Happy Valentine’s Day everyone… well, unless you were expecting hints for supersymmetry (SUSY) at the LHC. Last night the ATLAS collaboration posted the results for one of its supersymmetry searches to the arXiv. They corroborate last month’s results from CMS on a similar type of search. (The CDF site has an excellent public summary that should be at the right level for physics enthusiasts with no formal background.)

### What is supersymmetry?

**Supersymmetry** is an extension of the Standard Model in which every particle and anti-particle has a superpartner particle with a silly name, such as “gluinos” as the partners of gluons and “squarks” as the partners of quarks. The neat thing about supersymmetry is that the partner of a matter particle is a force particle (with a prefix *s*-), while the partner of a force particle is a matter particle (with a suffix *-ino*). SUSY does a lot of great stuff for us theoretically, but it must be broken so that the Standard Model particles and the SUSY particles are split up and have different masses. Because this is Valentine’s day, let’s leave the details of this splitting up to another post.

### What is the LHC telling us?

Here’s one of the key plots from the ATLAS paper (which includes the CMS result):

I’ll not get into the details here and will keep the discussion as accessible as possible. The axes of the plot are parameters in a particular supersymmetric model. The horizontal axis is the “universal scalar mass” *m0* (related to the mass of the squarks) while the vertical axis is the “universal gaugino masses” (related to the mass of the gluinos and its cousins). The area inside the curves (lighter masses) are ruled out. The red line is the ATLAS result, the black line is the recent CMS result, and the other lines are various exclusions from older experiments.

These parameters aren’t quite the same as the masses of the superparnters, but they are related by some formulae which experts in the field have memorized. A good estimate for the stringency of the bounds on the actual superpartner masses come from the conclusion of the paper:

For a chosen set of parameters within MSUGRA/CMSSM, and for equal squark and gluino masses, gluino masses below 700 GeV are excluded at 95% CL.

Some translations:

**MSUGRA/CMSSM**: These stand for “minimal supergravity” and “constrained minimal supersymmetric Standard Model.” The most general supersymmetric version of the Standard Model has over 115 free parameters… this would be a nightmare to plot. For simplicity, experimentalists typically plot their results against simplified reference models with much smaller parameter spaces.**Squark**and**gluino masses**: squarks are the partners of quarks and gluinos are the partners of gluons. The experiment is setting a lower bound on these masses. (Recall: heavier things are harder to produce.) The 700 GeV lower bound on the squark/gluino mass (in the case where they’re equal) is much heavier than any particle in the Standard Model—recall that the top quark is ‘only’ 172 GeV.**95% CL**. This is a**confidence level**that explains the statistical strength of this bound. Roughly it answers the question, “based on the data, how sure are you of the statement you’re making?” Here’s a great explanation.

### What’s actually happening at the LHC?

The general idea is that a common feature of most SUSY models is that when supersymmetric partner is produced at a collider, it will eventually decay into familiar stuff and a particle which escapes undetected. This escaping particle is called the **lightest supersymmetric particle** (LSP) and is a natural **dark matter **candidate, but its presence is only experimentally determined because the measured momenta of all the familiar stuff doesn’t balance. Thus a good way to search for the presence of supersymmetric partners is to look for:

- A high energy “normal” particles (typically QCD “jets”)
- Large “missing energy,” i.e. momentum that doesn’t add up

The high energies are important to tell us that something heavy (like a new particle) may have been involved, and the missing energy is important to tell us that something escaped undetected. By looking for decays of this type, ATLAS and CMS are able to constrain the existence of supersymmetric partners up to a certain mass. In fact, the reason why the LHC has been able to greatly improve the bounds on SUSY—even at such an early stage of running—is that the previous constraints from the Tevatron were limited not by how much data they could take, but by the energy scale of the collision.

Here’s an example, another plot from the ATLAS paper:

This plot shows the number of events in a particular range of “effective mass,” a kind of kinematic variable which characterizes the energy of an event. Here’s what’s happening:

- ATLAS records a
*bunch*of data over the past year or so. For each recorded particle collision (“**event**“), ATLAS records information about what its detectors see (“**signal**“). - Physicists go through this data when they want to search for new particles. The set of physicists who worked on this search focused only on the events whose signals included a lepton (
*e*or*μ*), QCD jets (quarks and gluons), and missing energy. - They then plot the number of events whose “effective mass” is in a certain energy range. This gives the data points on the plot above.
- In order to compare to the Standard Model, they run a “Monte Carlo” simulation of the kind of signal that
*known physics*would produce in this particular channel. These are all of the different colored pieces of the histogram—they represent events that we*expect*to be counted even if there is no new physics in these events. - If the data points line up with the sum of expected events, then we conclude (up to a certain statistical significance) that there was no new physics observed.

For reference, the dotted line is the expected contribution from one particular choice of SUSY parameters. That line would have to be added to the Standard Model sum (shown as a thin red line); clearly the data points do not show this excess.

### What does this mean for supersymmetry?

This isn’t great news for supersymmetry. One of the appealing features of supersymmetry is that it can solve the hierarchy problem of the Higgs mass. This problem is only really solved, however, if the SUSY particles are not *that* much heavier than their Standard Model partners. Thus the more we push up the lower bound on the super partner masses, the more trouble we have explaining the Higgs paradigm within the Standard Model.

I think I am not yet enough of an expert to comment on how severe the recent ATLAS/CMS results are in terms of current favorite models of supersymmetry. However, I will note that the particular model that was used to make these bounds represents a very *narrow* subset of possible supersymmetric extensions of the Standard Model. As explained above, this is by necessity: a plot over a 115-dimensional parameter space is simply not possible. Most of these parameters are related in plausible ways and the bounds from ATLAS and CMS are probably farily robust over huge swaths of parameter space, but in principle there is a lot of freedom to tweak a parameter here or there to try to evade particular experimental bounds. [For experts: last I heard there was some nit picking about the tan-*β *dependence of these results?]

This is actually a fairly important point. For the past two decades theorists have worked hard to come up with clever supersymmetric models which can either give novel experimental signatures or which are otherwise “generic” in a way that is not captured by the usual models used to experimentally constrain SUSY. With the advent of the LHC era, however, more thought has gone into better interfacing with our experimental colleagues to connect the results of the LHC to a more robust set of SUSY parameters. (This is part of a larger shift in the particle physics community over the past decade to have better communication between our theoretical and experimental practitioners.)

Anyway, there’s one thing that’s for sure: the Standard Model particles will be without super partners once again on Valentine’s day.

PS — [from Cosmic Variance] apparently the White House is also due to release its FY2012 budget request this Valentine’s day. Given the push towards spending cuts, it’s not looking like fundamental science will get much love… but I’m crossing my fingers anyway. (I don’t want to get political, but fundamental research *is *an investment in the American science and engineering infrastructure and the future of the American economy.)