The advent of supersymmetry (SUSY) has led the building of particle theory models linking a remarkably wide range of physical phenomena. While initially proposed on aesthetic grounds that nature should be symmetric between fermions and bosons, the fact that supersymmetry allows for the cancelation of the quadratic Higgs divergence allowed the building of consistent models valid up to the GUT (MG) or Planck scales. The extension of supersymmetry to a local gauge theory,
supergravity [1,2], led to the development of grand unified (GUT) models [3,4] giving a description of physics from the M_G down to the electroweak scale incorporating the successes of the Standard Model(SM). Subsequently, LEP data experimentally confirmed the validity of the idea of SUSY grand unification. Further, an additional feature of SUSY is that models with R parity invariance automatically give rise to a candidate, the lightest neutralino N_1, for the astronomically observed dark matter [5,6] deeply linking particle physics with cosmology, and detailed theoretical calculations confirm that GUT models can also achieve the experimentally observed amount of dark matter in a natural way. (For a review of current analyses see e.g. [7].) A large number of experiments are now under way to try to detect SUSY dark matter in the Milky Way. (For a review of the current dark matter experiments see e. g. [8].) Thus it is possible to construct models that encompass the full energy range of particle physics and simultaneously reach back into the early universe at times ~ 10^(-7) seconds after the Big Bang.
If supersymmetry ideas are correct, then the Large Hadron Collider(LHC) is expected to produce the N_1 particles. Similarly, the large one ton dark matter detectors, currently under development, will cover a large amount of the allowed SUSY parameter space and may detect directly the Milky Way dark matter particles. Theory predicts that these two should be the same, and the question arises as to how one might verify this. The direct approach to this problem would involve having the dark matter detectors measure the nuclear differential cross section for the incident dark matter particle scattering from the detector atomic nuclei, and comparing these with the differential cross sections occuring for the neutralinos produced in the LHC. Such measurements of course may be many years in the future, and one would like to see if more immediate measurements might give strong indications for the equivalence of the astronomical and accelerator phenomena. To investigate this it is necessary to chose a SUSY model, and we consider in this paper mSUGRA [1,2] (which has been used in many other LHC calculations).
mSUGRA depends upon four parameters in addition to those of the SM: m_0, the universal scalar soft breaking parameter at M_G; m_1/2, the universal gaugino mass at M_G; A_0, the universal cubic soft breaking mass; and tanbeta = H2/H1 at the electroweak scale (where H_(1,2) gives rise to (up, down) quark masses). The current accelerator and cosmic microwave background (CMB) data of WMAP limit the allowed parameter space to three regions: (1) the co-annihilation region where m_0 and m_1/2 are both relatively small, (2) the focus/hyperbolic region where m_0 is large (>~ 1 TeV) and m_1/2 is small and (3) the funnel region where both m_0 and m_1/2 are large. If, however, the muon magnetic moment anomaly, which currently shows a 2.7 sigma deviation from the SM prediction [9] is a valid deviation, then as seen e. g. in Fig. 1,only the co-annihilation region survives. We examine in this paper the possibility that the dark matter allowed region is in fact the co-annihilation band. It should be noted that the existence of the co-annihilation region is not a special property of mSUGRA, but also arises in a wide variety of other SUGRA models with non-universal scalar and non-universal gaugino masses at M_G, so that the type of analysis given here can be used in other models.
The special feature of the co-annihilation region is the near degeneracy of the N_1 and the light stau, i. e. a mass difference of only 5 - 15 GeV. The narrowness of the allowed band seen in Fig. 1 is not due to a fine tuning but rather from the rapid variation of the exponential Boltzman factor that governs the amount of dark matter in the relic density calculation [see e. g. 10]. Thus if the stau is too much heavier than the neutralino, not enough dark matter is created in the early universe, while if it lies too close to the neutralino too much will be created. This near degeneracy, however, gives a unique accelerator signal required by the hypothesis that the N_1
is the dark matter particle. If, indeed, the LHC were to verify this near degeneracy it would not of course prove that that the N_1 is the dark matter particle (only a direct detection of the dark matter would be able to do this), but it would give a strong indication of this possibility.
The question thus is whether such a small mass difference is measurable at the LHC. At the LHC one expects that gluinos and squarks will be the primary SUSY particles produced, and these will generally cascade down to lighter particles e. g. pairs of the heavier neutralino N_2. Each N_2 can then decay according to
N_2 -> tau + stau -> tau + (tau + N_1) (1)
The first tau will be hard (since the N_2 - N_1 mass difference is large), while the second tau is soft (since the stau and N_1 mass difference is only ~ (5 - 15) GeV). We consider therefore the signal of two hard taus + one soft tau + E_Tmiss to isolate the co-annihilation band, and use this signal to determine the mass difference. There are of course SM backgrounds that need to be eliminated (e. g. t - tbar production, etc.) before a realistic determination of the mass difference can be made. One might also ask how unique the signal of Eq. (1) is. For example, if the light stau was heavier but nearly degenerate with the N_2 (rather than the N_1), one would also get a signal similar to Eq. (1). In this case the N_1 could no longer be the dark matter candidate. One could,
however, check whether this possibility occurs by an LHC measurement of the selectron or smuon mass (which effectively determines m_0).