METing SUSY on the Z peak

Recently the ATLAS experiment announced a 3 $\sigma$ excess at the Z-peak consisting of 29 pairs of leptons together with two or more jets, $E_T^{\rm miss}>225$ GeV and $H_T \geq 600$ GeV, to be compared with $10.6 \pm 3.2$ expected lepton pairs in the Standard Model. No excess outside the Z-peak was observed. By trying to explain this signal with SUSY we find that only relatively light gluinos, $m_{\tilde g} \lesssim 1.2$ TeV, together with a heavy neutralino NLSP of $m_{\tilde \chi} \gtrsim 400$ GeV decaying predominantly to Z-boson plus a light gravitino, such that nearly every gluino produces at least one Z-boson in its decay chain, could reproduce the excess. We construct an explicit general gauge mediation model able to reproduce the observed signal overcoming all the experimental limits. Needless to say, more sophisticated models could also reproduce the signal, however, any model would have to exhibit the following features, light gluinos, or heavy particles with a strong production cross-section, producing at least one Z-boson in its decay chain. The implications of our findings for the Run II at LHC with the scaling on the Z peak, as well as for the direct search of gluinos and other SUSY particles, are pointed out.

well-motivated experimental programme to search for SUSY effects is of the highest interest.
Within this scenario, the ATLAS Collaboration has recently presented an intriguing excess at the 3 sigma level of e + e − and µ + µ − pairs just at the Z peak [9], accompanied by hadronic activity and missing transverse energy (MET). With an integrated luminosity of 20.3 fb −1 at a p − p CM energy of 8 TeV, the experiment observes a total of 29 pairs of electrons and muons with an invariant mass compatible with the Z boson mass, with an expected background of 10.6 ± 3.2 pairs. No excess over the expected background is observed outside the Z peak 1 . The question that immediately arises is whether SUSY, or some other extension of the Standard Model (SM), is able to explain that excess of Z + MET events taking into account the current limits on beyond the SM physics. A study in those terms within a SUSY framework is presented in this paper.
As we will show, the observed signal can only be explained if one has a large production crosssection of heavy SUSY particles (gluinos or squarks) whose decay chain contains about one Z-boson per parent particle. If such an explanation is indeed the answer to the observed excess, our study points out the way to confirm it in the Run II of LHC, as well as cosmological implications, in particular the particle content of dark matter in the Universe. The resulting scheme of SUSY particle mass hierarchy, including charginos and neutralinos, will be apparent.

II. ATLAS EXCESS IN l + l − ON THE Z PEAK
In order to motivate and clarify the assumptions that will be made in the next sections, a simplified summary of the mentioned ATLAS search is given here.
The main focus of the search in [9] are the decays of squarks and gluinos with two leptons (electrons or muons), jets and E miss T in the final state, where the two leptons originate from a Z-boson.
In order to discriminate between SM background events and a possible signal, the following requirements are applied: • At least two same-flavoured leptons with opposite electric charge are required in each event.
If more than two leptons are present in the event, the two with the largest values of p T are selected. The leading lepton, i.e. the lepton with highest p T , must have p T > 25 GeV , whereas the subleading lepton p T can be as low as 10 GeV . Their invariant mass must fall within the Z boson mass window, here considered as 81 < m ll < 101 GeV . 1 A similar analysis on Z plus E miss T has been performed by CMS [10]. However, among other differences, no cut on HT has been applied. No deviation from SM expectations has been observed here.
• All events are further required to contain at least two jets with p T > 35 GeV and |η| < 2.5, to have E miss T > 225 GeV and H T > 600 GeV , where H T is the p T sum over all the jets with p T > 35 GeV and |η| < 2.5 and the two leading leptons: H T = i p jet,i T + p lepton,1 T + p lepton,2 T .
• Furthermore, the azimuthal angle between each of the two leading jets and E miss T is required to be higher than 0.4.
A great effort has been made to accurately estimate the number of SM events that survive the previous selection. An enumeration of these expected SM processes together with some of their characteristics follows: • The main background, namely tt, together with W W , W t and Z → τ τ , which add up to ∼ 60% of the predicted background, have been estimated using a data-driven method that has been thoroughly cross-checked with different techniques.
• Diboson backgrounds with real Z-boson production (∼ 25%) and "rare top" (tt + W, tt + Z, tt + W W and t + Z) backgrounds (< 5%) are estimated using MC simulation. These are subject to carefully assessed theoretical and experimental uncertainties.
• Processes with "fake leptons", i.e. leptons originating from the mis-identification of a jet, (∼ 10%) are estimated using a data-driven method used regularly in most of ATLAS analyses.
• Finally, particular care has been taken to suppress the Z/γ * + jets background as much as possible, given that it could mimic a possible signal (the cut in the azimuthal angle between each of the two leading jets and the E miss T has been applied to serve this purpose). Nonetheless, a data-driven technique has been used to estimate this small (< 1%) but important background.
The total number of expected SM model events passing all the requirements is 10.6 ± 3.2 and the number of observed data events is 29. This corresponds to a 3.0 σ significance.

III. Z-BOSON PRODUCTION IN THE MSSM
As explained above, if the observed excess is confirmed, it would clearly point to a new nonstandard process producing additional Z-bosons at LHC energies. Z-bosons are regularly produced in the decay chains of most of the SM extensions. Still, this signal would require a significant production of Z-bosons without conflicting with all other experimental searches of beyond the SM particles. In fact, using the central value for the expected background and taking into account the Z-branching ratio to muon and electron, this would imply that we have produced 273 ± 48 additional Z-bosons (with 20.3 fb −1 ). Assuming the Z-bosons are produced in the decay-chains of beyond the SM particles, Y , produced in the collision, we need to produce at least 273/N (Y → Z) Y particles, with N (Y → Z) the average number of Z-bosons produced in the decay of a Y particle. On the other hand, as we will see next, the experimental cuts used in the experiment, namely n jets ≥ 2, E miss T > 225 GeV and H T > 600 GeV , define further the characteristics of the Y particle and its decays.
Now, the following question is whether it is possible to produce these extra Z-bosons with the associated event-attributes in some SUSY extension of the SM, while at the same time all the constraints imposed by present new-physics searches at LHC and other experiments are satisfied.
In this section, we will assume that the acceptance of the applied selection, also taking into account the reconstruction efficiencies is ideally equal to unity. In Section IV, we will perform a "realistic" simulation in a SUSY model using Delphes [11] to take into account the signal acceptance and detector efficiencies.

A. Production cross-section of MSSM particles
We need to produce 273 (225 at one-σ) Z-bosons if we want to accommodate the observed excess in lepton-pairs. Assuming that R-parity is conserved, supersymmetric particles are produced in pairs in processes of the type pp → YȲ . Thus, the required cross-section for this process would be, where we take into account that two Y particles are produced in each event. So, if we obtained one Z-boson for each Y -particle produced, we would need a production cross-section of (6.7 ± 1.1) fb at the LHC with a CM energy of 8 TeV. Then, the first thing we must do is to determine whether it is still possible to have these production cross-sections for some supersymmetric particle taking into account the constraints from direct searches at LHC. Here, we consider the production cross sections of different supersymmetric particles separately to identify the relevant processes. However, in a full simulation, as done in Section IV, different sparticles contribute to the final Z plus jets plus MET signal and the different contributions must be added.
Naively, the first option to consider in a hadron collider would be strong production of squarks or gluinos (assuming they produce Z bosons in their decays). However, current experimental searches of jets plus missing energy at LHC force the masses of these coloured particles to be high [12][13][14].
Nevertheless, as we will see below, in some cases we can still find cross-sections of the required size.
Production cross-sections of gluinos and squarks depend only on their masses and are basically independent of other MSSM parameters. In the case of gluino and squarks of the first generation, the cross-section depends both on the squark and gluino masses due to t-channel contributions, but in the case of stops or sbottoms it depends only on the stop or sbottom mass. In Fig. 1 we present the production cross-section of gluino pairs and light-flavour squark pairs 2 calculated at NLL+NLO with NLL-fast [15][16][17][18][19][20][21] as a function of the gluino or squark mass. Fig. 2 shows the squark plus gluino cross-section as a function of the squark or gluino mass with the second mass fixed at different values. The different bands in these figures correspond to the cross-section at oneσ with fixed squark or gluino masses: the blue (dashed) band corresponds to mq ,g = 1000 GeV, the brown (dash-dotted) band to mq ,g = 1500 GeV, the orange (dotted) band has mq ,g = 2500 GeV and the red (solid) band corresponds to decoupled squarks or gluinos. In all these plots, the horizontal grey lines represent the required cross-section at one-σ needed to reproduce the referred ATLAS excess.  As we can see in these figures, the required cross-section is reached only for light gluino and squark masses. In the case of gluino production, the needed cross-section is obtained only for mg 1200 GeV and favours heavy squark masses. In fact, these gluino masses are in the boundary of the allowed region obtained from jets plus missing E T searches at LHC [12][13][14] and would contribute significantly only if everyg produces at least a Z-boson in its decay. For the production of squark pairs, present limits are mq 1400 GeV for heavy gluinos and mq 1650 GeV for degenerate squarks and gluinos [12][13][14]. Under these conditions, σ(pp →qq) is always well-below the required cross-section, even for mq 1400 GeV. Here, we do not show the cross-section σ(pp →qq * ) as it is typically one order of magnitude smaller than σ(pp →qq), and thus irrelevant.
Another important process is the simultaneous production of squark and gluino shown in Fig.   2. However, we see that we would need both squark and gluino to be light, which is not possible if we take into account the bounds from LHC searches [12][13][14]. In summary, the best option seems to be gluino pair production with mg 1200 GeV with relatively heavy squarks mq 3000 GeV, if we can get at least one Z boson in every gluino decay.
Yet, we can also consider the strong production of stop pairs, where the current bounds on stop masses are much lower, mt 650 GeV [22,23]. The totaltt * production cross-section is shown in  and only a small fraction of the events are able to overcome the cut on H T . Therefore, we must conclude that it is not possible to generate the required cross-section and fulfil the requirements of the observed excess through stop production.
Apart from the production cross-sections of coloured sparticles, we could still consider the weak production of charginos/neutralinos which can be large enough for light gauginos. Taking into account that the current bounds on chargino and neutralino masses are not very stringent, electroweak production is worth exploring [24,25]. It is well-known that the largest electroweak production cross-sections are those corresponding toW 0W ± andW +W − , in terms of gauge eigenstates. This would correspond to χ 0 2 χ ± 1 and χ + 1 χ − 1 in terms of mass eigenstates. However, the observed signal requires Z-boson on-shell, at least two jets, E miss T > 225 GeV and a minimum H T of 600 GeV. As an example, we present, in Figure 5, the production cross-section Then, we can expect the cross-section σ(pp → χ 0 1 χ + ) at larger √ŝ values to be strongly reduced. This is shown by the red (solid) line in Figure 5: a relatively mild cut on the hadronic H T reduces the cross-section by more than one-order of magnitude.
Thus we must conclude that, although electroweak production could contribute efficiently to the production of additional Z-bosons, these events can not overcome the experimental cuts and can not give rise to the observed signal.
With this channel, we have reviewed all relevant production cross-sections of different supersymmetric particles that could potentially explain the signal. The next step would be to calculate the average number of Z-bosons per parent particle Y , that we use in Eq. The main sources of Z-bosons are the decays of neutralinos and charginos and also in some squark decays. The couplings of charginos/neutralinos to Z are given by, Therefore, we can obtain Z bosons in the decays of higgsino-like neutralinos and charginos. For instance in a usual mSugra spectrum, the second neutralino will only produce Z-bosons through its (relatively small) higgsino component while the two heavier neutralinos can be expected to produce a sizeable number of Z-bosons. On the other hand, charginos can produce Z-bosons both through the wino and from the higgsino component but only in decays of the heavier charginos, as the lightest one will only decay to a W -boson and a neutralino (or lepton-slepton if ml ≤ m χ + ).
In Fig. 6 we can see the values of N (χ 0 2,3 → Z) as a function of m χ 0 2,3 in an mSugra model. Here, we obtain N (χ 2 → Z) around 0.1, as expected if the higgsino content is relatively small. Then, N (χ 3 → Z) can reach at most 0.45 while the other 50% of the decays go to χ ± W ∓ . Similarly the heavy charginos produce Z-bosons in their decay as can be seen in Fig. 7. In this case N (χ + 2 → Z) can be 0.3, while we have similar branching ratios to χ 0 1 W + and χ + 1 h.
As we can see, the Z couplings are chirality diagonal and therefore, in decays, they can only enter through chirality mixing. Although these couplings could be flavour changing, flavour mixing is bounded to be small due to the stringent flavour changing neutral current constraints. Therefore we can expect a sizeable amount of Z-bosons produced only through chirality mixing in third generation sfermions in decays liket 2 →t 1 + Z, orb 2 →b 1 + Z in the large tan β regime.
In addition, we obtain Z-bosons in the decay chains of strongly produced sparticles. We can obtain Z-bosons at different steps of the decay chain, either through the couplings of Z to sfermions or to charginos/neutralinos that we saw above. For instance, if we produce a pair of gluinos a possible decay chain would beg Therefore taking into account the corresponding branching ratios, this decay chain would contribute , the number of Z-bosons produced perg produced. given the size of production cross-sections consistent with the present searches, we need to obtain nearly one Z-boson per Y particle produced. Therefore, from the expected numbers of Z-bosons that we have seen in this section, we have to conclude that it is not possible to reproduce the observed signal in a MSSM with a stable (and light) neutralino.

Nevertheless, we can still consider different variations of the MSSM:
• A first possibility would be to have a light gluino below 1 TeV that can evade the bounds from jets plus missing E T if it decays to a sufficiently heavy neutralino LSP in a sort of compressed spectrum. Under these conditions the gluino would be abundantly produced at LHC and even a small number of Z-bosons per gluino could fulfil the requirements to explain the observed signal. However, this would require strongly non-universal gaugino masses and very heavy LSP's and we will not follow this path here.
• A second option is to consider an MSSM where the lightest neutralino decays to a lighter gravitino plus some Z-boson. This is the case in gauge mediated MSSM [26][27][28][29] and it could be also possible in gravity mediated MSSM if the gravitino is lighter than the neutralino which then becomes the NLSP [30]. In this case, the neutralino decays to Z-boson and gravitino if it is allowed by phase-space and the branching ratio will depend on the lightest neutralino composition. This is the possibility we will explore in the following.
Thus, we will analyze a situation where the neutralino is the next to lightest supersymmetric particle and the LSP is the gravitino. All supersymmetric particles will decay to the lightest neutralino which then decays to gravitino plus a photon, a Z-boson or a Higgs. The decay width of the lightest neutralino to photon, h or Z plus gravitino [30][31][32] is given by, with F (x, y, z) a function of the particle masses non relevant for our discussion that can be obtained from [30]. As we can see, if the lightest neutralino is bino-like, N 11 1, and the mass difference between neutralino and gravitino is larger that the Z-mass, the branching ratios are BR(χ 1 → Although in gauge mediation models the LSP is always the gravitino, the gaugino masses in minimal models are proportional to the gauge couplings and therefore the LSP is mostly bino with small wino and higgsino components. Then, we will have to consider other extensions of the gauge mediation idea, like the so-called General Gauge Mediation (GGM) where the gaugino and sfermion masses depend on hidden sector current correlators which can be different for different gauge groups or particle representations. As we will show in the following section, in these models it is possible to obtain general neutralino NLSP as required to explain the excess.

IV. A POSSIBLE EXPLANATION IN GENERAL GAUGE MEDIATION
Minimal gauge mediation predicts that all scalar and gaugino masses originate from a single scale and powers of the gauge couplings [29]. Recently a model-independent generalization of gauge mediation was proposed under the name of General Gauge Mediation [33,34], where all the dependence of soft masses on the hidden sector is encoded in three real and three complex parameters obtained from a small set of current-current correlators. In these models the gaugino and sfermion masses are given by, Having six parameters,B 1/2 r (0) andÃ r , to fix the soft masses in the observable sector, it is clear now that we have much more freedom in GGM [35][36][37][38] and, in particular, we have as required to reproduce the observed signal at ATLAS. In particular, we need the NLSP to decay to gravitino and a Z-boson with a branching ratio close to one. Fortunately, this is possible in GGM as shown in Ref. [38,39].
In this GGM scenario we have used SPheno-3.3.3 [40,41] to obtain the full supersymmetric spectrum at LHC energies. We define the GGM1 parameter point with the following parameters, On the other hand the relatively large NLSP mass is needed to overcome the E miss T cut.
2. The gluino is relatively light mg = 1088.0 GeV which allows for a sizeable production crosssection and taking into account the squark masses of order ∼ 3 TeV, this mass is allowed by the latest LHC bounds. and Thomas [42]. Here, we assume that this problem is solved by one of these mechanisms, given it does not affect the observed phenomenology on the Z-peak  Under these conditions, the lightest neutralino width is Γ χ 1 = 4.097 × 10 −10 GeV and the decay branching ratios are BR(χ 0 1 →Gγ) = 1.14 × 10 −3 , BR(χ 0 1 →GZ) = 0.997 and BR(χ 0 1 →Gh) = 1.35 × 10 −3 . Therefore, gluinos are produced at LHC with a cross-section of 8.4 ± 1.6 fb at NLL+NLO and after going through different decay chains all of them produce a Z-boson plus a gravitino. In this case, the strong production represents approximately 20% of the total production cross-section.
We simulate the production of supersymmetric particles at LHC at 8 TeV (LHC8) with this spectrum using Pythia 8.1 [43] with Prospino2 [15,16,44] K-factors and the response of the ATLAS detector using Delphes [11]. The selection of events for this study is done as close as possible to that performed in ATLAS [9]. The dashed red line in Fig. 9 and Fig. 10 shows the H T and E miss T distributions respectively for the GGM1 point after applying all the selection detailed in section II except for the H T and E miss T cuts. In the H T distribution, we can distinguish the two peaks corresponding to electroweak production at low H T values and gluino production at higher H T . From here, we can expect that the cut on H T will eliminate most of the electroweak production but not the gluino production. This can be seen in Fig. 10, where the E miss T distribution is presented separately for strongly produced events (solid blue line) and for the electroweak component of the production (dashed red line) for the same selection as in Fig. 9  With these parameters we obtain the spectrum shown in Table II. The neutralino mixing matrix in point GGM2 is similar to the corresponding mixing matrix in GGM1, and the BR(χ 0 1 →GZ) = 0.94. However, gluino is now much lighter and the gluino-gluino cross-section is now (41.6 ± 7.5) with Prospino at NLL+NLO, thus we can expect many more gluino pairs to be produced and a larger contribution in the final selection for this point.
The simulation for this GGM2 point is presented by the solid blue line in Fig. 9. The H T distribution peaks at slightly lower values than in the case of GGM1, due to the slightly lower gluino mass, but it is still enough to overcome the H T cut at 600 GeV. The E miss T distributions are similar for both GGM points, due to the very similar neutralino masses in both cases. However,  in the case of GGM2 the strong production cross-section is larger and much more important in relation with the electroweak production: for the GGM2 point, the strong production represents ∼ 70% of the total cross-section. As seen in Fig. 11, after applying the selection we obtain an expected signal of 28.0 ± 4.7 events, compatible with the excess reported by ATLAS. We have to emphasize here that it is not difficult to obtain the observed excess for light gluino masses, and a gluino mass in between the two presented examples, mg ∈ [900, 1100] GeV, could reproduce the observed signal. However, these points may be in conflict with direct searches of jets plus E miss T [12][13][14]. There is a tension between this excess and the bounds from gluino searches in jets plus E miss T . This tension will only be solved by the new data at LHC13. Therefore, we have proved that it is indeed possible to construct a Supersymmetric model that accommodates the observed excess of lepton pairs on the Z-peak. The simulations presented here are only a proof of existence and the final model may be very different. Nevertheless, this model will have to share the main features of the examples that we presented here.

V. PROSPECTS FOR SUSY AT LHC13
As we have shown in the previous sections, the excess observed in ATLAS, if due to SUSY, requires a gluino of a mass ∼ 1 TeV producing nearly one Z-boson per gluino in its decay. This scenario would also require relatively heavy squarks of the first generation with mq 2.5 TeV. If this is indeed the correct explanation to the observed excess, such light gluinos would be abundantly produced at Run II in LHC together with other SUSY particles. Therefore, the results obtained at pp collisions at 13 TeV will immediately confirm or reject this supersymmetric explanation of the ATLAS excess.
Using NLL-Fast with the spectrum of point GGM1, the gluino pair production cross-section at In any case, for both points this would have unambiguous signatures, both on the Z-peak with a scaling of the signal found at LHC8 and in direct searches for gluinos using jets plus missing E T in the extension of the analysis in [12][13][14].
To confirm that it is indeed SUSY behind the excess found at the Z-peak, we should search for other sparticles at LHC13. As shown in Section III A, squarks of the first generation are preferred be heavy to increase the gluino production cross-section, namely above 2.5 TeV. Then their production cross-section at LHC13 would be around 1 fb which would make direct detection very challenging. Charginos and neutralinos are expected to be well-bellow the gluino mass in general and could be abundantly produced at LHC. Although our analysis does not fix the masses of χ ± 1 and χ 0 1,2 , they are expected to be rather heavy m χ 0 1 300 GeV and degenerate. In some cases, the production cross-section could be large. For instance σ(pp →χ + 1 χ 0 1 ) NLO LHC8 = 60.2 ± 0.9 fb and σ(pp →χ + 1 χ 0 1 ) NLO LHC13 = 154 ± 5 fb calculated with Prospino for m χ 0 1 = 313 GeV and m χ + 1 = 314 GeV (with largeW component in χ 0 1 ). Notice that, as explained above, electroweak production is also large for these points at 8 TeV, but is eliminated by the cuts on H T and number of jets.
Thus, a large electroweak production could be expected at LHC13 and dedicated searches should be encouraged, specially taking into account the requirement of a large production of Z-bosons in chargino and neutralino decays. Finally, the signal does not constrain the masses of sleptons or third generation squarks and, a priory, we can not make any prediction on their production at LHC13.
Before closing, we should comment on the nature of dark matter in our scenario. As we have seen the signal seems to prefer a non-stable neutralino decaying to a very light gravitino and a Zboson. Under these conditions the neutralino mass has no relation with the dark matter abundance of the universe and its role as dark matter compon ent would be played by the gravitino. The gravitino mass is not bounded by the observed signal but regardless of its exact mass, unfortunately no signal of dark matter is to be expected in direct search experiments.

VI. CONCLUSIONS
Recently the ATLAS experiment announced a 3 σ excess at the Z-peak consistent of 29 pairs of leptons observed to be compared with 10.6 ± 3.2 expected lepton pairs. No excess outside the Z-peak was observed. By trying to explain this signal with SUSY we found that only relatively light gluinos, mg 1.2 TeV, together with a heavy neutralino NLSP of mχ 400 GeV decaying predominantly to Z-boson plus a light gravitino, such that nearly every gluino produces at least one Z-boson in its decay chain, could do it.
Unfortunately, this is not possible withing minimal SUSY models, as mSugra, minimal gauge mediation or anomaly mediation. The requirement of a neutralino NLSP decaying to Z plus gravitino points to models of General Gauge mediation as the simplest possibility. We have shown that a model of this class is able to reproduce the observed signal overcoming all the experimental cuts. Needless to say, more sophisticated models could also reproduce the signal, however, they will ALWAYS share the above mentioned features, i.e. light gluinos (or heavy particles with a strong production cross-section) with an effective N (g → Z) 1.