1 Introduction
###### Abstract

We re-assess the exclusion limits on the parameters describing the supersymmetric (SUSY) electroweak sector of the MSSM obtained from the search for direct chargino-neutralino production at the LHC. We start from the published limits obtained for simplified models, where for the case of heavy sleptons the relevant branching ratio, , is set to one. We show how the decay mode , which cannot be neglected in any realistic model once kinematically allowed, substantially reduces the excluded parameter region. We analyze the dependence of the excluded regions on the phase of the gaugino soft SUSY-breaking mass parameter, , on the mass of the light scalar tau, , on as well as on the squark and slepton mass scales. Large reductions in the ranges of parameters excluded can be observed in all scenarios. The branching ratios of charginos and neutralinos are evaluated using a full NLO calculation for the complex MSSM. The size of the effects of the NLO calculation on the exclusion bounds is investigated. We furthermore assess the potential reach of the experimental analyses after collecting at the LHC running at .

Direct Chargino-Neutralino Production at the LHC:

Interpreting the Exclusion Limits in the Complex MSSM

A. Bharucha***email: Aoife.Bharucha@desy.de, S. Heinemeyeremail: Sven.Heinemeyer@cern.ch, F. von der Pahlenemail: pahlen@ifca.unican.es§§§MultiDark Fellow

II. Institut für Theoretische Physik, Universität Hamburg, Lupurer Chaussee 149, D–22761 Hamburg, Germany

Instituto de Física de Cantabria (CSIC-UC), E-39005 Santander, Spain

## 1 Introduction

The LHC is actively searching for physics beyond the Standard Model (BSM). Many of those searches rely on the predictions of specific models. A well motivated model is the Minimal Supersymmetric Standard Model (MSSM) [1], which provides a framework in which such predictions can be made. Provided  parity is conserved [2], the final particle of any SUSY decay chain is the lightest supersymmetric particle (LSP), e.g. the lightest neutralino. It was shown that this particle is a natural candidate for Cold Dark Matter (CDM) [3]. The MSSM also contains a rich Higgs phenomenology, particularly relevant in light of the exciting recent discovery by ATLAS and CMS of a scalar resonance at  [4], as the requirement of an additional Higgs doublet results in a total of five physical Higgs bosons, the light and heavy -even Higgs bosons, and , the -odd and the charged Higgs bosons, .

The search for supersymmetry (SUSY) at the LHC has not (yet) led to a positive result. In particular, bounds on the first and second generation squarks and the gluinos from ATLAS and CMS are very roughly at the TeV scale, depending on details of the assumed parameters, see e.g. [5]. On the other hand, bounds on the electroweak SUSY sector, where and denote the charginos and neutralinos (i.e. the charged (neutral) SUSY partners of the SM gauge and Higgs bosons) are substantially weaker. Here it should be noted that models based on Grand Unified Theories (GUTs) naturally predict a lighter electroweak spectrum (see Ref. [6] and references therein). Furthermore, the anomalous magnetic moment of the muon shows a more than deviation from the SM prediction, see Ref. [7] and references therein. Agreement of this measurement with the MSSM requires charginos and neutralinos in the range of several hundreds of GeV. This provides a strong motivation for the search of these electroweak particles, which could be in the kinematic reach of the LHC. One promising channel is the direct production of a chargino and neutralino, . Although the cross sections are generically lower than for the direct production of colored particles, the searches at ATLAS and CMS have lead to several limits in the range of the order of several hundreds of GeV, see e.g. Refs. [8, 9], which are independent of the mass scale of colored SUSY particles. The highest sensitivity comes from multi-lepton final states, including tau leptons, which offer the possibility to distinguish a signal from the large hadronic background. As an additional advantage the theoretical calculation is cleaner than that of the production of electroweak SUSY particles via cascade decays of colored particles.

Early on, studies had proposed the clean trilepton signal at the LHC, coming either from intermediate sleptons (particularly of the first and second generation) or gauge boson decays to which the experiments are more sensitive (see e.g. Ref. [10]). More recently there have been several studies investigating the LHC sensitivity to this decay mode, e.g. in the region where decays to trileptons via and bosons dominate [11]. Direct production of electroweak SUSY particles has also been investigated in more challenging scenarios where the lightest chargino and two neutralinos are higgsino-like, and thus nearly degenerate, such that their decay signals are lost in the SM background [12], but a same sign diboson signal from gaugino production could be detectable for wino masses up to with at LHC14 [13]. Other recent studies have focused on improving the reach of searches using e.g. a kinematic observable, the visible transverse energy for final states [14]. Furthermore, there has been an increasing interest in the final state [15], including a decay, for which the use of jet substructure was found to improve results [16, 17]. This improvement is particularly helpful in gauge-mediated scenarios, in which the GUT relation is broken (), and boosted Higgs bosons could be observed with at LHC14 for values of  [16].

As discussed before, ATLAS [8, 18, 19, 20, 21] and CMS [9, 22] are actively searching for the direct production of charginos and neutralinos, in particular for the process with the subsequent decays and , resulting a three lepton signature. These searches are performed mostly in so-called “simplified models”, where the branching ratios of the relevant SUSY particles are set to one, assuming that all other potential decay modes are kinematically forbidden. The results are (often) presented in the parameter plane.

To compare with these experimental results, precise predictions for the final state are required, involving both calculations for the gaugino production cross section and the branching ratios of the subsequent chargino and neutralino decays. The production cross section in the -conserving real MSSM (rMSSM) was calculated at NLO and incorporated into the code Prospino 2.1 [23], as well as at NLL accuracy and investigated in the context of the LHC8111With LHC we denote the LHC running at . in Ref. [24]. Chargino and neutralino cross sections for the LHC8 in the complex MSSM have not been analyzed so far. Chargino and neutralino decays have been calculated at the one-loop level in the rMSSM [26, 27, 28, 29] and in the complex MSSM [30, 31, 32, 33, 34, 35], where our evaluations are based on the first full one-loop (NLO) calculation (of all non-hadronic decays) presented in Refs. [33, 34]. A phenomenological analysis in the complex MSSM, where these state-of-the-art results are combined to make predictions for the LHC is still lacking. Turning to the neutralino decays, in Ref. [34] the NLO results for all possible neutralino decays were considered as a function of , under the assumption that colored particles are kinematically excluded. It was found that a change of the phase of can significantly alter the dominant decay mode when the decay modes to neutralinos and Higgs bosons are allowed. The NLO corrections have been found to be sizeable, particularly for channels involving Higgs bosons.

In this paper we define and analyze a set of scenarios for the production and decay of charginos and neutralinos at the LHC8, where we take and as free parameters. The starting point is the scenario used by ATLAS to present their results for [20], which so far constitutes the most sensitive test of direct electroweak SUSY production. We show the effect on the chargino and neutralino searches of the inclusion of the decay (with ). Direct and indirect effects from decays to the recently discovered Higgs boson [4] must not be neglected in any realistic analysis. Subsequently, we deviate from the ATLAS scenario in several ways, motivated by current limits on the MSSM parameter space. In particular, we vary the phase of the gaugino soft SUSY-breaking mass parameter, , which has a strong impact on the branching ratios of the and thus on the limits of the exclusion regions in the plane. We furthermore analyze the scenario with a light scalar tau in the so-called -coannihilation region, where the provides a good CDM candidate. We vary other parameters, such as (the ratio of the two vacuum expectation values of the two Higgs doublets, ), the higgsino mass parameter , and the masses that set the scale for the scalar leptons or the scalar quarks. By analyzing these variations we aim to provide a more realistic interpretation of current ATLAS and CMS limits on the electroweak SUSY particles. Finally we investigate which limits can be expected from the first at the LHC13 (i.e. with ), which could be obtained in the years 2015-2017.

The paper is organized as follows: We begin with a short review of the relevant parameters and couplings as well as the calculations employed in our analysis in Sec. 2. Then in Sec. 3 we review in more detail the existing experimental analyses and define the various scenarios in which the analysis will be performed. Sec. 4 contains the numerical results, i.e. the re-interpretation of the existing mass limits in the benchmark scenarios, as well as our extrapolation to the LHC13. We conclude in Sec. 5.

## 2 Details of the calculation

In this section, after having introduced the necessary notation, we will illustrate the dependence of the couplings on the fundamental parameters via a simple expansion, and then go on to describe the details of the calculations employed in our (NLO) analysis in Sec. 4.

### 2.1 Notation

In the chargino case, two matrices and are necessary for the diagonalization of the chargino mass matrix ,

 M~χ−=V∗X⊤U†=(m~χ±100m~χ±2)withX=(M2√2sinβMW√2cosβMWμ) , (1)

where is the diagonal mass matrix with the chargino masses as entries, which are determined as the (real and positive) singular values of and is the mass of the  boson. The singular value decomposition of also yields results for and .

In the neutralino case, as the neutralino mass matrix is symmetric, one  matrix is sufficient for the diagonalization

 M~χ0=N∗YN†=\bf diag(m~χ01,m~χ02,m~χ03,m~χ04) (2)

with

 Y =⎛⎜ ⎜ ⎜⎝M10−MZswcosβMZswsinβ0M2MZcwcosβ−MZcwsinβ−MZswcosβMZcwcosβ0−μMZswsinβ−MZcwsinβ−μ0⎞⎟ ⎟ ⎟⎠ . (3)

is the mass of the  boson, and . The unitary 44 matrix and the physical neutralino (tree-level) masses () result from a numerical Takagi factorization [36] of .

When working in the complex MSSM it should be noted that the results for physical observables are affected only by certain combinations of the complex phases of the parameters. It is possible, for instance, to rotate the phase away, which we adopt here. In this case the phase is tightly constrained [37]. Consequently, we take to be a real parameter. Further note that in the case of the complex MSSM, the three neutral Higgs bosons , and mix at the loop level [38, 39, 40, 41], resulting in the (mass ordered) , and , which are not states of definite -parity. In the following we denote the light Higgs with , independent whether the parameters are chosen complex or real. The Higgs sector predictions have been derived with FeynHiggs 2.9.4 [42, 43, 44, 45].

### 2.2 φM1 dependence of neutralino amplitudes

In this section we investigate the dependence of amplitudes for decays in the limit ; ; , which will be relevant for most of the analyzed benchmark scenarios. The full couplings take the form (with denoting the electric charge, , and is the angle that diagonalizes the -even Higgs sector at tree-level)

 CL~χ0i~χ0jZ =−e2cwsw[Ni3Nj3∗−Ni4Nj4∗] (4) CL~χ0i~χ0jh1 =−e2cwsw[(sinαNi3∗+cosαNi4∗)(swNj1∗−cwNj2∗)+(i↔j)] , (5)

showing the left-handed (LH) parts, with the right-handed (RH) parts following from hermiticity of the Lagrangian, see e.g. Ref. [46],

 CR~χ0i~χ0jZ=−CL∗~χ0i~χ0jZ,CR~χ0i~χ0jh1=CL∗~χ0i~χ0jh1 . (6)

In the limit of interest to us, the two lightest neutralinos are almost purely bino and wino-like states, , . Here we neglect the mixing between the bino and wino components, which has a subleading effect in our approximation, such that , while . Note that in the Higgs decoupling limit [47] one has . In this limit we obtain for Eqs. (4) and (5)

 CL~χ01~χ02Z ≈e2M2Zμ2exp(iφM12) , (7) CL~χ01~χ02h1 ≈e2MZμ(M1+M2μ+4tanβ)exp(−iφM12) , (8)

where the neglected terms are of higher order in and . Eqs. (7) and (8) also show that the absolute value of the Higgs coupling is largest (smallest) for positive (negative) . The partial decay widths, however, also depend on the relative intrinsic factor of the neutralinos and that of the Higgs boson. (the -boson is -even). This effect leads to a larger (much larger near the threshold) dependence on the -phases than the one resulting from the change in the absolute value of the couplings, provided , as we illustrate below.

Using the relation (6) between the LH and RH couplings we express the tree-level partial decay widths as

 Γtree(~χ02→~χ01Z)= β∗(~χ01,~χ02,Z)16πm~χ02|CL~χ01~χ02Z|2 (9) ×⎛⎜⎝m2~χ02+m2~χ01−2M2Z+(m2~χ02−m2~χ01)2M2Z+6cos(φ~χ01~χ02Z)m~χ02m~χ01⎞⎟⎠ , Γtree(~χ02→~χ01h1)= β∗(~χ01,~χ02,h1)16πm~χ02|CL~χ01~χ02h1|2 ×(m2~χ02+m2~χ01−m2h1+2cos(φ~χ01~χ02h1)m~χ02m~χ01) , (10)

with

 cos(φ~χ01~χ02Z) (11)

and , where . The coefficients defined by Eq. (11) are related to the relative phase factor of the particles involved. In this section we will further assume, for the sake of simplicity, that is -even. However, the generalization to the general case is straightforward. When the relative parity of the neutralinos and the Higgs boson or boson is positive, allowing this process in s-wave. When the situation is the opposite, with negative relative parity. In this case only odd-values of the total angular momentum allowed, leading to p-wave suppressed processes near the corresponding decay thresholds.

In the limit of interest the partial decay widths, Eqs. (9) and (2.2), are given by

 Γtree(~χ02→~χ01Z)≈ e2β∗(~χ01,~χ02,Z)64πm~χ02M4Zμ4 ×⎛⎜⎝m2~χ02+m2~χ01−2M2Z+(m2~χ02−m2~χ01)2M2Z+6cos(φM1)m~χ02m~χ01⎞⎟⎠ , (12) Γtree(~χ02→~χ01h1)≈ e2β∗(~χ01,~χ02,h1)64πm~χ02M2Zμ2∣∣∣M1+M2μ+4tanβ∣∣∣2 ×(m2~χ02+m2~χ01−m2h1+2cos(φM1)m~χ02m~χ01) . (13)

These expressions show explicitly the large dependence of the tree-level partial decay widths to the Higgs boson, both from the couplings as well as from the relative of initial and final states.

### 2.3 Calculation

Here we briefly review the calculations used for the direct production cross section of , and for the branching ratios for the subsequent decay of the neutralino into a boson and of the chargino into a boson and the LSP. The main production channels for at the LHC, as well as their two-body decays to gauge and Higgs bosons and the neutralino decay to a tau-stau pair are shown in Figs. 1 and 2, respectively.

The production of neutralinos and charginos at the LHC is calculated using the program Prospino 2.1 [23]. The effect of complex parameters on these cross sections can only enter via chargino or neutralino mixing effects. We have evaluated these cross sections at the parton level to estimate its effect, which turns out to be negligible in our analysis222 The same holds for the production .. Consequently, the Prospino results can be taken over also for the complex MSSM results. Small differences for the calculation of and of are neglected. The NLL corrections to the gaugino production cross section calculated in Ref. [24, 25] are not included, and we estimate their effects to be at the per-cent level.

The production is dominated by wino pair production, where the largest contribution is from the -channel gauge boson diagrams. If one assumes that , as is the case when the GUT relation for the gaugino mass parameters holds, then the neutralino with the largest wino component is either the second lightest neutralino (for ) or the heaviest one. Therefore, and will have the largest production cross sections. Note that although the and -channel contribution to pair production are suppressed due to squark propagators if one assumes the first generation squarks to be heavy, the destructive interference of the -channel with left-handed squark exchange and the -channel gauge boson channel can be significant, as will be discussed in Sec. 4.

In Refs. [33, 34] we have calculated the full one-loop (NLO) corrections to the branching ratios for all non-hadronic chargino and neutralino decays for arbitrary parameters in the complex MSSM. The calculation is based on FeynArts/Formcalc [48, 49], and the corresponding model file conventions [46] are used throughout. In particular, the results were analyzed and found to be reliable as a function of . We will employ this NLO calculation for our investigations. The benchmark scenarios defined in the following section are such that the decays as well as , , are the only relevant ones. As analyzed in the previous subsection the decays of a wino-like to are most sensitive to due to the relative between the bino-like and the wino-like , which is controlled by . This, however, can be modified when loop corrections are taken into account as discussed in Sec. 4.6. Furthermore, the NLO corrections are largest for decays to Higgs bosons [34] and thus have to be taken into account in a precision analysis. The production cross sections and decay branching ratios have been evaluated numerically using the OpenStack infrastructure as described in Ref. [50].

## 3 Benchmark scenarios and experimental motivation

### 3.1 Overview of current experimental results

In Refs. [9, 8, 22, 18, 19, 20, 21], ATLAS and CMS have studied the sensitivity to electroweak gaugino pair production, particularly to the production of the second lightest neutralino and lightest chargino via multi-lepton signatures. Here the chargino and neutralino decay either via sleptons or via gauge bosons, depending on the slepton masses, which are parameterized via (where ). Exclusion limits are then obtained within specific models, primarily simplified models which set all relevant branching ratios to one, assuming that all other channels are kinematically forbidden. The ATLAS results at are presented in Ref. [8] for , and the updated results including data are given in Refs. [18] for and [19, 20, 21] for up to . An update of CMS including the data was published in Ref. [22] for , where opposite sign (OS) dileptons inconsistent with a boson are also studied. The results were published in Ref. [9] for .

In addition to the lepton events (electrons, muons and hadronically reconstructed taus) analyzed by ATLAS, CMS also considers the case when one of the leptons is unidentified, selecting events with same the sign (SS) lepton pairs , and . Further, OS lepton pairs and 2 jets for on-shell and events where one decays to or and the other gauge boson decays hadronically are considered. Simplified models are used to obtain exclusion limits, tuned to search for decays via sleptons or gauge boson, mainly for but also for and . Here models with different couplings to leptons are considered, i.e. the sleptons may be left-handed or right-handed or a mixture, such that the final state leptons are predominantly light, flavor independent, or mostly taus.

ATLAS, on the other hand, presents its results for this channel by combining 3-lepton (electrons or muons) searches in various signal regions, the primary criterion being whether the invariant mass same-flavor-opposite-sign (SFOS) lepton pair lies around the boson mass or not, thus defining -enriched and -depleted regions respectively. By making requirements on the reconstructed mass of the SFOS lepton pair () and on the transverse momentum () of the third lepton, the depleted region is further subdivided into regions targeting either small mass splittings between the neutralinos (here the is off-shell and this region is discussed later), mass splittings close to the -boson mass, or decays via sleptons by requiring high transverse momentum of the third-leading lepton. In the simplified models, a number of assumptions are made, first and foremost that the neutralino and chargino are wino-like and the lightest neutralino bino-like. As for the sleptons, either in which case the branching ratio to all sleptons is assumed to be , or is very large (where the precise value is not quoted) such that the decay to sleptons may be ignored, and the branching ratio to gauge bosons is assumed to be .

### 3.2 Definition of benchmark scenarios

Since so far only ATLAS reported an analysis using the full 2012 data set with numerical values for the excluded cross sections [20], we will use their results for our baseline analysis. In order to interpret the ATLAS exclusions in terms of the complex MSSM, we calculate the cross section in benchmark scenarios similar to those used by ATLAS, including NLO corrections as described in Sec. 2.3. We re-analyze the ATLAS  CL exclusion bounds in the simplified analyses in the plane, taking and as free parameters with central values:

 M1=100GeVandM2=250GeV. (14)

The other parameters are chosen as in the ATLAS analysis presented in Ref. [20]333 Not all parameters are clearly defined in Ref. [20]. We select and choose our parameters to be as close to the original analysis as possible.,

 μ=1TeV,tanβ=6,M~q1,2=M~q3=M~ℓ=2TeV,At=2.8TeV . (15)

denotes the diagonal soft SUSY-breaking parameter in the scalar quark mass matrices of the first and second generation, similarly for the third generation and for all three generations of scalar leptons. If all three mass scales are identical we also use the abbreviation . We will clearly indicate where we deviate from the “unification” for scalar leptons. is the trilinear coupling between stop quarks and Higgs bosons, which is chosen to give the desired value of . The other trilinear couplings, set to zero in Ref. [18, 20], we set to for squarks and to zero for sleptons. Setting also the to zero would have a minor impact on our analysis. The effect the large sfermion mass scale is a small destructive interference of the -channel amplitude with the -channel squark exchange. The large higgsino mass parameter results in a gaugino-like pair of produced neutralino and chargino. The lightest Higgs boson mass (as calculated with FeynHiggs 2.9.4 [42, 43, 44, 45]) is evaluated to be , defining the value of in Eq. (15). In order to scan the plane we use the ranges

 |M1|=0…200GeV ,M2=100…400GeVwith~{}|M1|≤M2 . (16)

The main aim of this paper, as discussed above, is the interpretation of the ATLAS exclusion limits in several “physics motivated” benchmark scenarios. Taking the parameters in Eq. (15) as our baseline scenario, we deviate from it in the following directions.

1. We take , the phase of , to be a free parameter. Note that for the considered central benchmark scenario, as is low and is high, the full range is allowed by current electric dipole moment (EDM) constraints [51, 52, 53], as verified explicitly via both CPsuperH 2.3 [54, 55, 56] and FeynHiggs 2.9.4 [42, 43, 44, 45].

2. The variation of can have a strong impact on the couplings between the neutralinos and the Higgs boson, see Eq. (8). We therefore analyze the effect of variation of in the range .

3. Although in general the sleptons are assigned a common mass , in order to consider the possibility that neutralino decays to sleptons could compete with the decays to and Higgs bosons, we consider , where denotes the “right-handed” soft SUSY-breaking parameter in the scalar tau mass matrix, see Eq. (87) in Ref. [34]. This scenario is motivated by the measured relic density of dark matter. For this choice of parameters one finds , i.e. the stau co-annihilation region. We have confirmed (using micrOMEGAs3.1 [57]) that in our scenario the relic density is in agreement444 Small changes in the parameters which can have a drastic impact on the predicted CDM density, but only a small impact on the chargino/neutralino phenomenology are not relevant.  with the latest measurements presented by Planck [58] earlier this year, .

4. As shown in Eqs. (7), (8) the lighter neutralino-Higgs couplings depend strongly on , and consequently also the Born amplitudes. We investigate two scenarios: (i) with . This scenario shows similar characteristics as the ATLAS baseline scenario, but decouples the parameter further, as will be discussed briefly in Sec. 4.6. (ii) with . In this scenario the lighter neutralinos and chargino possess a substantial higgsino component.

5. Although has a negligible impact on the decays of the electroweak SUSY particles to gauge bosons, it plays an important role in the production, as the -channel squark exchange and the -channel gauge boson exchange amplitudes interfere destructively. We consider the range from to .

The various scenarios are summarized in Tab. 1

Besides interpreting the current results in the scenarios summarized in Tab. 1 we also evaluate possible future limits (assuming the absence of a signal). We analyze the following two (future) scenarios:

• A combination of ATLAS and CMS data, which for simplicity we take as resulting in a doubling of the luminosity, i.e. assuming analyzed by ATLAS. The change in the experimental limit on the production cross section (times branching ratio) is evaluated by assuming a purely statistical effect, thus dividing the current limit by .

• The first run at that could take place in 2015-2017. We assume that ATLAS collects . The new limit is evaluated from the existing limits by a simple rescaling of signal and background cross sections. More details are given in Sec. 4.7.

## 4 Interpretation of ATLAS exclusion limits

We re-analyze the ATLAS results of Ref. [20] in the scenarios defined in Tab. 1. In all scenarios the decay is taken into account. Production cross sections and branching ratios are evaluated as described in Sec. 2.3. Note that in the simplified model analyses, , which is not the case in the MSSM. However, for lighter gauginos, corresponding to , this relation holds to a good approximation. In our analysis, we chose to take the convention that our corresponds to the ATLAS , and our is calculated accordingly. Note that in almost all of the parameter space explored the difference will be less than , where larger values are indicated explicitly.

### 4.1 Effect of ~χ02 decays to Higgs bosons and sign of M1

We begin by re-interpreting the ATLAS simplified model exclusion bounds, taking full NLO branching ratios into account. Including has a considerable impact on the , thus weakens the existing conclusion limits. Keeping real, we analyze the excluded parameters allowing two possibilities for , namely 0 and . (The case of a complex will be addressed in Sec. 4.3.)

In Fig. 3 we show as a black line the production cross section for pair-production at the LHC8 as a function of and for in the upper right, upper left, lower right, lower left plot, respectively.555 It should be noted that a massless neutralino is not excluded by experimental searches [59]. The parameters are chosen according to , except for and which are varied. In order to avoid the lines in the lower plots start at (left) and (right). The production cross section times the is also shown for (green) and (blue), except for (upper left plot), where the sign is irrelevant. The chargino decays with as . The dashed green and blue lines correspond to the tree-level evaluation, whereas the solid lines are obtained by our full one-loop evaluation. The difference in Fig. 3, however, is barely visible. Below the kinematical threshold for the green/blue lines are on top of the black line, i.e. . The green/blue lines stop at the dashed vertical line, indicating the kinematical threshold for . The  CL exclusion cross sections from ATLAS [20] are given as red dots, connected by solid red lines. These lines do not correspond to true experimental analyses and are only indicative. Also shown as dotted red line is the projection for a combination of ATLAS and CMS data (see the end of the previous section and the discussion below).

The crossing point between the black and the red line corresponds to the highest value that is excluded by ATLAS, see Ref. [20]. However, taking into account the decay as well as a variation of the sign of , resulting in the green and blue lines, moves the highest excluded to substantially smaller values. In the case of , as shown in the upper left plot in Fig. 3, the exclusion bound for moves from down to . For positive the decay to a Higgs boson is enhanced, resulting in a reduced , while a smaller reduction is obtained for negative . This can be understood from the dependence of the decay amplitudes for as discussed in Sec. 2.2. From those expressions it is clear that the enhancement of the decay to Higgs bosons increases with . The corresponding strong variation of the partial decay widths leads to a strong variation in .666In Ref. [15] it was pointed out that, in the large regime, the gaugino pair production process with subsequent decay of a neutralino to a Higgs boson and the LSP would have the highest reach sensitivity for very large luminosities at LHC14. Notice that, for , the phase of could have a significant effect on this reach.  Consequently, the differences of the excluded values for opposite signs of becomes larger with increasing , as is visible comparing the green and the blue curves in the four plots in Fig. 3. The term in Eq. (2.2) further increases this ratio of couplings, suppressing the branching ratio to , especially for small . We discuss this effect in Sec. 4.2, where we compare the limits for (Fig. 3) and (Fig. 4).

A similar conclusion holds for the projected combination of ATLAS and CMS results, shown as red-dotted lines. The reduced statistical error leads to an increase of the excluded values of by for . For , where the current analysis just barely sets a limit, the exclusion is larger, while for neither the current nor the combined analysis yield any exclusion limit.

As explained in Sec. 2.2 a change in the phase of (here from to ) does not only change the couplings but also has a dynamical effect on the decay processes, which depends on the relative of the two neutralinos and the Higgs or gauge boson. The corresponding p-wave suppressed (s-wave) amplitude for opposite (equal) relative of the neutralinos and the Higgs or boson is most pronounced at the corresponding neutralino decay thresholds, while it becomes negligible for boosted Higgs bosons or gauge bosons777Analyses for neutralino decays to boosted Higgs bosons have been presented in [15, 16, 17, 60]. The p-wave suppression effect in the scenario, compared to the s-wave decays is reflected in the softer rise of the green curve at the threshold for the decay to the Higgs boson. Since both the and the lightest Higgs boson are -even888In case of a complex the lightest Higgs will receive a very small -odd admixture., the effect cancels out in the branching ratio for larger mass differences. Notice, however, that this will not be the case if there are additional decay channels open, as will be discussed in Sec. 4.4 for the DM-motivated scenario .

We also briefly investigate the effects of a variation of the overall sfermion mass scale, , i.e. the  scenario. In the upper left plot of Fig. 3, besides the production cross section using the default value shown as a black line, we also show as dotted (dot-dashed) gray line the production cross section for . Choosing the squarks of the first two families at (roughly) their experimental lower mass limit increases the destructive interference of the -channel squark exchange with the -channel gauge boson exchange production channels. The effect is negligible for the smaller neutralino/chargino masses where the -channel dominates, while it results in a suppression of over for the largest masses shown. Accordingly, we observe a smaller (larger) production cross section for a smaller (larger) value of . While the effects are small in comparison to taking into account the decay to Higgs bosons (green line), one can observe that the low value has an effect as sizable as the combination of ATLAS and CMS data. We will not investigate the effects of a variation of further.

### 4.2 tanβ dependence

As the change in has a negligible effect on the production cross section, by definition the ATLAS limits do not depend on . However, as seen in Eqs. (8), the couplings of the neutralinos to the Higgs bosons are strongly affected by , resulting in a larger branching ratio of the second neutralino to a boson and the LSP. The experimentally excluded region changes accordingly, with chargino and second lightest neutralino masses excluded up to higher masses than for . This is illustrated in Fig. 4, where we show the production cross section times the branching ratios for the same parameters as in Fig. 3 except for , which is increased from 6 to 20, i.e. for scenario . The mass exclusion limits lie at and for a massless LSP, for the tree-level and NLO results, respectively.

For an LSP of the exclusion limits are found to be very close to the threshold for Higgs decay for positive and between and for negative . For LSP masses above no chargino masses are excluded once the decay of the second lightest neutralino to the Higgs boson is open. In this region a more meaningful quantity to consider is the ratio of the excluded cross section divided by the theoretical production cross section times branching ratios, indicating the required “improvement” necessary for an exclusion. For instance, for , and this ratio is, respectively, and for positive and negative. For the same masses but for , this ratio is smaller, and , respectively.

The results presented in Figs. 3 and 4 are summarized in Fig. 5, where we show the exclusion region in the plane for (upper plot) and (lower plot). The solid lines (shaded areas) correspond to the currently analyzed data. The dashed lines are the projection for the combination of ATLAS and CMS LHC8 data, where the exclusion limit is calculated as for the dotted red line in Fig. 3. The red lines show the ATLAS analysis, the green lines take into account the decays for , and the blue ones for . The exclusion curves are not smooth, reflecting the fact that excluded cross sections obtained from ATLAS are only available for a sparse grid of points in the plane, and are given by the points in Fig. 3 and 4 where the red lines cross the black, blue and green lines, both for the ATLAS data and for LHC8 combined data. Technically, this is achieved by interpolating the cross section as a function of for fixed values of . Note that above the light (dark) gray line the on-shell decay is kinematically forbidden. Above the light gray line only off-shell decays of are allowed, which is discussed in Sec. 4.8.

The results for scenario , i.e. with , are shown in the upper figure. The dramatic reduction of the excluded area from the ATLAS result in comparison when the decay is taken into account is clearly visible. Only the region where is kinematically forbidden, extended by small strips close to the kinematic limit can be excluded by the current ATLAS analysis. The excluded area grows only marginally taking into account the projection for the LHC8 full data set, i.e. the projected combination of ATLAS and CMS data.

The results for scenario , i.e. with , are displayed in the lower figure of Fig. 5. While, by definition the curves with are identical for and , the regions excluded taking into account are somewhat larger for . Still a substantial reduction of the excluded regions remains visible. Again, the observations in Fig. 5 can easily be understood in terms of Eq. (8) and (7), where we see that for smaller and large the decay to the Higgs dominates, and the branching ratio to the boson substantially smaller than one.

Altogether these results show, on the one hand, how important it is to look at a realistic spectrum (i.e. where the decays to a Higgs boson are not neglected), and on the other hand that dedicated searches for the channel are beneficial [15].