Light Sneutrino Dark Matter at the LHC

In supersymmetric (SUSY) models with Dirac neutrino masses, a weak-scale trilinear A-term that is not proportional to the small neutrino Yukawa couplings can induce a sizable mixing between left and right-handed sneutrinos. The lighter sneutrino mass eigenstate can hence become the lightest SUSY particle (LSP) and a viable dark matter candidate. In particular, it can be an excellent candidate for light dark matter with mass below ~10 GeV. Such a light mixed sneutrino LSP has a dramatic effect on SUSY signatures at the LHC, as charginos decay dominantly into the light sneutrino plus a charged lepton, and neutralinos decay invisibly to a neutrino plus a sneutrino. We perform a detailed study of the LHC potential to resolve the light sneutrino dark matter scenario by means of three representative benchmark points with different gluino and squark mass hierarchies. We study in particular the determination of the LSP (sneutrino) mass from cascade decays involving charginos, using the mT2 variable. Moreover, we address measurements of additional invisible sparticles, in our case the lightest neutralino, and the question of discrimination against the MSSM.


Introduction
There is abundant and compelling evidence that the bulk of matter in the universe is made of massive, electrically neutral particles: dark matter (DM) [1]. While the density of DM has been precisely determined, the identity of the DM particle (or particles) is a complete mystery. Remarkably, many extensions of the Standard Model (SM) of electroweak and strong interactions-designed to address theoretical issues related to the breaking of the electroweak symmetry-require the introduction of new particles, some of which are excellent DM candidates. This is most notably the case in R-parity conserving supersymmetry (SUSY) [2].
If the origin of DM is indeed new physics beyond the SM, in particular SUSY, there are high hopes that DM will be produced in abundance at the LHC, through cascade decays of the new matter particles produced in the pp collisions [3]. The ambitious goal will then be to determine the properties of the DM candidate and reconstruct its thermal relic abundance from collider data. On the one hand this may then be used further to make testable predictions for direct and indirect DM searches. On the other hand, if the DM mass determined at colliders and non-accelerator experiments agrees, it may be used to constrain the cosmological model. This would enormously enhance the interplay between particle physics, astrophysics and cosmology. The LHC phenomenology of DM-motivated SUSY scenarios has hence been discussed in great detail in the literature [2,3].
Another experimental evidence that the SM misses something fundamental is the observation of neutrino oscillations [4]. This can be resolved by including right-handed neutrinos in the model. Current observations, however, do not allow to establish the Majorana or Dirac nature of neutrinos. While the smallness of the neutrino mass can be naturally explained by introducing Majorana mass terms and making use of the see-saw mechanism, Dirac masses for neutrinos with very small Yukawa couplings are a viable and interesting alternative. In supersymmetric theories, one may naturally obtain very light Dirac neutrino masses from F-term SUSY breaking [5,6]. In addition to providing an explanation for neutrino masses, this class of SUSY models offers an interesting alternative to the conventional neutralino DM candidate: the sneutrino.
The crucial point is that in these models one can have a weak-scale trilinear Aν term that is not proportional to the small neutrino Yukawa couplings and can hence induce a large mixing between left-handed (LH) and right-handed (RH) sneutrinos even though the Yukawa couplings are extremely small. The lightest sneutrino can thus become the lightest SUSY particle (LSP) and a viable thermal DM candidate.
Note that the mainly RH sneutrino LSP is not sterile but couples to SM gauge and Higgs bosons through the mixing with its LH partner. Sufficient mixing provides efficient annihilation so that the mixed sneutrino can be a viable thermal DM candidate with a relic density of Ωh 2 ≃ 0.11 as extracted from cosmological observations [7,8]. On the other hand the amount of mixing is constrained by limits on the spin-independent scattering crosssection, for which the LH sneutrino component receives an important contribution from Z exchange; this cross-section is suppressed by the sneutrino mixing angle. Because of the gauge and Higgs interactions, the presence of the mixed sneutrino can also significantly impact Higgs and SUSY signatures at the LHC [5].
In [9], some of us investigated the case of mixed sneutrinos as thermal DM with special emphasis on the mass range below ∼10 GeV. We examined the viable parameter space and discussed implications for direct and indirect dark matter searches, as well as consequences for collider phenomenology. Regarding the latter, we found that the SUSY signatures greatly differ from the expectations in the conventional Minimal Supersymmetric Standard Model (MSSM) with a Z 1 LSP: while squarks and gluinos have the usual cascade decays through charginos and neutralinos, with the same branching ratios as in the corresponding MSSM case, the charginos and neutralinos decay further into theν 1 LSP. In particular, with practically 100% branching ratio over most of the parameter space. At the LHC, the typical cascade decays therefore areq R → q Z 1 → qνν 1 ,q L → q Z 2 → qνν 1 andq L → q W 1 → q ′ l ±ν 1 , all giving different amount of missing transverse energy, E T . Moreover, gluino-pair production followed by decays into qq ′ W 1 through either on-or off-shell squarks leads to same-sign (SS) and opposite-sign (OS) dilepton events with equal probability. Besides, the light Higgs decays invisibly into a pair of LSPs, h 0 →ν 1ν1 .
In this paper, we now perform a detailed study of the LHC potential to resolve the light sneutrino DM scenario. This includes in particular the determination of the DM mass fromg → qq ′ W 1 → q ′ l ±ν 1 and/orq → q ′ W 1 → q ′ l ±ν 1 events. To this end we rely on the subsystem m T 2 method [10]. Moreover, we address the question of measuring the masses of additional invisible sparticles. The case of a ∼ 100 GeV mixed sneutrino LSP was studied in [11].
The paper is organized as follows. First, in Section 2, we briefly recall the main features of the mixed sneutrino model. In Section 3 we present three benchmark points and their characteristic signatures. This sets the framework of the analysis. We then go on in Section 4 to study the discovery potential at the LHC with 7 TeV center-of-mass energy. Measurements at the 14 TeV LHC are discussed in detail in Section 5. A summary and conclusions are given in Section 6.

Mixed sneutrinos
The framework for our study is the model of [5] with only Dirac masses for sneutrinos. In this case, the usual MSSM soft-breaking terms are extended by where m 2Ñ and Aν are weak-scale soft terms, which we assume to be flavor-diagonal. Note that the lepton-number violating bilinear term, which appears in case of Majorana neutrino masses, is absent. Neglecting the tiny Dirac masses, the 2 × 2 sneutrino mass matrix for one generation is given by Here m 2 L is the SU(2) slepton soft term, v 2 = v 2 1 + v 2 2 = (246 GeV) 2 with v 1,2 the Higgs vacuum expectation values, and tan β = v 2 /v 1 . The main feature of this model is that the m 2 L , m 2 N and Aν are all of the order of the weak scale, and Aν does not suffer any suppression from Yukawa couplings. In the following, we will always assume m N < m L so that the lighter mass eigenstate,ν 1 , is mostly aν R . This is in fact well motivated from renormalization group evolution, since for the gauge-singletν R the running at 1 loop is driven exclusively by the Aν term: A large Aν term in the sneutrino mass matrix will induce a significant mixing between the RH and LH states, leading to mass eigenvalues where m 2 ± ≡ m 2 L ± m 2Ñ + m 2 Z /2, and mν 1 < mν 2 by convention. Notice that a large value of Aν can induce a large splitting between the two mass eigenstates even if m 2 L and m 2 N are of the same order, leading to scenarios where mν 1 ≪ mν 2 , ml L . In this way,ν 1 can naturally be driven much below the neutralino masses.
Taking mν 1 , mν 2 and θν as input, the soft terms m N , m L and Aν entering the sneutrino mass matrix Eq. (2.2) are fixed. This also fixes the corresponding LH charged slepton mass, − m 2 Z cos 2β sin 2 θ W , we assume m R ≡ m L for simplicity. We use an appropriately modified version of SuSpect [12] for the spectrum calculation, which includes in particular radiative corrections induced by the Aν term, as given in [9].
A full scan of the relevant parameter space was done in [9], taking into account constraints from the Z invisible decay width, the Higgs and SUSY mass limits, as well as DM constraints from the relic abundance and direct and indirect DM searches. It was found that light mixed sneutrino DM consistent with all constraints populates the region 1 GeV mν 1 8 GeV and 0.1 sin θν 0.4 . (2.7) Moreover, over most of the parameter space, mν 2 200 GeV and ml L,R > m Z 1 , W 1 . For LHC physics this means that the final steps of the cascade decays will be dominated by Z 1,2 → ν +ν 1 and W 1 → l +ν 1 . The remaining relevant parameters are the squark and gluino masses, which determine the production cross sections.

Benchmark points and characteristic signatures
In order to study the light mixed sneutrino DM (SNDM) scenario at the LHC, we pick a parameter point from [9] with aν 1 LSP of 7.6 GeV as the DM candidate. The other sneutrino parameters are mν 2 = 524 GeV, sin θν = 0.225 and tan β = 10 (A ν = 348 GeV). The neutralino/chargino sector is given by M 2 = 2M 1 = 221 GeV and µ = 800 GeV. Together with m R = m L = 514 GeV, this fixes the properties of the weakly interacting sparticles. Note we assume flavor degeneracy. Based on this setup we define in Table 1 three benchmark points (SN1-SN3) with the same electroweak sector but different gluino-squark mass hierarchies. The squark and gluino production cross sections, computed using Pythia [13], are given in Table 2, and the relevant decay branching ratios are given in Table 3.
Employing GUT relations for gaugino-mass parameters, point SN1 has a gluino mass of mg = 765 GeV, while squark soft terms are set to 1.5 TeV, resulting in mq ≃ 2mg. Point SN1 is therefore characterized by heavy quarks and a light gluino, which decays through 3-body final states into charginos and neutralinos, which will then decay exclusively to l ±ν and νν 1 , respectively. We hence expect dominantly gluino-pair production leading to 4 jets plus E T . Moreover, about half of the events will have an isolated charged lepton, and about 25% of the events will have two leptons with uncorrelated flavor (assuming three roughly degenerate light sneutrinos, 2/3 of the leptons are electrons or muons and 1/3 are taus).
Since the gluino is a Majorana particle, same-sign and opposite-sign dileptons should have equal rates. However, same-sign dileptons have less SM background. Promising signatures to look for are hence (a) 4 jets, 0 leptons, large E T ; (b) 4 jets, same-sign dileptons, moderate E T ; (c) 4 jets, opposite-sign dileptons, moderate E T .
Point SN2 has the same gluino mass as SN1 but lighter squarks with mq ∼ mg. Therefore SN2 has a much larger overall SUSY production, since the squark-pair and gluino-squark associated production give the main contributions to the total cross-section, as shown in Table 2. The gluinos have the same decay modes as above, while the squarks decay dominantly through q + W 1 / Z 1,2 . Events with only 2 or 3 jets are predominant and result fromqq orgq production, with the squark decaying into a neutralino or chargino (99% of theq L and 98% of theq R decays).
Finally, point SN3 is characterized by light squarks and heavy gluinos (achieved through non-universal gaugino masses). We hence expect dominantly squark-pair production followed by decays into quarks plus charginos or neutralinos, see Table 3. These events have   2 hard jets plus E T , often accompanied by 1-2 leptons fromq L → q W 1 → qlν 1 . Again, events without leptons are expected to have larger E T on average than events with leptons.
It is also interesting to compare the phenomenology of the three SNDM benchmark points with the corresponding MSSM cases. To this end we consider points MSSM1-MSSM3 with the same masses as SN1-SN3 in Table 1 but with theν 1 removed from the spectrum. The MSSM points thus have a neutralino LSP with a mass of 109 GeV. The W 1 decays exclusively into Z 1 W , while the Z 2 decays into Z 1 Z (12%) or into Z 1 h (88%). 1 The larger rate of multilepton events in the SNDM scenario is a clear difference to the MSSM case. On the other hand one can expect MSSM events to have higher jet multiplicity.
Another general feature of the SNDM scenario is that, due to the invisible Z 2 decay, we expect a harder E T spectrum as compared to a similar MSSM point. This is illustrated in Fig. 1, where we show the E T distribution for the SN1/MSSM1 and SN3/MSSM3 points at detector level without any cuts (for details on the event simulation, see next Section). Notice moreover that the subset of events with W 1 → l ± + LSP has a slightly harder E T spectrum in the SNDM case. This is because the lightν 1 LSP is more boosted than the Z 1 LSP in the MSSM case; this difference becomes less significant if the LSP's mother already has a large boost. On the other hand, the E T spectrum coming fromq/g → Z 1 events are identical in both models, since the lightest neutralino decays invisibly in the SNDM.
Before studying the LHC phenomenology in more detail, a comment is in order concerning the assumption of flavor degeneracy. As discussed in [9], the exact mass splitting between theν 1 's of different flavors strongly influences the DM-allowed parameter space. There is, however, no difference between one or three light sneutrinos if the mass splitting is 1 GeV. This is because a 1 GeV mass splitting is enough to suppress any co-annihilation contributions to Ωνh 2 . Such a mass splitting is easily induced by small splittings in the soft terms, which are in fact rather generic even if one starts out with universal soft terms at a high scale. If we have, for instance, mν 1e,µ > mν 1τ , then the heavierν 1e,µ decays to theν 1τ LSP through 3-body modes [14]. The dominant decay is into neutrinos, while visible decays (e.g.,ν 1e → e ∓ τ ±ν 1τ ) have at most a few percent branching ratio. From the perspective of LHC signatures, the difference to the case of three exactly degenerate light sneutrinos is negligible. We therefore take mν 1e = mν 1µ = mν 1τ ≡ mν 1 for simplicity. Note, however, that interesting non-trivial flavor structures beyond the scope of this study may appear in the presence of lepton-flavor violation [15,16].

Discovery Potential at LHC7
We now turn to the discovery potential of the SNDM model at the

Event Simulation
For the SM background, we include in our calculations all relevant 2 → n processes for the multi-lepton and multi-jet searches. Since in this Section we restrict our results to the first LHC physics run ( 1 fb −1 and √ s = 7 TeV) we generate (at least) the equivalent of 1 fb −1 of events for each process, except for our QCD samples (see Table 4).
For the simulation of the background events, we use AlpGen [17] to compute the hard scattering events and Pythia [13] for the subsequent showering and hadronization. For the final states containing multiple jets (namely Z(→ ll, νν) + jets, W (→ lν) + jets, bb + jets, tt + jets, Z + bb + jets, Z + tt + jets, W + bb + jets, W + tt + jets and QCD), we use the MLM matching algorithm [17] to avoid double counting. All the processes included in our analysis are shown in Table 4 as well as their total cross-sections and number of events generated. The SNDM spectrum was generated with a modified version of Suspect [12], which includes right-handed sneutrinos, while the decay table was computed with CalcHEP [18]/micrOMEGAs2.4 [19,9]. Finally, using the SLHA [20] interface, signal events were generated using Pythia6.4 [13].
• Electrons and muons are considered isolated if they have |η| < 2.5, p T (l) > 10 GeV with visible activity within a cone of ∆R < 0.2 about the lepton direction, Σp cells T < 5 GeV.

Signal Distributions
In Fig. 2a-c we show the E T , n(l) and n(j) distributions for the benchmark points along with the SM background (BG) after the following set of cuts: where S T is the transverse sphericity and p T (j 1 ) is the p T of the hardest jet.
Despite having a softer E T spectrum than the SM BG, the point SN1 has a much harder n(j) distribution, which peaks at n(j) = 4, as expected from the discussion in Sec. 3. As shown in Fig. 2b, the signal exceeds the SM BG in the n(j) = 6, 7 bins. Furthermore, with this set of cuts, the lepton number distribution for point SN1 is already at the BG level for  Table 1 along with SM background for LHC7. In frames a − c the following cuts have been applied: While frame d has weaker cuts: E T > 300 GeV, n(j) > 2, p T (j 1 ) > 100 GeV, p T (j) > 50 and S T > 0.2 n(l) = 1, easily surpassing the BG in the dilepton channel. However, due to its small cross section, the SN1 signal requires several fb −1 of integrated luminosity in order to become visible. We estimate that approximately 5(2) fb −1 are required to claim a 5σ(3σ) evidence for the SN1 benchmark. As mentioned in Sec. 3, point SN2 has some distinct signatures from the benchmark point SN1. While for the latter the sparticle production cross-sections is dominated bygg, SN2 has the bulk of its signal coming fromqq andqg events. As a result the signal has a softer jet distribution, due to squark decays to charginos and neutralinos, as shown by the decay branching ratios (BRs) in Table 3. The same is valid for the SN3 signal, which is dominated by squark pair production. This is clearly seen in the n(j) distribution shown in Fig. 2b, once the overall signal normalization is taken into account. On the other hand, since the 2-body squark decay tends to produce boosted charginos and neutralinos, and because of the larger production cross-section, points SN2 and SN3 have a harder E T spectrum as compared to point SN1 (and the background), as shown in Fig. 2a. Therefore, the LHC7 should be able to discover the SN2 and SN3 points with hard E T ( 300 GeV) and p T (j 1 ) ( 250 GeV) cuts in the n(j) = 2 or 3 channels. We estimate that a 5σ evidence for both SN2 and SN3 points can be achieved with 1 fb −1 of integrated luminosity. Furthermore, from Fig. 2c we see that both points are also visible in the dilepton channel.
Since the SNDM signal is rich in boosted leptons, we show in Fig. 2d the ratio between the scalar sum of the lepton and jet E T 's, E T (l/j) ≡ E T (l)/ E T (j), for a weaker set of cuts: • E T > 300 GeV, n(j) > 2, p T (j 1 ) > 100 GeV, p T (j) > 50 GeV and S T > 0.2 As we can see, both the signal and BG distributions peak at low E T (l/j) values. However the SM BG falls much more sharply than the SN2 and SN3 signals, which are above background for E T (l/j) 0.2. Since the signal and SM distributions have very distinct shapes, E T (l/j) can be used to discriminate between signal and background even for SNDM models with smaller signal cross-sections. Nonetheless, point SN1 still is well below the SM BG to be seen at LHC7.
So far each of the SNDM signatures described above are common in standard MSSM scenarios, including the CMSSM. Let us now discuss how the distributions shown in Fig. 2 can help to distinguish between the MSSM and the SNDM models. For this purpose we also show the respective distributions for a MSSM case (MSSM3) with a spectrum identical to point SN3, but without RH sneutrino. 2 As expected, MSSM3 has a softer E T spectrum than the SNDM point SN3, although the difference after cuts is not very large. Another distinction between the MSSM and SN points is their jet multiplicity. In the SN case all charginos/neutralinos decay toν 1 + l/ν, while this channel is absent for the MSSM points and neutralinos and charginos decay instead to the Z 1 LSP plus h, Z or W , see Sec. 3. Therefore we expect SNDM models to have a softer n(j) distribution when compared to a similar MSSM case. This is confirmed in Fig. 2b, which shows that the n(j) distribution for the MSSM3 model is suppressed in the n(j) = 3 bin and enhanced in the higher bins when compared to the SN3 point (once the total signal normalization is taken into account).
The main distinct feature of the SNDM scenario appears, nevertheless, in the multilepton distribution. As discussed in Sec. 3, SNDM models are expected to be rich in hard leptons coming almost exclusively from W 1 decays. As a result, the leptons in dilepton events will have uncorrelated flavors and kinematics. Furthermore, higher lepton multiplicities only appear, at much smaller rates, from top decays. In corresponding MSSM scenarios, W 1 's and Z 2 's decays to leptons are sub-dominant: in case of W 1 , they are given by the BRs of the W , while in case of Z 2 , they are suppressed by the high BR into h 0 . To give concrete numbers, the ratio of dilepton/0-lepton events is ∼ 0.12, 0.06 and 0.06 for points SN1, SN2 and SN3, respectively, see Fig. 2c, while for the MSSM1, MSSM2 and MSSM3 points it is ∼ 0.04, 0.01 and 0.01. Furthermore, dilepton events in MSSM models often come from Z 2 decays to l + l − Z 1 and hence consist of same-flavor OS dileptons. Therefore the ratio of OS and SS dilepton events is another useful discriminant. For the set of cuts used in Fig. 2c we have SS/OS = 0.94, 0.94 and 0.62 for points SN1, SN2 and SN3, respectively. The SS/OS ratio is considerably smaller for SN3 than for the other points, because its signal is dominated by squark pair production, leading to less SS dileptons. Although the SN2 point also has a largeqq production cross-section, the n(j) ≥ 3 cut suppresses the contribution fromqq events to the SN2 signal, enhancing the SS/OS ratio in this case. For the corresponding MSSM models and the same set of cuts, we have SS/OS = 0.75, 0.54 and 0.39 for MSSM1, MSSM2 and MSSM3, respectively. As we can see, the SS/OS ratio is significantly enhanced in SNDM models, when compared to the MSSM. Furthermore, as seen in Fig.2d, the E T (l/j) distribution for the MSSM is much softer than in the SNDM case, which, together with the n(j) and n(l) distributions can also point to a light sneutrino LSP.
We conclude that, while the E T and n(j) distributions are more model dependent and more sensitive to NLO and detector systematics, the n(l) and E T (l/j) distributions are promising candidates for an early distinction between the MSSM and SNDM cases. Although the first LHC run will probably not accumulate enough luminosity to make use of the dilepton invariant mass, depending on the signal cross-section, the dilepton channel may already indicate which is the relevant model. However, a more decisive answer will have to wait for the later physics run with higher energy. In the next section we discuss how LHC14 ( √ s = 14 TeV) with an integrated luminosity of 100 fb −1 can give information on the SNDM spectrum and thefore provide stronger evidence that the SNDM case is realized.

Measuring Masses at LHC14
Despite the distinct features of the SNDM model discussed in the previous sections, information on the sparticle spectrum can give a more decisive evidence for sneutrino DM. While in most MSSM models, a neutralino LSP consistent with DM and collider constraints implies m Z 1 50 GeV (assuming gaugino mass unification), the SNDM model has a much lighter LSP. Since several fb −1 are required for any mass measurement, from now on we will present all our results for LHC14 ( √ s = 14 TeV and L = 100 fb −1 ). We include both SUSY and SM backgrounds, which include all the relevant processes listed in Table 4, but at √ s = 14 TeV (for more details see [22]).

Method
Recently much improvement has been made on mass measurement methods at hadron colliders and several distinct mass measurement techniques have been suggested, such as kinematic endpoints and shapes (invariant mass, s min , ...) and transverse mass methods (m T 2 , m CT ,...). See [23,24] for comprehensive reviews and references. Here we adopt the subsystem m T 2 method, described in detail in Ref. [10]. It consists in applying the m T 2 endpoint technique to particular subsets of the event topology.

Gluino-pair production
First, we consider gluino-pair production, with each gluino going through the cascade decay:g → qq + W 1 → qq + l +ν 1 (5.1) From this event topology we can form three subsystems: where the upper index labels the decay branch and the final states are grouped into a visible (vis) and a daughter (D) component. For instance, in the first case the gluinos are the parents (P), while qql andν 1 are the visible and daughter components, respectively. On the other hand, for the third subsytem, the charginos are the parents and l andν 1 are the visible and daughter components. The (subsystem) m T 2 variables are then constructed as defined in [25,26], but using the visible and daughter components defined within each subsystem: and m x is the trial daughter mass. Since m T 2 (m x = m D ) ≤ m P , the value of m max T 2 (m D ) determines the parent's mass in each subsystem. For the above example we have: where m qql T 2 , m qq T 2 and m l T 2 are the m T 2 subsystem variables for the subsystems 1, 2 and 3 defined in Eq. (5.2), respectively. Note that for the second subsystem the daughter is defined as lν 1 , which has invariant mass m W 1 . However, as the above relations show, in order to obtain the parent's mass, the daughter mass has to be known. The strength of the m T 2 method comes from the fact that analytical expressions are known for the function m max T 2 (m x ) and can be used to simultaneously extract both the parent and daughter masses from data. For the subsystems 1 and 2 in Eq. (5.2), we have: The above expressions were derived in Refs. [27,10] under the assumption of no initial state radiation (ISR), so the total parent p T (|p T (g (1) ) + p T (g (2) )|) is zero. In Ref. [10] it is shown that, unless p T mg, this is a reasonable approximation. Therefore for mg 700 GeV, we can safely neglect the ISR effect. On the other hand, for the subsystem 3, the parent system ( W 1 ) is expected to have large p T , since they are produced from gluino decays and are much lighter than their parents (m W 1 = 227 GeV for the cases we consider). In this case we have to include the transverse momentum effect in m l,max T 2 (m x ) [10]: and p T is the chargino pair total transverse momentum. Note that, neglecting initial state radiation for the gluino pair, we have Therefore, selecting events with a fixed p trans T , Eq. (5.7) can be used to obtain m W 1 and mν 1 . However this cut considerably reduces the statistical significance of the m T 2 distribution.

Squark production
The decay chain (5.1) is relevant for point SN1, where the signal is dominated by gluino pair-production, while for points SN2 and SN3, the sparticle production cross-section is dominated by squark pair production or squark-gluino production. In this case we will consider the following event topology: The subsystems in this case are analagous to the ones defined in Eq. (5.2), but with one less quark in the final state. Using the same notation as before, we label them as m ql T 2 , m q T 2 and m l T 2 , with: The new m max T 2 functions now obey [27,10]: while m l,max T 2 (m x ) is identical to Eq. (5.7). Note that, for a pair of m x values (m x = 0 and m x ≫ m D ), the gluino subsystems provide 6 constraints on the 3 masses involved, while the squark subsystems provide 5 constraints on 3 masses 3 . Therefore in both cases there is an arbitrariness on how to extract the mass values. Since the m l T 2 distribution requires an extra cut on p T in order to allow for the determination of m W 1 and mν 1 , it will necessarily have a much smaller statistical significance than the other m T 2 distributions. Hence we will make use only of the first two subsystems, which are already sufficient to determine all the masses involved in the process. For that, we adopt the following procedure: • For discrete values of m x , we extract the value of m max T 2 (m x ) for the subsystems 1 and 2, from the respective m T 2 distributions, following the algorithm defined in Appendix A; • We then simultaneously fit the results to the appropriate m max T 2 functions, Eqs. (5.5), (5.6), (5.10) or (5.11); • The mass values and their uncertainties are then extracted from the best fit result.
Although only two m max T 2 measurements at two different m x values are already sufficient to obtain all masses, fitting the m max T 2 (m x ) expressions for a wide range of m x values has two main advantages. First, it is less sensitive to uncertainties in extracting m max T 2 from the m T 2 distributions. Second, it allows us to test our underlying model asssumptions since a poor fit would indicate that the events selected do not correspond to the topologies (5.1) or (5.9).

Zero-lepton channel
In principle we can also determine the Z 1 and Z 2 masses if we look at the 0 lepton plus E T channel. For point SN1 this channel is dominated by gluino decays to neutralinos: The m max T 2 (m x ) function for this process obeys Eq. (5.6) with m W 1 → m Z 1 ,2 . In this case, the m T 2 distribution (for a fixed m x ) would present two endpoints, one fromg → qq + Z 2 and one fromg → qq + Z 1 . Since the latter will necessarily be at higher m T 2 values, a simple extraction of m max T 2 will always give the Z 1 endpoint, with the Z 2 endpoint partially obscured by the m T 2 distribution from Z 1 events. We have verified that, for the SN1 point, the signal/BG ratio is too small in the 4 jets, 0 lepton plus E T channel, making such a measurement unviable for L ∼ 100 fb −1 . For points SN2 and SN3 the 0 lepton plus E T channel is dominated byq decays: and the m max T 2 (m x ) function obeys Eq. (5.11) with m W 1 → m Z 1 ,2 . Since BR(q R → Z 1 ) ≃ 100%, while BR(q L → Z 2 ) ≃ 33%, the 2 jets, 0 lepton plus E T channel comes mainly fromq R decays and will have a large cross section. Therefore in this case it is possible to extract m Z 1 , once mq R is known. Hence, after determining the mq, m W 1 and mν 1 values fromq → W 1 + q decays, we will use the zero lepton channel to determine m Z 1 under the assumption that left and right-handed squarks are degenerate.
The results obtained applying the procedure described here to the benchmark points SN1-SN3 are presented below in sections 5.2 and 5.3. In our analysis we include all relevant SUSY and SM backgrounds, as well as detector and combinatorics systematics. We always assume √ s = 14 TeV and L = 100 fb −1 .

Results for SN1
To apply the m T 2 subsystem method for the SN1 point, we consider the event topology Eq. (5.1), which can be selected with the following set of cuts: E T > 100 GeV, n(j) = 4, n(l) = 2, n(b) = 0, p T (j 1 ) > 100 GeV, p T (j) > 50 GeV, p T (l) > 30 GeV . (5.14) Furthermore, to reduce the Z/γ + jets background, we veto OS-dilepton events with 80 GeV < m(l + l − ) < 100 GeV or m(l + l − ) < 40 GeV . include the full SM background in our results, the effect is subdominant. A more relevant issue is the jets and lepton combinatorics. For the subsystem 1 (2), defined in Eq. (5.2), it is necessary to group the 4 jets and 2 leptons (4 jets) into 2 visible groups, vis (1) and vis (2) . Several methods have been proposed to deal with the combinatorics issue [27,28], which usually rely on kinematical correlations between the final states. However, since we are only interested in obtaining m max T 2 , for each event we select the grouping which gives the minimum m T 2 value for that event. This way the m T 2 < m max T 2 (m x ) relation is still preserved even if the wrong grouping is selected. Nevertheless, initial and final state radiation (FSR), signal background and detector energy smearing still affects the m T 2 distribution, resulting in a tail for values above m max T 2 (m x ). In Fig. 3, we present the m qql T 2 and m qq T 2 distributions for the SN1 signal plus the SM background, where the trial mass was chosen as the respective daughter mass. For comparison purposes we also present the exact parton level distributions (dashed lines) for the signal. The spikes in the (solid) m T 2 distributions come from MC fluctuations in the SM background. As can be seen from Fig. 3

, both distributions have an edge at
• m qql T 2 ∼ 760 GeV and m qq T 2 ∼ 760 GeV .
The above values agree well with the expected value, mg. Figure 3 also shows that the m qql T 2 and m qq T 2 distributions are strongly affected by the cuts, ISR, FSR and energy smearing effects, when compared to the parton level distributions. Furthermore, our solution to the combinatorics usually shifts the m T 2 distribution to lower values, what diminishes the peak, resulting in a less evident edge.
The distributions in Fig. 3 assume a specific value for the trial mass m x , which was chosen to be the exact daughter mass in each case. However, as discussed in Sec.5, the value of m max T 2 as a function of m x allows us to extract both the parent and daughter masses, through Eqs. (5.5) and (5.6). Figure 4 shows the results obtained from fitting the m max T 2 (m x ) functions to the m max T 2 values extracted from the simulated data using the algorithm outlined in the Appendix. As can be seen from Figs. 4a Table 5: Measured mass values in GeV for the points SN1-SN3, obtained using the m T 2 subsystem method described in the text. The error shown only includes statistical uncertainties and assumes an integrated luminosity of 100 fb −1 .
(solid lines). The final result for the three masses, taken as the best simultaneous fit to both m max T 2 curves, is shown in Table 5. The approximate precision for mg and m W 1 is under a few percent, while the precision for theν 1 mass is much worse, around 50%, with the central value 1.8σ from the true one. This is due to its small mass, when compared to the other mass scales, which renders the m max T 2 expressions weakly dependent on mν 1 . Nonetheless, the results clearly point to a very light LSP, with a mass scale much smaller than the other particles involved in the cascade decay.
From the results in Fig. 4 and Table 5 we conclude that, despite the lack of precision in determining the LSP mass, the m T 2 subsystem method can still show that the LSP state is much lighter than expected in most MSSM scenarios. This would provide strong evidence for a sneutrino DM scenario, at least for the case of a light gluino/heavy squark spectrum, such as in the SN1 point.

Results for SN2 and SN3
For points SN2 and SN3 we must consider the squark cascade decay shown in Eq. (5.9). To selectq L → W 1 + q events we use the following set of cuts: E T > 100 GeV, n(j) = 2, n(l) = 2, n(b) = 0, p T (j 1 ) > 100 GeV, p T (j) > 30 GeV, p T (l) > 30 GeV (5.16) and once again veto OS-dilepton events with 80 GeV < m(l + l − ) < 100 GeV or m(l + l − ) < 40 GeV. The cross-section after cuts for points SN2 and SN3 are 32 fb and 36 fb, respectively, while for the SM background we obtain 29 fb. Despite the large background, the bulk of the SM events are concentraded at low m T 2 values (< 500 GeV). Thus the position of the m T 2 end point extraction is almost unaffected by the SM BG, as seen in Fig. 5.
For point SN2 only ∼ 65% of the signal comes from squark pair production, due to contamination from gluino pair production and gluino-squark production. On the other hand, the SUSY background is much smaller for point SN3, with ∼ 82% of the signal coming from squark pair production. After repeating the same procedure used for extracting the masses in the SN1 case, but using the appropriate m max T 2 expressions for the squark decay chain, Eqs. (5.10) and (5.11), we obtain the best fit result for mq, m W 1 and mν 1 shown in Table 5. As we can see, for both points the statistical error bars are smaller than the ones for point SN1, due to the larger signal cross-section. Once again the least precise measurement corresponds to mν 1 , due to its small value. Nonetheless we can still conclude that the LSP is much lighter than the chargino and squark.
As mentioned before, the largeqq production cross-section for points SN2 and SN3 can still provide one more piece of information about the spectrum. From Table 3, we have BR(q R → q + Z 1 ) ∼ 100%. Therefore, if instead ofq L pair production we consider theq RqR events, we can use the usual m T 2 variable withq R as the parent, Z 1 (νν 1 ) as the daughter and the jet as the visible component to measure the Z 1 mass once mq R is known. In the scenarios considered we have mq L ≃ mq R , so we can use the mq value obtained from our previous results. To select the right-handed squark signal we require: E T > 200 GeV, n(j) = 2, n(l) = 0, n(b) = 0, p T (j 1 ) > 100 GeV (5.17) The SN2 (SN3) signal in this channel is 133 (176) fb, while for the SM BG we have 68 fb. Once again, the distribution for the SM background peaks at low m T 2 and has almost no impact on the m max T 2 value. In Fig. 6 we show the m T 2 distribution for SN3 with m x = m Z 1 , where we see a clear edge at m T 2 ∼ 690 GeV, very close to the mq R input value.
The m q,max values as a function of m x for the SN3 point are shown in Fig. 7. We see that the extracted endpoints are very close to their exact value and due to the large signal statistics and low BG, the error bars are barely visible. Fitting Eq. (5.11) to the data points in Fig. 7 we obtain: which agrees extremely well with the theoretical value, 342 GeV. Assuming mq L = mq R and using the mq L value obtained from theq LqL signal (see Table 5), we can compute m Z 1 : where the error in mq R has been included when computing the uncertainty on m Z 1 . Repeating the same procedure for point SN2 we obtain: The result in this case is worse than for point SN3 because of the larger SUSY background present in the SN2 signal. This mainly affects the determination of mq, as seen in Table 5, which propagates to the central value and uncertainty in m Z 1 . Nonetheless, theq RqR channel still shows that the measured spectrum has a neutral NLSP with mass ≈ m W 1 /2. Such a neutral NLSP is consistent with a bino state, if gaugino mass unification is assumed. Therefore, the combined results of theq LqL andq RqR channels would point to the usual MSSM scenario with gaugino mass unification, but with an additional LSP state, which is neutral and very light. This would be another strong evidence for the SNDM model.

Dilepton Invariant Mass at LHC14
From the results in Table 5 we see that the m T 2 method can indicate the presence of a very light LSP neutral particle in the signal. Moreover, in case of SN2-3, the m q T 2 distribution can give information on an additional invisible sparticle, consistent with the Z 1 in case of universal gaugino masses. Additional evidence for a sneutrino LSP can be obtained from the properties of dilepton events, as already discussed in Sec. 4.2. Although at 7 TeV the dilepton signal is likely too small to allow for the use of the dilepton invariant-mass distributions, at LHC14 these may be exploited to probe the nature of the LSP.
In Fig. 8 we show the OS and SS dilepton invariant masses for the three SNDM benchmark points as well as for the corresponding MSSM models. The cuts applied are the same used for the m T 2 analyses, namely Eq. (5.14) for point SN1 and Eq. (5.16) for points SN2-3. We assume that the shape of the SM background distributions can be extracted from data and/or MC, so we neglect their contribution. As we can see, the m l + l − and m l ± l ± distributions are drastically different between the SNDM and MSSM scenarios. Besides the larger overall rate of dilepton events, the SNDM points show a much harder m ll distribution. This is due to the large W 1 −ν 1 mass gap, resulting in a much harder p T (l) spectrum. Moreover, for the gaugino masses considered here, the Z 2 has a significant BR to Z + Z 1 , giving rise to the Z-peak seen in the MSSM OS distributions; in the SNDM scenario, no such peak is present since BR( Z 2 →ν 1 + ν) ≃ 100%.

Conclusions
A mainly right-handed sneutrino with large L/R mixing is an excellent candidate for light cold dark matter with mass below ∼ 10 GeV. If DM is indeed realized in the form of light sneutrinos, there are important consequences to the SUSY signatures at the LHC. In particular, neutralinos Z 1 and Z 2 appearing in squark and gluino cascades decay invisibly into ν 1 ν, so that there can be up to three different invisible sparticles in an event. Charginos, on the other hand, decay dominantly into charged leptons plus theν 1 LSP. SUSY events will therefore present a harder E T distribution than expected in MSSM scenarios with a similar sparticle spectrum, and dilepton events will appear at much larger rates both in the OS and SS channels. During the first LHC run, at √ s =7 TeV and with ∼ 1 fb −1 , a signal could already be seen if gluinos and squarks have masses up to ∼ 1 TeV. Signal distributions such as the lepton and jet number, as well as SS/OS dilepton rates may already indicate a light sneutrino as the lightest SUSY particle in the early phase of LHC running.
Precision measurements enabling a model discrimination should be possible at higher energy and luminosity. For √ s =14 TeV and L = 100 fb −1 we have shown that the sneutrino mass can be measured using the m T 2 technique with a ∼ 50% precision, which is already sufficient to distinguish between the SNDM and MSSM scenarios with gaugino mass unification. Furthermore, the dilepton invariant mass distributions can also point to the presence of a light LSP which carries lepton number. The presence of additional invisible sparticles in the decay chains may be inferred from the E T and transverse-mass distributions. We have shown that indeed, for mq R ≈ mq L the Z 1 mass might be measurable with ∼ 10% precision.
Regarding alternative scenarios with possibly similar signatures, a 7-8 GeV Z 1 LSP in the MSSM with non-universal gaugino masses [29] (see however [30]) could be distinguished from the case studied here by exploiting, e.g., same-flavor opposite-sign (SFOS) dileptons from Z 2 → Z 1 + Z, which is absent in the SNDM case. Indeed the absence of kinematical structure and flavor correlations typical for the SNDM case will point to W 1 → l ±ν 1 decays. 4 Quite similar signals as in the SNDM case can in principle arise in the next-to-MSSM, with < 10 GeV neutralinos as viable DM candidates that can have large (10 −5 − 10 −4 pb) elastic scattering cross sections [30,31,32]. In this case one may have dominantly invisible Z 2 decays through Z 2 → h 2 Z 1 followed by h 2 → Z 1 Z 1 . Here possible ways of discrimination are, e.g., the W 1 → W ± Z 1 decays and the presence of additional light Higgs states h 1 and a 1 .
We conclude that the LHC offers very good prospects to resolve the light mixed sneutrino DM case. Finally, recall that a corroborating signal is expected in direct dark matter searches, as there is a lower limit on the spin-independent scattering cross section of σ SI 10 −5 pb.