarly, if SUSY is discovered, the plot I showed will cease to be an argument against SUSY, but rather a puzzle that theorists will struggle to explain (by invoking new physics beyond the MSSM ;-). But in the current reality the plot is handy to jeer and sneer SUSY fanatics.

Thanks Jester, that's the proper way to look at it. If you already discount the fact that the ew scale is what it is then the SM Higgs mass should be in the range I quoted and the fact that "we seem to have excluded all Higgs masses above 200 GeV"

is not that meaningful (in the context of Lubos argument). His argument still works for the "ew scale" (or Higgs vev, or Higgs mass parameter)

Thanks for cleaning up!

"new physics beyond the MSSM"???

I thought it should be beyond the SM?

I guess Lubos remember from where the 5 sigma proof comes? He was very aggressive about the 'hints of a fourth generation' at Tommasos blog, among other against me. Maybe he begins to eat his hat now?

It is very hard to explain living matter without SUSY, but the coupling to MSSM, as suggested above, must be broken. MSSM is probably not the solution.

Could technicolor still be better? Or the Skyrme model? What has been done in that field lately?

"But in the current reality the plot is handy to jeer and sneer SUSY fanatics."

Oh, I see, so you admit that this whole stuff is just dishonest demagogy and you realize that? Why didn't you say it in advance?

Whether you do such things or not, your attitudes may turn out to be very expensive for you, Jester.

It sounds that some here would insist that not only dice is played by God, yet hide and seek is also a game the great architect enjoys to play regularly. On the other hand if this is not to be taken as nature being malicious, it then could only mean its subtleties are too great to be fathomed by these same sages, as them not being able to forecast as to have anticipated such non-occurrences :-)

“It has been often said, and certainly not without justification, that the man of science is a poor philosopher. Why, then, should it not be the right thing for the physicist to let the philosopher to the philosophizing? Such might indeed be the right thing at a time when the physicist believes he has at his disposal a rigid system of fundamental concepts and fundamental laws which are also well established that waves of doubt cannot reach them; but, it cannot be right at a time when the very foundations of physics itself become problematic as they are now. At a time like the present, when experience forces us to seek a newer and more solid foundation, the physicist cannot simply surrender to the philosopher the critical contemplation of the theoretical foundations; for, he himself knows best, and feels more surely where the shoe pinches. In looking for a new foundation he must make clear in his own mind just how far such concepts which he uses are justified, and are necessities.”-Albert Einstein,“Physics and Reality” The journal of the Franklin Institute [Volume.221, No. 3, March 3, 1936]

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