1. The ALEPH searches  for Lightest Chargino pair production at centre-of-mass energies up to 208 GeV
2. The LEP combined result of slepton searches from the LEP SUSY WG
3. The LEP combined result of Higgs searches in the hZ channel from the LEP HIGGS WG

1. ALEPH Collaboration,  Absolute mass lower limit for the lightest neutralino of the MSSM from e+e- data at sqrt(s) up to 209 GeV, Phys. Lett. B583 (2004) 247 .
2. LEP SUSY Working Group, Combined LEP Selectron/Smuon/Stau Results 183-208 GeV, LEPSUSYWG/04-yy.1
3. LEP Higgs Working Group,  Search for the Standard Model Higgs boson at LEP,  CERN-EP/2003-011

The Model considered is a MSSM with lowest order Gaugino and Sfermion Mass Unification at GUT scale.  The free parameters are:

1. tanß   Higgs v.e.v. ratio
2. M₂     SU(2) gaugino mass
3.  µ       Higgs mixing mass term
4. M₀     Common Sfermion Mass term at GUT
5. A_t      Trilinear coupling in the stop sector
6. M_A     Pseudoscalar Neutral Higgs Mass

Method

The method follows the one described in detail in ALEPH 2000-019,CONF 2000-016 (see also Phys. Lett. B499 (2001) 67).
The most recent calculations of the radiative corrections in the Higgs sector (see Nucl.Phys. B580 (2000) 29 ) , have
been used (as implemented in the  HZHA generator ). The effect of the large top Yukawa couplings are
conservatively neglected in the renormalization group equations used to calculate the weak scale stop masses.
For a given set of tanß, M₀and M₂ values, the largest predicted Higgs boson mass M_h,maxis determined setting a
large value for M_A (2 TeV/c²) and maximizing the stop mixing with respect to the A_t - µ cotß combination.
In the limit of large M_A the lightest MSSM neutral Higgs bosons behaves as in the Stantard Model (decoupling limit),
and it is sufficient to compare M_h,max with the lower limit on the SM Higgs boson mass set by the experiments,
i.e. 114.4 GeV/c²  (at 95% C.L.). In this way  a lower limit on M₂ , hence on M_LSP, is obtained; this limit is the
strongest for low values of tanß and low values of M₀. As shown, for example, in Eur.Phys. J. C17 (2000) 223 ,
the result is robust against possible pathological situations that could arise when scanning over M_A.
A lower limit on M₂ can be derived independently from the negative result of slepton searches. This in general depends
on M₀, µ and tanß. However, when focussing on the so-called corridor (chargino -sneutrino degeneracy) the µ dependence
is removed and a lower limit on M_LSP as a function of tanß is obtained by minimizing with respect to M₀.

These constraints coming from Higgs boson and slepton searches are combined with those  derived by the negative
result of chargino and neutralino searches.
Theoretical uncertainties on M_h have been taken into account by increasing the calculated mass by 2 GeV/c².

Description of the plot:

       1.  For tanß < 3.3 the lower limit is set at large M₀:

            + by Higgs boson searches for tanß < 2.1 ;
            + by chargino searches for 2.1 < tanß< 3.3

       2.  For tanß > 3.3 the limit is set at small M₀ :

             + by the Higgs boson searches for tanß < 3.45 ;
             + by slepton searches for tanß > 3.45 .

           and depends on the degree of coverage of the chargino-sneutrino corridor by these searches.

Under these hypothesis the lower limit on M_LSP is found at large tanß at about 47 GeV/c².

The results should be intented at 95% C.L. and are valid for  M₀ < 1 TeV/c²  and  M_top = 178 GeV/c². For comparison, the result obtained for M_top=175 GeV/c² is also shown, illustrating the strong dependence of the Higgs constraints on the choice of the top mass (see also ALEPH 2000-019,CONF 2000-016). However the bounds
at large tanß, being set by slepton searches, are not affected, under these hypothesis, by the value used for M_top.

Finally, a theoretical uncertainty O(GeV) affects the lower mass limit due to the use of tree-level gaugino masses
and of the lowest order relation for gaugino unification.