Simplified Gaugino-Higgsino Models in the Mssm

M.P.A. SUNDER Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster,
Wilhelm-Klemm-Straße 9, 48149 Münster, Germany

We present a tool to produce benchmarks with realistic mass spectra and realistic mixing in the gaugino-higgsino sector of the MSSM. We suggest as a next-to-minimal approach the use of benchmarks, whose mass spectra and mixing matrix elements are the result of a proper matrix diagonalisation at treelevel. We scan over the four relevant parameters for a specific grid of neutralino and chargino masses. We demonstrate how to define a measure for the quality of a fit, including a method to maximise properties such as the gaugino or higgsino content.

1 The gaugino-higgsino sector

The gauginos and higgsinos are the fermionic superpartners of the electroweak gauge-bosons and the two -valued complex scalar Higgs doublets that appear in the Minimal Supersymmetric Standard Model (MSSM). Through electroweak symmetry breaking (EWSB) these fermionic states mix to form either neutral neutralinos  or electrically charged charginos .

The neutralinos are mixed states of neutral bino , wino and higgsino fields ,


The charginos are mixed states of charged winos and higgsino fields ,


The other particles in the MSSM, such as the gluino and the squarks, are decoupled at values of around , in accordance with the current mass limits from supersymmetry (SUSY) searches [1, 2, 3, 4, 5, 6]. We shall focus on simplified MSSM models that have neutralinos and charginos as their lightest supersymmetric particles, considered in experimental studies such as [7, 8, 9].

These simplified gaugino-higgsino models are governed by only four additional MSSM parameters, which gives them some predictive value. These parameters are,


where is the effective higgsino mass parameter originating from the superpotential , is the ratio of the two scalar Higgs vacuum expectation values (vevs) and , whilst and are the gaugino mass parameters that originate from the soft supersymmetry breaking (SSB).

2 The minimal vs. non-minimal approach

The minimal approach for SUSY searches in this sector, e.g. as used by  [10, 11, 12, 9], is to set a mass spectrum without any actual mixing among the gauginos and between gauginos and higgsinos. This approach is applicable in three different scenarios, namely in case of:

Figure 1: Here, we visualise the regions of parameter space wherein the minimal approach is valid, these are the shaded areas corresponding to either or both .
  • a bino lightest supersymmetric particle (LSP) with mass and an additional doublet of degenerate wino next-to lightest supersymmetric particles (nLSPs) at , which requires and .

  • a doublet of degenerate wino LSPs with masses and an additional bino nLSP at , which requires and .

  • a triplet of degenerate higgsino LSPs with masses , which requires that .

Independently of these three scenarios are applicable in two regions of the parameter space spanned by as depicted in Fig. 1. We suggest a next-to-minimal approach in [13] to obtain benchmarks that are applicable in cases where gaugino and higgsino states mix, as demonstrated in [14]. This method is applicable in the whole parameter space depicted in Fig. 1.

Instead of setting the mass spectrum, we scan over the parameters in Eq. 3 and compute the mass spectrum by proper diagonalisation of the mass matrices at tree-level. In this way, benchmarks that are extremely fine-tuned or unphysical will not be found, one can explore the relationships between mass-splittings and coupling strengths by using the appropriate mixing matrix elements and constrain certain regions in the MSSM parameter space more directly.

The search region must be defined, whilst taking into account approximate relations and parameter transformations that do not affect the mass spectra or particle content.

3 Case-Study: Higgsino-like benchmarks with equidistant mass splitting

We present an example scenario of higgsino-like benchmarks with equidistant mass splitting to clarify how one sets up a parameter scan for a specific scenario.

The chosen scenario of an equidistant mass-splitting between the chargino and the two neutralinos and motivates a parametrisation of the mass spectrum in terms of , the mass of at the intermediate scale, and , the total size of the mass-splitting between and . The neutralino masses are then given by,


This parametrisation was used to define a grid from which we sampled benchmarks in a region that would be accessible for LHC searches given in Tab. 1. The targeted spectra in Tab. 1 and the general parameter dependencies of the mass spectrum motivate an initial scan-range given by,


where either sign of the -parameter yields equally good benchmarks, though with a lower higgsino content once .

The randomly selected benchmarks were scored using three dimensionless selection criteria, as shown in Eq. 6. The deviation between found and targeted benchmarks was constrained by an upper limit on the benchmark’s score at .

Targeted mass(-splitting) Min. Max.
GeV GeV 1 GeV
Table 1: The targeted chargino masses and mass-splitting in the parameter scan for the scenario of higgsino-like benchmarks with equidistant mass-splittings. The column refers to the used grid-spacing of either or .

The average higgsino content of was maximised by reweighting the score with


which preferentially selects the benchmark with the higher higgsino content in case of a comparable agreement with the targeted mass spectrum. A redefinition of is usable to maximise other benchmark properties.

Figure 2: This figure shows the average higgsino content of of and a fine-tuning measure of the benchmarks that were found for the subscenario wherein . If the fine-tuning for two benchmarks relates as then the number of found acceptable benchmarks for is a factor less than for .

In Fig. 2 we demonstrate the feasibility of finding benchmarks for the subscenario with . We succeeded in finding benchmarks with reasonable higgsino contents of for independent of the targeted . Although, from the amount of fine-tuning made it increasingly more difficult to find these benchmarks, which can be seen by the absence of benchmarks or the poor maximisation of the higgsino content. The fine-tuning measure was chosen as the logarithms of the product of the allowed acceptable variation of the benchmark parameters divided by the total search range for each of those parameters.

4 Conclusions

We argue that the discussed minimal approach has only a limited applicability and does not constrain directly the parameter space of the MSSM in the gaugino-higgsino sector. We suggested here and in [13] a next-to-minimal approach wherein the whole parameter space in the gaugino-higgsino sector can be explored by scanning over the MSSM parameters . Use of this approach constrains the MSSM parameter space more directly and guarantees that the used benchmark is representative of a true non-simplified MSSM benchmark. We demonstrate that this approach is feasible in finding a high resolution grid of benchmarks for the particular scenario of higgsino-like benchmarks with equidistant mass-splitting, which would not be treatable in the minimal approach.


This work has been supported by the BMBF under contract 05H15PMCCA and the DFG through the Research Training Network 2149 ”Strong and weak interactions - from hadrons to dark matter”.



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