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:

• 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.

Unfortunately, most of this available parameter space has already been excluded by the LEP experiment back in the 90s. The failure to observe any superpartners of the Standard Model at LEP left only a narrow sliver of the parameter space close to the "vev=0". Now, the latest LHC results excluded a part of the remaining sliver, which is marked in the plot as the darker red 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.