title: The Scale of Superpartner Masses and Electroweakino Searches at the High-Luminosity LHC
authors: Jia Liu Navin McGinnis Carlos E. M. Wagner Xiao-Ping Wang
text: 
  
  EFI-20-16
  
  
  
  
  
  
  
  jialiu@pku.edu.cn
  School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
  Center for High Energy Physics, Peking University, Beijing 100871, China
  
  
  
  
  nmmcginn@indiana.edu
  Physics Department, Indiana University, Bloomington, IN 47405, USA
  High Energy Physics Division, Argonne National Laboratory, Argonne, IL, 60439
  
  
  cwagner@anl.gov
  
  High Energy Physics Division, Argonne National Laboratory, Argonne, IL, 60439
  
  
  
  hcwangxiaoping@buaa.edu.cn
  
  High Energy Physics Division, Argonne National Laboratory, Argonne, IL, 60439
  
  
  
  
  
  
          
  
  
  
  
  
  
  
  
  
  
  Searches for weakly interacting particles is one of the main goals of the high luminosity
  LHC run. In this work we study the well motivated cases of electroweakinos with mostly
  Wino and Bino components. We show the relevance of squark induced t-channel production in defining the production cross section and hence the LHC reach.
   Moreover, a realistic evaluation of the decay branching ratios show a strong dependence
   on the sign of μ and, for negative values of μ, on the relative size of the ratio of 
   μ to the gaugino masses compared with tanβ.  Overall, unless it is kinematically
   suppressed, or specific conditions are fulfilled, the Higgs decay channel is the most significant 
   one, and the trilepton channel becomes subdominant with respect to final states including
   bottom quarks.  Although the properties are different than in the Higgsino-Bino case,
   also in this case the discovery reach extends to mass values that are significantly larger than the 
   ones  probed at current luminosities, leading to a strong motivation for the search for 
   electroweakinos in the high luminosity LHC run.
  
  
  
  
  
  
  
  
  
  
  The Scale of Superpartner Masses and Electroweakino Searches 
  at the High-Luminosity LHC
      Xiao-Ping Wang
      December 30, 2023
  ========================================================================================
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  § INTRODUCTION
  
  
  Searches for new particles at the LHC have so far provided no evidence of the existence of new physics 
  at the TeV scale. These searches are quite sensitive to strongly interacting particles and have excluded
  the presence of vector like quarks or, in the case of supersymmetry, squarks and gluinos, for masses beyond 1 TeV. For examples of recent searches see Refs. <cit.>.   It is, however, premature to announce the absence of new physics at the 
  electroweak scale due to these observations.  On one hand, these searches have been mostly interpreted within
  simplified models with simple decay channels designed to maximize the observability of new particles and
  hence the bounds may be relaxed in the case of more complicated decay channels. More 
  importantly, the searches become mostly insensitive to weakly interacting particles for which
  the production cross sections become much weaker than the strongly interacting particle ones.
  
  Weakly interacting particles are naturally involved in one of the main hints for physics at the weak
  scale, namely Dark Matter <cit.>.  The Dark Matter particle appears naturally as part of the weakly
  interacting sector of extensions of the Standard Model, in a similar way to the appearance of
  the neutrino in the Standard Model (SM) of particle physics.  For heavy particles with masses
  of the order of the weak scale, the Dark Matter particle is identified with the lightest of these
  new particles and the stability of these neutral and weakly interacting particles demand the 
  presence of a symmetry, usually discrete (such as R-parity in the MSSM), that forbids the decay of this particles into SM ones.   
  Production of these beyond the SM particles leads to decays into Higgs and
  weak gauge bosons and the Dark Matter particle which is observed as missing energy.
  
  A particularly well motivated electroweak sector that has been studied in quite detail both
  theoretically as well as experimentally is the one implied by low-energy supersymmetric extensions,
  and in particular the one associated to the Minimal Supersymmetry Extension of the SM
  (MSSM)  <cit.>. In this case, the electroweak sector consists of two Higgs doublets and their
  corresponding superpartners (Higgsinos) as well as the superpartners of the weak and
  hypercharge gauge bosons (Winos and Bino, respectively).  The couplings of these
  particles to the gauge bosons and the Higgs bosons are dictated by the invariance 
  under gauge and supersymmetry transformations, the latter being violated only softly 
  by dimensionful parameters.   These mass parameters include the Wino M_2 and Bino
  M_1 masses, as well as the Higgsino  mass parameter μ.  The Higgs sector
  is characterized by the mass of the CP-odd Higgs m_A and tanβ, the ratio
  of the Higgs vacuum expectation values.   Due to the supersymmetry relations, the
  mass of the colored particles also play a role in determining the lightest Higgs mass
  and also contribute to the t-channel production cross section for gaugino-like particles (the Higginos
  couple very weakly to the first and second generation quarks.) <cit.>.
  
  In a previous article <cit.>, we studied the search for particles in the Higgsino-Bino sector
  of this model, assuming that the Wino mass is of order of a few TeV and a decoupled sfermion spectrum. We demonstrated
  the complementarity of the production of electroweakinos via the heavy Higgs
  bosons with the ones induced by the direct production of these particles via 
  gauge bosons and, due to the smaller production cross sections, 
  we  showed that the regions probed at present  are far weaker than
  the ones that are usually displayed experimentally for the Wino  case.
  Moreover, we showed that the discovery reach of the high luminosity 
  LHC go far beyond the current probed region.  The final states including gauge
  and Higgs bosons played a similarly relevant role in this analysis.
  
  In this work, we extend this analysis to the Wino case, which differs from the
  Higgsino case in several relevant aspects. On one hand the production cross
  section has a relevant dependence on the masses of the first and second generation
  squarks.  On the other hand, the branching ratios of the decay of the neutral
  Winos into Higgs and Z final states depend  on the sign of μ,
  the Higgs decay being in general dominant for positive μ, and also
  for negative values of μ unless one is in the proximity of a so-called
  blind spot solution, that occurs when the ratio of |μ| to the average gaugino
  masses is of order tanβ/2.  This implies a more complex (and weaker)
  reach for Winos to the one that is usually shown in experimental searches, 
  that rely on large branching ratios and very heavy squark masses. 
  
  This work is organized as follows. In section <ref>, we briefly review the mass eigenstates
  and mixing for the Wino case and calculate its decay branching ratio to Z and SM Higgs.
  In section <ref>, we point out the squark mass dependence for the production 
  cross section and show the parametric dependence of the Wino decay branching ratios on μ and tanβ.
  In section <ref>, we show the resultant, current bounds and future reach of the electroweakino 
  searches. We reserve section <ref>, for our conclusions.
  
  
  
  
  
  § MASS EIGENSTATES AND COUPLINGS TO Z AND SM HIGGS
  
  
  
  The mass eigenstates and decays modes of all electroweakinos are determined by only four parameters, the Wino and Bino masses M_2 and M_1, the Higgsino mass μ, and the ratio of vacuum expectation values of the Higgs doublets tanβ. The resulting mass matrices for the neutralinos and charginos in terms of these parameters are given by 
  
  
  M_N=   [         M_1           0  -c_βs_Wm_Z   s_βs_Wm_Z;           0         M_2   c_βc_Wm_Z  -s_βc_Wm_Z;  -c_βs_Wm_Z   c_βc_Wm_Z           0          -μ;   s_βs_Wm_Z - s_βc_Wm_Z          -μ           0 ],
  
     M_C=[        M_2 √(2)s_βm_W; √(2)c_βm_W          μ ],
  
  where c_W=cosθ_W, s_W=sinθ_W, m_Z and m_W are the Z and W gauge boson masses, and θ_W is the weak-mixing angle. For further details of the couplings and mass matrices of neutralinos and charginos see, for instance, Ref. <cit.>.
  
  The neutralino mass eigenstates are given after diagonlization Z_N^T M_N Z_N = m̃_χ where m̃_χ= diag(m_χ_1^0,m_χ_2^0,m_χ_3^0,m_χ_4^0) and the mixing matrix, Z_N, encodes the admixtures of the gauge eigenstates in the neutralinos. In general, the particular form of Z_N is not particularly illuminating. However, in this paper we will focus on the case when the Higgsinos are heavy and the low energy spectrum consists of Wino- and Bino-like states. In the limit of |μ| ≫ M_1, M_2, we find for the mixing matrix Z_N
  
  
  
      (
      [                1-m_Z^2s_w^2/2μ^2( 1+m_Z^2c_w^2s^2_2β/( M_2-M_1)^2) m_Z^2s_2w/2μ^2( M_2-M_1)[ μ s_2β + M_2 +m_Z^2s^2_2β c_2w/ M_2-M_1]                             -m_Zs_w( sin_β +cos_β)( μ+M_1)/√(2)μ^2                              m_Zs_w( cos_β -sin_β)(μ-M_1 )/√(2)μ^2; m_Z^2s_2w/2μ^2( M_1-M_2)[ μ s_2β + M_1 +m_Z^2s^2_2β c_2w/ M_2-M_1]                1-m_Z^2c^2_w/2μ^2(1+m_Z^2s_w^2s^2_2β/2( M_1-M_2)^2)                              m_Zc_w( sin_β +cos_β)( μ+M_2)/√(2)μ^2                             -m_Zc_w( cos_β -sin_β)(μ -M_2)/√(2)μ^2;      m_Z  s_w/μ^2[( μ s_β + M_1c_β)+m_Z^2c^2_ws_2β s_β/( M_2-M_1)]         -m_Zc_w /μ^2[μ s_β + M_2c_β+m_Z^2s_w^2s_2β s_β/( M_1-M_2)]                                 1/√(2) -m_Z^2s_β(s_β+c_β)/2√(2)μ^2                                  1/√(2)+m_Z^2s_β(c_β-s_β)/2√(2)μ^2;          -m_Zs_w/μ^2[μ c_β + M_1s_β+m_Z^2c^2_ws_2β c_β/( M_2-M_1)]         m_Z c_w/μ^2[ μ c_β+M_2s_β + +m_Z^2 s_2β c_β s^2_w/M_1-M_2]                                 -1/√(2)+m_Z^2c_β(s_β+c_β)/2√(2)μ^2                                 1/√(2) +m_Z^2c_β(s_β-c_β)/2√(2)μ^2 ]).
  
  
  
  Assuming M_2 > M_1, the mass eigenvalues of the NLSP and LSP are then simply approximated by
  
      m_χ^0_1   =M_1-m_Z^2/μs_w^2 (sin_ 2β +M_1/μ)≃ M_1 , 
      
      m_χ^0_2   =M_2-m_Z^2/μc_w^2 (sin _2β +M_2/μ)≃ M_2,
  
  where for large |μ| we see that χ_2^0 and χ_1^0 are almost pure Wino and Bino mixtures respectively.
  
  
  The parameters that determine the mass eigenstates and mixing also determine the couplings of electroweakinos to gauge and Higgs bosons through mixing of D-terms. In particular, the couplings of χ_2^0 to h/Z and χ_1^0, g_hχ^0_1χ^0_2 and g_Zχ^0_1χ^0_2,  can be simplified assuming large μ, |m_χ_1^0 - m_χ_2^0| > m_h, m_Z, and the Higgs alignment condition α≈β - π/2. 
  We find [Our result in g_hχ^0_1χ^0_2 has a minor difference with Ref. <cit.>, which omitted m_χ_1^0,  probably  assuming it to be small.]
  
  
  
      g_hχ^0_1χ^0_2   = - e m_Z /μ[ s_2β +m_χ_1^0 + m_χ_2^0/2μ  + m_Z^2s^2_2β c_2w/μ(m_χ_2^0-m_χ_1^0)], 
      
      g_Zχ^0_1χ^0_2   = - e m_Z^2 /2 μ^2[c_2β+m_Z^2s_4βc_2w/2μ( m_χ_2^0-m_χ_1^0)].
  
  
  
  We see that when μ < 0, the Higgs coupling g_hχ^0_1χ^0_2 has a blind spot when s_2β +(m_χ_1^0 + m_χ_2^0)/(2μ)  ∼ 0, and thus along this direction the coupling to the Higgs is suppressed and the neutral Wino decays almost exclusively through the Z-channel. Further, for a given pair of neutralino masses the blind spot is determined by the values of tanβ and μ. For example, given m_χ_1^0 + m_χ_2^0 = 800 GeV, the cancellation happens for {tanβ,  μ (GeV)} ={ 5,  -1040 }, { 10,  -2020 } or { 20,  -4010 }. 
  
  
  The decay widths of χ_2^0 →χ_1^0  h and χ_2^0 →χ_1^0  Z are given by
  
      Γ_h     = g_hχ^0_1χ^0_2^2/8π p_h (m_χ_1^0 + m_χ_2^0)^2 -m_h^2 /m_χ_2^0^2 , 
      Γ_Z     = g_Zχ^0_1χ^0_2^2/8π p_Z (m_χ_1^0 + m_χ_2^0)^2 -m_Z^2 /m_χ_2^0^2 ×(m_χ_2^0 - m_χ_1^0)^2 + 2 m_Z^2 /m_Z^2  ,
  
  where p_h and p_Z are the momentum of h and Z in the final state. These results are in agreement with Ref. <cit.>. For a review of electroweakino scenarios in the MSSM and corresponding decay modes see Ref. <cit.>.
  
  
  
  
  
   §.§ Comments on the anomalous Magnetic Moment and Dark Matter for large values of |μ|
  
  
  The SM prediction for the muon anomalous magnetic moment, (g-2)_μ differs by about 3.5 standard deviations with respect
  to the current experimental value measured at the Brookhaven g-2 experiment <cit.>, 
  
  
      δ a_μ^ exp≃( 27 ± 7 ± 5   ) × 10^-10,
   
  where the errors are associated with experimental and theoretical uncertainties. 
  
  The dominant contribution to the muon anomalous magnetic moment in the MSSM <cit.>, comes from the chargino induced diagram.  
  This contribution relies on the presence of a relevant Higgsino and Wino component of the light charginos and hence is suppressed when |μ| becomes sizable. For large values of |μ|, like the ones
  analyzed in this article, the neutralino contribution may be also relevant. Contrary to Winos, Binos couple to both left- and right-handed muons and tend to provide the most 
  relevant contributions through mixing in the slepton sector, with the parameter μ providing the necessary left-right slepton mixing.  Since this mixing is proportional to tanβ, sizable neutralino contributions may be obtained for large 
  values of μtanβ and sleptons that may easily be heavier than the characteristic Wino mass scale discussed in this article.   We verified these properties quantitatively by using the code 
  CPsuperH <cit.>. As an explicit example, if one takes the extreme values of μ = 10 TeV
  and tanβ = 50, considered in this article, values of M_1 of the order of the weak scale and first and second generation slepton masses of order 700 GeV will be necessary to get the current experimental 
  central value for the muon g-2.  On the other hand, the third generation sleptons must be heavy in order to avoid problems in the slepton spectrum. 
  For smaller values of μ and tanβ, the chargino contributions become relevant. For instance, for μ = 2 TeV and tanβ = 50, M_2 = 400 GeV and 
  M_1 =250 GeV, sleptons with masses of order 450 GeV will lead to the proper g-2 contribution, with neutralinos providing about 60 percent of the total contribution.
  
  
  Dark Matter, on the other hand, may be obtained either by resonant annihilation with scalars or by co-annihilation with the slepton states <cit.>.
  For co-annihilation, light sleptons should be close in mass to the Bino states and therefore will lead to additional decays of the the heavier Winos into charged and neutral Wino states, which would be in conflict
  with the heavy scalar assumption of the current work. This can only be avoided in the case of light right-handed sleptons, with small mixing with their left-handed partners.  Such small mixing would
  suppress the neutralino contribution to (g-2)_μ and is difficult to achieve for large values of |μ| and tanβ, but is still possible if one assumes a very large hierarchy between the left- and right-slepton
  masses.  Regarding the resonant annihilation via the Higgs states, this may be achieved for moderate values of tanβ and values of the Bino mass close to a half of the heavy Higgs masses (the
  resonant annihilation contribution via the lightest Higgs (or the Z) is highly suppressed for large values of μ  <cit.> ).  Heavy Higgs
  boson annihilation, on the other hand, will be subject to strong LHC constraints, unless tanβ is not very large <cit.>.  For instance, we verified using MicrOmegas <cit.> that the proper relic density can be obtained for tanβ = 5, μ = 2 TeV,  and  M_H ≃ 600 GeV [Masses of the heavy Higgs bosons ≳ 500 GeV will have a negligable effect on the discussion of electroweakino branching ratios in the following section.] provided M_1 is of order 290 GeV, where this value increases to  298 GeV for μ = 5 TeV. The
  direct detection cross section tends to be suppressed, an order of magnitude or more below the current bounds, due to the large Higgs and Z coupling suppression induced by the large
  values of |μ|.    
  
  
  
  
  § PRODUCTION AND BRANCHING RATIOS
  
  
  
   
  
  At the LHC, the production of Wino-like electroweakinos, χ_1^± and χ_2^0, proceeds mostly through s-channel exchange of a W boson. However, for heavy squarks, the χ_1^±-χ_2^0 pair is subdominantly produced through t-channel exchange of first- and second- generation squarks <cit.>, see Fig. <ref> [The same is true for other scenarios such as the Higgsino-Bino scenario. However, in such cases the dependence of the couplings to squarks is proportional to their Yukawa couplings and hence negligible.]. Apart from the parametric dependence described in the previous section, the overall production modes of χ_1^± and χ_2^0 will also have a dependence on the scale of superpartners, M_SUSY. The measurement of the Higgs boson mass indicates that stop masses are around 1-10 TeV in the MSSM <cit.>. Further, exclusion of squarks and gluinos have reached well into the 1-2 TeV range <cit.>. Thus, in our discussion we will assume a range of scalar superpartners M_SUSY = M_3=m̃_q_1,2,3 = m̃_l_1,2,3 = 1 -10 TeV. For simplicity, we will assume |μ| = M_SUSY in the main results. However, we will comment on other cases in later sections.
  
  
  
  
   
  
  
  In Fig. <ref>, we show the NLO production cross section of Wino-like electroweakinos with respect to the Wino mass for M_SUSY= |μ| = 1 - 10 TeV. For large Wino masses, the scalar interactions in the production cross section tend to destructively interfere compared to scenarios when superpartners are decoupled well above the weak scale, with the exception of when M_SUSY=1 TeV for which the mixing of the Wino with the Higgsinos becomes relevant when M_2 approaches μ. In the range of m_χ_1^±≃ 500 - 1000 GeV, we find that the difference in the production cross section can be close to a factor of ∼ 2 - 4. This range of masses is currently in the region of interest of exclusion and/or discovery limits for future searches of electroweakinos at the LHC. Thus, despite being decoupled from the typical searches, the scale of superpartners can have striking consequences on the interpretation of many channels currently being explored.
  
  
  
  As discussed in the previous section, the Wino will decay either through a Z or Higgs boson to χ_1^0. In the traditional searches, these decay modes are considered to be maximal over the whole range of masses considered. However, as we have pointed out these branching ratios have non-trivial dependence on the same set of parameters that determine the masses eigenstates. In Figs. <ref> & <ref> we show the branching ratios of χ_2^0 into Z and h for M_SUSY=2 & 10 TeV respectively. In each case, we show branching ratios for μ = ± M_SUSY. For M_SUSY=2 TeV we show branching ratios for tanβ = 5 & 10, while for M_SUSY=10 TeV we take tanβ = 10 & 50 to show the region of parameters where the blind spot in the Higgs decay is realized. The spectrum and branching ratios are produced using FeynHiggs <cit.> and SUSY-HIT <cit.>, respectively, by scanning M_1 = [5,500] and M_2 = [100,1000].
  
   
  
   
  
  We see that for M_SUSY = 2 TeV the Higgs decay mode is dominant over most of the region of interest. However, for μ < 0 and tanβ = 10 we see that the previously discussed blind spot condition may be fulfilled and the Z decay mode becomes dominant. While for M_SUSY=10 TeV the Higgs decay mode reaches maximum strength in most of the parameter space whereas the decay of Winos through the Z boson is negligible everywhere except in the compressed region, m_χ_2^0≃ m_Z + m_χ_1^0 and for μ < 0 and tanβ = 50 in this case. We note that such patterns of the branching ratios are not themselves strictly dependent on the scale of the scalar superpartners. Leaving μ = -2 TeV fixed and increasing the scale of the scalar superpartners will have the dual effect of increasing the production cross section and leaving the blind spot in a range accessible to, for instance, trilepton searches. 
  
  
  
  
  
  These findings show that, except for particular regions of parameter space, the Higgs decay channel stands out as the most promising decay mode for searches of Wino-like electroweakinos at the LHC. In particular, if μ > 0 this decay channel is the only relevant production mode beyond the compressed region, m_χ_2^0≃ m_Z + m_χ_1^0. This, together with the dependence of the production cross section on masses of the scalar superpartners, gives pertinent information when interpreting current bounds and projecting the future reach of the HL-LHC for electroweakinos.
  
  
  
  
  
  
  § REACH OF ELECTROWEAKINO SEARCHES ACCORDING TO SUSY SCENARIOS
  
  
  
  
  
   §.§ Current bounds
  
  
  
  The current reach of electroweakinos at the LHC has been presented in numerous studies by the ATLAS  and CMS collaborations Ref. <cit.>. For definiteness, in this article we will concentrate on the studies presented by the ATLAS collaboration. The existing searches present bounds on the masses of charginos and neutralinos at the 13 TeV LHC for luminosities ranging from 36 fb^-1 to 139 fb^-1 assuming Wino-like crosses sections with superpartners decoupled and maximal branching ratios of χ_2^0 to either Z or SM Higgs bosons. In this section, we recast the current bounds comparing the reach of electroweakino searches with respect to the scale of superpartners.
  
   
  
  
  
  The production cross sections and associated branching ratios are obtained over the Wino-Bino parameter space, M_1 = [5,500] and M_2 = [100,1000], using and  Prospino-2.1 <cit.> and SUSY-HIT respectively. For each point in the scan, we compare the result with the experimental upper limits on the cross section for decays leading to trilepton or h→ bb̅ channels <cit.>,
  
  
      pp→χ_1^± + χ_2^0→ W^± + Z/h + E_T= 
                          3 ℓ  + E_T    for Z→ℓℓ
      
                           1(0)ℓ + bb̅ + E_T    for h→ bb̅.
  
  
   
  
  
  In this and subsequent sections, we focus mainly on two scenarios when M_SUSY=|μ| = 2 TeV and M_SUSY=|μ| = 10 TeV. [Lower squark masses 1 TeV would result in abysmal reach for electroweakinos as the interference in the production cross section is maximal.] As discussed in the previous section, for a given |μ| the blind spot in the Higgs decay occurs for different regions of tanβ. Thus, in order to present both the worst and best case scenario for the reach of the searches we consider tanβ = 5 & 10 when M_SUSY=|μ| = 2 TeV, and tanβ = 10 & 50 when M_SUSY=|μ| = 10 TeV. In each case, since we are recasting the current bounds taken from the data available on HEP-data, we do not extend our results beyond what has already been explored by the experimental collaborations as such an analysis would require an artificial presentation of signal and background efficiencies which would typically improve with increased data. Thus, we consider our results conservative in this sense.
  
  
  
  
   
  
  
  In Fig. <ref>, we show the result of recasting the current bounds for M_SUSY=|μ| = 2 TeV. The gray and magenta shaded regions show the bounds from a search of the decay χ_2^0 χ_1^±→ hW+2χ_1^0, followed by h→ bb̅, in final states  with a pair b-quarks and zero or one leptons respectively <cit.>. We have denoted these channels as 0ℓ bb and 1ℓ bb. The cyan region shows the corresponding bound from an independent search of the 1ℓ bb channel <cit.>. The orange shaded region, denoted as 3ℓ(2ℓ+j), shows our recasting of the bounds resulting from a search of the χ_2^0 χ_1^±→ ZW+2χ_1^0 decay, followed by Z→ℓ^+ℓ^-, in the statistical combination of final states with 3 leptons and 2 leptons plus jets <cit.>. Finally, the dark yellow region shows the bounds from a similar trilepton search focused in the compressed electroweakino spectrum <cit.>. 
  
  
  Due to the decrease in the production cross section, the resulting bounds from the Higgs channel are  weaker than what is typically presented, reaching slightly above chargino masses m_χ_1^±≃ 600 GeV and neutralino masses m_χ_1^±≃ 200 GeV. Meanwhile the trilepton searches lose sensitivity almost over the whole range of masses, except in the region of parameters where the blind spot appears in the Higgs decay mode, see Fig. <ref>. In contrast, when M_SUSY=|μ| = 10 TeV, Fig. <ref>, we find similar reach in the Higgs channel as is currently expected (in this and subsequent figures, regions of parameters that were left unexplored by the experimental analyses are shown at the edge of the bounds by sharp edges without solid lines). The trilpeton searches again lose sensitivity everywhere beyond the compressed region, and except when μ <0 and tanβ = 50 due to the suppression of the branching ratio of χ_2^0 to Z. However, in this case the overall reach also improves due to the increase in the production cross section.
  
  
  
  
  The assumption that M_SUSY=|μ| places strong constraints on both the production cross section, patterns of decays for the lightest electroweakino states, and thus the resulting bounds. Other scenarios with different hierarchies, such as in Split Supersymmetry <cit.> where sfermions are much heavier than the gauginos, are also well motivated. In Fig. <ref> we show the bounds for tanβ = 10, |μ|=2 TeV, and M_SUSY=10 TeV. The overall effect on the bounds is twofold. The decoupling of scalars gives an increase in the production cross section yeilding a slightly larger reach in both the Higgs and trilepton channels, and for negative μ the trilepton searches remain sensitive to the blind spot resulting in an even larger reach compared to the case of a universal SUSY scale (bottom right panel of  Fig. <ref>).
  
   
  
  
  
   §.§ Future reach and discovery potential
  
  
  
  
  
  In this section, we assess the ultimate reach and discovery potential of Wino-like electroweakinos at the HL-LHC. As in the previous section, we show the projected bounds resulting from the dependence of the scale of superpartners, |μ|, and tanβ. Throughout this section, we stress the ultimate reach of electroweakino searches with respect to the squark masses. The current bounds shown in the previous section suggest electroweakino masses well above 100 GeV. From Fig. <ref> it is clear that in this region of parameters, squarks with masses of 10 TeV can boost the Wino cross section by close to a factor of 2 compared to 2 TeV. Thus, in this section we project the bounds and discovery potential of electroweakinos for the HL-LHC for M_SUSY=2 and 10 TeV. The lower bound, M_SUSY=2 TeV, is chosen to conservatively satisfy current bounds on squark masses, while M_SUSY=10 TeV gives the maximum boost to the electroweakino production cross section leading to the strongest potential reach for these particles. For other theoretical projections of electroweakino searches in the (N)MSSM see  <cit.>.
  
   
  
  
  
  
  In Fig. <ref>, we show the projected bounds for integrated luminosity of 3 ab^-1 with M_SUSY=|μ|=2 TeV and tanβ = 5 (10) in the top (bottom) panels. As before, the Higgs decay channel remains the dominant search channel for most of the range of chargino and neutralino masses, with the ultimate reach extending the bound for m_χ_1^± beyond 850 GeV and m_χ_1^0 to almost 400 GeV when μ > 0 and tanβ = 5. However, we see again that these conclusions differ significantly when the coupling of χ_2^0 to the SM Higgs crosses the blind spot. In this case, the trilepton channel dominates covering a similar range of masses. In Fig. <ref>, we show the 5-σ discovery regions for the same set of parameters. Comparing each panel to the respective bound in Fig. <ref> we see that there is a significant region of masses in the discovery region at the HL-LHC not excluded by the current searches. Such a region includes m_χ_1^±≳ 600 GeV, m_χ_1^0≳ 200 GeV, and a far better coverage of the compressed region m_χ_1^± - m_χ_1^0≃ m_Z.
  
   
  When M_SUSY=10 TeV the production cross section reaches maximal values over the whole range of masses giving the strongest expected reach at the HL-LHC. In Fig. <ref> and Fig. <ref>, we show the corresponding 95% CL and 5-σ discovery bounds with M_SUSY=|μ|. Here the 95% CL bounds on chargino masses from Higgs decay searches begin to reach the TeV scale and beyond 400 GeV for neutralinos. In this case, the discovery region extends to m_χ_1^±≳ 750 GeV and m_χ_1^0≳ 250 GeV, and is significantly stronger than the current bounds, shown in Fig. <ref>, implying again a strong discovery potential at the HL-LHC run.
  
   
  
  
  
  
  § CONCLUSIONS
  
  
  
  The search for electroweak interacting particles is, together with precision measurements of the Higgs couplings, one of the most
  promising activities in the HL-LHC era. In this article, we critically reanalyzed the search for electroweakinos in the
  case of a Higgsino mass parameter significantly larger than the weak scale.  We showed that the signatures of Wino production
  depend crucially on three parameters :  The first and second generation squark masses, which control the t-channel contribution
  to the Wino production cross section, the sign of μ, which control the mixing parameter determining the decay of the neutral
  Winos into Z or h final states, and finally the relative size of the ratio of the Higgsino mass parameter to the average gaugino mass
  to tanβ, which control the proximity to the blind spot for the decay of the neutral Wino into Higgs states for negative values of μ.
  
  The t-channel contribution to the cross section interferes destructively with the s-channel one and hence the cross section becomes
  larger for larger squark masses.  This destructive interference is still sizable for squark masses of the order of 2 TeV, but becomes
  weak for squark masses above the 5 TeV scale, for which the maximal reach is  therefore achieved.  These very large values of the squark
  masses are implicitly assumed in the experimental presentation of the LHC bounds for Wino-like particles decaying into
  lighter Bino states.  It is important to stress that such dependence is not present in the production of Higgsino states, which couple
  with the first and second generation squarks via their small Yukawa couplings. We refer to Ref. <cit.> for the 
  Higgsino search analysis. 
  
  In general, the Higgs decay mode provides the dominant decay branching ratio of the neutral Winos and hence the tri-lepton channel
  looses significance unless the mass difference between the neutral Winos and Binos are below the Higgs mass scale or
  one is in the proximity of the previously mentioned blind spot. For positive values of μ with respect to the average
  gaugino masses and large mass differences, the Branching ratio of the Higgs decay is very close to one. The blind spot
  only occurs for negative values of μ, in which case there may be a rich interplay between the Higgs decay and Z decay
  searches.
  
  Two relevant conclusions of this study is that, depending on the parameters, the current exclusions limits may be
  significantly weaker than the ones displayed in experimental searches and, most importantly, the discovery reach
  of the HL-LHC greatly exceeds the region probed at current luminosities. This, together with 
  similar results obtained in the case of Higgsino searches <cit.>,  provides a strong
  motivation for the future electroweakino searches in the high luminosity LHC era. 
  
  
  
  
  § ACKNOWLEDGMENTS
  
  Work at University of Chicago is supported in part by U.S. Department of Energy grant
  number DE-FG02-13ER41958. Work at ANL is supported in part by the U.S. Department
  of Energy under Contract No. DE-AC02-06CH11357. NM acknowledges support by the U.S.
  Department of Energy, Office of Science, Office of Work- force Development for Teachers and
  Scientists, Office of Science Graduate Student Research (SCGSR) program. The SCGSR
  program is administered by the Oak Ridge Institute for Science and Education (ORISE) for
  the DOE. ORISE is managed by ORAU under contract number de-sc0014664.
  JL acknowledges support by Peking University under Special Research grant number 7101502458. 
  
  
  
  
  
  
  JHEP   
  
  
  
  
  