“L = R” - U(1)R lepton number at the LHC

We perform a detailed study of a variety of LHC signals in supersymmetric models where lepton number is promoted to an (approximate) U(1)R symmetry. Such a symmetry has interesting implications for naturalness, as well as flavor- and CP-violation, among others. Interestingly, it makes large sneutrino vacuum expectation values phenomenologically viable, so that a slepton doublet can play the role of the down-type Higgs. As a result, (some of) the leptons and neutrinos are incorporated into the chargino and neutralino sectors. This leads to characteristic decay patterns that can be experimentally tested at the LHC. The corresponding collider phenomenology is largely determined by the new approximately conserved quantum number, which is itself closely tied to the presence of “leptonic R-parity violation”. We find rather loose bounds on the first and second generation squarks, arising from a combination of suppressed production rates together with relatively small signal efficiencies of the current searches. Naturalness would indicate that such a framework should be discovered in the near future, perhaps through spectacular signals exhibiting the lepto-quark nature of the third generation squarks. The presence of fully visible decays, in addition to decay chains involving large missing energy (in the form of neutrinos) could give handles to access the details of the spectrum of new particles, if excesses over SM background were to be observed. The scale of neutrino masses is intimately tied to the source of U(1)R breaking, thus opening a window into the R-breaking sector through neutrino physics. Further theoretical aspects of the model have been presented in the companion paper [1].

The recent discovery at the LHC of a Higgs-like signal at ∼ 125 GeV has put the general issue of electroweak symmetry breaking under a renewed perspective. In addition, the absence of other new physics signals is rapidly constraining a number of theoretically wellmotivated scenarios. One of these concerns supersymmetry, which in its minimal version is being tested already above the TeV scale. In view of this, it is pertinent to consider alternate realizations that could allow our prejudices regarding e.g. naturalness to be consistent with the current experimental landscape, within a supersymmetric framework. At the same time, such scenarios might motivate studies for non-standard new physics signals. One such non-standard realization of supersymmetry involves the possible existence of an approximately conserved R-symmetry at the electroweak scale [2][3][4][5][6][7][8][9][10][11][12][13]. It is known that one of the characteristics of such scenarios, namely the Dirac character of the gauginos (in particular, gluinos), can significantly soften the current exclusion bounds [14,15]. At the same time, an approximate R-symmetry which extends to the matter sector, could end up playing a role akin to the GIM mechanism in the SM, thereby allowing to understand the observed flavor properties of the light (SM) particles. As advocated in ref. [16], a particularly interesting possibility is that the R-symmetry be an extension of lepton number (see also [17]). In a companion paper [1], we classify the phenomenologically viable Rsymmetric models, and present a number of theoretical and phenomenological aspects of the case in which R-symmetry is tied to the lepton number. Such a realization involves the "R-parity violating (RPV) superpotential operators", W ⊃ λLLE c + λ LQD c where, unlike in standard RPV scenarios, there is a well-motivated structure for the new λ and λ couplings, some of them being related to (essentially) known Yukawa couplings. Although, at first glance, one might think that such a setup, possibly with a preponderance of leptonic signals should be rather constrained, we shall establish here that this is not the case. In fact, the scenario is easily consistent with most of the superparticles lying below the TeV scale. Only the Dirac gauginos are expected to be somewhat above the TeV scale, which may be completely consistent with naturalness considerations. As we will see, the light spectrum is particularly simple: there is no LR mixing in the scalar sector, and there is only one light (Higgsino-like) neutralino/chargino pair. At the same time, it turns out that the (electron) sneutrino vev can be sizable, since it is not constrained by neutrino masses (in contrast to that in standard RPV models). This is because the Lagrangian (approximately) respects lepton number, which is here an R symmetry, and the sneutrinos do not carry lepton number. Such a sizable vev leads to a mixing of the neutralinos/charginos above with the neutrino and charged lepton sectors (ν e and e − to be precise), which results in novel signatures and a rather rich phenomenology. Although the flavor physics can in principle also be very rich, we will not consider this angle here.
We give a self-contained summary of all the important physics aspects that are relevant to the collider phenomenology in section 2. This will also serve to motivate the specific spectrum that will be used as a basis for our study. In section 3, we put together all the relevant decay widths, as a preliminary step for exploring the collider phenomenology. In section 4 we discuss the current constraints pertaining to the first and second generation JHEP05(2013)012 squarks, concluding that they can be as light as 500 − 700 GeV. We turn our attention to the third generation phenomenology in section 5, where we show that naturalness considerations would indicate that interesting signals could be imminent, if this scenario is relevant to the weak scale. In section 6, we summarize the most important points, and discuss a number of experimental handles that could allow to establish the presence of a leptonic R symmetry at the TeV scale.

U(1) R lepton number: general properties
Our basic assumption is that the Lagrangian at the TeV scale is approximately U(1) R symmetric, with the scale of U(1) R symmetry breaking being negligible for the purpose of the phenomenology at colliders. Therefore, we will concentrate on the exact R-symmetric limit, which means that the patterns of production and decays are controlled by a new (approximately) conserved quantum number. We will focus on the novel case in which the R-symmetry is an extension of the SM lepton number. Note that this means that the extension of lepton number to the new (supersymmetric) sector is non-standard.

The fermionic sector
As in the MSSM, the new fermionic sector is naturally divided into strongly interacting fermions (gluinos), weakly interacting but electrically charged fermions (charginos) and weakly interacting neutral fermions (neutralinos). However, in our framework there are important new ingredients, and it is worth summarizing the physical field content. This will also give us the opportunity to introduce useful notation.

Gluinos
One of the important characteristics of the setup under study is the Dirac nature of gauginos. In the case of the gluon superpartners, this means that there exists a fermionic colored octet (arising from a chiral superfield) that marries the fermionic components of the SU(3) C vector superfield through a Dirac mass term: M D 3g a αõ aα + h.c., where a is a color index in the adjoint representation of SU(3) C and α is a Lorentz index (in 2-component notation). Whenever necessary, we will refer toõ as the octetino components, and tog as the gluino components. For the most part, we will focus directly on the 4-component fermions G a = {g a α ,ō aα } and we will refer to them as (Dirac) gluinos, since they play a role analogous to Majorana gluinos in the context of the MSSM. However, here the Majorana masses are negligible (we effectively set them to zero) and, as a result, the Dirac gluinos carry an approximately conserved (R) charge. In particular, R(g) = −R(õ) = 1, so that R(G) = 1. Rcharge (approximate) conservation plays an important role in the collider phenomenology.
The Dirac gluino pair-production cross-section is about twice as large as the Majorana gluino one, due to the larger number of degrees of freedom. Assuming heavy squarks, and within a variety of simplified model scenarios, both ATLAS [18][19][20] and CMS [21][22][23][24] have set limits on Majorana gluinos in the 0.9 − 1 TeV range. As computed with Prospino2 [25] in this limit of decoupled squarks, the NLO Majorana gluino pair-production cross-section is σgg Majorana (Mg = 1 TeV) ≈ 8 fb at the 7 TeV LHC run. Although, for the JHEP05(2013)012 same mass, the Dirac gluino production cross-section is significantly larger, it also falls very fast with the gluino mass so that the above limits, when interpreted in the Dirac gluino context, do not change qualitatively. Indeed, assuming a similar K-factor in the Dirac gluino case, we find a NLO pair-production cross section of σgg Dirac (M D 3 = 1.08 TeV) ≈ 8 fb. Nevertheless, from a theoretical point of view the restrictions on Dirac gluinos coming from naturalness considerations are different from those on Majorana gluinos, and allow them to be significantly heavier. We will take Mg ≡ M D 3 = 2 TeV to emphasize this aspect. This is sufficiently heavy that direct gluino pair-production will play a negligible role in this study. 1 At the same time, such gluinos can still affect the pair-production of squarks through gluino t-channel diagrams, as discussed later (for the gluinos to be effectively decoupled, as assumed in e.g. [15], they must be heavier than about 5 TeV).

Charginos
We move next to the chargino sector. This includes the charged fermionic SU(2) L superpartners (winos)w ± and the charged tripletino components,T + u andT − d , of a fermionic adjoint of SU(2) L (arising from a triplet chiral superfield). It also includes the charged components of the Higgsinos,h + u andr − d . The use of the notationr − d instead ofh − d indicates that, unlike in the MSSM, the neutral "Higgs" component R 0 d does not acquire a vev. Rather, in our setup, the role of the down-type Higgs is played by the electron sneutrinõ ν e (we will denote its vev by v e ). As a result, the LH electron e − L mixes with the above charged fermions, 2 and becomes part of the chargino sector (as does the RH electron field e c R ). 3 Besides the gauge interactions, an important role is played by the superpotential [1]. The pattern of mixings among these fermions is dictated by the conservation of the electric as well as the R-charges: R(w ± ) = R(e c R ) = R(r − d ) = +1 and R(T + u ) = R(T − d ) = R(e − L ) = R(h + u ) = −1. In 2-component notation, we then have that the physical charginos have the compositionχ where i = 1, 2. The notation here emphasizes the conserved electric and R-charges, by 1 However, at 14 TeV, with σgg Dirac (M D 3 = 2 TeV) ≈ 3 fb, direct gluino pair-production may become interesting. The K-factor (≈ 2.6) is taken from the Majorana case, as given by Prospino2. This production cross-section is dominated by gluon fusion, and is therefore relatively insensitive to the precise squark masses. 2 Ref. [26] has previously pointed out the possibility of such a potentially large mixing in the charged fermion sector, although in that case it arises from a RH sneutrino vev, while in our case it arises from a LH sneutrino vev (there is no RH neutrino/sneutrino in our setup). 3 As discussed in ref. [1], the electron mass arises from R-preserving, but SUSY-breaking higher-dimension operators. In particular, in the absence of such higher-dimension operators the chargino mass matrix has a zero eigenvalue, and the corresponding eigenstate would be identified with e − . Note that the same physics that generates the electron mass is expected to generate small contributions to the masses of the heavier leptons, as well as flavor-changing effects. As explained in the above reference the latter are easily consistent with current lepton flavor-violating constraints.

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indicating them as superindices, e.g.χ +− i denoting the two charginos with Q = +1 and R = −1. The U ± , V ± are 2 × 2 unitary matrices that diagonalize the corresponding chargino mass matrices. The superindex denotes the product R × Q, while the subindices in the matrix elements should have an obvious interpretation. We refer the reader to ref. [1] for further details. In this work we will not consider the possibility of CP violation, and therefore all the matrix elements will be taken to be real. The above states are naturally arranged into four 4-component Dirac fields, , for i = 1, 2, whose charge conjugates will be denoted byX −− i andX −+ i . In this notation, e =X −− 1 corresponds to the physical electron (Dirac) field. As explained in the companion paper [1], precision measurements of the electron properties place bounds on the allowed admixtures V + 1w and U + 1t , that result in a lower bound on the Dirac masses, written as . This lower bound can be as low as 300 GeV for an appropriate choice of the sneutrino vev. However, a sizably interesting range for the sneutrino vev requires that M D 2 be above about 1 TeV. For definiteness, we take in this work M D 2 = 1.5 TeV, which implies that 10 GeV v e 60 GeV. Thus, the heaviest charginos are theX ++ Dirac fields, which we will simply call "winos". The lightest chargino is the electron, e ≈ (e − L , e c R ), with non-SM admixtures below the 10 −3 level. The remaining state is expected to be almost pureh u -r d , with a mass set by the µ-term. 4 Naturalness considerations suggest that this parameter should be around the EW scale, and we will take µ = 200 − 300 GeV. However, it is important to note that the gaugino component of this Higgsino-like state, U − 1w , although small, should not be neglected. This is the case when considering theX +− 1 couplings to the first two generations, which couple to the Higgsino content only through suppressed Yukawa interactions. In the left panel of figure 1, we exhibit the mixing angles of the two lightest chargino states as a function of the sneutrino vev, v e , for M D 2 = 1.5 TeV, µ = 200 GeV, λ S u = 0 and λ T u = 1. The V -type matrix elements are shown as solid lines, while the U -type matrix elements are shown as dashed lines (sometimes they overlap). In the right panel we show the chargino composition as a function of λ T u for v e = 10 GeV. This illustrates that there can be accidental cancellations, as seen for thew − component ofX −+ 1 at small values of λ T u . For the most part, we will choose parameters that avoid such special points, in order to focus on the "typical" cases. It is also important to note that the quantum numbers of these two lightest chargino states (the lightest of which is the physical electron) are different. This has important consequences for the collider phenomenology, as we will see.

Neutralinos
The description of the neutralino sector bears some similarities to the chargino case discussed above. In particular, and unlike in the MSSM, it is natural to work in a Dirac   Figure 1. Composition of the two lightest chargino states as a function of the sneutrino vev (left panel) and as a function of λ T u (right panel). We fix M D 2 = 1.5 TeV, µ = 200 GeV and λ S u = 0. In the left panel we take λ T u = 1 and in the right panel we take v e = 10 GeV. We plot the absolute magnitude of the rotation matrix elements V ± ik (solid lines) and U ± ik (dashed lines). Not plotted are V + 1w = 0 and V + 1e = 1.X ++ 1 is the physical (charge conjugated) electron, andX +− 1 is the lightest BSM chargino state (which is Higgsino-like). For reference, we also show in the upper horizontal scale the values of tan β = v u /v e . basis. The gauge eigenstates are the hypercharge superpartner (bino)b, the neutral winõ w, a SM singlet,s, the neutral tripletinoT 0 , the neutral Higgsinos,h 0 u andr 0 d and, finally, the electron-neutrino ν e (which mixes with the remaining neutralinos when the electron sneutrino gets a vev). If there were a right-handed neutrino it would also be naturally incorporated into the neutralino sector. In principle, due to the neutrino mixing angles (from the PMNS mixing matrix) the other neutrinos also enter in a non-trivial way. However, for the LHC phenomenology these mixings can be neglected, which we shall do for simplicity in the following. Besides the gauge interactions and the λ T u superpotential coupling introduced in the previous subsection, there is a second superpotential interaction, W ⊃ λ S u SH u R d , where S is the SM singlet superfield, that can sometimes be relevant [1]. In two-component notation, we have neutralino states of definite U(1) R chargẽ where V N ik and U N ik are the unitary matrices that diagonalize the neutralino mass matrix (full details are given in ref. [1]). These states form Dirac fermionsX 0+ where, as explained in the previous subsection, the superindices indicate the electric and R-charges. In addition, there remains a massless Weyl neutralino: which corresponds to the physical electron-neutrino. With some abuse of notation we will refer toχ 0− 4 as "ν e " in subsequent sections, where it will always denote the above mass  we will refer toX 0+ 1 as the "lightest neutralino", with the understanding that strictly speaking it is the second lightest. Nevertheless, we find it more intuitive to reserve the nomenclature "neutralino" for the states not yet discovered. The heavier neutralinos are labeled accordingly.
Given that both the gluino and wino states are taken to be above a TeV, we shall also take the Dirac bino mass somewhat large, specifically M D 1 = 1 TeV. This is mostly a simplifying assumption, for instance closing squark decay channels into the "second" lightest neutralino (which is bino-like). Thus, the lightest (non SM-like) neutralino is Higgsino-like, and is fairly degenerate with the lightest (non SM-like) chargino,X +− 1 . In figure 2, we show the composition of the physical neutrino (χ 0− 4 ) and of the Higgsinolike neutralino state (X 0+ 1 ). Note that, as a result of R-charge conservation, the neutrino state has no wino/bino components. In addition, its (up-type) Higgsino component is rather suppressed. As a result, the usual gauge or Yukawa induced interactions are very small. Instead, the dominant couplings ofχ 0− 4 to other states will be those inherited from the neutrino content itself. The associated missing energy signals will then have a character that differs from the one present in mSUGRA-like scenarios. However, it shares similarities with gauge mediation, where the gravitino can play a role similar to the neutrino in our case. 5 By contrast, the "lightest" neutralino,X 0+ 1 , typically has non-negligible wino/bino components that induce couplings similar to a more standard (massive) neutralino LSP. Nevertheless, here this state decays promptly, and is more profitably thought as a neutralino LSP in the RPV-MSSM (but with 2-body instead of 3-body decays).

The scalar sector
In this section, we discuss the squark, slepton and Higgs sectors, emphasizing the distinctive features compared to other supersymmetric scenarios.

Squarks
Squarks have interesting non-MSSM properties in the present setup. They are charged under the R-symmetry (R = +1 for the LH squarks and R = −1 for the RH ones), and as a result they also carry lepton number. Thus, they are scalar lepto-quarks (strongly interacting particles carrying both baryon and lepton number). This character is given by the superpotential RPV operator λ ijk L i Q j D c k , which induces decays such ast L → b R e + L . In addition, and unlike in more familiar RPV scenarios, some of these couplings are not free but directly related to Yukawa couplings: λ 111 = y d , λ 122 = y s and λ 133 = y b . The full set of constraints on the λ couplings subject to these relations was analyzed in ref. [1]. The λ 333 coupling is the least unconstrained, being subject to where y b = m b /v e , tan β = v u /v e and we took m b (µ ≈ 500 GeV) ≈ 2.56 GeV [27]. In this work, we will assume that the only non-vanishing λ couplings are those related to the Yukawa couplings, together with λ 333 . We will often focus on the case that the upper limit in eq. (2.4) is saturated, but should keep in mind that λ 333 could turn out to be smaller, and will comment on the relevant dependence when appropriate. It is also important to keep in mind that the R-symmetry forbids any LR mixing. As a result, the squark eigenstates coincide with the gauge eigenstates, at least if we neglect intergenerational mixing. 6 We will assume in this work that the first two generation squarks are relatively degenerate. As we will see, the current bound on their masses is about 500 − 700 GeV. We will also see that the third generation squarks can be lighter, possibly consistent with estimates based on naturalness from the Higgs sector.

Sleptons
The sleptons are expected to be among the lightest sparticles in the new physics spectrum. This is due to the intimate connection of the slepton sector with EWSB, together with the fact that a good degree of degeneracy between the three generation sleptons is expected. The possible exception is the LH third generation slepton doublet, if the RPV coupling λ 333 turns out to be sizable. As a result, due to RG running, the LH stau can be several tens of GeV lighter than the selectron and smuon, while the latter should have masses within a few GeV of each other. Note that the sleptons are R-neutral, hence do not carry lepton number. This is an important distinction compared to the standard extension of lepton number to the new physics sector.
Since the electron sneutrino plays the role of the down-type Higgs, naturalness requires its soft mass to be very close to the electroweak scale. To be definite, we take m 2 L ∼ m 2Ẽ ∼ (200-300 GeV) 2 . Depending on how this compares to the µ-term, the sleptons can be heavier or lighter than the lightest neutralino,X +− 1 . WhenX +− 1 is lighter than the sleptons we will say that we have a "neutralino LSP scenario". The other case we will JHEP05(2013)012 consider is one where the LH third generation slepton doublet is lighter thanX +− 1 , while the other sleptons are heavier. Given the possible mass gap of several tens of GeV between the (ν τ ,τ L ) pair and the other sleptons, this is a rather plausible situation. We will call it the "stau LSP scenario", although the τ -sneutrino is expected to be up to ten GeV lighter than the stau. 7 The possibility that several or all the sleptons could be lighter thanX +− 1 may also deserve further study, but we will not consider such a case in this work.
We also note that some of the couplings in the RPV operator λ ijk L i L j E c k are related to lepton Yukawa couplings: λ 122 = y µ and λ 133 = y τ . The bounds on the remaining λ ijk 's under these restriction have been analyzed in [1], and have been found to be stringent. We note that, in principle, it could be possible to produce sleptons singly at the LHC through the λ ijk L i Q j D c k operator, with subsequent decays into leptons via the λ ijk L i L j E c k induced interactions. We have studied this possibility in ref. [1], and found that there may be interesting signals in the µ + µ − and e ∓ µ ± channels. However, in this work we do not consider such processes any further, and set all λ couplings to zero, with the exception of the Yukawa ones. The tau Yukawa, in particular, can play an important role.

The Higgs sector
The "Higgs" sector is rather rich in our scenario. The EW symmetry is broken by the vev's of the neutral component of the up-type Higgs doublet, H 0 u , and the electron sneutrino,ν e , which plays a role akin to the neutral down-type Higgs in the MSSM. We have also a scalar SM singlet and a scalar SU(2) L triplet, the superpartners of the singlino and tripletino discussed in the previous section. These scalars also get non-vanishing expectation values. However, it is well known that constraints on the Peskin-Takeuchi T -parameter require the triplet vev to be small, v T 2 GeV. We will also assume that the singlet vev is in the few GeV range. This means that these two scalars are relatively heavy, and not directly relevant to the phenomenology discussed in this paper. Note that all of these states are R-neutral.
There is another doublet, R d , the only state with non-trivial R-charge (= +2). It does not acquire a vev, so that the R-symmetry is not spontaneously broken, and therefore this state does not mix with the previous scalars. Its (complex) neutral and charged components are relatively degenerate, with a mass splitting of order 10 GeV, arising from EWSB as well as the singlet vev. For simplicity, we will assume its mass to be sufficiently heavy (few hundred GeV) that it does not play a role in our discussion. Nevertheless, it would be interesting to observe such a state, due to its special R-charge.
The upshot is that the light states in the above sector are rather similar to those in the MSSM: a light CP-even Higgs, a heavier CP-even Higgs, a CP-odd Higgs and a charged Higgs pair. The CP-even and CP-odd states are superpositions of the real and imaginary 7 Again, we remind the reader that we are using standard terminology in a non-standard setting. In particular, a rigorous separation of the SM and supersymmetric sectors is not possible, due to the mixings in the neutralino and chargino sectors. Also, the supersymmetric particles end up decaying into SM ones, similar to RPV-MSSM scenarios. Furthermore, the light gravitino could also be called the LSP, as in gaugemediation. However, unlike in gauge mediation, here the gravitino is very rarely produced in superparticle decays, hence not phenomenologically relevant at the LHC. Thus, we will refer to either the (ντ ,τL) pair orX +− 1 as the "LSP", depending on which one is lighter. Our usage emphasizes the allowed decay modes.

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components of h 0 u and the electron sneutrino (with a small admixture of the singlet and neutral triplet states). Given our choice for the slepton soft masses, the heavy CP-even, CP-odd and charged Higgses are expected to be relatively degenerate, with a mass in the 200 − 300 GeV range (the charged Higgs being slightly heavier than the neutral states). The charged Higgs is an admixture of H + u and the LH selectronẽ L (and very suppressed charged tripletino components). The RH selectron, as well as the remaining neutral and charged sleptons do not mix with the Higgs sector, and can be cleanly mapped into the standard slepton/sneutrino terminology.
The light CP-even Higgs, h, is special, given the observation of a Higgs-like signal by both the ATLAS [29] and CMS [30] collaborations at about 125 GeV. This state can also play an important role in the decay patterns of the various super-particles. Within our scenario, a mass of m h ≈ 125 GeV can be obtained from radiative corrections due to the triplet and singlet scalars, even if both stops are relatively light (recall the suppression of LR mixing due to the R-symmetry). This is an interesting distinction from the MSSM: a heavy triplet scalar is significantly more efficient in increasing the Higgs mass than the well-known mechanism involving stops, as already emphasized in ref. [1]. Therefore, reproducing the observed m h within the framework can be achieved with relatively mild fine-tuning through such radiative corrections. A more detailed study of this issue will be dealt with in a separate paper [31]. Here we point out that these arguments suggest that λ S u should be somewhat small, while λ T u should be of order one. This motivates our specific benchmark choice: λ S u = 0 and λ T u = 1 (although occasionally we will allow λ S u to be non-vanishing). These couplings affect the neutralino/chargino composition and are therefore relevant for the collider phenomenology.

Summary
Let us summarize the properties of the superpartner spectrum in our scenario, following from the considerations in the previous sections. All the gauginos ("gluino", "wino" and "bino") are relatively heavy, in particular heavier than all the sfermions. The first two generation squarks can be below 1 TeV, while the third generation squarks can be in the few hundred GeV range. These bounds will be discussed more fully in the remaining of the paper. The sleptons, being intimately connected to the Higgs sector, are in the couple hundred GeV range. So are the "lightest" neutralino and chargino states, which are Higgsino-like. Mixing due to the electron sneutrino vev, induces interesting couplings of the new physics states to the electron-neutrino and the electron, while new interactions related to the lepton and down-quark Yukawa couplings give rise to non-MSSM signals. The collider phenomenology is largely governed by a new (approximately) conserved Rcharge, and will be seen to be extremely rich, even though the spectrum of light states does not seem, at first sight, very complicated or unconventional. Finally, we mention that there is also an SU(3) C octet scalar (partner of the octetinos that are part of the physical gluino states) that will not be studied here (for studies of the octet scalar phenomenology, see [32,33]).

JHEP05(2013)012 3 Sparticle decay modes
In this section we discuss the decay modes of the superparticles relevant for the LHC collider phenomenology. We have checked that three-body decays are always negligible and therefore we focus on the two-body decays.

Neutralino decays
From our discussion in the previous section, the lightest (non SM-like) neutralino is a Higgsino-like state (that we callX 0+ 1 ), while the truly stable neutralino state is none other than the electron-neutrino. It was also emphasized thatX 0+ 1 has small, but not always negligible, gaugino components. The other two (Dirac) neutralino states are heavy. We therefore focus here on the decay modes ofX 0+ 1 . As explained in subsection 2.2.2, we consider two scenarios: a "neutralino LSP scenario", whereX 0+ 1 is lighter than the LH third generation slepton doublet, and a "stau LSP scenario" with the opposite hierarchy. The decay modes of the lightest neutralino depend on this choice and we will consider them separately.
Neutralino LSP scenario. IfX 0+ 1 is lighter than the (ν τ ,τ − L ) pair, the possible decay modes forX 0+ 1 have partial decay widths [in the notation of eqs. (2.1)-(2. 3)]: where we denote theX 0+ 1 mass by mX0 1 , and R 1i are the mixing angles characterizing the composition of the lightest Higgs, h. In our scenario all the other Higgs bosons are heavier than the lightest neutralino. We note that the above expressions contain an explicit factor of 1/ √ 2 for each occurrence of a neutralino mixing angle, compared to the standard ones [34][35][36]. This is because the mixing matrix elements, U N ij and V N ij are defined in a Dirac basis, whereas in the usual approach the neutralinos are intrinsically Majorana particles. Recall also that, for simplicity, we are assuming here that all quantities are real. The generalization of these and subsequent formulas to the complex case should be straightforward.
The above decay modes can easily be dominated by the neutrino-neutralino mixing angles, since the contributions due to the higgsino (U N 4u ) and tripletino components are highly  suppressed. This mixing angles, in turn, are controlled by the sneutrino vev. Note that in the RPV-MSSM such decay modes are typically characterized by displaced vertices due to the extremely stringent bounds on the sneutrino vev arising from neutrino physics [37]. By contrast, in our scenario the sneutrino vev is allowed to be sizable (tens of GeV), and is in fact bounded from below from perturbativity/EWPT arguments, so that these decays are prompt.
The left panel of figure 3 shows that the decay width into hν e is the dominant one in the small sneutrino vev limit, while in the large sneutrino vev limit the channels involving a gauge boson can be sizable. We also note that it is possible for the W − e + L decay channel to be the dominant one, as shown in the right panel of figure 3. In this case we have chosen λ S u = λ T u = 0.4, which leads to a cancellation between the mixing angles such that Zν e is suppressed compared to W − e + L . For such small couplings, the radiative contributions to the lightest CP-even Higgs are not large enough to account for the observed m h ≈ 125 GeV, while stops (due to the absence of LR mixing) are also not very effective for this purpose. Therefore, without additional physics such a situation may be disfavored. We mention it, since it is tied to a striking signal, which one should nevertheless keep in mind.
andν τντ channels open up with partial decay widths given by In eq. (3.4) we have suppressed additional terms proportional to the τ Yukawa coupling, that give negligible contributions compared to the ones displayed. Although we have included the full expressions in the numerical analysis, we choose to not display such terms to make the physics more transparent. The only cases where contributions proportional to the Yukawa couplings are not negligible occur when the top Yukawa is involved. 8 We then see that eqs. (3.4) and (3.5) are controlled by the gaugino components, even for the suppressed V N 1w and V N 1b shown in figure 2. Thus, these decay channels dominate over the ones driven by the neutrino-neutralino mixing, as shown in figure 4. Here theν τντ channel is slightly suppressed compared to the one into the charged lepton and slepton due to a cancellation between the mixing angles in eq. (3.4). In other regions of parameter space such a cancellation may be more or less severe.

Chargino decays
The lightest of the charginos (other than the electron) isX +− 1 . It is Higgsino-like, which follows from its R = −Q nature, and the fact that the winos are heavy. Note that, in contrast, the electron and the other charged leptons have R = Q. Therefore, the two-body decays ofX +− 1 can involve a charged lepton only when accompanied with an electrically neutral, |R| = 2 particle, the only example of which is the R 0 d scalar. However, this state does not couple directly to the leptons. 9 We take it to be heavier thanX +− 1 , which has important consequences for the allowed chargino decay modes. For instance, in the region whereτ L is heavier thanX +− 1 the potentially allowed decay modes ofX +− 1 are into W + ν e and W +X 0− 1 , whereX 0− 1 denotes the antiparticle ofX 0+ 1 . However, the second channel is closed in most of the parameter space sinceX 0+ 1 andX +− 1 are relatively degenerate (with a mass splitting of order ten GeV). The dominant decay mode in this "neutralino LSP scenario" has a partial decay width given by: Even the contribution from the bottom Yukawa coupling (with possible large tan β enhancements) is negligible, given the typical mixing angles in the scenario. 9 Recall that the R d SU (2) Figure 5.τ L (solid lines) andν τ (dashed lines) decay modes for two masses: mτ L ≈ mν τ = 180 GeV (left panel) and mτ L ≈ mν τ = 250 GeV (right panel). It is assumed thatX 0+ 1 is heavier than the (ν τ ,τ L ) pair, and that λ 333 saturates eq. (2.4).
where we denote the mass ofX +− 1 by mX± 1 . Therefore, for sufficiently heavy sleptons the chargino always decays into W + ν e .
If insteadτ L is lighter thanX +− 1 one can also haveX +− Typically, this decay channel dominates, but the W + ν e can still have an order one branching fraction.

Slepton decays
We focus on the decays of the (ν τ ,τ L ) pair since it may very well be the "LSP", i.e. the last step in a cascade decade to SM particles. In this case the charged slepton decay modes areτ − L → τ − Rν e andτ − L →t L b R , with partial decay widths given by: The decay widths for the SU(2) L related processes,ν τ → τ − R e + L andν τ →b L b R , are obtained from eqs. (3.8) and (3.9) with the replacements mτ L → mν τ and m t → m b . In figure 5, we show the branching fractions as a function of the sneutrino vev, assuming that λ 333 saturates eq. (2.4), and taking m τ = 1.7 GeV. We see that thet L b R channel can be sizable in the large sneutrino vev/small tan β limit, in spite of the phase space suppression when mτ L ∼ m t + m b (left panel). Away from threshold, it can easily dominate (right panel).

Squark decays
As already explained, we focus on the case where the gluinos are heavier than the squarks and, therefore, the squark decay mode into a gluino plus jet is kinematically closed. The lightest neutralinos and charginos are instead expected to be lighter than the squarks since naturalness requires the µ-term to be at the electroweak scale, while we will see that the first and second generation squarks have to be heavier than about 600 GeV. Thus, the squark decays into a quark plus the lightest neutralino or into a quark plus the lightest chargino should be kinematically open. However, the decay mode of the left handed uptype squarks, which have Q = 2/3 and R = 1, into the lightest charginoX +− 1 plus a (R-neutral) jet is forbidden by the combined conservation of the electric and R-charges: The decay mode into the second lightest neutralino, which can be of the (++) type, could be allowed by the quantum numbers, but our choice M D 1 > mq ensures that it is kinematically closed. Note also that since u R has Q = 2/3 and R = −1, one can haveũ R →X +− 1 j.

First and second generation squarks
• The left-handed up-type squarks,ũ L andc L , decay intoX 0+ 1 j and e + L j with: and analogous expressions forc L (in eq. (3.10), we do not display subleading terms proportional to the Yukawa couplings). The second decay is an example of a leptoquark decay mode. However, taking into account the smallness of the Yukawa couplings for the first two generations, together with theX 0+ 1 composition shown in figure 2, one finds that the dominant decay mode is the one into neutralino and a jet. Therefore, in the region of parameter space we are interest in,ũ L andc L decay intoX 0+ 1 j with almost 100% probability.
• The down-type left-handed squarks,d L ands L , have the following decay channels: with analogous expressions fors L . The relative minus sign in the gaugino contributions to the neutralino decay channel is due to the SU (2)   squarks, and should be compared to the up-type case, eq. (3.10). This leads to a certain degree of cancellation between the contributions from the bino and wino components, which together with the factor of 1/18 results in a significant suppression of the neutralino channel. Since the Yukawa couplings are very small, it follows that the chargino channel is the dominant decay mode of the down-type squarks of the first two generations.
• The right-handed up-type squarks,ũ R andc R , decay according to with analogous expressions forc R . The chargino decay mode foũ R is suppressed since the up-type Yukawa coupling is very small. Therefore, the right-handed up-type squark decays intoX 0+ 1 j with almost 100% probability. However, the charm Yukawa coupling is such that the various terms in eqs. (3.15) and (3.16) are comparable when the mixing angles are as in figures 1 and 2. For this benchmark scenario, both decay channels happen to be comparable, as illustrated in the left panel of figure 6. Here we used [27].
• The right-handed down-type squarks,d R ands R , decay according to with analogous expressions fors R . Again, for the down squark the Yukawa couplings are negligible so that it decays dominantly into neutralino plus jet. For the strange squark, however, the various channels can be competitive as illustrated in the right panel of figure 6. Here we used y s = m s /v e with m s (µ ≈ 600 GeV) ≈ 49 MeV [27].

Third generation squarks
For the third generation we expect the lepto-quark signals to be visible in all of our parameter space, although they may be of different types. The point is that the bottom Yukawa coupling can be sizable in the small sneutrino vev/large tan β limit (as in the MSSM), thus leading to a signal involving first generation leptons through the λ 133 ≡ y b ≈ 1.15 × 10 −2 sec β coupling. In the large sneutrino vev/small tan β limit, on the other hand, the RPV coupling λ 333 1.4 cos β can be of order of g , and may lead to third generation leptons in the final state.
• The left-handed stop,t L , has the following decay modes: When kinematically allowed, the decay mode into neutralino plus top is the dominant one since it is driven by the top Yukawa coupling, as shown in figure 7. However, this figure also shows that the two lepto-quark decay modes can have sizable branching fractions. 10 In particular, at small sneutrino vev the electron-bottom channel is the dominant lepto-quark decay mode (since it is proportional to the bottom Yukawa), while in the large vev limit the third generation lepto-quark channel dominates [we have assumed that λ 333 saturates the upper bound in eq. (2.4)]. The existence of lepto-quark channels with a sizable (but somewhat smaller than one) branching fraction is a distinctive feature of our model, as will be discussed in more detail in the 10 Here we used yt = mt/ √ v 2 − v 2 e and y b = m b /ve with mt(µ ≈ 500 GeV) ≈ 157 GeV and m b (µ ≈ 500 GeV) ≈ 2.56 GeV [27]. following section. We also note that in the case that λ 333 is negligible and does not saturate the bound in eq. (2.4), thet L → τ + L b R channel is no longer present, so that the BR(t L → e + L b R ) and BR(t L →X 0+ 1 t) increase in the large sneutrino vev limit (but are qualitatively the same as the left panel of figure 7).
• The left-handed sbottom,b L , has several decay modes as follows: When kinematically open, the dominant decay mode is into a chargino plus top since it is controlled by the top Yukawa coupling. The decays into neutrino plus bottom have always a sizable branching fraction, as can be seen in figure 8. However, one should note that when λ 333 is negligible, so that theb L →ν τ b R channel is unavailable, the decay involving a neutrino (ν e only) decreases as the sneutrino vev increases (being of order 0.3% at v e = 50 GeV). The other two channels adjust accordingly, but do not change qualitatively.   • For the right-handed stop,t R , the decay widths are: • The right-handed sbottom,b R , has a variety of decay modes: The lepto-quark signals are the dominant ones. Adding the two neutrino channels, the decay mode into νb has a branching fraction of about 50% as shown in the right panel of figure 9. The charged lepton signals can involve a LH electron or a τ plus a top quark. Note also that the decay mode intoX 0+ 1 b is very suppressed. We finally comment on the modifications when λ 333 is negligible. Once theb R → τ − L t L and b R → ν τ b L channels become unavailable, one has that BR(b R → e − L t L ) ≈ 0.6 and BR(b R → ν e b L ) ≈ 0.4, independent of the sneutrino vev. Theb * R →X 0+ 1b R channel remains negligible.

1 st and 2 nd generation squark phenomenology
In the present section we discuss the LHC phenomenology of the first and second generation squarks, which are expected to be the most copiously produced new physics particles. Although these squarks are not required by naturalness to be light, flavor considerations may suggest that they should not be much heavier than the third generation squarks. Therefore, it is interesting to understand how light these particles could be in our scenario. As we will see, current bounds allow them to be as light as 500 − 700 GeV, while in the MSSM the LHC bounds have already exceeded the 1 TeV threshold. The bounds can arise from generic jets + E T searches, as well as from searches involving leptons in the final state.

Squark production
We compute the cross section to produce a given final state X in our model as follows: where i =q 1q2 ,gq,gg, and the squark pair production can in principle come in several flavor and chirality combinations. We generate the production cross section for each independent i-th state with MadGraph5 [38]. Here we note that, due to the assumption of gluinos in the multi-TeV range, and the fact that we will be interested in squarks below 1 TeV, our cross section is dominated by the production of squark pairs. We have also computed the corresponding K-factor with Prospino2 [25], as a function of the squark mass for fixed (Majorana) gluino masses of 2 − 5 TeV. We find that for squark masses below about 1 TeV, the K-factor is approximately constant with K ≈ 1.6. Since, to our knowledge, a NLO computation in the Dirac case is not available, we will use the previous K-factor to obtain a reasonable estimate of the Dirac NLO squark pair-production cross-section. One should note that the Dirac nature of the gluinos results in a significant suppression of certain t-channel mediated gluino diagrams compared to the Majorana (MSSM) case, as already emphasized in [14,15] (see also figure 10). Nevertheless, at Mg = 2 TeV such contributions are not always negligible, and should be included. For instance, we find that for degenerate squark with mq = 800 GeV, the production ofũ LũR ,ũ LdR andũ RdL is comparable to the "diagonal" production ofq Lq * L andq Rq * R for all the squark flavors q =ũ,d,s,c taken together. As indicated in eq. (4.1) we include separately the BR for each i-th state to produce the final state X, since these can depend on the squark flavor, chirality or generation.

"Simplified Model" philosophy
We have seen thatũ L ,ũ R ,d R andc L decay dominantly through the neutralino channel, the LH down-type squarks,d L ands L , decay dominantly through the chargino channel,

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andc R ands R can have more complicated decay patterns (see figure 6). The striking lepto-quark decay mode,s R → e − L j, will be treated separately. In this section we focus on the decays involving neutralinos and charginos. Since the signals depend on how the neutralino/chargino decays, it is useful to present first an analysis based on the simplified model (SMS) philosophy. To be more precise, we set bounds assuming that the neutralinos/charginos produced in squark decays have a single decay mode with BR = 1. We also separate the "neutralino LSP scenario", in whichX 0+ 1 /X +− 1 decay into SM particles, from the "stau LSP scenario", where they decay intoτ − L τ + L ,ν τντ orτ + L ν τ . We will give further details on these subsequent decays below, where we treat the two cases separately.
Here we emphasize that we regard the jets plusX 0+ 1 /X +− 1 stage as part of the production. The point is that an important characteristic of our scenario is that different types of squarks produce overwhelmingly only one of these two states. For instance, if we are interested in two charginos in the squark cascade decays, this means that they must have been produced through LH down-type squarks (with a smaller contribution from c Rc * R production), and the production of any of the other squarks would not be relevant to this topology. Conversely, if we are interested in a topology with two neutralinos, the LH down-type squarks do not contribute. We denote by σ 1 the corresponding cross sections, computed via eq. (4.1) with X = "X +− 1X −+ 1 jj or X = "X 0+ 1X 0− 1 jj , taking the BR's as exactly zero or one, according to the type of squark pair i. 11 At the same time, since in other realizations of the R-symmetry these production patterns may not be as clear-cut, we will also quote bounds based on a second production cross section, denoted by σ 2 , where it is assumed that all the squarks decay either into the lightest neutralino or chargino channels with unit probability. This second treatment is closer to the pure SMS philosophy, but could be misleading in the case that lepton number is an R-symmetry. We show the corresponding cross-sections in figure 11.
It should also be noted that the great majority of simplified models studied by ATLAS and CMS consider either mq = Mg, or mq Mg. Therefore, at the moment there are only a handful of dedicated studies of our topologies, although we will adapt studies performed for other scenarios to our case. In the most constraining cases, we will estimate the acceptance by simulating the signal in our scenario 12 and applying the experimental cuts, but for the most part a proper mapping of the kinematic variables should suffice (provided the topologies are sufficiently similar). A typical SMS analysis yields colored-coded plots for the upper bound on σ × BR (or A × ) for the given process, in the plane of the produced (strongly-interacting) particle mass (call it mq), and the LSP mass (call it m LSP ). In most cases, the LSP is assumed to carry E T . Often, there is one intermediate particle in the decay chain. Its mass is parametrized in terms of a variable x defined by m intermediate = xmq +(1−x)m LSP . In our "neutralino LSP scenario", the intermediate particle is either the 11 The only exception is the RH charm squark,cR, for which we take BR(c * R →X 0+ 1 j) = BR(cR → X +− 1 j) = 0.5, although the characteristics of the signal are not very sensitive to this choice. We also neglect the decays ofsR into neutralino/neutrino plus jet. 12 We have implemented the full model in FeynRules [39], which was then used to generate MadGraph 5 code [38]. The parton level processes are then passed through Pythia for hadronization and showering, and through Delphes [40] for fast detector simulation.  Figure 11. Cross-sections for the separate production ofX 0+ trough squark pair-production in the SMS approach (see main text). The solid and dotted lines correspond to σ 1 , according to the case. The dashed line marked as σ 2 corresponds to the full pair-production of squarks, irrespective of how they decay. The cross-sections are computed for Mg = 2 TeV for a 7 TeV LHC run, with a K-factor, K = 1.6. lightest neutralinoX 0+ 1 or the lightest charginoX +− 1 , whose masses are set by the µ-term. Since the particle carrying the E T is the neutrino, i.e. m LSP = 0, we have x ≈ µ/mq.
We will set our bounds as follows: we compute our theoretical cross section as described above (i.e. based on the σ 1 or σ 2 production cross-sections) as a function of the squark mass, and considering the appropriate decay channel for the X 0+ 1 /X +− 1 (with BR = 1 in the SMS approach). Provided the topology is sufficiently similar, we identify the x-axis on the color-coded plots in the experimental analyses (usually mg) with mq, take m LSP = 0 (for the neutrino), and identify "x" as µ/mq (from our discussion above). Then, we increase the squark mass until the theoretical cross-section matches the experimental upper bound, defining a lower bound on mq. In a few cases that have the potential of setting strong bounds, but where the experimentally analyzed topologies do not exactly match the one in our model, we obtain the signal × A from our own simulation and use the 95% C.L. upper bound on σ × × A to obtain an upper bound on σ that can be compared to our model cross-section. If there are several signal regions, we use the most constraining one.

Neutralino LSP scenario
In the neutralino LSP scenario, and depending on the region of parameter space (e.g. the sneutrino vev or the values of the λ S and λ T couplings), the lightest neutralino,X 0+ 1 , can dominantly decay into Zν e , hν e or W − e + L . The "lightest" charginoX +− 1 always decays into W + ν e . Following the philosophy explained in the previous subsection, we set separate bounds on four simplified model scenarios:

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as well as on two benchmark scenarios (to be discussed in subsection 4.3.1) that illustrate the bounds on the full model. There are several existing searches that can potentially constrain the model: • jets + E T , • 1 lepton + jets + E T , • Z(ll) + jets + E T , • OS dileptons + E T + jets , • multilepton + jets + E T (with or without Z veto).
We postpone the detailed description of how we obtain the corresponding bounds to the appendix, and comment here only on the results and salient features. We find that typically the most constraining searches are the generic jets + E T searches, in particular the most recent ATLAS search with 5.8 fb −1 [19]. In addition, some of the simplified topologies can also be constrained by searches involving leptons + jets + E T . For example, those involving a leptonically decaying Z are important for theX 0+ 1 → Zν e case, while a number of multi-lepton searches can be relevant for the topologies that involve a W . We summarize our findings in table 1, where we exhibit the searches that have some sensitivity for the given SMS topology. We show the lower bounds on the squark masses based on both the σ 1 and σ 2 production cross-sections, as described in subsection 4.2. We see that these are below 650 GeV (based on σ 1 ; the bound from σ 2 is provided only for possible application JHEP05(2013)012 to other models). We also show the bounds for two benchmark scenarios (which depend on the sneutrino vev), as will be discussed in the next subsection. These are shown under the σ 1 column, but should be understood to include the details of the branching fractions and various contributing processes. We have obtained the above results by implementing the experimental analysis and computing the relevant × A from our own simulation of the signal, and using the model-independent 95% CL upper bounds on σ × × A provided by the experimental analysis. Whenever possible, we have also checked against similar simplified model interpretations provided by the experimental collaborations. Such details are described in the appendix, where we also discuss other searches that turn out to not be sensitive enough, and the reasons for such an outcome. In many cases, it should be possible to optimize the set of cuts (within the existing strategies) to attain some sensitivity. This might be interesting, for example, in the cases involving a Higgs, given that one might attempt to reconstruct the Higgs mass.
We turn next to the analysis of the full model in the context of two benchmark scenarios.

Realistic benchmark points
Besides the "simplified model" type of bounds discussed above, it is also interesting to present the bounds within benchmark scenarios that reflect the expected branching fractions for the neutralinos/charginos discussed in subsections 3.1 and 3.2. One difference with the analysis of the previous subsections is that we can have all the combinations of X 0+ 1 jj in squark decays, with the corresponding BR's. In figure 11 we have shown the individual cross-sections in the SMS approach. These give a sense of the relative contributions of the various channels. In particular, we see that thẽ X 0+ • jets + E T , • OS dileptons + E T + jets , • dileptons (from Z decay) + jets + E T , • multilepton + jets + E T (without Z cut). We apply the model-independent bounds discussed in the previous sections, and find that the jets + E T search is the most constraining one. Using σ j+ & E T 20 − 40 fb, we find mq 620 − 690 GeV (mq 590 − 650 GeV) for v e = 10 GeV (v e = 50 GeV). We show in the left panel of figure 12 the cross-sections for several processes, for mq = 700 GeV. These are computed from eq. (4.1) using the actual BR's for the chosen benchmark. Although there is some dependence on the sneutrino vev, the global picture is robust against v e .   figure 3). In the right panel of figure 12, we show the cross-sections for the main processes. We see that, for this benchmark, the "leptonic channels" have the largest cross sections (especially the multilepton + jets + E T one). However, taking into account efficiencies of at most a few percent for the leptonic searches (as we have illustrated in the previous section), we conclude that the strongest bound on the squark masses arises instead from the jets + E T searches (as for benchmark 1). Using σ j+ & E T 20 − 40 fb, we find mq 520 − 580 GeV (mq 500 − 560 GeV) for v e = 10 GeV (v e = 50 GeV). Note that there is a sizable "no missing energy" cross section. However, this could be significantly lower once appropriate trigger requirements are imposed.

Stau LSP scenario
In this scenario the dominant decay modes ofX 0+ 1 are intoτ − L τ + L orν τντ (about 50-50), while the charginoX +− 1 decays intoτ + L ν τ . The decay modes ofτ − L depend on the sneutrino vev: for large v e it decays dominantly intot L b R (assuming λ 333 is sizable), while for smaller values of v e it decays dominantly into τ − Rν e trough the τ Yukawa coupling. Similarly,ν τ decays intob L b R for large sneutrino vev, and into τ − R e + L for small sneutrino vev. In the "stau LSP scenario" we prefer to discuss the two limiting cases of small and large sneutrino vev, rather than present SMS bounds (recall from figure 11 that the squarks produce dominantlỹ X 0+ 1X 0− 1 pairs). This scenario is, therefore, characterized by third generation signals.

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4.4.1τ − L → τ − Rν e andν τ → τ − R e + L decay modes These decays are characteristic of the small sneutrino vev limit. In this case all the final states would contain at least two taus: i) for theX 0+ 1X 0− 1 topology the final state contains 2 jets, missing energy and 2τ + 2e, 3τ + 1e or 4τ 's; ii) for theX 0+ 1X +− 1 topology the final state contains 2 jets, missing energy and 2τ + 1e or 3τ 's; iii) for theX −+ 1X +− 1 topology the final state contains 2 jets, missing energy and 2τ 's. It is important that cases i) and ii) can be accompanied by one or two electrons, given that many searches for topologies involving τ 's 13 impose a lepton (e or µ) veto.
Thus, for instance, a recent ATLAS study [45] with 4.7 fb −1 searches for jets + E T accompanied by exactly one (hadronically decaying) τ + one lepton (e or µ), or by two τ 's with a lepton veto. Only the former would apply to our scenario, setting a bound of σ × × A = 0.68 fb −1 . A previous ATLAS search [46] with 2.05 fb −1 searches for at least 2τ 's (with a lepton veto), setting a bound of σ × × A = 2.9 fb −1 . However, the efficiency of such searches is lower than the one for jets plus missing energy (also with lepton veto). Since in our scenario the cross sections for these two signatures is the same, the latter will set the relevant current bound.
There is also a CMS study [47] sensitive to 4τ signals in the context of GMSB scenarios, which has a similar topology to our case (SMS:gg production withg → qqχ 0 1 and χ 0 1 → τ + τ −G µ ). From their figure 9b, we can see that the 95% CL upper limit on the model cross section varies between 0.3 − 0.03 pb for 400 GeV < mg < 700 GeV. Including the branching fractions, and reinterpreting the bound in the squark mass plane, 14 we find a bound of mq 600 GeV at v e = 10, where the cross section is about 45 fb. When the sneutrino vev increases the bound gets relaxed so that for v e 20 GeV there is no bound from this study.
The generic searches discussed in previous sections (not necessarily designed for sensitivity to the third generation) may also be relevant: • jets + E T , • jets + E T + 1 lepton , • jets + E T + SS dileptons , • jets + E T + OS dileptons , where the leptons may arise from theν τ decay as in cases i) and ii) above, or from leptonically decaying τ 's. 15 It turns out that, as in the "neutralino LSP scenario", the strongest bound arises from the jets + E T search. We find from simulation of the signal efficiency times acceptance for the ATLAS analysis [19] in our model that the most stringent bound arises from signal region C (tight), and gives an upper bound on the model cross section of about 120 fb. Thus, we find that mq 500 GeV for v e = 10 GeV.

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4.4.2τ − L →t L b R andν τ →b L b R decay modes When the third generation sleptons decay through these channels, as is typical of the large sneutrino vev limit, the signals contain a bb and/or a tt pair, as well as τ 's. Note that when the τ 's and tops decay hadronically one has a signal without missing energy. However, the branching fraction for such a process is of order BR(q →X 0+ few per cent (in the large sneutrino vev limit, where all of these branching fractions are sizable). Indeed, we find that the "no E T " cross section for 700 GeV squarks in the "stau LSP scenario" is of order 1 fb, which is relatively small. Rather, the bulk of the cross section shows in the jets + E T and 1 lepton + jets + E T channels (with a smaller 2 lepton + jets + E T contribution). Simulation of the ATLAS j+ E T search [19] in this region of our model indicates that again the most stringent bound arises from signal region C (tight) of this study, and gives an upper bound on the model cross section of about 70 fb. This translates into a bound of mq 550 GeV for v e = 50 GeV.

Third generation squark phenomenology
We turn now to the LHC phenomenology of the third generation squarks. We start by studying the current constraints and then we will explain how the third generation provides a possible smoking gun for our model. We separate our discussion into the signals arising from the lepto-quark decay channels, and those that arise from the decays of the third generation squarks into states containingX 0+ 1 orX +− 1 (or their antiparticles).

Lepto-quark signatures
Due to the identification of lepton number as an R-symmetry, there exist lepto-quark (LQ) decays proceeding through the LQD c couplings. These can be especially significant for the third generation squarks. As discussed in subsection 3.4.2, in our scenario we expect: It may be feasible to use the channels involving a top quark in the final state [48], but such searches have not yet been performed by the LHC collaborations. Thus, we focus on the existing eejj [49,50], ννbb [51] and τ τ bb [52] searches, where in our case the jets are really b-jets. 16 The first and third searches have been performed with close to 5 fb −1 by CMS, while the second has been done with 1.8 fb −1 . In the left panel of figure 13, we show the bounds from these searches on the LQ mass as a function of the branching fraction of the LQ into the given channel. The bounds are based on the NLO strong pairproduction cross-section. We see that the most sensitive is the one involving electrons, while the one involving missing energy is the least sensitive. This is in part due to the lower luminosity, but also because in the latter case the search strategy is different since one cannot reconstruct the LQ mass.
In the right panel of figure 13 we show the corresponding branching fractions in our scenario as a function of the sneutrino vev, assuming m LQ = 400 GeV (which, as we will see, turns out to be the mass scale of interest). We have fixed M D 2 = 1.5 TeV and M D 1 = 1 TeV, and scanned over µ ∈ [−300, 300] GeV and λ S u , λ T u ∈ [0, 1], which is reflected in the width of the bands of different colors. We assume that λ 333 saturates eq. (2.4). The BR's are rather insensitive to λ S u and λ T u , but depend strongly on µ, especially when |µ| 200 GeV. The reason is that for larger µ the neutralinos and charginos become too heavy, the corresponding channels close, and the LQ channels can dominate. This affects the decays oft L andb L , but not those ofb R as can be understood by inspecting figures 7, 8 and the right panel of figure 9. 17 The darker areas correspond to the region |µ| ∈ [0, 200], while the lighter ones correspond to |µ| ∈ [200, 300]. We can draw a couple of general conclusions: 1. The ννbb branching fractions are below the sensitivity of the present search, except when the neutralino/chargino channels are suppressed or closed for kinematic reasons. Even in such cases, the lower bound on mb L is at most 350 GeV. Note thatb R is unconstrained.
2. The τ τ bb search, which is sensitive to BR's above 0.3, could set some bounds at large v e in some regions of parameter space. Such bounds could be as large as 520 GeV, but there is a large region of parameter space that remains unconstrained.

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3. The eejj search , which is sensitive to BR's above 0.15, could set some bounds at small v e in some regions of parameter space. Such bounds could be as large as 815 GeV if v e ∼ 10 GeV and the neutralino/chargino channels are kinematically closed. However, in the more typical region with µ 200 GeV the bounds reach only up to 550 GeV in the small v e region. Nevertheless, there is a large region of parameter space that remains completely unconstrained.
The latter two cases are particularly interesting since the signals arise from the (LH) stop, which can be expected to be light based on naturalness considerations. In addition to the lessons from the above plots, we also give the bounds for our benchmark scenario with M D 1 = 1 TeV, M D 2 = 1.5 TeV, µ = 200 GeV, λ S u = 0 and λ T u = 1, assuming again that eq. (2.4) is saturated. We find that the ννbb search requires mb L 350 GeV, and gives no bound on mb R . The τ τ bb search gives a bound on mt L that varies from 380 to 400 GeV as v e varies from 20 − 50 GeV. The eejj search gives a bound on mt L that varies from 470 down to 300 GeV as v e varies from 10 − 30 GeV. The other regions in v e remain unconstrained at present. In our benchmark, when mb L ∼ 350 GeV, we expect mt L ∼ 380 − 390 GeV, depending on the scalar singlet and (small) triplet Higgs vevs (and with only a mild dependence on v e ). We conclude that in the benchmark scenario a 400 GeV LH stop is consistent with LQ searches, while offering the prospect of a LQ signal in the near future, possibly in more than one channel.
Comment on LQ signals from 2 nd generation squarks. We have seen that the RH strange squark has a sizable branching fraction into the LQ channel,s R → e − L j, of order 0.4 − 0.65. From the left panel of figure 13, we see that the eejj CMS lepto-quark search gives a bound of ms ≈ 530 − 630 GeV, which is quite comparable to (but somewhat weaker than) the bounds obtained in section 4. Thus, a LQ signal associated to the RH strange squark is also an exciting prospect within our scenario.

Other searches
There are a number of searches specifically optimized for third generation squarks. In addition, there are somewhat more generic studies with b-tagged jets (with or without leptons) that can have sensitivity to our signals. We discuss these in turn.
Direct stop searches. In the case of the top squark, different strategies are used to suppress the tt background depending on the stop mass. However, the searches are tailored to specific assumptions that are not necessarily satisfied in our framework: • Perhaps the most directly applicable search to our scenario is an ATLAS GMSB search [53] (t 1t * 1 pair production witht 1 → tχ 0 1 ort 1 → bχ + 1 and finallyχ 0 1 → ZG or χ + 1 → W +G ), so that the topologies are identical to those for LH and RH stop pairproduction in our model, respectively, with the replacement of the light gravitino by ν e (although the various branching fractions are different; see figures 7 and 9 for our benchmark scenario). Ref.
[53] focuses on the decays involving a Z, setting bounds of σ× ×A = 18.2 (9.7) fb for their signal region SR1 (SR2). Simulation of our signal for JHEP05(2013)012 our benchmark parameters and taking 400 GeV LH stops gives × A ≈ 1.9% (1.7%) for SR1 (SR2), which include all the relevant branching fractions. The corresponding bound on the model cross section would then be σt LtL ≈ 1 (0.6) pb. However, a crosssection of 0.6 pb is only attained for stops as light as 300 GeV, and in this case the efficiency of the search is significantly smaller, as the phase space for thet L →X 0+ 1 t decay closes (recall that due to the LEP bound on the chargino, and the Higgsino-like nature of our neutralino, the mass ofX 0+ 1 must be larger than about 100 GeV). We conclude that this search is not sufficiently sensitive to constrain the LH stop mass. Also, the requirement that the topology contain a Z gauge boson makes this search very inefficient for the RH stop topology:t R →X +− 1 b R ,X +− 1 → W + ν e , so that no useful bound can be derived on mt R .
• There is a search targeted for stops lighter than the top (t → bχ + 1 , followed bỹ χ + 1 → W +χ0 1 ). This is exactly the topology fort R production in our scenario (with m LSP = 0 for the neutrino), but does not apply tot L since its decays are dominated by lepto-quark modes in this mass region. Figure 4c in [54] shows that for a chargino mass of 106 GeV, stop masses between 120 and 164 GeV are excluded. As the chargino mass is increased, the search sensitivity decreases, but obtaining the stop mass limits would require detailed simulation in order to compare to their upper bound σ× ×A = 5.2 − 11 fb.
• There are also searches for stop pair production witht → tχ 0 1 . A search where both tops decay leptonically [55] would yield the same final state as fort Rt * R production in our case (bbW + W − + E T with the W 's decaying leptonically). However, the kinematics is somewhat different than the one assumed in [55] which can impact the details of the discrimination against the tt background, which is based on a M T 2 analysis. Indeed, we find from simulation that the M T 2 variable in our case tends to be rather small, and × A for this analysis is below 0.1% (including the branching ratios). Therefore, this search does not set a bound on the RH stop in our scenario.
There is a second search focusing on fully hadronic top decays [56], that can be seen to apply fort Lt * L production witht L → tX 0+ 1 followed byX 0+ 1 →ν e Z/h. For instance, when both Z gauge bosons decay invisibly the topology becomes identical to the one considered in the above analysis (wheret L → t + E T ). Also when both Z's decay hadronically one has a jet + E T final state. In fact, although the analysis attempts to reconstruct both tops, the required 3-jet invariant mass window is fairly broad. We find from simulation that when BR(X 0+ 1 → Zν e ) = 1, the × A of our signal is very similar to that in the simplified model considered in [56]. However, when BR(X 0+ 1 → hν e ) = 1 we find that × A is significantly smaller. Due to the sneutrino vev dependence of these branching fractions in our model, we find (for benchmark 1 ) that this search can exclude mt L in a narrow window around 400 GeV for a large sneutrino vev (v e ∼ 50 GeV). For lower stop masses the search is limited by phase space in the decayt L → tX 0+ 1 , while at larger masses the sensitivity is limited by the available BR(X 0+ 1 → Zν e ) (see figure 3). At small sneutrino vev no bound on JHEP05(2013)012 mt L can be derived from this search due to the suppressed branching fraction of the Z-channel. We also find that the RH stop mass can be excluded in a narrow window around 380 GeV from the decay chaint R →X +− 1 b R followed byX +− 1 → W + ν e . Although there are no tops in this topology, it is possible for the 3-jet invariant mass requirement to be satisfied, and therefore a bound can be set in certain regions of parameter space.
There is a third search that allows for one hadronic and one leptonic top decay [57]. We find that it is sensitive to the LH stop in a narrow window around mt L ∼ 380 GeV (for benchmark 1 ). However, we are not able to set a bound on mt R from this search.
We conclude that the present dedicated searches for top squarks are somewhat inefficient in the context of our model, but could be sensitive to certain regions of parameter space. The most robust bounds on LH stops arise rather from the lepto-quark searches discussed in the previous section. However, since the latter do not constrain the RH stop, it is interesting to notice that there exist relatively mild bounds (below the top mass) for t R , as discussed above, and perhaps sensitivity to masses around 400 GeV.
Direct sbottom searches. Ref. [58] sets a limit on the sbottom mass of about 420 GeV, based onbb * pair production followed byb → tχ − 1 andχ − 1 → W −χ0 1 (for mχ0 1 = 50 GeV, and assuming BR's = 1). This is essentially our topology whenb L → tX −+ ≈ 430 GeV, again independent of µ. We note that the bound on mb L sets indirectly, within our model, a bound on the LH stop, since the latter is always heavier thanb L (recall that the LR mixing is negligible due to the approximate R-symmetry). Typically, mt L − mb L ∼ 30 − 50 GeV. Generic searches sensitive to third generation squarks. In table 2, we summarize a number of generic searches with b-tagging and with or without leptons. We see that the JHEP05(2013)012  bounds on σ × × A range from a few fb to several tens of fb. We find that our model cross section for these signatures (from pair production of 400 GeVt L ,t R ,b L orb R ) are in the same ballpark, although without taking into account efficiencies and acceptance. Thus, we regard these searches as potentially very interesting, but we defer a more detailed study of their reach in our framework to the future. We summarize the above results in figure 14, where we also show the bounds on the first two generation squarks (section 4), as well as the lepto-quark bounds discussed in section 5.1 (shown as dashed lines). The blue region, labeled "b L (SUSY search)", refers to the search via two b-tagged jets plus E T , which has more power than the LQ search that focuses on the same final state. The region labeled "t L (model)" refers to the bound ont L inferred from the SUSY search onb L . We do not show the less sensitive searches, nor the bound onb R , which is independent of µ, and about 470 GeV in our benchmark scenario.

Summary and conclusions
We end by summarizing our results, and emphasizing the most important features of the framework. We also discuss the variety of signals that can be present in our model. Although some of the individual signatures may arise in other scenarios, taken as a whole, one may regard these as a test of the leptonic R-symmetry. The model we have studied departs from "bread and butter" SUSY scenarios (based on the MSSM) in several respects, thereby illustrating that most of the superpartners could very well lie below the 1 TeV threshold in spite of the current "common lore" that the squark masses have been pushed above it.
There are two main theoretical aspects to the scenario: a) the presence of an approximate U(1) R symmetry at the TeV scale, and b) the identification of lepton number as the R-symmetry (which implies a "non-standard" extension of lepton number to the new physics sector). The first item implies, in particular, that all BSM fermions are Dirac particles. A remarkable phenomenological consequence is manifested, via the Dirac nature of gluinos, as an important suppression of the total production cross section of the strongly interacting BSM particles (when the gluino is somewhat heavy). This was already pointed out in ref. [15] in the context of a simplified model analysis. We have seen here that the main conclusion remains valid when specific model branching fractions are included, and even when the gluino is not super-heavy (we have taken as benchmark a gluino mass of 2 TeV). We find that: • The bounds on the first two generation squarks (assumed degenerate) can be as low as 500 − 700 GeV, depending on whether a slepton (e.g.τ L ) is lighter than the JHEP05(2013)012 lightest neutralino [X 0+ 1 in our notation; see comments after eq. (2.3)]. There are two important ingredients to this conclusion. The first one is the above-mentioned suppression of the strong production cross section. Equally important, however, is the fact that the efficiencies of the current analyses deteriorate significantly for lower squark masses. For example, the requirements on missing energy and m eff (a measure of the overall energy involved in the event) were tightened in the most recent jets + E T analyses (∼ 5 fb −1 ) compared to those of earlier analyses with 1 fb −1 . As a result, signal efficiencies of order one (for 1.4 TeV squarks and 2 TeV gluinos in the MSSM) can easily get diluted to a few percent (as we have found in the analysis of our model with 700 GeV squarks and 2 TeV gluinos). This illustrates that the desire to probe the largest squark mass scales can be unduly influenced by our prejudices regarding the expected production cross sections. We would encourage the experimental collaborations to not overlook the possibility that lighter new physics in experimentally accessible channels might be present with reduced production cross sections. Models with Dirac gluinos could offer a convenient SUSY benchmark for optimization of the experimental analyses. It may be that a dedicated analysis would strengthen the bounds we have found, or perhaps result in interesting surprises.

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It is important to keep in mind that the previous phenomenological conclusions rely mainly on the Dirac nature of gluinos, which may be present to sufficient approximation even if the other gauginos are not Dirac, or if the model does not enjoy a full U(1) R symmetry. Nevertheless, the presence of the U(1) R symmetry has further consequences of phenomenological interest, e.g. a significant softening of the bounds from flavor physics or EDM's [6] (the latter of which could have important consequences for electroweak baryogenesis [12,62]). In addition, the specific realization emphasized here, where the R-symmetry coincides with lepton number in the SM sector, has the very interesting consequence that: • A sizable sneutrino vev, of order tens of GeV, is easily consistent with neutrino mass constraints (as argued in [1,16]; see also ref. [13] for a detailed study of the neutrino sector). The point is simply that lepton number violation is tied to U(1) R violation, whose order parameter can be identified with the gravitino mass. When the gravitino is light, neutrino Majorana masses can be naturally suppressed (if there are RH neutrinos, the associated Dirac neutrino masses can be naturally suppressed by small Yukawa couplings). We have also seen that there are interesting consequences for the collider phenomenology. Indeed, the specifics of our LHC signatures are closely tied to the non-vanishing sneutrino vev (in particular the neutralino decays: X 0+ 1 → Zν e /hν e /W − e + L , or the chargino decay: This should be contrasted against possible sneutrino vevs in other scenarios, such as those involving bilinear R-parity violation, which are subject to stringent constraints from the neutrino sector. Note also that the prompt nature of the above-mentioned decays may discriminate against scenarios with similar decay modes arising from a very small sneutrino vev (thus being consistent with neutrino mass bounds in the absence of a leptonic U(1) R symmetry). In addition, the decays involving a W gauge boson would indicate that the sneutrino acquiring the vev is LH, as opposed to a possible vev of a RH sneutrino (see e.g. [26,63] for such a possibility).
A further remarkable feature -explained in more detail in the companion paper [1]is that in the presence of lepto-quark signals, the connection to neutrino physics can be an important ingredient in making the argument that an approximate U(1) R symmetry is indeed present at the TeV scale. In short: • If lepto-quark signals were to be seen at the LHC (these arise from the LQD c "RPV" operator), it would be natural to associate them to third generation squarks (within a SUSY interpretation, and given the expected masses from naturalness considerations). In such a case, one may use this as an indication that some of the λ i33 couplings are not extremely suppressed. The neutrino mass scale then implies a suppression of LR mixing in the LQ sector. From here, RG arguments allow us to conclude that the three Majorana masses, several A-terms and the µ-term linking the Higgs doublets that give mass to the up-and down-type fermions (see footnote 4) are similarly suppressed relative to the overall scale of superpartners given by M SUSY , which is the hallmark of a U(1) R symmetry. Therefore, the connection to neutrino masses via a LQ signal provides strong support for an approximate U(1) R symmetry

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in the full TeV scale Lagrangian, and that this symmetry is tied to lepton number, which goes far beyond the Dirac nature of gluinos. In particular, it also implies a Dirac structure in the fermionic electroweak sector, which would be hard to test directly in many cases. Indeed, in the benchmark we consider, the lightest electroweak fermion states are Higgsino-like and hence have a Dirac nature anyway, while the gaugino like states are rather heavy and hence difficult to access. What we have shown is that the connection to neutrino masses can provide a powerful probe of the Dirac structure even in such a case.
The (approximately) conserved R-charge, together with electric charge conservation can impose interesting selection rules (e.g. allowing 2-body decays of the LH squarks, includingt L , into a state involving an electron but not involving the next lightest chargino, X +− 1 ). Of course, eventually the approximate R-symmetry should become evident in the decay patterns of the BSM physics. The above lepto-quark signals, and perhaps signals from resonant single slepton production [1] that may be present in more general RPV scenarios, can be amongst the first new physics signals discovered at the LHC. Although by themselves, these may admit interpretations outside the present framework, the "L = R" model has a variety of signals that provide additional handles. Some of them are summarized below.
The presence of fully visible decay modes, in addition to those involving neutrinos, may give an important handle in the reconstruction of SUSY events. An example is displayed in the left diagram of figure 15, where one of the squarks decays viaq → jX 0− followed byX 0− → e − L W + (with a hadronic W ), while the other squark gives off missing energy in the form of neutrino(s), which can help in increasing the signal to background ratio. Although the combinatorics might be challenging, there are in principle sufficient kinematic constraints to fully reconstruct the event.
Perhaps more striking would be the observation of the lepto-quark decay mode of the RH strange squark, as discussed at the end of section 5.1. The pure LQ event (eejj) would allow a clean measurement of ms R , which could then be used in the full reconstruction of "mixed" events involving missing energy, such as displayed in the right diagram of figure 15. Furthermore, if the gluinos are not too heavy, associated production of different flavor squarks (one beings R ) through gluino t-channel exchange, may allow an interesting measurement of the second squark mass. Both of these would offer discriminatory power between scenarios with relatively light squarks (∼ 700 GeV, as allowed by the R-symmetry) versus scenarios with heavier squarks (e.g. 1 TeV with ultra-heavy gluinos, as might happen within the MSSM), by providing information on the scale associated with a putative excess in, say, the jets + E T channel.
An important possible feature of the present scenario is the presence of final states with large third-generation multiplicities. We have seen how in the "stau LSP scenario" squark pair production can result in final states with multiple τ 's, often accompanied by one or more leptons (e or µ). Although these may not be the discovery modes due to a reduced efficiency compared to more standard squark searches, they remain as an extremely interesting channel to test the present scenario. Similarly, processes such as Figure 15. Examples of processes with one fully visible decay chain (thus allowing for mass reconstructions), while containing a significant amount of missing energy from the second decay chain (that can help for triggering and discrimination against backgrounds). The arrows indicate the flow of L = R number.
RbR t LtL , display all the heavy third generation fermions in the final state, and it would be extremely interesting to conduct dedicated searches for this kind of topology. Another extremely interesting 'no missing energy" topology arises in the "neutralino LSP scenario":qq * → jjX 0+ In the lepto-quark sector, signals such asb Rb * R → e + L e − L t LtL /τ + L τ − L t LtL have not been looked for experimentally, but have been claimed to be feasible in ref. [48]. Needless to say, experimentalists are strongly encouraged to test such topologies given the expected importance of the third generation in connection to the physics of electroweak symmetry breaking.
Finally, it is important to note that there may be alternate realizations of an approximate U(1) R symmetry at the TeV scale. For example, in the realization in which the R-symmetry is identified with baryon number [64,65], the "LSP" decays predominantly to jets, giving rise to events with very little missing energy and hence evading most of the current LHC bounds. So, these models may hide the SUSY signals under SM backgrounds. A remarkable feature of the realization studied in this paper is that fairly "visible" new physics could still be present just were naturalness arguments could have indicated. It is certainly essential to test such (and possibly other) realizations if we are to address one of the most important questions associated to the weak scale: whether, and to what extent, EWSB is consistent with naturalness concepts as understood within the well-tested effective field theory framework.  . For reference, we show the MSSM total strong production cross-section (squarks and gluinos). The dashed lines are the SMS upper limit from the CMS searches for the channel Z(ll) + jets + E T , assuming mχ = 100 GeV and mχ = 300 GeV [23].
We start with the dilepton Z(ll) + jets + E T channel, basing our discussion on a CMS analysis with 4.98 fb −1 (gg production withg → qqχ and χ → Z LSP 18 ) [24,41]. Bounds are given for x = 1/4, 1/2 and 3/4. Identifying mq with the "gluino mass", taking m LSP = 0, and adjusting the squark mass until the experimental upper bound on σ is matched by our theoretical cross section, we find for x = 1/2: σ 1 (mq ≈ 585 GeV) ≈ 0.07 pb and σ 2 (mq ≈ 650 GeV) ≈ 0.06 pb. What this means is that this topology/analysis gives a lower bound of mq ≈ 585 GeV whenX 0+ 1 is produced as in our scenario, and of mq ≈ 650 GeV in a scenario where all the squarks decay into neutralino plus jet, followed by the decaỹ X 0+ 1 → Zν e with BR = 1 (σ 1 and σ 2 are computed as explained in subsection 4.2). For a lighterX 0+ 1 (x = 1/4), the corresponding bounds are mq ≈ 360 GeV and 440 GeV, respectively. All of these can be read also from figure 16. 18 Note that this topology is not identical to ours, having two extra jets.

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As a check, and to evaluate the effect of the additional two jets in the topology considered in [41] compared to the squark pair-production of our case, we have obtained the × A from simulation of our signal (qq production withq → qX 0+ 1 andX 0+ 1 → Zν e , taking mX 0 = 200 GeV) in the various signal regions of the CMS analysis. 19 We find that the strongest bound arises from the "MET Search" with E T > 300 GeV (with ×A ≈ 1.5%, including the branching fractions of the Z), and corresponds to a model cross-section of about 40 fb. This translates into the bounds mq 640 GeV (based on σ 1 ) and mq 690 GeV (based on σ 2 ), which are somewhat stronger than above.
For the jets + E T signal we use an ATLAS search with 5.8 fb −1 [19], which includes five different signals regions depending on the jet multiplicity. In order to apply this analysis, we estimate the efficiency times acceptance in our model in the different signal regions by simulating our signal (X 0+ 1X 0− 1 jj production via the processes defining σ 1 , followed byX 0+ 1 → Zν e with BR = 1), and then applying the cuts in [19]. Our topology, and our model in general, is distinguished by long cascade decays, and we find that the strongest bound arises from signal region D (tight), i.e. a 5 jet region, setting a bound on the signal cross-section of about 20 fb. We find a lower limit of mq ∼ 635 GeV (based on σ 1 ), and mq ∼ 685 GeV (based on σ 2 ). We conclude that the bounds from this analysis are very comparable to those from the Z(ll) + jets + E T channel. We note that CMS has a M T 2 -based Simplified Model analysis of the jets + E T signature with 4.73 fb −1 [21] (SMS:gg production withg → qq + LSP). Applying the procedure detailed at the end of subsection 4.2, we find that σ 1 (mq ≈ 350 GeV) × BR(Z → jj) 2 ≈ 0.9 pb and σ 2 (mq ≈ 440 GeV) × BR(Z → jj) 2 ≈ 0.4 pb. The fact that these limits are much weaker than those obtained from the ATLAS study may be related in part to the additional hard jets that differentiate the gluino from the squark pair production topology.
There are no SMS limits on multilepton searches applicable to our topologies, but there are a number of model-independent upper bounds on σ × × A, as summarized in table 3. However, putting in the BR(Z → l + l − ) and taking into account the general lessons from the computed efficiencies for "Topologies (3) and (4)" below, we conclude that such searches are less sensitive than the previous two searches.
A.2 Topology (2):X 0+ 1 → hν e For this topology we use the ATLAS jets + E T search [19] since the Higgs decays mostly into hadrons. This topology is characterized by a high jet multiplicity, as was the case with the hadronic Z of the previous topology. The efficiency times acceptance is the same as in the case studied above (with a Z instead of h), so that the bound on the model cross section is about 20 fb. We find a lower limit of mq ∼ 605 GeV (based on σ 1 ), and mq ∼ 655 GeV (based on σ 2 ).
Note that, since the Higgs decays predominantly into bb, searches with b tagged jets are interesting for this topology. In a search for final states with E T and at least three b-jets (and no leptons), ATLAS sets a bound on the corresponding visible cross section of JHEP05(2013)012  about 2 fb [61]. However, simulating our signal (for 700 GeV squarks) in MG5 + Pythia + Delphes, we find an extremely small efficiency for the present topology: × A ≈ 10 −4 for their signal regions SR4-L and SR4-M (and much smaller efficiencies for the other SR's). This arises from the aggressiveness of the E T requirement and the combined efficiency of tagging three b-jets. As a result we infer a very mild bound on the model cross section of about 18 pb, and no meaningful bound on the squark masses, as such a cross section can be reached only for squarks as light as a couple hundred GeV, where the × A would be even smaller. Nevertheless, it would be interesting to optimize such an analysis for the present model (with suppressed production cross sections), and furthermore to try to reconstruct bb resonances at about 125 GeV.
The leptonic searches are not constraining due to the significant suppression from the Higgs branching fraction into final states that might involve leptons. In this case the two relevant searches are: jets + two leptons without E T , and multileptons + jets + E T . The first signal has a branching fraction of BR(W → jj) 2 ≈ 0.45. However, at the moment there are no searches that constrain this topology, since these typically include important cuts on the missing transverse energy. It would be interesting to perform a dedicated search for this signal. Here we focus on the existing multilepton searches. CMS has a detailed analysis including a large number of channels [68]. Unfortunately, the results are model-dependent and no information on σ × × A for the different signal regions is provided. ATLAS has a ≥ 4 leptons (+ jets + E T ) search with and without Z veto [42]. Their upper limit (with a Z veto) is σ × × A ≈ 1.5 fb. 20 We find from simulation of our signal that, for this analysis, × A ≈ 0.02 (which includes the branching fractions of the W decays). We can therefore set a limit of mq 580 GeV (based on σ 1 ) and mq 630 GeV (based on σ 2 ), corresponding to a model cross section of about 75 fb.
We can use again the ATLAS bound on jets + E T discussed above. In this case, however, the efficiency times acceptance turns out to be smaller. 21 The strongest constraint arises again from signal region D (tight) in [19], and gives an upper bound on our model cross section of about 60 fb. This translates into mq 530 GeV (based on σ 1 ) and mq 650 GeV (based on σ 2 ).
In a multi-lepton study, the ATLAS collaboration has considered our simplified model (model C in [43]), except that all the squarks are assumed to decay with unit branching fraction through the chargino channel (i.e. the process characterized by σ 2 ). If we assume the same efficiency times acceptance for the process in our scenario, i.e. based on σ 1 , we read from their figure 10 the bounds mq 410 GeV (based on σ 1 ), and mq 500 GeV (based on σ 2 ), which correspond to model cross sections of about 0.35 pb.
ATLAS also has a search for exactly 1 lepton + ≥ 4 jets + E T , setting a bound on σ × × A ≈ 1.1 − 1.7 fb, depending on whether the lepton is an electron or a muon [44]. Simulation of the above process (qq production withq → qX +− 1 followed byX +− 1 → W + ν e , taking mX ± = 200 GeV) gives that the ATLAS analysis has × A ≈ 10 −3 (this includes the branching fractions for the W decays). We see that the efficiency is quite low. This is due, in part, to the fact that the analysis requires at least four jets with p T > 80 GeV. While the two jets from squark decays easily pass the p T cut, the other two jets arise from a W decay and are softer (the other W decaying leptonically). But when the quarks are sufficiently boosted to pass the p T cut, they also tend to be collimated, and are likely to be merged into a single jet. As a result, using an upper bound on the model cross section of order 1 pb, we get a rather mild bound of mq 350 GeV (based on σ 1 ), and mq 430 GeV (based on σ 2 ).
For the OS dilepton signal CMS sets a bound of σ × ×A 1−5 fb with 4.98 fb −1 [66]. Our simulation gives × A ∼ 10 −3 (including the W BR's), resulting again in an upper bound on the model cross section of about 1 pb, and the same mild bounds as above.
CMS studies a simplified model (gg production withg 1 → qqχ 0 andg 2 → qqχ ± ) with 4.98 fb −1 [23], where the neutralino χ 0 is the LSP, while χ ± decays into W ± χ 0 . Therefore, as in our scenario, a single lepton is produced via W decay, although there are two extra hard jets compared to our case from the gluino versus squark production. From figure 8 of [23], with m LSP = 0, we find that our cross section, in the range 300 GeV < mq < 800 GeV, is more than an order of magnitude below the current sensitivity. Here we used our σ 1 including the branching for exactly one of the W's to decay leptonically.

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Finally, our model has very suppressed SS dilepton signals due to the Dirac nature of the gluino, 22 so that no interesting bounds arise from this search. In conclusion, for this simplified topology, the strongest bounds again arise from the generic jets + E T searches, although it should be possible to optimize the leptonic searches to our signal topologies to obtain additional interesting bounds.
Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
[53] ATLAS collaboration, Search for scalar top quark pair production in natural gauge mediated supersymmetry models with the ATLAS detector in pp collisions at √ s = 7 TeV, Phys. Lett.