The Scale of Superpartner Masses and Electroweakino Searches at the High-Luminosity LHC

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 $\mu$ and, for negative values of $\mu$, on the relative size of the ratio of $\mu$ to the gaugino masses compared with tan$\beta$. 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.

Refs. [1,2]. 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 [3,4]. 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) [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. 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 tan β, 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.) [21][22][23][24][25].
In a previous article [26], 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 tan β/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 II, 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 III, 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 tan β.
In section IV, we show the resultant, current bounds and future reach of the electroweakino searches. We reserve section V, for our conclusions.

II. 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 tan β. The resulting mass matrices for the neutralinos and charginos in terms of these parameters are given by where c W = cos θ W , s W = sin θ 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. [9].
The neutralino mass eigenstates are given after diagonlization Z T N M N Z N =m χ wherẽ m χ = diag(m χ 0 1 , m χ 0 2 , m χ 0 3 , m χ 0 4 ) 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 where p h and p Z are the momentum of h and Z in the final state. These results are in agreement with Ref. [28]. For a review of electroweakino scenarios in the MSSM and corresponding decay modes see Ref. [29]. 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 [30][31][32], where the errors are associated with experimental and theoretical uncertainties. Since this mixing is proportional to tan β, sizable neutralino contributions may be obtained for large values of µ tan β 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 [39,40]. Higgs boson annihilation, on the other hand, will be subject to strong LHC constraints, unless tan β is not very large [49,50]. For instance, we verified using MicrOmegas [51] that the proper relic density can be obtained for tan β = 5, µ = 2 TeV, and M H 600 GeV 2 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 2 Masses of the heavy Higgs bosons 500 GeV will have a negligable effect on the discussion of electroweakino branching ratios in the following section.
the current bounds, due to the large Higgs and Z coupling suppression induced by the large values of |µ|. At the LHC, the production of Wino-like electroweakinos, χ ± 1 and χ 0 2 , proceeds mostly through s-channel exchange of a W boson. However, for heavy squarks, the χ ± 1 -χ 0 2 pair is subdominantly produced through t-channel exchange of first-and second-generation squarks [21][22][23][24][25], see Fig. 1 3 . Apart from the parametric dependence described in the previous section, the overall production modes of χ ± 1 and χ 0 2 will also have a dependence on the scale of superpartners, M SU SY . The measurement of the Higgs boson mass indicates that stop masses are around 1 − 10 TeV in the MSSM [52][53][54][55][56]. Further, exclusion of squarks and gluinos have reached well into the 1 − 2 TeV range [1,2]. Thus, in our discussion we will assume a range of scalar superpartners M SU SY = M 3 =m q 1,2,3 =m l 1,2,3 = 1 − 10 TeV.

III. PRODUCTION AND BRANCHING RATIOS
For simplicity, we will assume |µ| = M SU SY in the main results. However, we will comment on other cases in later sections.
In As discussed in the previous section, the Wino will decay either through a Z or Higgs boson to χ 0 1 . 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    M SU SY = |µ| = 2TeV. The 0 bb (gray) [16] and 1 bb (magenta, cyan) [17] bounds are projected from searches of the χ 0 2 χ ± 1 → hW + 2χ 0 1 channel, with h →bb and W decay to hadronic or leptonic final states. The 3 (dark yellow) [19] and 3 /2 + j (orange) [15] bounds are projected from the In this and subsequent sections, we focus mainly on two scenarios when M SU SY = |µ| =         Fig. 6, we find similar reach in the Higgs channel as is currently expected. The trilpeton searches again lose sensitivity everywhere beyond the compressed region, and except when µ < 0 and tan β = 50 due to the suppression of the branching ratio of χ 0 2 to Z. However, in this case the overall reach also improves due to the increase in the production cross section.
The assumption that M SU SY = |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 [66][67][68] where sfermions are much heavier than the gauginos, are also well motivated. In Fig. 7 we show the bounds for tan β = 10, |µ| = 2 TeV, and M SU SY = 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. 5).

B. 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 tan β. For other theoretical projections of electroweakino searches in the (N)MSSM see [43,[69][70][71].   In Fig. 8, we show the projected bounds for integrated luminosity of 3 ab −1 with M SU SY = |µ| = 2 TeV and tan β = 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 0 1 to almost 400 GeV when µ > 0 and tan β = 5. However, we see again that these conclusions differ significantly when the coupling of χ 0 2 to the SM Higgs crosses the blind spot. In this case, the trilepton channel dominates covering a similar range of masses. In Fig. 9     When M SU SY = 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. 10 and Fig. 11, we show the corresponding 95% CL and 5 − σ discovery bounds with M SU SY = |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 0 1 250 GeV, and is significantly stronger than the current bounds, shown in Fig. 6, implying again a strong discovery potential at the HL-LHC run.

V. 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 tan β, 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. [26] 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