Mass Degeneracy of the Higgsinos

The search for charginos and neutralinos at LEP2 can become problematic if these particles are almost mass degenerate with the lightest neutralino. Unfortunately this is the case in the region where these particles are higgsino-like. We show that, in this region, radiative corrections to the higgsino mass splittings can be as large as the tree-level values, if the mixing between the two stop states is large. We also show that the degree of degeneracy of the higgsinos substantially increases if a large phase is present in the higgsino mass term μ. CERN–TH/95–337 December 1995 On leave of absence from INFN Sezione di Padova, Padua, Italy. The search for charginos (χ̃) at LEP2 is one of the most promising ways of discovering low-energy supersymmetry. If the χ̃ decays into the lightest neutralino (χ̃) and a virtual W, it can be discovered at LEP2 (with a ∫ L = 500 pb) whenever its production cross section is larger than about 0.1–0.3 pb and mχ̃0 is within the range mχ̃0 >∼ 20 GeV and mχ̃+ −mχ̃0 >∼ 5–10 GeV [1]. Therefore, the chargino can be discovered almost up to the LEP2 kinematical limit, unless one of the following three conditions occurs: i) The sneutrino (ν̃) is light and the chargino is mainly gaugino-like. In this case the ν̃ t-channel exchange interferes destructively with the gauge-boson exchange and can reduce the chargino production cross section below the minimum values required for observability, 0.1–0.3 pb. However, in a large fraction of the parameter space where this effect is important, the two-body decay mode χ̃ → ν̃l is kinematically allowed and dominates over the conventional three-body decays χ̃ → χ̃lν, χ̃q̄q. The resulting signal, quite similar to the one caused by slepton pair production, allows the chargino search for much smaller production cross section, possibly as small as 20–60 fb [1]. ii) The χ̃ is very light (mχ̃0 <∼ 20 GeV). In this case the χ̃-detection efficiency diminishes, as the decrease in missing invariant mass makes the signal more similar to the WW background. Such a light χ̃ is allowed by LEP1 data, if the weak-gaugino mass (M) is small, M ≪ MW . It is however ruled out by gluino (g̃) searches at the Tevatron [3] in models which assume gaugino mass unification, M = αMg̃/(αs sin 2 θW ). It should also be mentioned that no study has attempted to optimize the analysis in the low-mχ̃0 region, while specially designed experimental cuts could improve the chargino detection efficiency. iii) ∆+ ≡ mχ̃+ −mχ̃0 is small (∆+ <∼ 5–10 GeV) and the χ̃ detection is problematic because of the lack of energy of the visible decay products [1]. In this letter, we concentrate on case (iii). Small values of ∆+ occur when the gaugino masses are much larger than MW . In this region, the lightest chargino and the two lightest neutralinos (χ̃,χ̃) are mainly higgsino-like and are nearly degenerate with mass ∼ μ. In ref. [5] it has been suggested that this parameter region (M ≫ MW and μ ∼ MW ), although problematic for chargino searches, can nevertheless be covered by neutralino searches. Indeed, in this case the χ̃–χ̃ production cross section at LEP2 is large (∼ pb) The parameter region where M and the higgsino mass (μ) are both small has been recently studied in ref. [2]. It has been recently shown [4] that single-photon tagging cannot be used to observe charginos in the higgsino region under consideration. Ref. [4] has also considered a gaugino-like region where ∆+ can become small in models without gaugino mass unification. and the mass difference ∆0 ≡ mχ̃0′ − mχ̃0 is always greater than ∆+, allowing a better identification of the visible decay products than in the chargino case. It is also worth recalling that the parameter region where M ≫ MW and μ ∼ MW has a special interest as a light higgsino-like chargino (together with a light stop) can increase the Standard Model prediction for Rb [6]. Here we point out that, for M ≫ MW and μ ∼ MW , ∆0 and ∆+ receive one-loop corrections proportional to m3t , which can be as large as their tree-level values. We will also show that in the small tan β region, the tree-level values of ∆0 and ∆+ can be reduced if the μ parameter has a non-trivial phase. Finally, we will comment on the implications for chargino and neutralino searches at LEP2. First let us recall that, in the higgsino region under consideration (M ≫ MW , μ ∼ MW ), the tree-level values of ∆0 and ∆+ are well approximated by a 1/M expansion 3 ∆0 = 2a M W M + 2b sin 2β μM W M +O(1/M) , ∆+ = [a + (a− 1)ε sin 2β] M W M + [(b− 1) + bε sin 2β] |μ|M 2 W M − a 2 2 cos 2β M W |μ|M2 +O(1/M ) , (1)