Here in France this time of the year is known as winter holidays among schoolkids, or winter conferences among particle physicists, which amounts to the same thing (unless you're a PhD student working 24h/day to meet the deadline). These days new experimental results pop up like mushrooms with the peak expected middle March at the Moriond conference. Last week new results from LHC SUSY searches were presented at the Aspen conference, both by CMS and ATLAS. The latest additions are the jets+MET search from ATLAS, and the photons+MET and dileptons+MET searches from CMS. The new ATLAS search provides the current best limits on the mSUGRA parameter spaceUnfortunately, for the moment ATLAS and CMS present their theoretical interpretations only in this obscure and contrived way. So it might be worthwhile to discuss the physics behind the above plot and its more general consequences.

At the current stage, SUSY searches are in fact searches for squarks and gluinos, the superpartners of the Standard Model quarks and gluons. That's because only superpartners carrying the QCD charge have had a chance to be produced at the LHC in reasonable quantities. With 45pb-1 of luminosity acquired so far, the LHC is sensitive to cross sections of order a picobarn. As can be read off the plot on the right, this roughly translates to a sensitivity to 600 GeV gluinos and squarks, slightly less than what you might naively guess from the mSUGRA plot. However, if squarks and gluinos have comparable masses one can profit from the squark+gluino associated production which has the largest cross section of all the production channels. The proximity of squark and gluino masses occurs in a large portion of the mSUGRA parameter space, that's why the exclusion limits extend up to 800 GeV masses in this case.

Thus the production processes are relatively straightforward, it's the decay where the supersymmetric hell breaks loose. In the popular SUSY scenarios squarks and gluinos decay to the lightest superpartner, usually a neutralino, who is an electrically neutral stable particle that escapes the detector. In the simplest case, the squark decays to 1 quark + 1 neutralino, while gluino decays to 2 quarks + 1 neutralino (via an off-shell squark). Thus the experimental signature of both squarks and gluinos is a number of energetic jets accompanied by missing energy carried off by the neutralino. This is precisely what is targeted by the jet+MET search in ATLAS and CMS, and it is the most robust signature of supersymmetry. However things can get infinitely more complicated. For example, if charginos (superpartners of W bosons and charged Higgs fields) are lighter than squarks, as is always the case in mSUGRA, a squark may choose to first decay to a chargino who then decays down the lightest neutralino. These cascade decays may spit electrons or muons on the way. Thus, ATLAS and CMS also search for jets and missing energy associated with one, two, or three leptons. This is slightly less robust, as the presence of light charginos is not guaranteed, but at the same time the leptons in the final state help to reduce the Standard Model background. Comparing the recent ATLAS 0-lepton and 1-lepton searches one finds that the former gives slightly better limits on mSUGRA, but that might be different in other SUSY scenarios.

So the cord tightens. With several final states already covered, and more to appear soon, it's getting harder to avoid the stringent LHC limits in most popular SUSY scenario. Nevertheless, the possibility of sub-TeV superpartners has not been completely excluded yet. Firstly, uncolored superpartners are not constrained by the LHC. Furthermore, gluinos and/or squarks with masses 500 GeV or less are still allowed as long as the mass splitting with the lightest neutralino is small enough, such that the supersymmetric events fail the missing energy cuts. Stops, that is the scalar superpartners of the top quark, are even less constrained due to the smaller production cross section and the pesky t-tbar background. As a last resort one can turn to R-parity violating scenarios which are not constrained by the current LHC searches.

To conclude this post and fulfill my weekly quota of malice and scoff, here is a picture shown at the end of the ATLAS talk in Aspen:

Hmmm. Sorry to disappoint you guys but it's not the "stop", it's the "wrong way"; a symbolic mistake in this context. Let's hope future discovery claims from ATLAS will be more carefully scrutinized ;-)

See also Peter's comments.

## Monday 21 February 2011

## Wednesday 16 February 2011

### What LHC tells about SUSY

The first SUSY searches using the full 2010 LHC dataset are out now, one from CMS and one from ATLAS. The nagging question is what are their implications for low-energy supersymmetry. Some answers can be found in this talk of Alessandro Strumia who provides a cute visualization of the impact of the latest LHC results:

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:

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.

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.

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