So far, no signal consistent with supersymmetry has been found. Experiments have set a number of direct and indirect limits, which are briefly summarised in the following.
As already mentioned in Section 7.1.3, indirect limits arise from processes that are either very rare or forbidden in the SM but have contributions from sparticle loops. These includeµ → eγ, b → sγ, neutral meson mixing, electric dipole moments for the neutron and the electron, etc.
There are also virtual sparticle effects on SM predictions like the anomalous magnetic moment of the muon.4 The measurements of such processes already exclude some otherwise viable super-symmetry models.
The WMAP total cold dark matter limit,Ωh2 <0.14[134], can be taken as an indirect constraint from experimental cosmology. In supersymmetry with exactR-parity conservation, the LSP might be this cold dark matter. The best supersymmetric dark matter candidate (for detection) is the lightest neutralino [43]. The sneutrino has been largely ruled out: the mass range550to2300GeV gives a cosmologically interesting relic density, but the scattering cross section of a sneutrino in this range with nucleons is much larger than the limits found by direct dark matter detection experiments [135]. A gravitino LSP, as is commonly found in GMSB models, might be the cold dark matter but would be impossible to directly detect because it interacts too weakly. In order
4The latest BNL measurements ofaµdeviate by3.4σfrom the SM predictions [2]. This could be interpreted as a hint for new physics, in particular supersymmetry.
7.3. EXPERIMENTAL CONSTRAINTS 97
to get the observed dark matter density today, the thermal-averaged effective annihilation cross section times the relative speedvof the LSPs should be abouthσvi ∼1pb∼α2/(150GeV)2[43].
To first approximation, a neutralino LSP has the correct electroweak interaction strength and mass.
More detailed and precise calculations reveal that an efficient neutralino LSP pair annihilation is required in order to not exceed the observed cold dark matter density. This can be turned into a limit for the MSSM (or mSUGRA) parameter space. Fig. 7.7 shows the mSUGRA parameter space taking into account a cold dark matter density consistent with WMAP data [136].
However, it is important to point out that simple extensions can completely change the predicted relic dark matter density in supersymmetry models, without changing much the predictions for collider experiments. Thus, the dark matter limit must be taken with care.
The most significant direct constraints on supersymmetric particles have been obtained at LEP and at the Tevatron collider. All following limits are at95%confidence level and assume the MSSM, in particular with exactR-parity conservation. Further constraints in less canonical modes can be found in Ref. [2].
The lower mass limits for charged sparticles from the LEP experiments are nearly half of the beam energy, which reached a centre-of-mass energy of209GeV. Fig.7.8 shows in the left plot the combined LEP constraints for sleptons, depending on the lightest neutralino mass. These constraints are very robust, as few model assumptions have been made. Smuon masses below95 to 99GeV, depending on the χ˜01 mass, are excluded as long as theµ˜R −χ˜01 mass difference is larger than5GeV [2,137].
In the case of staus, the subsequent decays of τ-leptons lead to reduced selection efficiencies.
Furthermore, the enhanced mixing of left and right-handed components has to be considered, since it influences the coupling to theZboson. In the worst case of no coupling between the stau and Z boson, stau masses smaller than86 to 95GeV are excluded, depending again on the χ˜01 mass, and assuming a stau-χ˜01mass difference of at least7GeV [2,137].
Selectrons are excluded with masses below 100GeV, for χ˜01 masses < 85GeV, and for µ =
−200 GeVandtanβ = 1.5[2,137]. Additionally, a lower limit of73GeV can be set indepen-dently of theχ˜01 mass.
The LEP chargino mass bound is 92GeV, assuming gaugino and sfermion mass unification [2, 137]. Lower mass limits for the lightest neutralino can be derived indirectly at LEP from: chargino pair production, slepton, and Higgs boson searches. The absolute lower limit ismχ˜0
1 >47GeV.
The most constraining squark and gluino mass limits come in general from Tevatron Run II. The canonical supersymmetry searches performed at the Tevatron experiments CDF and DØ select multiple jets plus missing transverse energy or three isolated leptons in the final state. Results from DØ, based on an integrated luminosity of∼2.1fb−1, exclude squark masses below379GeV and gluino masses smaller than 308GeV, within the framework of mSUGRA with tanβ = 3, A0= 0, andµ <0[138]. This exclusion together with previous results from other experiments is shown in the right plot of Fig.7.8.
Comparable exclusion results have been obtained by the CDF experiment, based on an integrated luminosity of2.0fb−1: in a mSUGRA scenario withA0 = 0,µ < 0andtanβ = 5, squark and
100 200 300 400 500 600 700 800 900 1000
100 200 300 400 500 600 700 800 900 1000 0
100 200 300 400 500 600 700 800 900 1000 0
100 200 300 400 500 600 700 800 900 1000 0 allowed by the older cosmological constraint0.1 <Ωh2 <0.3has medium blue shading, and the region allowed by the newer cosmological constraint0.094 < Ωh2 < 0.129 has very dark blue shading. The disallowed region wheremτ˜1< mχe0has dark red shading. The regions excluded byb→sγhave medium green shading, and those in plots a) and d) that are favoured bygµ−2at the 2-σlevel have medium pink shading. A dot-dashed line in plot a) delineates the LEP constraint on the selectron mass and the contours mχe± = 104 GeV(mh = 114 GeV) are shown as near-vertical black dashed (red dot-dashed) lines in plot a) (each panel).