How to find SUSY with near-degenerate masses? In SUSY models, you can have the case that sparticles and their decay products have near-degenerate masses. For example
$$ m(\tilde \chi^\pm_1) - m(\tilde \chi^0_1) < 1\,\mathrm{GeV}$$
Then in the leptonic decay mode
$$ \tilde \chi^\pm_1 \rightarrow \tilde \chi^0_1 + \bar\nu + e^-$$
you'd have the electrons basically produced at rest, or their momentum will be at least well below what you can comfortably detect at a hadron collider. How would you detect SUSY in such a scenario?
(Assume that you can't just search for other SUSY particles or decay chains, since you are either doing a model-independent search and don't know how heavy gluinos etc. are, or your other particles are  out of range, or also degenerate in masses. Nature can be nasty.)


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*You certainly can't just look for a drop in total cross section (disappearing events), since the SUSY cross sections are way too low.

*I was wondering if you could use associated production to find these kind of decays, for example if you produce a Z along with your SUSY particles, you'd see a boosted Z decay balanced by nothing to the other side. Would that work?

*I heard these scenarios would be easier to study with the ILC. Is that just because of the cleaner events, and that you'd be able to see those displaced decays easier?

 A: It depends on the degree of degeneracy. Winos are split primarily by loop effects (because the leading tree-level splitting arises only from a dimension 7 operator) and have a mass splitting $m_{{\tilde W}^+} - m_{{\tilde W}^0} \approx 166$ MeV. Due to this small splitting, the charged wino propagates distances of order centimeters before decaying (usually to a soft pion and the neutral wino). So the experiments can look for a disappearing track. ATLAS has done this and excluded wino LSPs below about 270 GeV.
Higgsino LSPs have a larger tree-level splitting: it arises from dimension 5 operators and is of order $\frac{m_Z^2}{M_{1,2} - \mu}$. This is typically of order 10 GeV. This makes higgsinos very difficult to find. Associated production is the way to look, either in the monojet channel (missing energy recoiling against a hard jet) or in the vector boson fusion channel (tagging the event with two forward jets). You can see some recent theoretical work on such signatures here, here, or here, for instance. (This is not a complete list, but it should get you started.) The conclusion is that the LHC is only sensitive in such channels if the masses are very small. This is probably why we haven't seen experimental results along these lines yet: the reach just isn't good enough to say anything interesting yet.
The ILC (or TLEP, or any other future $e^+ e^-$ collider that may be built) would be much cleaner and doesn't have huge QCD cross sections to contend with, so yes, it would do better. LEP, for instance, has ruled out higgsinos up to about 100 GeV (approximately its kinematic limit).
