Natural SUSY at LHC with right-sneutrino LSP

Journal of High Energy Physics, Jun 2018

Abstract We study an extension of the minimal supersymmetric standard model (MSSM) with additional right-handed singlet neutrino superfields. While such an extension incorporates a mechanism for the neutrino mass, it also opens up the possibility of having the right-sneutrinos (\( \tilde{\nu} \)) as the lightest supersymmetric particle (LSP). In this work, we focus on the viability of rather small (≲500 GeV) higgsino mass parameter (μ), an important ingredient for “naturalness”, in the presence of such a LSP. For simplicity, we assume that the bino and wino mass parameters are much heavier; thus we only consider (almost) pure and compressed higgsino-like states, with small \( \mathcal{O}\left(1{0}^{-2}\right) \) gaugino admixture which nevertheless still affect the decay of the low-lying higgsino-like states, thus significantly affecting the proposed signatures at colliders. Considering only prompt decays of the higgino-like states, especially the lightest chargino, we discuss the importance of leptonic channels consisting of up to two leptons with large missing transverse energy to probe this scenario at the Large Hadron Collider (LHC). In addition we also comment on the dark matter predictions for the studied scenario.

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Natural SUSY at LHC with right-sneutrino LSP

Revised: March Natural SUSY at LHC with right-sneutrino LSP Arindam Chatterjee 0 1 Juhi Dutta 0 1 Santosh Kumar Rai 0 1 Harish-Chandra Research Institute, HBNI, 0 203 B. T. Road, Kolkata-700108 , India 1 Chhatnag Road, Jhusi , Allahabad-211019 , India We study an extension of the minimal supersymmetric standard model (MSSM) with additional right-handed singlet neutrino super elds. tension incorporates a mechanism for the neutrino mass, it also opens up the possibility of having the right-sneutrinos ( ) as the lightest supersymmetric particle (LSP). In this work, we focus on the viability of rather small (. 500 GeV) higgsino mass parameter ( ), an important ingredient for \naturalness", in the presence of such a LSP. For simplicity, we assume that the bino and wino mass parameters are much heavier; thus we only consider (almost) pure and compressed higgsino-like states, with small O(10 2) gaugino admixture which nevertheless still a ect the decay of the low-lying higgsino-like states, thus signi - cantly a ecting the proposed signatures at colliders. Considering only prompt decays of the higgino-like states, especially the lightest chargino, we discuss the importance of leptonic channels consisting of up to two leptons with large missing transverse energy to probe this scenario at the Large Hadron Collider (LHC). In addition we also comment on the dark matter predictions for the studied scenario. Supersymmetry Phenomenology - 2.1 2.2 2.3 4.1 4.3 4.4 4.5 4.6 5 Conclusion 1 Introduction 1 Introduction 2 The model 4 Survey of the relevant parameter space Constraints on electroweakino sector from LHC 4.2 Impact of additional related searches at LHC Benchmarks Collider analyses impressing the fact that low j j is of more essence to the \natural" scenarios at EW scale. While the constraints on stop squarks and gluinos are rather stringent due to their large production cross-section at the LHC, the weakly interacting sector with rather light { 1 { electroweakinos in general, and higgsinos in particular, remain viable [11, 12]. There have been several analyses on light electroweakinos, assuming a simpli ed spectra with one or more speci c decay channels [13{26]. Further, the constraints on the mass of the light higgsino-like states have been studied in detail because of their importance in a \natural" supersymmetric scenario [19, 27{33]. However, note that these analyses assume the lightest neutralino as the lightest supersymmetric particle (LSP). In scenarios with conserved Rparity, the search strategies, and therefore the limits of various sparticle masses, depend on the nature of the LSP. This is because in such scenarios the LSP appears at the end of the decay chain of each sparticle, therefore dictating the possible search channels. This warrants investigation of supersymmetric scenarios with di erent types of LSP. While within neutrino mass generation issue, has been widely studied in supersymmetric extensions. While the left-sneutrinos have been ruled out as a Dark Matter (DM) candidate long ago, thanks to the stringent limit from direct detection experiments [71], right-sneutrinos continue to be widely studied as a candidate for DM in simple extensions of the MSSM [59{ 63, 65{68, 72]. In its simplest incarnation as ours, the right-sneutrinos at EW scale remain very weakly interacting, thanks to the small Yukawa coupling O(10 6{10 7) determining their coupling strength to other particles. However, as in the case of charged sfermions, a rather large value of the corresponding tri-linear soft supersymmtry breaking parameter can induce signi cant left-admixture in a dominantly right-sneutrino and therefore can substantially increase the interaction strengths [66, 67, 72]. In both of these scenarios, DM aspects as well as search strategies at LHC have been studied for certain choices of the SUSY spectra [64, 73{79]. We note that in the light of \naturalness", it becomes equally important to investigate the supersymmetric spectrum in such a scenario. In particular we focus on a minimalistic spectrum, motivated by \naturalness" at the EW scale, with light higgsino-like states and a right-sneutrino LSP. However, analysing collider signatures from the third generation squarks and gluinos will be beyond the scope of the present work and will be addressed in a subsequent extension. For the present case, the strongly interacting sparticles have been assumed to be very heavy adhering to the \naturalness" scheme proposed in refs. [9, 10]. Further, we will also assume the gaugino mass parameters to be large enough (& O( 1 ) TeV). Thus the light electroweakinos are higgsino-dominated states. Note that the presence of a mixed right-sneutrino as the LSP can lead to a very di erent signature from the compressed higgsino-like states, mostly due to the leptonic decay of the light chargino. Although leptonic channels provide a cleaner environment for new physics searches at a { 2 { hadron machine such as the LHC, one expects that the level of compression in the mass spectra of the electroweakinos would also play a major role in determining the e cacy of the leptonic channels. We investigate the prospects of discovery of such channels at the 13 TeV run of LHC. We focus on the following apsects in our study: We consider a right-sneutrino LSP along with a compressed electroweakino sector sitting above the LSP, where the lighter states are almost Higgsino-like with a very small admixture of gauginos. We give a detailed account of how the decay of the light electroweakinos depend on the various supersymmetric parameters that govern the mixing, mass splitting and, in which region of the parameter space the decays are prompt. We also highlight how even the smallest gaugino admixture plays a signi cant role in their decays. We comment on the DM predictions for a thermal as well as non-thermal nature of the right-sneutrino DM candidate in regions of parameter space of our interest. We then look at possible leptonic signals that arise from such a spectrum and analyze the signal at LHC. The article is organized as follows. In section 2 we discuss the model and the underlying particle spectrum of interest in detail. In the following section 3 we focus on identifying the parameter space satisfying relevant constraints as well as implications on neutrino sector and a sneutrino as DM. In section 4 we discuss the possible signatures at LHC and present our analysis for a few representative points in the model parameter space. We nally conclude in section 5. 2 The model We consider an extension to the Minimal Supersymmetric Standard Model (MSSM) by introducing a right-chiral neutrino super eld for each generation. This extension addresses the important issue of neutrino mass generation which is otherwise absent in the MSSM. In particular, we adopt a phenomenological approach for \TeV type-I seesaw mechanism". The superpotential, suppressing the generation indices, is given by [59, 72, 80]: W WMSSM + y L^H^uN^c + MRN^cN^c 1 2 where y is the neutrino Yukawa coupling, L^ is the left-chiral lepton doublet super eld, H^u is the Higgs up-type chiral super eld and N^ is the right-chiral neutrino super eld. Besides the usual MSSM superpotential terms denoted by WMSSM, we now have an added Yukawa interaction term involving the left-chiral super eld L^ coupled to the up-type Higgs super eld H^u, and N^ . SM neutrinos obtain a Dirac mass mD after electroweak symmetry breaking once the neutral Higgs eld obtains a vacuum expectation value (vev) vu, such that mD = y vu. The third term 12 MRN^cN^c is a lepton-number violating (L= ) term (4L = 2). { 3 { In addition to the MSSM contributions, the soft-supersymmetry breaking scalar potential receives additional contributions as follows: 1 2 V soft VMSSM + m2RjNe j2 + soft BM Ne cNe c + T Le:HuNe c + h.c. where m2R is the soft-supersymmetry breaking mass parameter for the sneutrino, BM is the soft mass-squared parameter corresponding to the lepton-number violating term and T is the soft-supersymmetry breaking L-R mixing term in the sneutrino sector. We have suppressed the generation indices both for the superpotential as well as for the soft supersymmetry-breaking terms so far. Note that a small -parameter is critical to ensure the absence of any ne-tuning at the EW scale ( EW) [5{8]. Fine-tuning arises if there is any large cancellation involved at the EW scale in the right hand side of the following relation [1, 2]: MZ2 = 2 m2Hd + d (m2Hu + tan 2 1 u) tan 2 2 ; (2.1) where m2Hu ; m2Hd denote the soft-supersymmetry breaking terms for the up-type and the down-type Higgses at the supersymmetry breaking mass scale (which is assumed to be the geometric mean of the stop masses in the present context) and tan denotes the ratio of the respective vevs while u and d denote the radiative corrections. Note that, since we are not considering any speci c high-scale framework in the present context, we are only concerned about the EW ne-tuning. Typically EW . 30 is achieved with j j . 300 GeV [5{8]. The assurance of EW naturalness is the prime motivation in exploring small scenarios. However it is quite possible that obtaining such a spectrum from a high-scale theory may require larger ne-tuning among the high-scale parameters and the corresponding running involved, especially considering that mHu evolves signi cantly to ensure radiative EW symmetry breaking. Therefore, EW can be interpreted as a lower bound on ne-tuning measure [5{8]. Note that, stop squarks and gluinos contribute to the radiative corrections to mHu at one and two-loop levels respectively. It has been argued [9, 10] that an EW ne-tuning of less than about 30 can be achieved with . 300 GeV and with stop squarks and (gluinos) as heavy as about 3 TeV (4 TeV). It is, therefore, important to probe possible scenarios with low EW and therefore with low j j. 2.1 The (s)neutrino sector e o = feL; eRogT are given by, o e 2 e 2 In presence of the soft-supersymmetry-breaking terms BM , a split is generated between the CP-even and the CP-odd part of right-type sneutrino elds. In terms of CP eigenstates we can write: L = eLep+ieLo ; R = eRep+ieRo , where superscripts e, o denote \even" and \odd" respectively. The sneutrino (e) mass-squared matrices in the basis ee = feL; eRegT and e M 0m2LL mjLR2 mjL2R1 mjRR2 A C ; { 4 { (2.2) 1 2 m2LL = m2L + m2Z cos 2 + m2D; mjLR2 = (T mjRR2 = m2R + m2D + MR2 BM ; y MR)v sin mD cot ; (2.3) (2.4) (2.5) (2.6) and v = with j 2 fe; og and the `+' and the `-' signs correspond to j = e and j = o respectively, qvu2 + vd2 = 174 GeV, where vu; vd denotes the vevs of the up-type and the down-type CP-even neutral Higgs bosons. Further, we have assumed T to be real and with no additional CP-violating parameters in the sneutrino sector. The physical masses and the mass eigenstates can be obtained by diagonalizing these matrices. The eigenvalues The corresponding mass eigenstates are give by, The mixing angle = 2 ' is given by, e1j = cos 'j eLj sin 'j eRj e2j = sin 'j eLj + cos 'j eRj: sin 2 j = (T y MR)v sin mD cot mj22 mj12 ; where j denotes CP-even (e) or CP-odd (o) states. The o -diagonal term involving T is typically proportional to the coupling y , ensuring that the left-right (L-R) mixing is small. However, the above assumption relies on the mechanism of supersymmetry-breaking and may be relaxed. The phenomenological choice of a large T O(1)GeV leads to increased mixing between the left and right components of the sneutrino avor eigenstates in the sneutrino mass eigenstates [66, 67, 72]. Further, if the denominator in eq. (2.6) is suitably small, it can also lead to enhanced mixing. As for the neutrinos, at tree-level with MR 1 eV, their masses are given by m as in the case of Type-I see-saw mechanism [81{83]. Thus, with MR neutrino masses of O(0:1) eV requires y 10 6{10 7. Although we have ignored the avor indices in the above discussion of the sneutrino sector, the neutrino oscillation experiments indicate that these will play an important role in the neutrino sector. We will assume that the leptonic Yukawa couplings are avor diagonal, and that the only source of avor mixing arises from y [84]; see also [85, 86]. Further, at one-loop, avor diagonal BM can also contribute to the neutrino mass matrix [80, 87] which can be quite signi cant in the presence of large T in particular.1 The dominant contribution to the Majorana mass of the active neutrino arises from the sneutrino-gaugino loop as shown in gure 1. The 1Note that avor o -diagonal terms in BM can lead to avor mixing in the neutrino sector via higher order e ects which we avoid in our discussions for simplicity. ' MR y2vu2 , O(100) GeV, { 5 { additional contributions to the neutrino mass give signi cant constraints in the fT ; BM g parameter space. mass, then, requires a very small y ' 10 11. Finally, some comments on the scenario with MR = 0 and BM = 0 are in order. With MR = 0 (and BM = 0), only Dirac mass terms would be present for neutrinos, which is given by y vu. The oscillation data for neutrinos can only be satis ed by assuming y (and/or T , at one-loop order) to be avor o -diagonal. In addition, O(0:1) eV neutrino In the sneutrino sector, the relevant mass eigenstates may be obtained simply by substituting MR = 0 = BM in equations (2.2), (2.3), (2.4). Since the mass matrices for both CP-even and the CP-odd sneutrinos are identical in this scenario, any splitting between the corresponding mass eigenstates would be absent. Consequently there will be only two complex-scalar mass eigenstates ~1; ~2. Also, there will be no large one-loop contribution to the Majorana neutrino mass, relaxing the constraint on large T signi cantly. 2.2 The electroweakino sector The other relevant sector for our study is the chargino-neutralino sector, in particular the higgsino-like states. This sector resembles the chargino-neutralino sector of the MSSM. The tree-level mass term for the charginos, in the gauge eigen-basis, can be written as [88] are column vectors whose components are Weyl spinors. The mass matrix M c is given by c Lmass = T M c + + h:c: + = (Wf+; h~2+)T ; = (Wf ; h~1 ) T M c = p M2 2MW cos p 2MW sin ! : (2.7) (2.8) (2.9) In the above equation, M2 is the supersymmetry breaking SU( 2 ) gaugino (wino) mass parameter, is the supersymmetric higgsino mass parameter, MW is the mass of the W { 6 { boson, and tan is the ratio of vevs as described before. The non-symmetric M c can be diagonalized with a bi-unitary transformation using the unitary matrices U and V to obtain the diagonal mass matrix, M Dc = U M cV 1 = Diagonal(m ~+ m ~+ ): 1 2 The eigenstates are ordered in mass such that m ~+ 1 m ~+ . The left- and right-handed com2 ponents of the corresponding Dirac mass eigenstates, the charginos ~i+ with i 2 f1; 2g, are PL ~i+ = Vij j+; PR ~i+ = Uij j ; where PL and PR are the usual projectors, j = j y, and summation over j is implied. In the above mass matrix sW ; s ; cW and c stand for sin W ; sin ; cos W and cos respectively while W is the weak mixing angle. MZ is the mass of the Z boson, and M1 is the supersymmetry breaking U( 1 )Y gaugino (bino) mass parameter. M n can be diagonalized by a unitary matrix N to obtain the masses of the neutralinos as follows, MDn = N M nN 1 = Diagonal(m ~01 m ~02 m ~03 m ~04 ) m ~03 m ~04 . Again, without loss of generality, we order the eigenvalues such that m ~01 The left-handed components of the corresponding mass eigenstates, described by fourcomponent Majorana neutralinos ~i0 with i 2 f1; 2; 3; 4g, may be obtained as, PL ~i0 = Nij j0 ; 0 = B~0; Wf3; h~01; h~02 T The neutralino mass matrix M n can be written as , the tree level mass term is given by [88] n Lmass = 2 1 0T M n 0 + h:c: M n = BBB 0 M1 0 MZ sW c MZ sW s 0 M2 MZ cW c MZ cW s MZ sW c MZ cW c 0 MZ sW s MZ cW s C 0 1 C : C A where summation over j is again implied; the right-handed components of the neutralinos are determined by the Majorana condition ~ charge conjugation. ic = ~i, where the superscript c stands for Since the gaugino mass parameters do not a ect \naturalness", for simplicity we have assumed M1; M2 like states, ~01, ~ j j. In this simple scenario there are only three low-lying higgsino02 and ~1 . The EW symmetry breaking induces mixing between the gaugino and the higgsino-like states, via the terms proportional to MZ ; MW in the mass matrices above. The contributions of the right-chiral neutrino super elds to the chargino { 7 { and neutralino mass matrices are negligible, thanks to the smallness of y (' 10 6). Thus lightest neutralino and charginos are expected to be nearly the same as in the MSSM. Following [89] (see also [90]), in the limit M1; M2 for the masses below, j j, we give the analytical expression m ~ 1 = j j 1 m ~0a;s = M W2 sin 2 M2 MZ2 (1 2 sin 2 ) + O(M2 2) + rad:corr: sin W2 + M1 cos W2 M2 + rad:corr: (2.16) where the subscripts s (a) denote symmetric (anti-symmetric) states respectively, and the sign of the eigenvalues have been retained. For the symmetric state Ni3; Ni4 share the same sign, while for the anti-symmetric state there is a relative sign between these two receives di erent radiative corrections in M n and M c), M1; M2 and tan terms. Although the leading contribution to the mass eigenvalues are given by j j (which a ects the mass splitting between the three light higgsino-like states due to non-negligible gaugino-higgsino mixing. The radiative corrections, mostly from the third generation (s)quarks, contribute di erently for m ~ 1 and m ~01;2 and have been estimated in [89, 91{93]. As we are interested in a spectrum where the lighter chargino and the neutralinos play a major role and the knowledge of their mass di erences would become crucial, it is necessary to explore what role the relevant SUSY parameters have in contributing to the masses of the higgsino dominated states. It is quite evident from our choice of large M1 and M2 that the three states according to eq. (2.16) would be closely spaced. We now look at how the variation of the above gaugino parameters a ect the shift variation of the mass di erences in mass of m ~ 1 and m ~01;2 . Assuming have used SARAH [94, 95] to generate model les for SPheno [96, 97], and have used the same to estimate the masses. Since SLHA [98] convention has been followed, the input parameters, as shown in the gures above, are interpreted as DR parameters at 1:6 TeV. Note that the same model and spectrum generators have been used for all subsequent gures. The me01 and m2 = me02 m as a function = 300 GeV, tan = 5, in gure 2 we show the following features are noteworthy from gure 2:2 For > 0; M1; M2 : here ~02 is the heaviest higgsino-like state while ~1 remains between the two neutralinos. For a xed M1 j j, the mass di erence m1 increases as M2 decreases. This feature can be simply understood from eq. (2.16). A similar conclusion also holds for m2. Further, as shown in panels (a) and (b) of gure 2, the variation in m2 is larger compared to m1 in this case. For > 0;M1 < 0: we nd that negative M1 can lead to negative m1, since the lightest chargino can become lighter than this state for a wide range of M2 [29, 30, 38]. 2Although our numerical analysis, as shown in gure 2, includes radiative corrections, the generic features also appear at the tree-level for j j = 300 GeV, M1; M2 j j and tan = 5.We have checked this using a Mathematica code. { 8 { the palette. me01 ( m2 = me02 2 1 3 2 1 ] 3 eV 2 G 2 1 3 2 1 2 M ?3 ?2 ?1 1 2 3 ?3 ?2 ?1 As shown in gure 2(a), such a scenario occurs for large M2 values (& 2 TeV) with jM1j . 1 TeV. Further, for jM1j M2, as jM1j decreases one observes an upward kink in the attributed to the change in nature of the lightest neutralino state from anti-symmetric to the symmetric state. < 0; M1 > 0: as shown in gures 2(c) and 2(d), similar to the > 0 case, mi smoothly increases with decreasing M2 in this region as well. < 0; M1 < 0: in gure 2(c) we again see (due to the change in nature of LSP) a sharp rise of m1 for large M2 & 2 TeV and jM1j . 1:5 TeV. Note that in this case the ~1 can be the heaviest higgsino-like state in a substantial region of the parameter space for M2 & 2 TeV, as shown in gure 2(d). 2.3 Compressed Higgsino spectrum and its decay properties As we have already emphasized, the focus of this work is on higgsino-like NLSPs in a scenario with a right-sneutrino LSP where the choice of small j j is motivated by the \naturalness" criteria [6, 8, 9]. Thus we will restrict our discussions to scenarios where the higgsino mass parameter j j . 500 GeV. The gaugino mass parameters have been assumed { 9 { j j, and m~1 < j j. Here to be heavy for simplicity; thus the light higgsino-like states are quite compressed in mass ( gure 2). Note that since the gaugino mass parameters are much heavier, the gaugino fraction in the higgsino-like states are small (O(10 2)). However, M1 and M2 play signi cant role in determining m2 and also the hierarchy between the higgsino-like states. While for most parameter space the spectra shown in the left panel of gure 3 is realized, for M1 < 0 (i.e. sign(M1M2) = 1), it is possible to achieve the chargino as the lightest higgsino-like state which leads to a spectra as shown in the right panel of gure 3. Further, with ; M1 < 0 one can also have the chargino as the heaviest of the three higgsino-like state. However, as we will discuss subsequently in section 4, this does not contribute to any new signature. Figure 3 schematically shows the mass hierarchies of our interest. For the electroweakinos which are dominantly higgsino-like, their production rates and subsequent decay properties would have serious implications on search strategies at accelerator machines like LHC. This in turn would play an important role in constraining the higgsino mass parameter in the natural SUSY framework. ~ 1 ! ~01W We now try to brie y motivate the compositions of the LSP as well as the higgsinolike states of our interest and their decay properties. In the presence of ~01 as the lightest higgsino-like state, the decay modes available to the chargino are ~ 1 ! l ~kj and , where j; k corresponds to a particular lighter sneutrino species. The partial width to the 3-body decay modes, mostly from the o -shell W boson mediated processes, are suppressed by the small mass di erence while small y (. 10 6) suppresses the 2body decay mode. In such a scenario, the gaugino fraction in ~1 , can contribute to the 2-body mode signi cantly in the presence of small left-right mixing ( O(10 5)) in the sneutrino sector. We illustrate the decay properies of ~ 1 based on the composition of the LSP in gure 4.3 As shown in gure 4, for small T and therefore for small left admixture in 3The particular choice of gaugino mass parameters correspond to m1 . 1 GeV, and the partial width in the corresponding hadronic channel is quite small (' 10 16 GeV). Thus, the leptonic partial width resembles the total width of ~1 . ?9 ?10 ?11 ) ? epL ?12 to T , the soft left-right mixing parameter in the sneutrino sector. The plot shows the required T and mixing angle sin( j) for prompt decay of the chargino. We focus on the values of T in our study ensuring prompt decays of the chargino. the sneutrino sector, y dominates the decay of ~1 . As T increases past O(10 2), the gaugino fraction plays a crucial role, which explains the rise of the partial width in the 2-body leptonic decay mode. With y 10 6 prompt decay of the lightest chargino to the sneutrino and lepton is always ensured. However, for y 10 7 prompt decay of the chargino in the leptonic channel is not viable in the absence of adequate left admixture; T & O(10 2) GeV is required to ensure prompt decay in the leptonic channel. The dip in gure 4 appears as a consequence of possible cancellation between the gaugino and the higgsino contributions to the vertex factor (e.g. / (g2V11 sin j y V12 cos j ), g2 is the SU( 2 ) gauge coupling). It is of our interest to study the scenario where the 2-body decay mode into l ~ competes with the 3-body decay mode. Since the present work focuses on prompt decays, we ensure small left admixture with T & O(10 2) GeV in the dominantly right-sneutrino LSP to ensure prompt decay of ~1 in the 2-body leptonic decay mode. The mass splitting m1 & 1 GeV has been considered to ensure a competing 3-body mode. Since we have assumed a compressed higgsino spectrum, together with a mostly rightsneutrino LSP, the light higgsino states include ~10; ~02; ~ 1 and at least one generation of CP-odd and/or CP-even sneutrino LSP as described in section 2. In gure 2 we showed that for a xed j j, the hierarchy and the mass di erences between the higgsino-like states are a ected signi cantly by the choice of the gaugino mass parameters M1; M2, and sign( ). In a similar compressed scenario within the MSSM, the higgsinos ~02 and ~1 decay into soft leptons or jets [99] and ~01, producing E= T . Scenarios with compressed higgsinos in MSSM have been studied in the light of recent LHC data [27, 29{33]. For smaller mass di erences, 130 MeV . m1 . 2 GeV, the e ective two-body process ~ dominate the hadronic branching fraction. Further, when ~02 is also almost degenerate with 1 ! ~01 [100{102] can HJEP06(218)4 Parameters Values jM1j (GeV) (500{3000) jM2j (GeV) (500{3000) j j (GeV) 300 tan 5 T (GeV ) ~1 , for an even smaller mass di erence m2, ~02 ! ~01 can become signi cant [103{106]. Note that while the three-body decay modes (soft leptons/ jets and ~01) su er from phase space suppression ( m)5 , the two-body mode ( ~01) is also suppressed by a loop factor. In addition to the above decay channels of the compressed higgsino-like states, the present scenario with a sneutrino LSP o ers additional decay channels to the lighter sneutrinos. While a ~0 1 ! ~ would lead to missing transverse energy (as in the case for MSSM) without altering the signal topology if the neutralino was the LSP, ~ 1 ! l ~ would have a signi cant impact on the search strategies. For a pure right-sneutrino LSP this decay is driven by y . In the presence of large T and therefore a large left-right mixing in the sneutrino LSP, a gaugino fraction of & O(10 2) in the higgsino-like chargino begins to play a prominent role as the decay is driven by a coupling proportional to g where represents the gaugino admixture and represents the L-R mixing in the sneutrino sector. The presence of multiple avors of degenerate sneutrinos would lead to similar decay probabilities into each avor and would invariably increase the branching to the two-body leptonic mode when taken together. In the present context, as has been emphasized, only prompt decays into the leptonic channels such as ~ 1 ! l ~ and ~ i0 ! ~1 jsjs0, where js; js0 denote soft-jets or soft-leptons can give us a signal with one or more hard charged leptons in the nal state. Since the latter consists of ~ 1 in the cascade, it can also lead to leptonic nal states. These branching fractions would be a ected by any other available decay channels and therefore it is important to study the di erent regions of parameter space for all possible decay modes of the light electroweakinos. As shown in gure 2, while in most of the parameter space ~01 is the lightest higgsino-like state, and ~1 is placed in between the two neutralinos (i.e. m ~01 < m ~ 1 < m ~02 ), it is also possible to have ~1 as the lightest or the heaviest higgsino-like state. The important competing modes for ~1 and ~02 where m ~01 < m ~ 1 < m ~02 include (a) ~1 ! ~10jsjs0= ; (b) ~20 ! ~10jsjs= ; (c) ~20 ! ~1 jsjs0= where (c) is usually small. However, if ~1 is the lightest higgsino-like state, decay modes (b) and (c), together with ~ 0 1 ! ~1 jsjs0= heaviest higgsino-like state, decay modes (a), (b) and ~ although the latter would be sub-dominant. can be present. Similarly, when ~ 1 is the 0 1 ! ~2jsjs0= can be present, In gures 5 ( > 0) and 6 ( < 0) we show the variation of branching fraction in the 0 leptonic decay channels ~1 ! l ~i and ~i ! l ~i W . The relevant parameters for the scan can be found in table 1. HJEP06(218)4 ) 0.7 BR 0.3 0.9 0.8 1.5 0.5 (b) 2 1 bino soft mass parameter, M1 for the Higgsino mass parameter, parameter M2 is shown in the palette. ?3 ?2 ?1 0 bino soft mass parameter, M1 for the Higgsino mass parameter, = 300 GeV. The wino mass against the parameter M2 is indicated in the palette. Since the sneutrino masses and mixing matrices do not change in the scan, the two body partial decay widths ( ~1 ! l ~i) and ( ~i0 ! ~j ) are only a ected by the variation of the gaugino-admixture in the higgsino-like states. However, the choice of gaugino mass parameters do a ect the mass splittings m2 through mixing and can even alter the hierarchy. These alterations in the spectrum mostly a ect the 3-body decay modes described above which has a signi cant e ect on the branching ratio. As shown in gure 2(a), for sgn( ) = + (i.e. = 300 GeV) and for M1 < 0, m1 is almost entirely . 1 GeV. With large M2 and jM1j . 2 TeV, ~ 1 can become the lightest higgsino-like state making its leptonic branching probability close to 100% as shown in gure 5(a). However, for small jM1j, and large M2, where m1 increases, this branching is somewhat reduced to about 0.8 and the 3-body decays start becoming relevant. For M1 > 0 region the branching ratio increases as M1 increases. This can be attributed to the consistent decrease in m1 ( gure 2(a)) and therefore of the three-body partial decay width. For M1 < 0, generally the branching grows for larger m2 ( gure 2(b)) and decreases for smaller M2 as the mass splitting goes down. It is again worth pointing out here that for large M2 and with jM1j . 2 TeV, m1 < 0 and ~ 1 becomes the lightest state. Thus in this region the three-body mode into ~01 is more phase-space suppressed compared to the decay mode into ~ . 1 4 Further, as jM1j approaches , the symmetric state, which mixes well with the bino, acquires larger bino fraction and there can be a cancellation in the vertex factor / g2(N22 tan W N21) for the two-body decay width into sneutrino. This and consequently Br( ~02 ! ~1 jsjs0) is rather small. can reduce the corresponding width and then increase again as jM1j decreases. Thus the branching ratio for the three-body decay shows a discontinuous behavior in such regions. For positive M1, the branching ratio shows similar pattern as m2 variation, as expected. Larger m1 in this region implies that the three-body decay ( ~02 ! ~10jsjs) can be larger, For = 300 GeV, there are marked di erences in the decay probabilities as the ~ can become the heaviest when M1 < 0, for large regions of the parameter space in contrast to what was observed for > 0. Figure 6(a) shows the branching ratio of ~1 ! l ~j which decreases as M2 increases. Although, for large M2, the gaugino fraction in ~ small, thus possibly reducing the partial width in this two-body decay mode; smaller 1 would be in this region ensures that the competing three-body mode decreases even more. Therefore, the branching ratio in the two-body mode is enhanced. This holds true for almost the entire range of M1. The feature in the negative M1 region, as jM1j approaches j j, where the branching ratio rises faster for larger M2 values, corresponds to a similar fall in m1 (see 1 m1 gure 2(c)). In gure 6(b) we show the variation of Br( ~02 ! ~1 jsjs0) with M1; M2. For negative M1, this branching ratio increases with decreasing M2, since the corresponding mass difference m2 also increases (see gure 2). The larger M2 values are not shown for M1 < 0, since ~1 becomes the heaviest higgsino-like state in this region. Thus, m2 < 0 as shown in see gure 2(d), and this decay mode does not contribute. For M1 > 0 smaller M2 values correspond to larger branching fractions, since m2 becomes larger, increasing the partial width. However, for large M2 values, the partial width decreases rapidly as m2 decreases. Note that T = 0:5 GeV has been used in the gure. For smaller values of T the leptonic branching ratio of ~ 1 would generally be reduced when it is not the lightest higgsino-like state. However, the generic features described above would remain similar. Note that, y 10 6 can lead to prompt decay even in the absence of large left-admixture, as induced by large T . Therefore, even for small T . O(10 2), for certain choice of the gaugino mass parameters, the leptonic branching can be competing, and thus would be relevant to probe such scenario at collider. 4Note that, because of mi . 1:5 GeV, decay modes involving can dominate the hadronic branching fractions in this region. While we have estimated the same to be signi cant using routines used in SPheno-v4 [96, 97], see also refs. [100{102], the presence of large T typically ensures that the two-body decay mode shares rather large branching fraction in these regions. In the plot we have only included three-body partial widths. A similar strategy has been adopted for regions with small m2 as well. HJEP06(218)4 We now consider the model parameter space in light of various constraints. We implement the following general constraints on the parameter-space: The lightest CP-even Higgs mass mh has been constrained within the range: 122 mh (GeV) While the experimental uncertainty is only about 0.25 GeV, the present range of 3 GeV is dominated by uncertainty in the theoretical estimation of the Higgs mass, see e.g. [110] and references there.5 The lightest chargino satis es the LEP lower bound: m 103:5 GeV [111]. The LHC bounds, which depend on the decay channels of the ec1hargino, will be considered only for prompt channels in more detail in section 4. The light sneutrino(s) (with small left-sneutrino admixture) can contribute to the non-standard decay channels of (invisible) Higgs and /or Z boson. The latter requires the presence of both CP-even and CP-odd sneutrinos below ' 45 GeV. Constraints from the invisible Higgs decay (' 20%) [112] and the Z boson invisible width (' 2 MeV) [113] can impose signi cant constraints on the parameter space where these are kinematically allowed. We further impose Bs ! + [114] and b ! s constraints [115]. 3.1.1 Implication from neutrino mass Recent analyses by PLANCK [116] imposes the following constraint on the neutrino masses: P mi . 0:7 eV. In the present scenario, the neutrinos can get a tree-level mass, as is usual in the Type-I see-saw scenario. For y 10 6, and MR 100 GeV, the active neutrino mass is of O(0:1) eV. Further, as discussed in section 2.1, a non-zero Majorana mass term MR, and the corresponding soft-supersymmetry breaking term BM introduce a splitting between the CP-even and CP-odd mass eigenstates of right-sneutrinos. In the presence of sizable left-right mixing, signi cant contribution to the Majorana neutrino mass can be generated at one-loop level in such a scenario, the details depend on the gaugino mass parameters [80, 87]. Thus, regions of large BM , in the presence of large left-right mixing in the sneutrino sector (induced by a large T ) can be signi cantly constrained from the above mentioned bound on (active) neutrino mass. In gure 7 we show the allowed region in the T as follows: BM plane. We consider y 2 f10 6; 10 7 g while the other parameters are xed = 300 GeV, M3 = 2 TeV, MQ3 = 1:5 TeV, Tt = 2:9 TeV, ML1=2 = 600 GeV, ms~oft = 100 GeV and MA = 2:5 TeV. While in the former case the tree-level and radiative contributions to the neutrino mass can be comparable (with each being O(0:1) eV), the radiative corrections often dominate for the latter. As shown in the gure, clearly larger T values are consistent with neutrino mass for smaller BM . 5Note that, besides the MSSM contributions, rather large T can induce additional contributions to the Higgs mass [66]. Our numerical estimation takes this e ect into account. 2 ) 4e?10 2e?10 1e?10 0 0 1 2 3 4 5 6 7 8 9 10 T? (GeV ) O(10 2). The colored palette denotes the mass of the heaviest neutrino. mass and left-fraction. The right panel shows the allowed region respecting the direct detection constraint from XENON-1T. 3.1.2 Implications for dark matter Within the paradigm of standard model of cosmology the relic abundance is constrained as 0:092 h 2 0:12 [116]. Stringent constraints from direct search constraints require the DM-nucleon (neutron) interaction to be less than about 10 9 pb, which varies with the mass of DM, see e.g. LUX [117], PANDA-II [118] and Xenon-1T [119]. In gure 8, with y 2 f10 6; 10 7g; tan 2 f5; 10g; = 450 GeV; mA = 600 GeV and all other relevant parameters are xed as before, we scan over the set of parameters fT ; m~; BM g ( rst generation only). We plot the left-admixture (sin j ) in the LSP required to obtain the thermal relic abundance and direct detection cross section against its mass in the left and the right panel respectively. We have used micrOMEGAs-3.5.5 [120] to compute the thermal relic abundance and direct detection cross-sections. With T & O(10 3), which is the region of interest to allow left-right mixing in the sneutrino sector, the right-sneutrino LSP thermalizes with the (MS)SM particles via its interaction with left-sneutrino and Higgs bosons. The important annihilation processes involve s-channel processes mediated by Higgs bosons, as well as four-point vertices leading to hh; W W ; ZZ; tt nal states. However, large left-right mixing induces large direct detection cross-section. In gure 8 we have only shown parameter regions with a mass di erence of at least 1 MeV between the CP-even and the CP-odd states to prevent the Z boson exchange contribution to the direct detection [59, 121, 122].6 There are t-channel contributions mediated by Higgs bosons, mostly from the D-term, as well as the tri-linear term T , and is proportional to the left-right mixing (sin ) in the sneutrino sector. Note that, we have only shown points with spin-independent direct detection cross-section less than 10 9 pb. As shown in the left panel of gure 8, sin of O(0:1) is required to achieve the right thermal relic abundance. The right relic abundance is achieved soon after the dominant annihilation channels into the gauge bosons (and also Higgs boson) nal states are open (i.e. mDM & 130 GeV), while at the Higgs resonances (mh = 125 GeV and mA a lower admixture can be adequate. Further, co-annihilation with the low-lying higgsinolike states (j j 450 GeV), when the LSP mass is close to 450 GeV, can also be e ective. As shown in the right panel of the same gure, for mDM . 450 GeV, most parameter space giving rise to the right thermal relic abundance is tightly constrained from direct searches (spin-independent cross-sections) from Xenon-1T [119] (similar constraints also arise from LUX [117], PANDA-II [118]), the exceptions being the resonant annihilation and co-annihilation regions. Note that for very small T and y . 10 6, the e ective interaction strength of rightsneutrinos may be smaller than the Hubble parameter at T ' mDM. In such a scenario, non-thermal production, especially from the decay of a thermal NLSP, can possibly generate the relic abundance [60{63]. Further, non-thermal productions can also be important in certain non- standard cosmological scenarios, e.g. early matter domination or low reheat temperature, see e.g. [123, 124]. In addition, large thermal relic abundance can be diluted if substantial entropy production takes place after the freeze-out of the DM. For such regions of parameter space our right-sneutrino LSP is likely to be a non-thermal DM candidate. 4 Signatures at LHC We now focus on the LHC signal of the higgsino-like electroweakinos in the presence of a right-sneutrino LSP. As discussed, the various decay modes available to e1 , e02 and e1 0 in presence of a right-sneutrino LSP depend not only on the mixing among the various sparticle components but also crucially on the mass splittings. The LHC signals would 6We have checked that with 1 MeV mass splitting and a left-admixture of O(10 2), as is relevant for thermal relic, the heavier of the CP-even and the CP-odd state has a decay width of into the LSP and soft leptons/quarks via o -shell Z boson. This corresponds to a lifetime of . 10 3 s. Thus it would decay well before the onset of Big Bang Nucleosynthesis (BBN) and is consistent with constraints 10 20 GeV, mostly from the same. then re ect upon the above dependencies on the parameter space. We therefore look at all possible signals for di erent regions of m1=2 and T . While there are regions of m1=2 where the chargino decays non-promptly to pions that lead to the chargino traveling in the detector for some length and then decay into a soft pion and neutralino. In such cases, since both decay products are invisible, the relevant search channel at LHC is the disappearing tracks [32, 33, 125]. Our focus however, is primarily on the prompt decay of the chargino to hard leptons (small m1=2 and large T ) which would be clean signals to observe at LHC. The following production channels are of interest to us: 0 0 + 0 0 0 0 p p ! e1 e2; e1 e1; e1 e1 ; e1 e2; e1 e1; e20 e20; el el; el el ; el e; e e (4.1) the pair production cross-section of 0 where the sleptons and sneutrinos are heavier than the electroweakinos here. The LSP pair production is excluded in the above list. The processes as given in eq. (4.1) are in decreasing order of production cross-sections as obtained from Prospino [126{128]. The followed by the chargino pair production, 0 associated chargino neutralino pair, i.e e1 +e1=2 production has the largest cross-section e1 e10 and e2 e20 are negligible compared to the other e1 e1 0as in gure 9. In the pure higgsino limit, processes. Since the strong sector is kept decoupled and the compressed higgsino sector leads to soft jets and leptons, the only source of hard jets are from initial-state radiations (ISR). The suppressed jet multiplicity in the signal could prove to be a potent tool for suppressing SM leptonic backgrounds coming from the strongly produced tt and single top subprocesses which would give multiple hard jets in the nal state in association with the charged leptons. Therefore we shall focus on the following leptonic signals with low hadronic activity: Di-lepton + 0 jet + E= T ), and associated pair production, e1 ei0 with i = 1; 2 ( e1 ! l The mono-lepton signals would come from the pair production of e1 e1 , ( e1 ! l e and e2=1 ! e1 W e 0 and ei ! ) leading to missing energy. Among the di-lepton signals we look into both opposite sign leptons and same sign lepton signal with missing energy. Opposite sign leptons arise from the pair produced e1 e1 , with the chargino decaying leptonically as + e1 ! l e. In regions of the parameter space where 0 process may contribute to the di-lepton state via ei ! e1 W e2=1 is heavier than e1 , e1 ei0, i = 1; 2 0 followed by e1 ! l . e channels come from e10 e20 with e1=2 ! e1 W 0 In such cases, there could be either opposite sign di-lepton signal or same-sign di-lepton signal owing to the Majorana nature of the neutralinos ( ei0). A similar contribution to both . Also there are sub-leading contributions from slepton pair productions which can become relevant if light sleptons are also present in the spectrum. It is worth pointing out that in very particular regions of the parameter space e1 is the NLSP and therefore always decays to a hard lepton and sneutrino LSP. In such cases, signal rates for the di-lepton channel would be most interesting and dominant rates for same-sign di-lepton would be a particularly clean channel which will be important to 0.1 0.01 B = e1 e10, C = e1 e20 and D = e1 e2 can be estimated by using a K factor very e ectively. This is very particular of the parameter region when M1 is negative and one has a sneutrino LSP. 4.1 Constraints on electroweakino sector from LHC Before setting up our analysis on the above signals we must consider the role of existing LHC studies that may be relevant for constraining the parameter space of our interest. LHC has already looked for direct production of lightest e1 , e02 and e10 in both run 1 and prompt search results only. run 2 searches at 7, 8 and 13 TeV respectively albeit assuming simpli ed models. Search results have been reinterpreted both in terms of non-prompt as well as prompt decays of the Higgsinos. Since the focus of our study is on prompt decays of e1 , we consider the The LHC results have been reinterpreted assuming simpli ed models with and without intermediate left and right sleptons with e10 LSP contributing to E= T (see table 3). Assuming 100% leptonic branching of the sparticles and an uncompressed spectra, CMS has ruled out degenerate wino-like m 600 GeV from same-sign di-lepton, three lepteo1n and four lepton searches with at most 1 jet [129]. The limits vary slightly depending on the choice of slepton masses. For the nearly compressed higgsino sector and assuming mass degeneracy of the lightest chargino ( e1 ) and next-to-lightest neutralino ( e02) the alternate channels probed by LHC are soft opposite sign di-leptons searches [130]. The mass limits on the , me02 < 1:2 TeV for a bino-like me01 < compressed higgsino sector relax to 230 (170) GeV for me01 210 (162) GeV. corresponding leptons would be soft compared to BP1 and BP2-a. Therefore BP2-b and BP3 require higher luminosity 106 fb 1 and 613 fb 1 respectively for observation. The challenge in having a multi-lepton signal from the production of compressed higgsinolike electroweakinos comes from the fact that the decay products usually lead to soft nal states. However, with a sneutrino LSP and the possibility of the decay of the chargino to a hard lepton and the LSP leads to a healthy di-lepton signal with large missing energy + (from e1 e1 as well as e1 e20 pair production, provided the next-to-lightest neutralino decay yields a lepton via the chargino). A sub-dominant contribution also arises from e1 e20 with each of the neutralino decaying to a chargino and an o -shell W boson which 0 gives soft decay products. The chargino then decays to a charged lepton and sneutrino LSP. This happens most favorably when chargino is the lightest of the higgsinos. Owing to the Majorana nature of ei0 we can have signals for opposite-sign and same-sign di-lepton nal states with large missing transverse energy. Hence we look into both the possibilities: Opposite sign di-lepton + 0 jet + E= T Same sign di-lepton + 0 jet + E= T Opposite sign di-lepton + 0 jet + E= T signal + Opposite sign di-lepton signal arises mainly from e1 e1 production process. Sub-dominant 0 contributions arise from e1 e1 , e1 e20 and e1 e20 as discussed before. The dominant SM 0 contributions to the opposite sign di-lepton signal with missing energy come from tt, tW and Drell-Yan production. Among the di-boson processes, W +W (W + ! l + ; W ! l ), ZZ ( Z ! l+l ; Z ! jj= ) and W Z+jets (W ! jj; Z ! l+l ) also contribute substantially to the opposite sign di-lepton channel. The triple gauge boson processes may also contribute. However, these have a small production cross-section and are expected to be subdominant. There could also be fake contributions to missing energy from hadronic energy mismeasurements. In gure 12 we show the normalized distributions for important kinematic variables for two benchmarks BP2-a and BP2-b with M = 100; 40 GeV respectively along with the dominant SM backgrounds after selecting the opposite sign-di-lepton state (D1). We nd that as expected the lepton pT distribution for BP2-a is much harder than the SM backgrounds processes whereas for BP2-b with a lower mass gap between the chargino and LSP, the leptons are much softer and the distributions have substantial overlap with the backgrounds. We further use the other kinematic variables, E= T = j ip~Ti j and Ml2+l = (pl1 + pl2 )2 (4.4) (where i runs over all visible particles in the nal state) represent the transverse missing energy and invariant mass-squared of the di-lepton nal state respectively which peak at higher values for SUSY signals over backgrounds in BP2-a whereas BP2-b still retains a large overlap with the SM backgrounds. However, the largest source of background for the HJEP06(218)4 di-lepton background coming from Drell-Yan process can be removed safely by excluding the Z boson mass window for Ml+l . Since the SUSY signals do not arise from a resonance the exclusion of the Z mass window is expected to have very little e ect on the signal events. We further note that removing b-tagged jets would also be helpful in removing SM background contributions from the strongly produced top quark channels which have huge cross sections at the LHC. Another kinematic variable of interest to discriminate between SUSY signals and SM backgrounds is the MT2 variable [197] constructed using the leading and sub-leading lepton p~T and E=~T . For processes with genuine source of E= T there is a kinematic end point of MT2 which terminates near the mass of the parent particle producing the leptons and the invisible particle. In SM, channels such as tt; tW; W +W involving a W boson nally giving the massless invisible neutrino in the event, the end-point would be around 80 GeV. For SUSY events the invisible particle is not massless and therefore the visible lepton pT will depend on the mass di erence. Thus the end-point in the signal distribution would not have a cut-o at the parent particle mass anymore. For BP2-a which has a large M the end point is expected at larger values ( 200) GeV. However for BP2-b, where the available phase space is small for the charged lepton due to smaller M the MT2 distribution is not very wide and has an end-point at a much lower value. Thus a strong cut on this variable is not favorable when the sneutrino LSP mass lies close to the electroweakino's mass. Following the features of the kinematic distributions, we implement the following optimal selection criteria as follows for both signal and backgrounds: D1: the nal state consists of two opposite sign leptons and no photons. D2: the leading lepton has pT > 20 GeV and the sub-leading lepton has pT > 10 GeV. D3: Ml+l > 10 GeV helps remove contributions from photon mediated processes while the Z mass window is also removed by demanding that the opposite-sign same avor di-lepton invariant mass satis es 76 < Ml+l < 106 GeV. This helps to reduce a large resonant contribution form the Z exchange in Drell-Yan process. D4: we reject any b-jet by putting a b-jet veto (for pT > 40 GeV). This helps in suppressing background events coming from top quark production. D5: we demand a completely hadronically quiet event by choosing zero jet multiplicity (Njet = 0) in the signal events. This is e ective in suppressing contributions from background processes produced via strong interactions. D6: we demand E= T > 80 GeV to suppress the large Drell-Yan contribution. D7: we demand MT 2 > 90 GeV which helps reduce a majority of the other SM backgrounds. D8: E= T > 100 GeV is implemented to further reduce the SM backgrounds. In table 9 we show the signal events that survive the above listed kinematic selections (cut- ow). We nd that among all benchmarks, BP2-a is the most robust followed by dN dET 1 10?1 10?2 dN dNb 1 10?1 10?2 10?3 BP2-a BP2-b Drell Yan WW ET (GeV) BP2-a BP2_b tW ZZ Drell Yan WW 5 N b T210?1 M d / N d /1N10?2 10?3 200 250 300 350 MT2(GeV) BP4. Note that we avoid using the MT 2 cut on the benchmarks where the mass splitting between the chargino and the sneutrino LSP is small as D7 cut makes the signal events negligible. As pointed out earlier, the end-point analysis in MT 2 is not favorable for small M as seen in the signal and background distributions in gure 12. Thus BP2-b and BP3 have cuts D1{D6. In table 10 we plot the SM background events after each kinematic cuts. Quite clearly up to cut D6 the SM background numbers are quite large, and then drastically reduce after the MT 2 cut (D7) is imposed. In table 11 we give the required integrated luminosities to achieve a 3 and 5 statistical signi cance for the signal events of the benchmark points. Just like for the mono-lepton ZZ tt Drell Yan WW Signal tW Total BP1 BP2-a BP4 Signal BP2-b BP3 D2 129 271 298 D2 452 2394 D3 656 5399 Preselection (D1) 130 306 209 455 2424 Preselection (D1) Number of events after cut D3 112 265 246 D3 351 1840 D4 109 161 241 D4 345 1805 D5 68 108 153 D5 230 1186 D7 22 76 81 D6 45 189 nal state number of events at 100 fb 1 for SUSY signals. Note that the events have been rounded-o to the nearest integer. Cross-sections have been scaled using NLO K-factors obtained from Prospino. nal state number of events at 100 fb 1 for Standard Model backgrounds. Note that the events have been rounded-o to the nearest integer. Crosssections scaled with K-factors at NLO [178] and wherever available, NNLO [191{196] have been used. case, BP2-a requires the least integrated luminosity and is in fact gives a 3 signi cance for much lower luminosity compared to mono-lepton signal. However for the rest of the benchmarks mono-lepton channel is more favorable while the opposite-sign di-lepton can act as a complementary channel for BP1 with higher luminosity and BP3 with the very-high luminosity option of LHC. BP2-b type of spectrum for the model is strongly suppressed in the di-lepton channel. The signal rates can be attributed to the fact that the leptonic branching of the chargino is much larger for BP2-a ( 100%) than BP1 ( 12%) and hence the signal is much more suppressed for BP1 than in BP2-a. For BP4 where the NLSP is the chargino, the opposite sign dilepton signal is a robust channel for discovery. Thus this channel is not a likely probe for benchmarks with a smaller phase space, like BP2-b and BP3 in which cases, as seen in the previous section, mono-lepton signals fare better over di-lepton signals. Whereas for spectra like BP2-a and BP4, with a large phase space available, opposite sign di-lepton signals are much more sensitive than mono-lepton signals. In contrast spectra like BP1 with a lower leptonic branching of the chargino, mono-lepton + missing energy signal is still a better channel to look for than opposite sign di-lepton channel. BP1 BP2-a BP2-b BP3 BP4 568 51 1035 160 1:83 104 Same sign di-leptons + 0 jet + E= T signal A more interesting and unique new physics signal at LHC in the di-lepton channel is the same-sign di-lepton mode. The same-sign di-lepton in the absence of missing transverse energy is a clear signal for lepton number violation and forms the backbone for most studies of models with heavy right-handed Majorana neutrinos. Even with missing energy, the same-sign di-lepton is a di cult nal state to nd within the SM and therefore a signal with very little SM background. Thus nding signal events in this channel would give very clear hints of physics beyond the SM. In our framework of SUSY model the same-sign di-lepton signal with missing energy and few jets come from the production modes e1 e20 and=or e1 e10 where the lepton number violating contribution comes from the decay of the Majorana-like neutrali0 nos given by e2 ! W e1 with e1 ! le. grounds are rare in SM, with some small contributions coming from processes such as We note that same-sign di-lepton backp p ! W Z; ZZ; W +W +=W W +jets, ttW and ttZ as well as from triple gauge boson productions such as W W W where with two of the W bosons being of same sign and the other decaying hadronically. Other indirect backgrounds can arise from energy mismeasurements, i.e, when jets or photons or opposite sign leptons fake a same sign di-lepton signal.7 For our analysis we select the same-sign di-lepton events using optimal cuts for both signal and background using the following kinematic criteria: S1: the nal state consists of two charged leptons with same-sign and the leading lepton in pT must satisfy pT > 20 GeV with the sub-leading lepton having pT > 15 GeV. Additionally we ensure that there are no isolated photon and b-jets in the nal state. S2: a minimal cut on the transverse mass constructed with the leading charged lepton (l1), MT (l1; E=~T ) > 100 GeV is chosen to reject background contributions coming from W boson. S3: to suppress background from W W jj as well as those from ttW , ttZ with higher jet multiplicities than the SUSY signal, we keep events with only up to 2 jets. 7There may be additional contributions for same-sign di-lepton coming from non-prompt and conversions which we have not considered [129]. BP1 BP2-a BP2-b BP3 BP4 Preselection (S1) 5 3 32 2 30 S2 5 W +W +jj W W jj tW ttW tt Total background Preselection (S1) 3856 94 60 416 188 40 128 90 S3 5 nal state number of events at 100 fb 1 for SUSY signals. Note that the events have been rounded-o to the nearest integer where relevant. Cross-sections have been scaled using NLO K-factors obtained from Prospino. nal state number of events at 100 fb 1 for SM background. Note that the events have been rounded-o to the nearest integer where relevant. Cross-sections scaled with K-factors at NLO [178] and wherever available, NNLO [191{196] have been used. S4: a large missing energy cut, E= T > 100 GeV is implemented to reduce SM backgrounds. zero jets in the event. S5: nally we choose the events to be completely hadronically quiet and demand In tables 12 and 13 we show the signal and backgrounds events after each selection cuts are imposed. As the same-sign signal is strongly constrained by existing LHC data, our benchmarks have been chosen to comply with the existing limits. Thus we nd that our benchmark choices do not seem too robust in terms of signal rates, especially BP3 and BP4 which has the chargino as the NLSP. It is therefore important to point out that BP1 and BP2-a like spectra is naturally not favored to give a same-sign di-lepton signal while BP3 and BP4 are the most probable to give the same-sign signal but have been chosen to suppress the signal to respect existing constraints (by choosing very small branching for the neutralinos to decay to chargino) for two di erent values. However the spectra as re ected by BP2-b and BP4 satisfying existing constraints do present us with a signi cant number of event rates when compared to the background after cuts. BP2-b BP4 811 1052 2251 3845 energy at ps = 13 TeV LHC. From the above cuts, we nd that a large MT (l1) cut coupled with a large E= T and the requirement of jet veto removes a large fraction of the dominant W Z background as well as other fake contributions coming from tt. Other genuine contributions to this channel from and BP4 with BR( e02 ! e1 W ! l ) W W jj, ttW and W W W having a lower production cross-section and are e ciently suppressed by cuts on E= T , MT and applying a jet veto. Amongst all benchmarks, the most sensitive to the same sign di-lepton analysis are BP2-b where BR( e02 ! e1 W ! l ) 3:3% 10%. Note that BP2-b, with a smaller M gives soft leptons and is therefore slightly suppressed and requires larger integrated luminosity 810 fb 1 of data as shown in table 14. Although BP4 has a larger branching fraction, it requires 1052 fb 1 of data at LHC for observing a 3 excess owing to a higher value compared to BP2-b. Thus the same-sign di-lepton can be a complementary channel to observe for benchmarks of BP2-b and BP4. We must again point out here that for BP3-like spectra with e1 NLSP the same-sign di-lepton would be the most sensitive channel of discovery, for large j j and small M2, where the neutralino decay to chargino NLSP becomes 0 large (see gures 5 and 6) because of the small SM background. In such a case both e1 and e20 will decay to the NLSP along with soft jets or leptons. Thus both e1 e20 and e1 e1 0 production channels would have contributed to the signal leading to a two-fold increase of the number of signal events and would be more sensitive to detect a sneutrino LSP scenario. We conclude that conventional channels such as mono-lepton or opposite sign di-lepton channels however with low hadronic activity, i.e, with at most 1 jet or no jet would be extremely useful channels to look for cases of a sneutrino LSP. Detecting same sign dilepton signals at higher luminosities would further serve as a strong con rmatory channel for a sneutrino LSP scenario over a e10 LSP scenario as in the MSSM from the compressed higgsino sector and can exclude large portions of the regions with M1 < 0. Our analyses also shows better signal signi cance for a given integrated luminosity, when compared to the forecast shown in table 5. Note that our estimates do not include any systematic uncertainties that may be present and would be dependent on the speci c analysis of event topologies. However it is worthwhile to ascertain how our results fare in presence of such systematic uncertainties. To highlight this we assume a conservative 10% systematic uncertainty in each case. We nd that the required integrated luminosities follow a similar scaling and our results for the luminosity vary by atmost 10% in most cases. Dependence on involving the avor of eR LSP. LHC searches explore di erent search channels avor of the leptons owing to their high reconstruction e ciency at the detector, for instance, e+E= T , + E= T [161, 162], ee= =e nal states associated with E= T [130, 132]. As we have considered both rst and second generation sneutrinos to be light in this study, we qualitatively analyze the prospects of the signals studied by tagging the avor of the leptons as well as consequences of a single light generation of sneutrino LSP assuming the net leptonic branching to be the same in both cases.8 Hence, for a single light sneutrino LSP, the observed events in the mono-lepton and di-lepton signals contribute to only a single choice of lepton avor and vanishes for the rest. We compare the signal and background in this case for the same luminosity as before and comment on the results obtained for our benchmarks. For mono-lepton signals with degenerate sneutrino LSP ( rst two generations), say, we look at only an electron in the nal state. This would lead to reduction of both signal and background in table 6 and 7 by half such that the signi cance falls by a factor of p2. If a single generation of right-sneutrino was light, say e, then only the background would reduce by a factor 1/2. Since the signal remains unchanged as the chargino now decays e factor of completely to an electron and the lightest sneutrino the signal signi cance increases by a p2. Consequently no signal is observed for the other avor lepton channel, in this case , where although the background decreases by half, no signal events are present. For the di-lepton signal there are three possible channels ee; and e with net branching fraction of around 1/4, 1/4 and 1/2 respectively. We consider rst the oppositesign di-lepton channel. For e nal states, only di erent avor lepton backgrounds such as from W W; tt or tW contribute with a BR ' 2=3. However contributions from same avor di-lepton sources such as involving Z boson fall. The total background thus reduces to nearly 70%. Since signal in this channel also reduces to half thereby the signi cance falls. For channels with same avor (SF) leptons, i.e, ee= , dominant SF contributions are from Z boson whereas sub-dominant contributions from top quark production channel reduce. Although SM background reduces so does the signal statistics and hence the signi cance. However, in presence of a single generation of light sneutrino we the signal signi cance improves by a factor of about p2. Note that if the LSP is ee then the chargino decays to an electron and the LSP. Therefore ee + E= T channel signi cance nd that improves whereas and e channels vanish. Similarly, for an LSP, + E= T channels improve whereas the rest vanish. Similar conclusions may be drawn for same sign dilepton channel, where the dominant backgrounds are W Z and W W , the signi cance is e expected to improve only for a single light generation of sneutrinos. Some comments on the prospect of avor searches and other channels. In this context, we also explore the discovery prospects of a natural higgsino sector and a single light e as the LSP. LHC has looked at nal states with tau leptons, decaying hadronically, in the context of electroweakino searches. The electroweakino mass limits considerably reduce for tau lepton searches owing to the reduced reconstruction e ciency of hadronically decaying leptons ( 60%) [198] compared to that of the light leptons (e, ) 95%). From searches with one or two hadronically decaying tau leptons associated with light leptons lead to stronger limits from e1 , e02 production on m e1 ; me02 > 800 GeV for 8This may not correspond to the same parameter point since the presence of the other decay modes of the net leptonic branching is the same in both cases. e1 a ect the leptonic branching for the single light sneutrino LSP case. However, when e1 is the NLSP, HJEP06(218)4 0 a bino-like me01 < 200 GeV for stau mass midway between the e1 and e1 . For stau closer to the e1 , the limit [129], m e1 ; me02 1000 GeV for me01 on electroweakino searches from three tau lepton searches exclude wino-like degenerate 200 GeV. Limits > 600 GeV for a bino-like me01 < 200 GeV [129] for stau mass midway between . Limits from opposite sign tau lepton searches [199] reinterpreted from e1 e20 production and decaying via intermediate sleptons lead to me02 ; m me01 < 200 GeV. From opposite sign di-tau searches reinterpreted in context of chargino pair production leads to a bound close to 650 GeV on chargino for LSP masses up to > 760 GeV for e1 For the current scenario of a compressed electroweakino sector in presence of a light HJEP06(218)4 LSP, the signals from the low-lying compressed higgsino sector would be: me02 ; m e1 Mono- jet + E= T Di jets + E= T For the mono-tau channel, both signal and background scale by the tau reconstruction e ciency, R = 0:6 is the tau reconstruction e ciency. Further a factor of 12 comes in for the background since the branching of W or Z boson to light leptons is roughly twice that LSP. However, owing to the reduced tau reconstruction p R 0:78. Similarly, for the di-tau channels, 0:6. Hence, the estimated reach of the higgsino mass LSP compared to ee= LSP. to the tau lepton as for a ee= e ciency, the signal signi cance falls by the signi cance scales by R is expected to weaken for a Note that, the pionic decay modes of the ~ 1 and ~02 can dominate among the hadronic modes as the respective mass di erences become less than about a GeV. While we have used form factors to estimate the pionic branching fractions, we have not considered the possibility of late decay into pions in this work. This is because we have ensured that in the parameter space of our interest the two body mode to the lightest sneutrino(s) always remain prompt. Further, the potential of the loop-induced channel ~ 02 ! ~ 01 in deciphering the scenario has not been explored in the present work. While the photons, thus produced in the cascade, would be soft in the rest frame of ~02, it may be possible to tag hard photons in the lab frame. Note that the choice of light higgsinos are motivated by \naturalness" at the electroweak scale and we do not discuss the discovery potential for stop squarks and gluino in the present work which we plan to do in a subsequent extension. 5 To summarize, motivated by \naturalness" criteria at the electroweak scale, we have studied a simpli ed scenario with low parameter in the presence of a right-sneutrino LSP. For simplicity, we have assumed the gaugino mass parameters to be quite heavy & 1 TeV. In such a scenario, with O(100) GeV Majorana mass parameter the neutrino Yukawa coupling can be as large as 10 6 10 7. In contrast with the MSSM with light-higgsinos, in the present context, the higgsino-like states can decay to the sneutrino LSP. While the neutral higgsinos can decay into neutrino and sneutrino, the lightest chargino can decay into a lepton and sneutrino. We have demonstrated that the latter decay channel can lead to various leptonic nal states with up to two leptons (i.e. mono-lepton, same-sign di-lepton and opposite-sign di-lepton) and missing transverse energy at the LHC, which can be important in searching for or constraining this scenario. We have only considered prompt decay into leptons, which require y > 10 7 and/or small O(10 5{10 1) left-right mixing in the sneutrino sector. For smaller values of y , contribution from the latter dominates and the leptonic partial width on small gaugino-higgsino mixing (. O(10 2)). Further, the mass split between the three states, the lightest chargino and the two lightest neutralinos depend on the choice of the gaugino mass parameters, as well as on one-loop contributions. We have shown how these mass di erences signi cantly a ect the three-body partial widths, thus a ecting the branching ratios to the sneutrino. Therefore, even assuming the gauginolike states to be above a TeV, as in our benchmark scenarios, the viability of a low parameter depends crucially on the choice of M1; M2. This has been emphasized in great detail. Consequently, there are regions of the parameter space where BR(e1 ! l e) especially in the negative M1 parameter space. Such regions of parameter space would lead 100% to enhanced leptonic rates, thereby a large fraction of negative M1 parameter space can be excluded from current leptonic searches at LHC. For a given j j, we check the existing constraints by recasting our signal in CheckMATE against existing LHC analysis relevant for our model parameters to search for a viable parameter region of the model. We then choose some representative benchmarks and observe that mono-lepton signals with large E= T and little hadronic activity could successfully probe as low as 300 GeV at the ongoing run of LHC with 106 fb 1 of data at 3 . Additional con rmatory channels for the scenario are opposite-sign di-lepton and same-sign di-lepton signal which require and 800 fb 1 for observing 3 excess at LHC. While our benchmarks assume the rst two generations of sneutrinos to be degenerate and consider only e; for the charged leptons which can be detected e ciently at the LHC, the reach may be substantially reduced if only LSP e 50 fb 1 tau-sneutrino appears as the lightest avor due to the low tau reconstruction e ciency. Acknowledgments AC acknowledges nancial support from the Department of Science and Technology, Government of India through the INSPIRE Faculty Award: /2016/DST/INSPIRE/04 /2015/000110. The work of JD and SKR is partially supported by funding available from the Department of Atomic Energy, Government of India, for the Regional Centre for Accelerator-based Particle Physics (RECAPP), Harish-Chandra Research Institute. The authors would like to thank W. 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Arindam Chatterjee, Juhi Dutta, Santosh Kumar Rai. Natural SUSY at LHC with right-sneutrino LSP, Journal of High Energy Physics, 2018, 42, DOI: 10.1007/JHEP06(2018)042