SUSY Mass Upper Limits

Supersymmetry remains the most popular theoretical extension of the Standard Model of particle physics.  It's not hard to see why; in addition to its structural appeal, many people have spent years working on it.  With all that time invested, a minor detail like it not showing up at the LHC is hardly going to dissuade us.

What has changed is the perspective we take, especially as far as the motivation for supersymmetry is concerned.  The traditional arguments about avoiding regions of theoretical fine-tuning have taken a battering from the combination of the observed Higgs mass, and the high exclusion limits on superpartner masses.  These already force most models to be tuned to at least one part in a thousand, often worse.

But once we abandon fine tuning as a motivation for supersymmetry, we also remove one of the main arguments for electroweak supersymmetry; that is, for the superpartners to be light enough to show up at the  LHC.  And this is reflected in recent model building, with theorists increasingly willing to consider models where some or all of the superpartners are heavy; for example, mini-Split SUSY models put most of the new scalar particles at a hundred to a thousand TeV, with the new fermion masses around one to ten TeV.

Against this, a recent paper develops some interesting arguments for upper limits on superpartner masses.

The key argument relies on another popular motivation for SUSY: dark matter.  In most commonly considered models, SUSY automatically contains a dark matter candidate with the correct expected cosmological abundance.  Specifically it is usual to include a symmetry, R-parity, to prevent proton decay.  All the Standard Model particles have zero R-charge, so the lightest state with non-zero R-charge is automatically stable; and if electrically neutral, it can be dark matter.

The simpler case is a neutralino: a fermionic partner of the photon, Z or Higgs.  These objects interact through the electroweak force, so the WIMP miracle tells us they should have masses in the 100 GeV to 10 TeV range.  In fact for the Zino and Higgsino, it is well known that a mass of 2.5 TeV gives the correct abundance.  Lower masses are easy to achieve if their are cancellations in the annihilation processes, but not so larger masses.  This gives us one upper limit on superpartner masses.  (Unfortunately, this is probably already too heavy to find at the LHC without a lot of data.)

The paper I'm considering today examines the other standard example of SUSY dark matter, the gravitino.  This is the supersymmetric partner of the graviton, and so interacts gravitationally.  These interactions are much weaker than for the neutralino, so you usually require a different way to set the current cosmological density than in the case of the WIMP miracle.  Hall and his collaborators consider the different possibilities, and conclude that the mass of the other supersymmetric particles must be less than 20 TeV.  Unfortunately that doesn't quite prove they must be observable at the LHC, but it is close.

If the gravitino is very light, it can be in thermal equilibrium in the early Universe.  It has to be light due to the weak gravitational interactions; it takes a long time to reach equilibrium, but it must do so before the Universe cools too much.  Once the typical energy in particle collisions is less than the gravitino mass, it is out of equilibrium pretty much by definition.  The net result is that the gravitino must be a million times lighter than the electron or less.  We then have a theoretical upper limit on the superpartner masses, which is around 10 TeV.  Heavier masses would require couplings too large to be physical, roughly speaking leading to an error like probabilities bigger than one.

For gravitinos above this scale but lighter than the other superparticles, gravitinos are produced in the scattering and the decay of superpartners.  Usefully, these two processes not only depend on the gravitino and other superpartner masses, but in different ways.  In particular, scattering is enhanced for light gravitinos, simply on kinematic grounds.  In contrast the second-lightest R-charged particle must decay to the gravitino, so the number of gravitinos produced this way is independent of their mass, and hence the density is proportional to it.

Combining all of this, we find that the lightest visible superpartner must have a mass less than 20 TeV (which occurs for a gravition mass around 10 GeV).  The overall result is shown in this plot, figure 1 from the paper:

The coloured regions are ruled out by various observations, not all of which I discussed.  The white regions are allowed, the horizontal axis is the gravitino mass and the vertical axis the superpartner masses.  The left region is where the gravitino is produced thermally, the middle region through other means and the bottom-right is where the gravitino is no longer the dark matter particle.

There are a number of assumptions made here, some of which are relaxed in the paper.  The conclusions don't change much: the lightest superpartner is probably 20 TeV or less.  Of course, one of the biggest assumptions is that supersymmetry explains dark matter; relax that assumption and all limits disappear.  But I don't think that's a slight on this work, which makes assumptions that have been standard in the community for many years.  Rather, it's another point to consider in model building, to try and reign in the wilder flights of fancy.