PHYSICAL REVIEW D 101, 075040 (2020)
Identifying a Higgsino-like NLSP in the context of a keV-scale gravitino LSP
† ‡ Juhi Dutta ,* Biswarup Mukhopadhyaya, and Santosh Kumar Rai Regional Centre for Accelerator-based Particle Physics, Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhusi, Allahabad 211019, India
(Received 28 January 2020; accepted 19 March 2020; published 22 April 2020)
The presence of a Higgsino-like neutralino next-to-lightest sparticle (NLSP) and a keV scale gravitino (G˜ ) LSP opens up new decay modes of the NLSP, mainly to a Higgs=Z boson and the LSP. Besides, a keV- scale gravitino as a warm dark matter candidate salvages a relatively light Higgsino-like NLSP from dark matter constraints. We focus on the prospects of observing at least one b jet and two opposite sign leptons þ − with a large missing transverse momenta (≥ 1b þ l l þ =ET ) signal at the LHC. A distinguishing feature of this scenario is the production of longitudinal Z bosons in neutralino decays, unlike in the case of gauginolike neutralinos, where the Z is mostly transverse. The polarization information of the parent Z boson gets reflected in the angular distributions of the decay leptons and in some other variables derived therefrom.
DOI: 10.1103/PhysRevD.101.075040
I. INTRODUCTION be consistent with relic density as well as direct search constraints. However for a winolike LSP, SU (2)-driven In the light of the 13 TeV LHC run 2 results [1,2], both annihilation channels lead to strong constraints from γ-ray experimentalists and theorists are leaving no stone unturned [4] as well as positron data [5]. A light Higgsino-like LSP to interpret results of different supersymmetric (SUSY) is disfavored from direct dark matter searches [6,7]. scenarios, primarily to ensure no glaring gaps are left in the Conversely, the relic density being inversely proportional current search strategies such that the signals may slip to the annihilation cross section, shows an underabundance through them. Although bounds on sparticle masses from for wino or Higgsino-like LSP, whereas a binolike LSP can LHC are steadily increasing, they are derived in the context lead to an overabundance unless coannihilation occurs at an of simplified scenarios. However, generic features on adequate rate. Mixed bino-Higgsino or bino-wino dark collider signals are helpful to investigate, if such features matter scenarios could be more consistent from these reflect the spectrum and the composition of the super- standpoints [8]. The presence of a lighter particle such as particle states. a gravitino or an axino as the lightest SUSY particle relaxes The R-parity conserving minimal supersymmetric stan- these constraints on the composition of the lightest neu- dard model (MSSM) ensures a stable, neutral, colorless dark tralino χ˜0, which now serves as the next-to-lightest sparticle matter (DM) candidate, generally the lightest neutralino 1 (NLSP). Gravitinos are the LSP in models like gauge (χ˜0), which is the lightest SUSY particle (LSP). Depending 1 mediated supersymmetry breaking with low scale of on its composition, it could be either a democratic admix- SUSY breaking. Here, the gravitino mass scale may be ture of gaugino and Higgsino states or dominantly binolike, lighter than the MSSM sparticle masses if the scale of winolike, or Higgsino-like. The DM composition faces SUSY breaking is light enough to allow a light gravitino stringent constraints from direct search data and indirect mass governed by [9–11], evidence as well as from relic density measurements by χ˜0 Planck [3]. For example, a bino-dominated 1 with an hFi m ˜ ¼ pffiffiffi ; ð1Þ appropriate small admixture of Higgsinos can by and large G 3 MPl h i *[email protected] where mG˜ is the mass of the gravitino, F is the SUSY † [email protected] breaking scale, and MPl is the Planck scale. This means that ‡ [email protected] depending on the SUSY breaking scale hFi, the gravitino can be as light as O (keV). A light gravitino with mass of Published by the American Physical Society under the terms of few keV is motivated to be a warm dark matter candidate the Creative Commons Attribution 4.0 International license. – Further distribution of this work must maintain attribution to [12 14]. In this work, we consider the LHC signals of a the author(s) and the published article’s title, journal citation, Higgsino-dominated NLSP, where one has such a light and DOI. Funded by SCOAP3. gravitino LSP.
2470-0010=2020=101(7)=075040(16) 075040-1 Published by the American Physical Society DUTTA, MUKHOPADHYAYA, and RAI PHYS. REV. D 101, 075040 (2020)
0 Signals for a dominantly Higgsino-like χ˜1 NLSP with a studied by utilizing angular variables of the neg- gravitino LSP has been studied by experimental collabo- atively charged lepton. In order to distinguish it 0 from transversely polarized Z bosons coming from rations at the LHC. A primarily Higgsino-like χ˜1 NLSP is found to decay dominantly to either the Higgs or Z boson other sources, we compare our results with the along with gravitino. Since the light standard model (SM) complementary admixture of NLSP, especially gau- like Higgs has the largest decay probability to bb¯, this leads gino-dominated neutralinos as well as the SM back- to a final state dominated by hard b-tagged jets along with a ground. (iii) We observe that for a spectrum with a heavy NLSP, large missing transverse momentum (MET) =ET and addi- tional light jets/leptons arising from an accompanying Z reflecting overall compression with respect to the strong sector leads to an increased fraction of boson. Signatures for the Higgsino-like NLSP’s have been the longitudinal mode in the Z boson arising from studied in the context of Tevatron [15,16] and also at LHC, the NLSP decay. where both CMS [17] and ATLAS [18] have looked at (iv) New observables enhancing the asymmetry in the multiple b jets þ MET, dilepton, and multilepton states to angular distributions of the negatively charged constrain a Higgsino-like NLSP scenario. lepton have been proposed in order to characterize In this work, we aim to study signatures of a low-lying a longitudinally polarized Z boson in comparison to Higgsino sector in the presence of a light gravitino LSP with a transversely polarized Z boson. Such observables emphasis on determining how the NLSP nature can be distinctly vary, depending on the Higgsino-gaugino convincingly identified. To do this, one would like to admixture of the NLSP, and crucially capture the reconstruct the decay products of the NLSP. As the effect of the equivalence theorem for a heavy NLSP. Higgsino NLSP would decay to a light Higgs or a Z boson, The paper is organized as follows. In Sec. II, we discuss we may be able to observe their properties by appropriately the current scenario with the Higgsino NLSP and gravitino reconstructing the Higgs boson through the b jets arising LSP followed by the decay properties of the Higgsinos in from its decay as well as the Z boson through the opposite Sec. III. In Sec. IV, we discuss the experimental status of a sign dilepton pair from the gauge boson’s decay, respec- tively. We note here a very important and interesting feature Higgsino-like NLSP with a light gravitino LSP at LHC. In of the decay of the NLSP. It is expected that the Z boson Sec. V, we choose some benchmarks to study the available 0 parameter space. We perform the collider study and discuss arising from the Higgsino-like χ˜ decay would be domi- 1 our results at the high luminosity run of LHC in Sec. VI.In nantly longitudinal (Goldstone boson), primarily following Sec. VII, we distinguish between the features of longi- the equivalence theorem where, after electroweak symmetry tudinal and transverse gauge bosons. Section VIII summa- breaking, the neutral Goldstone boson constitutes the rizes the main conclusions of our work. longitudinal mode of the Z boson responsible for its mass. This property if observed in the decay of the NLSP would 0 exclusively point towards the presence of a Higgsino-like χ˜1, II. HIGGSINO-DOMINATED NLSP WITH KEV LSP helping us identify the nature of the NLSP. The direct In our work, we discuss light Higgsino-like NLSP as a production of the electroweak neutralino NLSP would be possible consequence of a general phenomenological limited at the LHC as their mass becomes larger. However, MSSM. Since no hint of SUSY has yet shown up at direct the property of the NLSP could still be studied if they are searches, various possible configurations of the lightest produced in cascade decays of strongly interacting spar- 0 neutralino, χ˜1, leading to distinct signals at colliders are of ticles. We therefore study the effect of including the strong 0 interest. Such a light Higgsino-like χ˜ is characterized by a sector in exploring the compositions of the NLSP as well as 1 low (≲800 GeV) μ parameter and heavy bino, wino soft from the direct production of the low-lying electroweakinos mass parameters, i.e., jμj ≪ M1, M2. μ in the aforesaid range (still allowed by experiments) and propose some new is also a preferred choice from the angle of naturalness kinematic observables which help identify the NLSP. [19–24]. However, χ˜0 may not be the LSP in many Thus, the salient points of our study are as follows: 1 (i) We consider a naturally compressed low-lying situations. In such cases, there can be several other candi- dates for LSP such as gravitinos, axinos, sneutrinos, etc. Higgsino sector as well as partially and/or fully 3 compressed spectra with the strongly interacting The gravitino is the spin 2 superpartner of the spin 2 sparticles sitting above the NLSP. The sparticles graviton in local SUSY. Upon spontaneous SUSY break- decay via cascades to the NLSP, which further ing, there arises a massless Weyl fermion known as the ˜ decays to a Higgs and a Z boson, thereby giving goldstino (G), owing to the breaking of the fermionic rise to at least 1b jet and opposite-sign same flavor generators of SUSY. After electroweak symmetry breaking, dileptons along with missing transverse energy in the gravitino acquires mass by absorbing the goldstino, 1 the final state. which form the spin 2 components of the massive gravitino. (ii) The characteristic features of a longitudinal Z boson We henceforth approximate a light gravitino by the gold- 0 arising from decay of the Higgsino-like χ˜1 are stino using the equivalence theorem.
075040-2 IDENTIFYING A HIGGSINO-LIKE NLSP IN THE CONTEXT … PHYS. REV. D 101, 075040 (2020)
˜ n T The goldstino (G) Lagrangian is [9], NM N ¼ diagðmχ˜0 ;mχ˜0 ;mχ˜0 ;mχ˜ 0 Þ; ð5Þ 1 2 3 4 1 L ¼ ˜ †σ¯ μ∂ ˜ − ˜ ∂ μ þ ð Þ where mχ˜0
c −1 III. HIGGSINO NLSP DECAYS U M V ¼ diagðm˜ ;m˜ Þ; ð7Þ χ1 χ2 0 A Higgsino-like χ˜ 1 is characterized by a large Higgsino fraction with suppressed wino and bino fractions, i.e., where mχ˜
MZsWsβ −MZcWsβ −μ 0 ð4Þ TABLE I. Relevant range of the input parameters for the parameter-space scan to study the decay probabilities of the lightest Here, sW ¼ sin θW, cW ¼ cos θW, where θW is the weak neutralino is shown. We keep other parameters at fixed values which ¼ 2 ¼ 2 ¼ 1 917 ¼ mixing angle, whereas sβ ¼ sin β, cβ ¼ cos β, where include: M1 TeV, M2 TeV, M3 . TeV, MQ3 vu 2 8 ¼ 2 8 ¼ 2 5 ¼ 3 tan β ¼ refers to the ratio of the vacuum expectation . TeV, MU3 . TeV, MA . TeV, At TeV, and vd ¼ 1 mG˜ keV. value’s of the up-type Higgs doublet (Hu) and the down- type Higgs doublet Hd. Diagonalizing the symmetric mass Parameters jμj (TeV) signðμÞ tan β n matrix M using a unitary matrix N lead to the neutralino – 1 – χ˜0ð ¼ 1 … 4Þ Values 0.2 1.5 2 45 mass eigenstates i i ; ; ,
075040-3 DUTTA, MUKHOPADHYAYA, and RAI PHYS. REV. D 101, 075040 (2020)
1 45 1 45 40 40 0.8 0.8
) 35 ) 35 ~ ~
30 β 30 β 0.6 0.6
25 tan 25 tan 1 1 -> h G -> h G 0 0 ~ ~ χ 0.4 20 χ 0.4 20
BR ( 15 BR ( 15 0.2 10 0.2 10 5 5 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 μ (TeV) μ (TeV)
1 45 1 45 40 40 0.8 0.8
) 35 ) 35 ~ ~
30 β 30 β 0.6 0.6
25 tan 25 tan 1 1 -> Z G -> Z G 0 0 ~ ~ χ 0.4 20 χ 0.4 20 15 15 BR ( BR ( 0.2 10 0.2 10 5 5 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 μ (TeV) μ (TeV)
0 ˜ FIG. 1. Variation of χ˜1 decay into a Higgs (top panel) or Z boson (bottom panel) along with the G LSP with μ and tan β in the colored palette. The parameters of the scan are listed in Table I.
¼ 1 ¼ 1 ¼ Γðχ˜0 → ˜ Þ ∝ j β þ βj2ð Þ−2 ð Þ where i , 2 and k , 2, 3, such that Hk h, H, A, 1 hG N14 cos N13 sin MPlmG˜ : 13 respectively. The coefficients ek and dk are as below, The interference term between the gaugino and the Higgsino vanishes [30] in the above decay mode due to e1 ¼ cos α;e2 ¼ − sin α;e3 ¼ − sin β the polarization states being physical states. We note ¼ − α ¼ − α ¼ β ð Þ 0 d1 sin ;d2 cos ;d3 cos ; 10 that for a Higgsino-like χ˜1, N13 ≃−N14 for μ > 0, whereas for μ < 0, N13 ∼ N14 [15]. This leads to an increase in th Γðχ˜0 → ˜ Þ and Nij refer to the ðijÞ entry of the neutralino mixing 1 hG as evident from Eq. (13). matrix N, α is the mixing angle between the CP-even Higgs bosons, h and H. In the decoupling limit, i.e., mA ≫ mh, A. Branching ratios β − α ∼ π 2 0 β π −π α 0 = (where, < < and < < ), the The decay branching ratios of the Higgsino-dominated lightest CP-even Higgs boson (h) behaves like the SM 0 χ˜1 NLSP are governed mainly by values of μ and tan β. Higgs boson [9]. The partial decay widths of the lightest Table I summarizes the relevant parameter ranges for the neutralino χ˜0 are as follows [15,29]: 1 scan performed using the package SPheno-v3.3.6 [31,32].In Fig. 1, we show the regions of the parameter space, having Γðχ˜0 → ˜ Þ ∝ j α − αj2ð Þ−2 ð Þ χ˜0 1 hG N14 sin N13 cos MPlmG˜ 11 the different branching ratios of the 1. We discuss the salient points of the parameter space as below: (i) The branching fractions to the Higgs and Z mode 0 ˜ 2 decreases with an increase in the gaugino admixture Γðχ˜ → ZGÞ ∝ jN11 sin θ − N12 cos θ j 1 W W in the NLSP at higher values of μ and tan β (as μ gets 1 closer to the choice of M1 and M2 shown in Table I). þ j β − βj2 ð Þ−2 ð Þ 2 N14 cos N13 sin MPlmG˜ : 12 This defines a range of the parameter space with comparable branching ratios for the Higgs and Z 0 boson decay modes of the χ˜1 NLSP. The terms proportional to N14 and N13 denote the (ii) For jμj > 400 GeV, Goldstone couplings.1 In the decoupling limit, sin α ¼ − β α ¼ β 0 ˜ 0 ˜ cos and cos sin ; thus, Eq. (11) reduces to BRðχ˜1 → hGÞ ≃ BRðχ˜1 → ZGÞ;
1See the discussion at the beginning of Sec. VII for the decay for large values of tan β (tan β ≥ 25) with small of the Z boson and the polarization of the gauge bosons. differences depending on signðμÞ. For signðμÞ¼þ1,
075040-4 IDENTIFYING A HIGGSINO-LIKE NLSP IN THE CONTEXT … PHYS. REV. D 101, 075040 (2020)
0 ˜ 0 ˜ BRðχ˜1 → hGÞ ≃ 0.47; BRðχ˜1 → ZGÞ ≃ 0.53; TABLE II. List of experimental searches from LHC reinter- preted for Higgsinos relevant for our current study with G˜ LSP. whereas for signðμÞ¼−1, The rate in each final state is the sum of rates in all channels listed in the corresponding rows. 0 ˜ 0 ˜ BRðχ˜1 → hGÞ ≃ 0.54; BRðχ˜1 → ZGÞ ≃ 0.46: Final state Contributing channels ATLAS CMS 2 3 4 þ 0 0 þ − 0 0 = = b =ET χ˜1χ˜1 ; χ˜2χ˜1 ; χ˜1 χ˜1 ; χ˜1χ˜2 [33] [17] (iii) For μ < 400 GeV and tan β ≃ 5, þ − 0 0 þ − 0 0 l l þ =ET χ˜1χ˜1 ; χ˜2χ˜1 ; χ˜1 χ˜1 ; χ˜1χ˜2 [17] ≥ 3l þ χ˜0χ˜ χ˜0χ˜ χ˜þχ˜− χ˜0χ˜0 0 ˜ 0 ˜ =ET 1 1 ; 2 1 ; 1 1 ; 1 2 [17] BRðχ˜1 → hGÞ ≃ 0.30; BRðχ˜1 → ZGÞ ≃ 0.70: hh þ =ET g˜ g˜ [34] 4l þ þ − 0 =ET χ˜1 χ˜1 ; χ˜1 χ˜2 [35] ¼ − due to N13 N14, such that the Z mode dominates ≥ 2j þ =ET g˜ g;˜ q˜ q˜ [36] −μ 400 ¯ χ˜0χ˜ over the Higgs mode. Whereas for > GeV bb þ =ET 2 1 [37] β ≃ 5 ¯ χ˜0χ˜ and tan , 1l þ bb þ =ET 2 1 [37] 0 3l þ =ET χ˜2χ˜1 [37] 0 ˜ 0 ˜ l l þ χ˜0χ˜ BRðχ˜1 → hGÞ ≃ 0.67; BRðχ˜1 → ZGÞ ≃ 0.33; =ET 2 1 [37]
where N13 ¼ N14 and the Higgs and Z decay modes 0 of the χ˜1 NLSP dominate over the others, (ii) Strong sector: Direct limits for a massless gravitino respectively. LSP scenario are placed on strong sector sparticles 0 ˜ þ In addition, as the χ˜1 becomes more gauginolike, the with G LSP from opposite sign dilepton additional decay mode of γG˜ would also open up and missing energy searches in ATLAS [38], excluding m˜ ≤ 1.8 TeV for mχ˜0 < 600 GeV. Stringent limits subsequently dominate the branching probabilities [16]. g 1 also arise from boosted Higgs searches [39] inter- preted in terms of a simplified scenario with a light IV. EXISTING LHC LIMITS 0 χ˜ LSP, excluding m˜ ≤ 2.2 TeV for m˜0 ¼ 1 GeV. 1 g χ1 The current bounds on the light Higgsinos as NLSP and Other indirect searches, which constrain the above ˜ G LSP are well studied at LHC for a light gravitino mentioned scenario, are multijets and/or multilep- ¼ 1 2 (mG˜ GeV [33]) assuming prompt decays. The rel- tons þ=ET searches [35,36], owing to the presence of evant analyses are summarized in Table II, and we list the h=Z from the NLSP decay which give rise to leptons constraints from LHC on the Higgsinos as well as on the or jets in the final state. strong sector sparticles as relevant for our study below: (i) Higgsinos: ATLAS and CMS impose stringent V. BENCHMARKS FOR OUR ANALYSIS limits on the mass of the Higgsinos from searches We choose representative benchmark points of the involving multiple b jets/leptons along with large =E T allowed parameter space to probe a low-lying Higgsino- assuming specific branching probabilities for its χ˜0 ˜ decay. The following are the exclusion limits on like 1 NLSP with light G LSP, focusing primarily on χ˜0 the Higgsino masses [17,33]: promptly decaying 1 signals. Our choice of benchmarks is motivated by the underlying aim of uncovering the char- 0 ˜ acteristics of a Higgsino-like NLSP in the presence of a BRðχ˜1 → hGÞ ∼ 1.0∶ mχ˜0 ≤ 880 GeV ðATLASÞ; 1 light G˜ LSP. Decays of the strong sector sparticles occur via mχ˜0 ≤ 760 GeV ðCMSÞ: ˜ 1 the following decay modes for a keV G: for gluinos 0 ˜ (m˜ 0 ˜ Among these decay modes, owing to the Higgsino-like BRðχ˜ 1 → hGÞ ∼ 1.0∶ mχ˜0 ≤ 775 GeV ðCMSÞ: 1 nature of the NLSP, the interaction strengths are governed 0 ˜ BRðχ˜1 → ZGÞ ∼ 1.0∶ mχ˜0 ≤ 650 GeV ðCMSÞ: by the Yukawa couplings. Hence, the third generation 1 ≤ squark channels dominate. For squarks (mq˜ 075040-5 DUTTA, MUKHOPADHYAYA, and RAI PHYS. REV. D 101, 075040 (2020) TABLE III. List of benchmarks chosen for our study. Mass Higgs mass is within the range 122–128 GeV [40,41]. In all parameters are in GeV unless specified otherwise. cases, both t˜1 and/or t˜2 are heavy or the trilinear coupling A , is too large to fit the lightest CP-even Higgs mass Parameters BP1 BP2 BP3 BP4 BP5 t [40–42]. Also, m adheres to the LEP lower limit of χ˜1 M1 2400 800 7000 2300 2400 103.5 GeV [43]. We choose the benchmarks after passing M2 2400 800 7000 2300 2400 them through the public software CheckMATE [44]. Among μ 800 2400 700 2250 −800 tan β 25 25 25 25 3.8 the searches implemented in CheckMATE, stringent con- straints come from multijet searches by ATLAS [36]. The At 3200 3200 100 3200 3740 mA 2500 2500 2500 2500 3000 benchmark points are generated using the spectrum gen- erator SPheno-v3.3.6 [31,32]. mh 125.3 125.3 127.1 124.5 122.2 mg˜ 2806.4 2807.1 7271.2 2840.1 2663.3 ˜ mqL 2303.3 2300.2 7156.4 2313.3 2280.6 VI. LHC SIGNALS m˜ 2302.2 2302.5 7155.4 2312.5 2283.7 qR We now discuss in detail the possible LHC signals m˜ 2357.5 2184.8 7057.0 2509.1 1581.1 t1 arising in the current scenario with a Higgsino-like χ˜0 m˜ 2340.9 2370.8 7104.0 2666.0 2271.4 1 t2 ˜ m˜ 2260.9 2266.4 7102.2 2583.4 2237.5 NLSP and keVpffiffiffi G LSP. A strong sector sparticles pair b1 0 ˜ produced at s ¼ 13 TeV LHC cascades down to the χ˜1 mb2 2299.0 2323.9 7129.0 2630.3 2295.6 m˜ 3331.8 3326.8 7337.2 3332.6 3329.4 NLSP along with additional jets arising from the cascade. lL m˜ 3335.6 3333.7 7336.3 3336.3 3334.1 In situations where the strong sector is not kinematically lR mχ˜0 810.9 797.9 718.8 2211.0 1214.8 accessible, it is worthwhile to explore signals from the 1 direct production of the low-lying Higgsinos decaying mχ˜0 −814.4 837.8 −723.7 −2254.8 −1217.2 2 0 promptly to the NLSP χ˜1, which then further decays to a mχ˜ 812.5 837.9 720.9 2223.1 1216.4 1 Higgs=Z gauge boson and the G˜ LSP. As discussed in mχ˜ 2415.7 2397.3 1925.9 2350.5 2420.9 2 Sec. III A, such a scenario would lead to hh=hZ=ZZ final mχ˜0 2386.3 −2394.8 1923.6 2290.1 2392.2 3 states with/without extra hard jets arising from the strong mχ˜0 2415.6 2397.4 1925.8 2350.5 2420.9 4 sector cascade. mG˜ (keV) 1.0 1.0 1.0 1.0 1.0 Motivated by the characteristics of a Higgsino NLSP 0 ˜ BRðχ˜1 → hGÞ 0.45 0.0 0.44 0.23 0.27 spectrum, among the multifarious signatures possible, we 0 ˜ BRðχ˜1 → ZGÞ 0.55 0.25 0.56 0.75 0.73 focus on a final state consisting of a Higgs and Z boson 0 ˜ BRðχ˜1 → γGÞ 0 0.75 0 0.02 0 along with large =ET as the primary signature of such a scenario. In addition, to study the characteristic polarization ðχ˜ → ˜ Þ BR 1 WG 0.024 0.0 0.003 0.0001 0.15 of the Z boson coming from the decay of the NLSP, we ðχ˜ → χ˜0Þ BR 1 W 1 0.976 1.0 0.997 0.9999 0.85 require an efficient and cleaner mode of reconstruction, which can only come through the leptonic decay of the weak gauge boson. Note that for the hadronic decays of a 0 0 0 q˜ → qχ˜ 1;qχ˜2;qχ˜1 : Higgs and Z boson contributing to the signal rates, the corresponding SM hadronic background would also be As discussed in Sec. III A, the dominant decay mode of the significantly bigger. We therefore choose a final state that 0 includes at least one b jet and two same-flavor opposite χ˜ NLSP is to either a Higgs or a Z boson along with the G˜ 1 sign leptons along with =E . Owing to the presence of LSP which contributes to the missing energy. We wish to T leptons in the final state, this is a relatively clean channel to study the collider prospects of observing the final state ≥ 1 þ lþl− þ observe at LHC as compared to an all hadronic final state. b =ET in the context of the upcoming high ˜ luminosity run of the LHC and explore kinematic variables Since the LSP is a very light G, the ensuing h=Z from the reflecting the composition of the NLSP. We discuss below NLSP decay and hence, the b jets and/or leptons have large the characteristic features of each of the chosen bench- transverse momentum (pT), thereby leading to a large =ET, ⃗ ¼ −⃗ marks as shown in Table III. We also include a benchmark where =ET pTvis (balancing the net transverse momenta, BP5 BP1 ⃗ similar to with a larger branching fraction into pTvis of the visible particles). No specific criteria is imposed the Higgs boson and gravitino mode, which would re- on the number of light jets in the scenario as will be present present the low tan β and negative μ region of the if the signal arises from the decay of the squarks or gluinos parameter space. to the NLSP. This is because our choice of an inclusive final For simplicity, M1 ≃ M2 ∼ 2.3–2.4 TeV, such that their state signal would be able to highlight the presence of a contribution to the signal region under study (directly or via Higgsino-like NLSP irrespective of the rest of the under- cascade decays of strong sector sparticles) is negligible. lying MSSM spectrum, i.e., with/without the strong sector Among the constraints on the parameter space, the light placed above the low-lying Higgsinos. 075040-6 IDENTIFYING A HIGGSINO-LIKE NLSP IN THE CONTEXT … PHYS. REV. D 101, 075040 (2020) A. Signal, background, and event selection criteria helps probe the heavy mass scale of the SUSY particles and We consider the following SUSY production processes would serve as an effective discriminator between the involving squarks as well as the low-lying Higgsinos to be SUSY signal and SM background. For an SM background, QCUT ¼ pair produced when kinematically accessible: we perform MLM matching [45] when needed with 20 − 30 GeV. pp → q˜ q˜ ; q˜ q˜ ; q˜ q˜ ; q˜ g;˜ χ˜0χ˜0; χ˜ χ˜0; χ˜ χ˜0; χ˜þχ˜−: i j i j i j 1 2 1 1 1 2 1 1 B. Primary selection criteria Note that the gluinos are heavier compared to the squarks We choose the following basic selection criteria to identify μ and Higgsinos, and their contribution to the signal is leptons (e, )andb jets in the signal and background: subdominant. When the signal is generated from the pair (i) The charged leptons are identified with pT > 10 GeV and jηj < 2.5. production of the strongly interacting sparticles, the final 30 state consists of at least two hard jets in the hh=hZ=ZZ final (ii) All reconstructed b jets have pT > GeV jηj < 2 5 state along with a pair of invisible gravitinos, which and . . (iii) Jets and leptons are isolated with ΔRij > 0.4 contribute to the large =ET. Among the possible combinations and ΔRll > 0.2. of the decay products of h and Z, we primarily focus on the ≥ 1b þ lþl− final state along with =E . Since the Z decays T b − jet l + l − leptonically, it gives a cleaner channel and better control C. Signal analysis: At least 1 + + E=T over the SM backgrounds as compared to a hadronic final We note that for the signal, since the NLSP-LSP mass state. gap is large, the transverse momenta carried by the decay We generate the signal events in MadGraph_v5 [45] using products are large thereby ensuring a large amount of =ET in the model UFO files available from FeynRules [46]. the event. Figure 2 shows the normalized differential Subsequently, parton level events are showered and hadron- distribution of a few kinematic variables (MEff and =ET) ized using PYTHIA [47,48], and a detector simulation is for BP1 and BP4 along with the background. The SUSY performed using DELPHES [49]. Jets (including b jets) are signal distributions for the missing transverse energy (=ET) reconstructed using the anti-kT algorithm [50], using FastJet and effective mass (MEff) are widely separated from the SM [51] with minimum transverse momentum, pT > 20 GeV background for BP4 in the presence of a heavy NLSP. within a cone ΔR ¼ 0.4. Charged leptons are reconstructed However, the signal events peak at a much lower value of ∼ 850 BP1 in a cone of ΔR ¼ 0.2 with a maximum energy deposit in MEff GeV for , while significant events of the ∼2 0 BP4 the cone from all other particles limited to 10% of the pT of signal are found at large MEff values . TeV for . the lepton. The significant contributions to the SM back- Note that for BP4, this is due to the high transverse ground for the given final state come from momentum of the jets and leptons arising from the decay (i) tt¯, ðt → bWþ;Wþ → lþνÞ cascades of the heavy Oð2Þ TeV range sparticles. However, (ii) hZþ jets, (h → bb¯, Z → lþl−) for BP1 with a light NLSP, there is considerable overlap of (iii) ttZ¯ , ðZ → lþl−Þ the kinematic distributions with the background while (iv) ZZ,(Z → bb¯, Z → lþl−) differing in the tail of the distribution. This happens (v) W W∓Z, ðZ → lþl−Þ because the dominant contribution to the signal comes (vi) lþl−bb¯ þ νν¯. from the direct production of the light Higgsino sector as Although the QCD background has a large cross section, it compared to the strong production cross section. We break has a negligible contribution to the signal region charac- our analysis in two parts to study different scenarios that terized by large =ET as well as effective mass (MEff ), which can present themselves at LHC. The signal from a heavy BP1 1 BP4 Zbbνν WWZ t Zt WZ ZZ −1 10 tt hZ T E dN d 1 N 10−2 0 500 1000 1500 2000 2500 ET (GeV) FIG. 2. Distribution of few useful kinematic variables before application of any selection cuts. 075040-7 DUTTA, MUKHOPADHYAYA, and RAI PHYS. REV. D 101, 075040 (2020) spectrum of Oð2Þ TeV, including the NLSP, that can only dominant fraction of signal events would come from the have a relevant signal contribution through the production light Higgsino production, and the cuts given below are not of strongly interacting sparticles at the LHC is optimized particularly optimized to study BP1. The BP3 signal, on using cuts in Analysis 1, while the signal for relatively the other hand, becomes very small. We shall discuss the lighter electroweakino states being directly accessible at BP1 and BP3 benchmarks separately in Analysis 2. LHC with smaller contributions from the strong sector is Additional cuts on the events are analyzed in Analysis 2. Appropriate cuts on the relevant (i) D4: Since nearly all the SUSY particles excluding BP4 BP5 kinematic variables will be crucial to remove SM back- the LSP are heavy for and , a large MEff is ground in the subsequent collider analyses to study the two expected for the signal over the SM background as scenarios discussed above. shown in Fig. 2. We therefore demand a strong cut of 2 MEff > TeV. This cut renders the signal for other D. Analysis 1 benchmarks to a relatively smaller value. As a crucial part of our analysis is dependent on the (ii) D5: In addition, we also put a strong cut on missing 300 reconstruction of the Z boson in the events through the transverse energy, =ET > GeV to further remove dilepton mode, the event rate for the signal will suffer due remaining contributions from SM background to the small branching fraction of the gauge boson to processes. charged leptons. In addition, if we intend to reconstruct the We show the cut-flow result of our analysis for the signal light Higgs boson too using double b-tag jets, we will end and SM background in Table IV. As expected, the signal rates coming from a 2 TeV squark sector yields quite small up restricting our search sensitivity significantly. We there- −1 fore need to select events using proper cuts to be able numbers, even with an integrated luminosity of 3000 fb . to identify the Z boson as well as imply a Higgs like event. The overwhelmingly huge SM background is brought in In order to select such a final state, we implement the control by primarily using the MT2 cut and is then rendered following event selection criterion to retain a significant negligibly small using the combination of MEff and =ET amount of signal against the SM background: cuts. We find that the sequence of cuts shown in Table IV (i) D1: We select a final state with two opposite sign affects the signal slightly with a suppression of the signal BP5 leptons of the same flavor (Nl ¼2 with pT >20GeV) rate of less than 50% for . Thus, we find a significant and at least one b jet with pT > 30 GeV. number of SUSY signal events surviving the event selec- (ii) D2: To reconstruct the Z boson, we demand that the tion. Note that while a ∼75% suppression of signal events invariant mass of a dilepton pair (opposite sign, happen for BP1, it is still quite large compared to the SM same flavor) in the signal events is within the Z mass background, unlike that for BP3. window satisfying 76 075040-8 IDENTIFYING A HIGGSINO-LIKE NLSP IN THE CONTEXT … PHYS. REV. D 101, 075040 (2020) TABLE V. Required luminosities forpffiffiffi observing the SUSY strong sector for the benchmarks in our study when they are signal for the different benchmarks at s ¼ 13 TeV LHC run. kinematically accessible and study the benchmarks BP1 The numbers in the parentheses include 10% systematic errors in and BP3. As the final state remains unchanged, the cuts the background. implemented on both signal and background in Analysis 1 L (in fb−1) L (in fb−1) would still be useful for background suppression. The Benchmark for 3σ excess for 5σ excess implemented cuts therefore remain similar except for the M BP1 excluded Eff cut, optimized for the two benchmarks 240 (250) 665 (695) (i) E1:AsinAnalysis 1, we select a final state with BP4 1112 (1178) 3090 (3270) two opposite sign leptons of same flavor (Nl ¼2 BP5 340 (356) 943 (988) with pT >20GeV) and at least one b jet with pT >30GeV. (ii) E2: To reconstruct the Z boson, we demand that the We compute the statistical significance (S) of the above invariant mass of the dilepton pair in the signal signals using the formula in Eq. (14) and show the required events is within the Z mass window, satisfying integrated luminosities to observe and discover the signal in 76 075040-9 DUTTA, MUKHOPADHYAYA, and RAI PHYS. REV. D 101, 075040 (2020) TABLE VII. Required luminosities forpffiffiffi observing the SUSY presence of longitudinal gauge bosons from heavy Higgs signal for the different benchmarks at s ¼ 13 TeV LHC run. decays have been studied in earlier works in the context of The numbers in the parentheses include 10% systematic errors in the Tevatron [60]. LHC analyses have also looked at the background. features of longitudinal gauge bosons in the SM [61].In L (in fb−1) L (in fb−1) case an excess over SM is observed, it is of crucial Benchmark for 3σ excess for 5σ excess importance to extend current search strategies to character- BP1 ize BSM scenarios by studying variables sensitive to the 310 (333) 862 (924) polarization information of the gauge bosons via their BP3 208 (226) 577 (626) decay products. Although there have been several studies in the context of eþe− colliders focusing on studies of polarizations of the incoming electron-positron beams or helps reduce a significant part of the remnant polarization of the final state particles, there are few contributions from SM background. analogous studies with respect to the LHC utilizing these The cut-flow table for the signal and SM background are Z as shown in Table VI. We rely on a slightly stronger cut on techniques [62]. The polarization of a boson has been studied briefly in [62] with respect to the LHC in a similar M to ensure substantial removal of the tt¯ background T2 scenario however in displaced dilepton final states arising while retaining the signal events. However, other back- θ þ − ¯ þ from the Z boson decay using the angular variable cos ground contributions, such as that from l l bb =ET, discussed below. We discuss analytically some basic remain. This still gives a significantly large event rate for variables found in the literature, which distinguish longi- the signal as compared to Analysis 1, and thereby allowing a tudinal and transverse gauge bosons. The differential decay ∼ð8–10Þσ L ¼ 3000 −1 discovery possible with fb .Since rates for the transversely polarized and longitudinally both the benchmarks have similar branching fractions into polarized Z boson in the rest frame of Z boson are [60] the Z and Higgs mode, the difference in the required integrated luminosity is due to the fact that the NLSP mass Γ d T ∝ ð1 θ Þ2 ð Þ is heavier in BP1 than in BP3. The required luminosity for cos 15 d cos θ observing a 3σ and 5σ significance at LHC are shown Table VII. We conclude that both BP1 and BP3 are well dΓ L ∝ sin2 θ ; ð16Þ within the discovery reach of the high luminosity run d cos θ of LHC. We are now set to study the efficacy of the signal that we 0 ˜ 0 ˜ where ΓT ¼ Γðχ˜1 → ZTGÞ and ΓL ¼ Γðχ˜ 1 → ZLGÞ are the have analyzed to identify the nature of the NLSP and its 0 partial decay widths of the χ˜1 to a transverse Z boson (ZT) inherent composition with respect to the gaugino-Higgsino and longitudinal Z (ZL) boson, respectively. The angle θ is admixture in the following section. defined as the angle the outgoing lepton (arising from the Z boson decay) makes with the Z boson in its rest frame with VII. A DISTINGUISHING FEATURE: the reference direction being the boost direction of the Z LONGITUDINAL VS TRANSVERSE boson in the laboratory frame. The dependence of the decay GAUGE BOSONS width; i.e., ð1 cos θ Þ2 corresponds to k ¼∓ 1 state and 2 0 sin θ corresponds to k ¼ 0 state, where k is the helicity of We are interested in a Higgsino-like lightest neutralino χ˜ 1 Z χ˜ 0 → ˜ the boson. To highlight the difference, we choose the for which 1 hG is an obvious decay channel. In addition, NLSP from a few of our benchmarks and generate a the Higgsino also couples to the imaginary parts of the normalized distribution for cos θ , where the NLSP is neutral component of the two Higgs doublets. This leads to decaying at rest and gives the Z boson as its decay product. Higgsino-goldstone-gravitino interactions. The goldstone, The simple illustration of this reconstruction is shown in on the other hand, approximates the longitudinal component Fig. 3, where BP1 represents a dominantly Higgsino-like of the Z, when the relevant energy scale is much larger than BP2 0 NLSP, represents a dominantly gauginolike NLSP, m . Thus, for a Higgsino-like χ˜1 with mχ˜0 ≫ m ,onealso Z 1 Z while BP4 represents a comparable admixture of gauginos 0 ˜ expects the decay χ˜1 → ZG, when the Z is longitudinal. and Higgsinos in the NLSP. Although our focus is on the polarization of Z boson in We now go ahead and consider the full analysis for the þ − the context of SUSY in this work, the polarization signal ≥ 1b þ l l þ =ET and focus on the negatively information of vector bosons may be extremely useful charged lepton. Note that we expect distributions in even for non-SUSY scenarios, where a polarized gauge cos θ , as highlighted in Fig. 3, for the Z polarization to boson is likely to be produced from the decay of a heavy be robust against the energy smearings in the detector and particle. Thus, the features of the longitudinal Z boson, the full detector simulation. To show this, we compare both which will be discussed in detail in this work, are also parton-level analysis to the signal events obtained after applicable for other scenarios as well. For example, the detector simulations. We plot the normalized distributions 075040-10 IDENTIFYING A HIGGSINO-LIKE NLSP IN THE CONTEXT … PHYS. REV. D 101, 075040 (2020) cone radius of R ¼ 0.5 for lepton identification and also 0.07 demand that a large energy deposit with respect to the pT of 0.06 the lepton is allowed in the cone (∼12% for electrons and * 25% for muons). The distribution still retains the gaugino- θ 0.05 like behavior for an isolation of ΔR>0.2 as in the parton dN 0.04 d cos level but starts agreeing with the Higgsino-like feature (as 1 N 0.03 in the parton-level case) when the separation between the Δ 0 05 0.02 BP1 charged leptons is chosen to be loose with R> . or BP2 ΔR>0.1 as can be seen in the bottom-right panel of Fig. 4. 0.01 BP4 The qualitative differences observed in the distributions 0 of the negatively charged lepton as the gaugino admixture −1 −0.5 0 0.5 1 cos θ * increases in the NLSP amongst the three cases may be effectively captured by defining asymmetry variables in FIG. 3. Normalized distribution of cos θ of the negatively cos θ , which could clearly discriminate between a longi- − 0 charged lepton ðl Þ arising from the χ˜1 NLSP decay at rest tudinal and transverse Z boson. Taking a cue from the corresponding to the benchmarks BP1, BP2, and BP4 with the features of cos θ , we construct a variable which highlights isolation variable ΔR>0.2 for the leptons. this difference through an asymmetry amongst the observed cos θ values for the Higgsino-like and gauginolike NLSP. for cos θ of the negatively charged daughter lepton of the The asymmetry variable, CθZ , as defined in Eq. (17), serves Z boson in Fig. 4 at the parton level (left) and detector level to enhance the features of the longitudinally polarized Z in (right-panel) for our benchmarks BP1, BP2, and BP4, comparison to the transversely polarized Z, such that they where one NLSP decays to a Z boson along with a G˜ . would be less affected if detector simulation effects smear Recall, BP1 has a purely Higgsino-like NLSP (∼99%), the polarization dependence of the angular or energy BP2 with purely gauginolike NLSP (∼100%), and BP4 observables. We define has ∼31% gaugino admixture in the NLSP. We observe in − − Fig. 4 that the distributions for the negatively charged NA NB NC Cθ ¼ ; ð17Þ BP1 BP2 Z lepton (for and ) are largely similar at both parton NA þ NB þ NC and detector level simulations, to the expected distributions 4 BP4 as shown in Fig. 3. For , where the NLSP is a more where NI’s stand for events whereas the subscript I ¼ A, B, C democratic superposition of the gaugino and Higgsino represent the angular regions in θ given by A ¼½π=3; 2π=3 , states, a slightly flat and broad peak for cos θ is observed. B ¼½0; π=3 ,andC ¼½2π=3; π . The numerator focuses In addition, the NLSP mass is around 2 TeV, which results only on the asymmetry features while the denominator is in a very boosted Z boson in the final state. The event the total number of events for −1 < cos θ < 1.Basedonthe selection criteria can in principle have adverse effects in construction of CθZ , a positive value is indicative of a this case and modify the distributions. The most notable Higgsino-like NLSP whereas negative values indicate a BP4 effect for is that the distribution starts to resemble gauginolike NLSP. Since Cθ is the normalized difference BP2 Z features similar to the gauginolike NLSP ( ) at both in the number of events corresponding to j cos θ j < 0.5 and parton and detector-level simulations. This we find is due to j cos θ j > 0.5, a Higgsino-like NLSP gives larger events the fact that when the Z boson is highly boosted, the pair of around cos θ ¼ 0 as NA > ðNB þ NCÞ, whereas for the charged leptons coming from the Z boson decay get more gauginolike NLSP, the distribution peaks around cos θ ∼ collimated with a very small opening angle. This in turn 0.8 i.e., ðNB þ NCÞ >NA. Therefore, the latter shows a would mean that a larger isolation requirement for the negative sign as compared to the former. We list the values of charged leptons would lead to loss of events and also affect rest Cθ for cases when the NLSP decays at rest (Cθ )and θ Z Z the cos distribution. parton compare this with parton-level (Cθ ) results and full In our analysis, we have used the default DELPHES card Z ¼ 0 2 using a small cone radius R . and a maximum energy detector-level simulation (CθZ )ofourAnalysis 1 in BP1 BP2 deposit in the cone being 10% of the pT of the lepton. A Table VIII, for the benchmarks and (which lepton-lepton isolation cut on ΔR>0.2 reduces the peak of correspond to an almost pure Higgsino and pure gaugino the cos θ plot. To counter the consequent reduction in compositions, respectively).5 BP4 signal events, for , a relatively relaxed lepton identi- Note that the values of CθZ are in good agreement with the parton fication criterion can be useful for our purpose. To highlight parton level Cθ results. For the pure Higgsino-like NLSP this, we identify the charged leptons with a much larger Z 5The results in Table VIII are produced by using only squark 4Similar distributions for cos θ are expected for the positively pair production. However, the generic feature remains unchanged charged leptons. even when all production modes are included. 075040-11 DUTTA, MUKHOPADHYAYA, and RAI PHYS. REV. D 101, 075040 (2020) 0.07 0.06 * 0.05 θ 0.04 dN d cos 0.03 1 N 0.02 BP1 BP2 0.01 BP4 0 −1 −0.5 0 0.5 1 cos θ * 0.09 BP4 0.08 0.07 * 0.06 θ 0.05 dN d cos 0.04 1 N 0.03 Δ R > 0.05 0.02 Δ R > 0.1 0.01 Δ R > 0.2 0 −1 −0.5 00.51 cos θ * − 0 FIG. 4. Normalized distribution of cos θ of the negatively charged lepton ðl Þ arising from the χ˜1 NLSP at the parton level (top left panel) and after detector simulation (top right panel) using Analysis 1, corresponding to the benchmarks BP1, BP2, and BP4. In the bottom panel, we present the plots for BP4 at the parton level (left) and at the detector level (right) for various ΔR values as discussed in the text. BP1 ( ), CθZ is large and positive, whereas the pure gaugino- requirement and identification of the charged lepton with like NLSP (BP2) shows a negative value. We find that the ΔR>0.05; 0.1 as against Cparton ¼ −0.214 for the tighter θZ CθZ value starts decreasing as the gaugino admixture in the isolation cut of ΔR>0.2. We expect that the same would be NLSP is increased when compared to BP1. Thus, with true when the events are passed through detector simula- increasing gaugino admixture the asymmetry value becomes tions, which would be consistent with observations made in negative as shown for BP2. The most notable change is the lower panels of Fig. 4. observed for the BP4 with an intermediate gaugino- An additional kinematic feature that can be used to study ∼0 021 Higgsino admixture. CθZ value is . when the NLSP the polarization of the Z boson, which in effect highlights decays at rest with the small positive value still hinting at a the composition of the NLSP, is the charged lepton energy. larger Higgsino admixture. However, it turns negative for the Among others, the ratio of the energy carried by the analysis where the NLSP appears from cascade decays of the charged lepton and antilepton also show a dependence squark, both at the parton and the detector level owing on the polarization of the Z boson with an energy E, via largely to the effect of isolation cuts and detector smearing dependence on the angle θ . The energy (El) of the leptons effects, which modify the cos θ distribution as seen in Fig. 4 in the laboratory frame [60] follows parton and discussed earlier. We note that the Cθ value becomes Z E parton ∝ ð1 β θ Þ ð Þ positive giving Cθ ¼ 0.04, 0.05 for the loose isolation El cos : 18 Z 2 rest parton TABLE VIII. Variation of the asymmetry variables Cθ , Cθ , Cθ , and CZ as defined in the text, at the parton level and detector D1 − D5 BP1 BP2Z Z Z level after cuts for benchmarks and . The numbers for CθZ and CZ include both signal and background in the computation of the observables and its associated 1σ error for L ¼ 3000 fb−1. rest parton Benchmark mχ˜ 0 (GeV) Higgsino admixture (%) Gaugino admixture (%) C C Cθ C 1 θZ θZ Z Z BP1 810.9 99.83 0.17 0.38 0.33 0.35 0.16 0.38 0.16 BP2 797.9 0.05 99.95 −0.18 −0.08 −0.05 0.21 −0.02 0.21 075040-12 IDENTIFYING A HIGGSINO-LIKE NLSP IN THE CONTEXT … PHYS. REV. D 101, 075040 (2020) 0.1 0.1 BP1 BP1 0.09 0.08 0.08 BP2 BP2 0.07 R 0.06 D 0.06 dN dZ dZ dN 0.05 1 N 1 N 0.04 0.04 0.03 0.02 0.02 0.01 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ZD ZR FIG. 5. Normalized distributions of the kinematic variables ZD and ZR as defined in the text for distinguishing between a Higgsino and 0 gauginolike χ˜1 NLSP before cuts D1 − D5 The variables are as defined in the text. Here, we have plotted the observables for the process 0 ˜ þ − q˜ q˜ with one of the squarks decaying as: q˜ → qχ˜1 → qZG, Z → l l . pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Using this, we define two kinematic observables ZD and ZR 1 − C (variations of such observables have been pointed out in σðCÞ¼ pffiffiffiffi ; ð21Þ N earlier papers [63,64] using jet substructure to study hadronic final states), where C ¼ Cθ , C , while N represents the total number of Z Z pffiffiffiffi events. The uncertainty goes down as 1= N, which means j − − þ j − El El El that a larger luminosity would help in improving the ZD ¼ ; ZR ¼ : ð19Þ El− þ Elþ El− þ Elþ statistical significance; therefore, we emphasize that the distribution of cos θ arising from the Z boson decay as well We study the usefulness of these observables using as the associated asymmetry variables, CθZ and CZ prove simple cuts on kinematic variables after detector simulation quite useful in identifying the nature of the NLSP. The effects are taken into account. For a predominantly longi- distinctive features of the variables discussed for distin- tudinal Z boson, there is an equal sharing of energy of the guishing a longitudinal and transversely polarized Z boson parent among its daughter particles whereas for a transverse are also applicable for new physics scenarios, where a Z boson, the energy sharing is unequal. The asymmetry is polarized gauge boson is likely to be produced and therefore, evident in Fig. 5, where the Higgsino-like NLSP peaks at can prove very important in studying BSM physics. ZD ¼ 0.1 as compared to ZD ¼ 0.8 for the gauginolike case. Similar effects are observed in the variable ZR, which VIII. SUMMARY AND CONCLUSIONS denotes the fraction of net leptonic energy carried away by the negatively charged lepton. The ratio peaks at Z ≃ 0.5 In this work, we have considered Higgsino-like NLSP in R ˜ for BP1 as compared to ZR ≃ 0.1 and ZR ≃ 0.8 for the the presence of a light keV G LSP in the framework of BP2, since for the former case, the leptons mostly have phenomenological MSSM. The keV scale G˜ serves as a equal energy sharing, whereas unequal energy sharing warm dark matter candidate, significantly relaxing con- occurs for the latter case. We define an asymmetry variable straints from dark matter searches on the MSSM spectrum μ similar to Cθ , now referred to as CZ to capture the and thereby, allowing low parameter values. In addition, Z ˜ asymmetry in the values of ZD at the detector level, presence of a light G allows decay of the NLSP to a Higgs=Z boson and G˜ leading to hard b jets and charged N − N ¼ A B ð Þ leptons in the final state along with large =ET carried away CZ ; 20 ˜ NA þ NB by the G. Such a scenario has been extensively explored by experiments, including the LHC, with a primary focus on where NA refers to the number of events for ZD < 0.5 and the low-lying electroweak sector, leading to stringent NB represents events for ZD > 0.5, respectively. We list the constraints on the parameter space. The question that CZ values in Table VIII and observe that CZ is positive for one ventures to answer in this study is as follows: What 0 the Higgsino-like NLSP and negative for gauginolike NLSP. are the future prospects of detecting a Higgsino-like χ˜1 Note that the effect observed for the highly boosted Z boson NLSP at LHC? If detected, how can we ascertain the nature in CθZ also shows up for CZ highlighting the consistency and of the NLSP? importance of the isolation of the charged leptons. The We address this question bypffiffiffi studying a specific final þ − statistical uncertainty in the observed asymmetry has been state: ≥ 1b þ l l þ =ET at s ¼ 13 TeV motivated by shown in Table VIII and is calculated using [65] the presence of at least one b jet from the Higgs boson and 075040-13 DUTTA, MUKHOPADHYAYA, and RAI PHYS. REV. D 101, 075040 (2020) an opposite sign same-flavor lepton pair from the Z boson charged lepton as a reference and highlight its importance decay besides large =ET. We choose a few representative in observing the polarization of the parent gauge boson. We benchmark points encompassing a light and heavy also propose new variables which utilize the observed Higgsino sector with/without strong sector sparticles within asymmetries between the angular variables for the charged the reach of LHC. We find that such a signal is discoverable lepton coming from a parent longitudinal and transverse Z in the upcoming runs of the high luminosity LHC after boson. We do a full detector level simulation of the events suitable cuts are applied. It is important to emphasize that and study the asymmetries that show the characteristic such a semileptonic channel will prove crucial in identify- features of a longitudinal Z boson and observe substantial ing the nature of the NLSP, being relatively clean compared differences between a Higgsino and gauginolike NLSP. to an all hadronic final state, which may have a better This highlights the robustness of the constructed asymme- discovery prospect. Thus, simultaneous use of both chan- tries. Our analysis is applicable to other BSM scenarios, nels could be advocated for the purpose of discovery and which predict preferential production of longitudinally identifying the nature of the NLSP. We focus on the polarized gauge bosons as a consequence of the equiv- presence of a dominantly longitudinal Z boson arising alence theorem. from the decay of a Higgsino-like NLSP owing to the presence of the Goldstone boson as the longitudinal mode ACKNOWLEDGMENTS of Z after electroweak symmetry breaking. This is quite a striking identification criteria if observable, for a Higgsino- The work is partially supported by funding available like NLSP in sharp contrast to a dominantly gauginolike from the Department of Atomic Energy, Government of NLSP, which would dominantly decay to a transversely India, for the Regional Centre for Accelerator-based polarized Z. It is thus important to characterize the features Particle Physics (RECAPP), Harish-Chandra Research of the longitudinally polarized Z boson to ascertain the Institute (HRI). The research of J. D. is also partially composition of the parent NLSP. 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