Prepared for submission to JHEP

The Light Higgsino-dominated NLSPs in theSemi-constrained NMSSM

Kun Wang and Jingya Zhu

Center for Theoretical Physics, School of Physics and Technology, Wuhan University, Wuhan430072, China

E-mail: wk2016@whu.edu.cn, zhujy@whu.edu.cn

Abstract: In the semi-constrained NMSSM (scNMSSM, or NMSSM with non-universalHiggs mass) under current constraints, we consider a scenario where h2 is the SM-likeHiggs, χ0

1 is singlino-dominated LSP, χ±1 and χ02,3 are mass-degenerated, light and higgsino-

dominated NLSPs (next-to-lightest supersymmetric particles). We investigate the con-straints to these NLSPs from searching for SUSY particles at the LHC Run-I and Run-II,discuss the possibility of discovering these NLSPs in the future, and come to the follow-ing conclusions regarding the higgsino-dominated 100 ∼ 200 GeV NLSPs in scNMSSM:(i) Among the search results for electrowekinos, the multilepton final state constrain ourscenario most, and can exclude some of our samples. While up to now, the search results byAtlas and CMS with Run I and Run II data at the LHC can still not exclude the higgsino-dominated NLSPs of 100 ∼ 200 GeV. (ii) When the mass difference with χ0

1 is smaller thanmh2 , χ0

2 and χ03 have opposite preference on decaying to Z/Z∗ or h1. (iii) The best channels

to detect the NLSPs are though the real two-body decay χ±1 → χ01W± and χ0

2,3 → χ01Z/h2.

When the mass difference is sufficient, most of the samples can be checked at 5σ level withfuture 300 fb−1 data at the LHC. While with 3000 fb−1 data at the High Luminosity LHC(HL-LHC), nearly all of the samples can be checked at 5σ level even if the mass differenceis insufficient. (iv) The a1 funnel and the h2/Z funnel are the two main mechanisms forthe singlino-dominated LSP annihilation, which can not be distinguished by searching forNLSPs.ar

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Contents

1 Introduction 1

2 Introduction to NMSSM and scNMSSM 22.1 The Higgs sector of NMSSM and scNMSSM 32.2 The electroweakino sector of NMSSM and scNMSSM 5

3 The Light Higgs-dominated NLSPs in scNMSSM 63.1 Constraints from the recent search results at the LHC 73.2 Possibility of discovery at the HL-LHC in the future 12

4 Conclusions 14

1 Introduction

As an internal symmetry between fermions and bosons, Supersymmetry (SUSY) is an at-tractive idea. In the framework of SUSY, the strong, weak and hypercharge gauge couplings(g3, g2, g1) can be unified at the GUT scale (∼ 1016 GeV), and the large hierarchy prob-lem between the electroweak scale and the Planck scale can be solved. Besides, with theR-parity conserved, the lightest SUSY particle (LSP) is stable and can be a good candidatefor weakly-interaction-massive-particle (WIMP) dark matter (DM).

SUSY at TeV scale is motivated by the possible cancellation of quadratic divergencesof the Higgs boson mass. And the simplest implementation of SUSY is the Minimal Su-persymmetric extension to the Standard Model (MSSM). Since the soft SUSY breakingparameters is totally free in the MSSM, a dynamic way to get these parameters is morefavoured. In the minimal supergravity (mSUGRA) framework, the dynamics is used toderive soft SUSY breaking parameters, which is a top-down approach and all soft SUSYbreaking parameters unified at the GUT scale. The fully constrained MSSM (CMSSM)is the MSSM with the boundary conditions same as the mSUGRA. But in order to getthe 125 GeV SM-like Higgs, the MSSM need very large one-loop radiative corrections toHiggs mass, which makes the MSSM not natural. And there is a so-called µ-problem [1]in the MSSM, where the superpotential contained a term µHuHd, and µ is a dimensionfulparameter and can be chosen at any value artificially.

The Next-to Minimal Supersymmetric Standard Model (NMSSM) can solve the µ-problem by introducing a complex singlet superfield S, which can generate an effectiveµ-term dynamically. And it can easily predict a SM-like 125 GeV Higgs, under all theconstraints and with low fine-tuning [2]. The fully constrained NMSSM (cNMSSM) containsnone or only one more parameter than the CMSSM/mSUGRA, thus both of them are intension with current experimental constraints including 125 GeV Higgs mass, high mass

– 1 –

bound of gluino, muon g-2, and dark matter [3, 4]. So, we consider the semi-constrainedNMSSM (scNMSSM), which relaxing the universality of scalar masses by decoupling thesquared-masses of the Higgs bosons and the squarks/sleptons, which is also called NMSSMwith non-universal Higgs mass (NUHM) [5–7]. In the scNMSSM, the bino and wino areheavy because the high mass bound of gluino and the unification of gaugino masses atGUT scale, thus the light neutralinos and charginos can only be singlino-dominated orhiggsino-dominated.

In recent years, the Atlas and CMS collaborations have carried out many searches forSUSY particles, which pushed the gluino and squarks masses bounds in simple models upto several hundreds GeV and even TeV scale. While it is still possible for the electroweakinosector to be very light. The electroweakino sector of NMSSM was studied in [8–14], amongwhich different search channels were provided, such as trileptons [11], multi-lepton [12], andjets with missing transverse energy (E/T ) [13]. These motivated us to check the current statusof higgsino, in special SUSY models such as the scNMSSM, under direct-search constraintsand their possibility of discovery by detailed simulation.

In this work, we discuss the light higgsino-dominated NLSPs (next-to-lightest super-symmetric particles) in the scNMSSM. We use the scenario of singlino-dominated χ0

1 andSM-like h2 in the scan result in our former work on scNMSSM [7], where we consideredthe constraints including theoretical constraints of vacuum stability and Landau pole, ex-perimental constraints of Higgs data, muon g-2, B physics, dark matter relic density anddirect searches, etc. Thus in this scenario the χ±1 and χ0

2,3 are higgsino-dominated, light andmass-degenerated NLSPs. We first investigate the constraints to these NLSPs, includingsearching for SUSY particle at the LHC Run-I and Run-II. We use Monte Carlo to do thedetailed simulations to add these constraints. Then we discuss the possibility of discoveringthe higgsino-dominated NLSPs in the future at the High Luminosity LHC (HL-LHC).

This paper is organized as follows. First, in Section 2, we briefly introduce the model ofNMSSM and scNMSSM, especially the Higgs and electroweakino sector. Latter in Section3, we discuss the constraints to the light higgsino-dominated NLSPs, and the possibility ofdiscovering them at the HL-LHC. Finally, we draw our conclusions in Section 4.

2 Introduction to NMSSM and scNMSSM

The superpotential of the NMSSM with Z3 symmetry :

WNMSSM = WMSSM |µ=0 + λSHu · Hd +κ

3S3 , (2.1)

where the superfields Hu and Hd are two complex doublet superfields, the superfield S is thesinglet superfield, the coupling constrats λ and κ are dimensionless, and the WMSSM |µ=0

is actually the Yukawa couplings of the Hu and Hd to the quark and lepton superfields.When electroweak symmetry breaking, the scalar component of superfields Hu , Hd andS get their vacuum expectation values(VEVs) vu, vd and vs respectively. The relationsbetween the VEVs are

tanβ = vu/vd (2.2)

– 2 –

v =√v2u + v2d = 174 GeV (2.3)

µeff = λvs , (2.4)

where the µeff is the mass of Higgsino, like in the MSSM. In the following, for the sake ofconvenience, we refer to µ as µeff .

The soft SUSY breaking terms in the NMSSM is only different from the MSSM inseveral terms:

− LsoftNMSSM = − LsoftMSSM |µ=0 +m2S |S|2 + λAλSHu ·Hd +

1

3κAκS

3 + h.c. , (2.5)

where the S, Hu and Hd is the scalar component of the superfields, the m2S is the soft SUSY

breaking mass for single field S, and the trilinear coupling constants Aλ and Aκ have massdimension.

In the semi-constrained NMSSM (scNMSSM), the Higgs sector are considered non-universal, that is, the Higgs soft mass m2

Hu,m2

Hdand m2

S are allowed to be different fromM2

0 , and the trilinear couplings Aλ, Aκ can be different from A0. Hence, in the scNMSSM,the complete parameter sector is usually chosen as:

λ, κ, tanβ, µ, Aλ, Aκ, A0, M1/2, M0 . (2.6)

2.1 The Higgs sector of NMSSM and scNMSSM

When the electroweak symmetry breaking, the scalar component of superfields Hu , Hd andS can be written as

Hu =

(H+u

vu + HRu +iHI

u√2

), Hd =

(vd +

HRd +iHI

d√2

H−d

), S = vs +

SR + iSI√2

, (2.7)

where HRu , HR

d , and SR are CP-even component fields, HIu, HI

u, and SI are the CP-oddcomponent fields, and the H+

u and H−d are charged component fieldsIn the basis (HR

d , HRu , S

R), the CP-even scalar mass matrix is [15]

L 3 1

2

(HRd , H

Ru , S

R)M2S

HRd

HRu

SR

(2.8)

with

M2S =

M2As

2β +M2

Zc2β (2λv2 −M2

A −M2Z)sβcβ Ccβ + C ′sβ

(2λv2 −M2A −M2

Z)sβcβ M2Ac

2β +M2

Zs2β Csβ + C ′cβ

Ccβ + C ′sβ Csβ + C ′cβ M2S,SRSR

(2.9)

where

M2A =

2µ(Aλ + κvs)

sin2β(2.10)

C = 2λ2vvs (2.11)

C ′ = λv(Aλ − 2κvs) (2.12)

M2S,SRSR = λAλ

vuvdvs

+ κvs(Aκ + 4κvs) (2.13)

– 3 –

and sβ = sinβ, cβ = cosβ. Actually, there is a more common basis H1, H2, SR, where

H1 = HRu cβ −HR

d sβ (2.14)

H2 = HRu sβ +HR

d cβ (2.15)

and the H2 is the SM-like Higgs field. In the basis (H1, H2, SR), the scalar mass matrix is

different from eq.(2.9). But, since the rotation of the basis do not touch the third componentSR, the M2

S,SRSR will keep the same as in eq.(2.13). The Higgs boson mass matrix M2S′ in

basis (H1, H2, SR) is given by [16]

M2S′,H1H1

= M2A +

(m2Z − λ2v2

)sin2 2β , (2.16)

M2S′,H1H2

= −1

2

(m2Z − λ2v2

)sin 4β , (2.17)

M2S′,H1SR = −

(M2A

2µ/ sin 2β+ κvs

)λv cos 2β , (2.18)

M2S′,H2H2

= m2Z cos2 2β + λ2v2 sin2 2β , (2.19)

M2S′,H2SR = 2λµv

[1−

(MA

2µ/ sin 2β

)2

− κ

2λsin 2β

], (2.20)

M2S′,SRSR =

1

4λ2v2

(MA

µ/ sin 2β

)2

+ κvsAκ + 4(κvs)2 − 1

2λκv2 sin 2β . (2.21)

And comparing eq.(2.21) with eq.(2.13), it’s not hard to get M2S′,SRSR = M2

S,SRSR .In order to get the physical CP-odd scalar Higgs bosons, one can rotate the Higgs fields,

A = HIucβ +HI

dsβ . (2.22)

Then the Goldstone mode can be dropped off, and the CP-odd scalar mass matrix in thebasis (A,SI) become [15]

L 3 1

2

(A,SI

)M2P

(A

SI

)(2.23)

with

M2P =

(M2A λv(Aλ − 2κvs)

λv(Aλ − 2κvs) M2P,SISI

)(2.24)

whereM2P,SISI = λ(Aλ + 4κvs)

vuvdvs− 3κvsAκ . (2.25)

The mass eigenstates of the CP-even Higgs hi (i = 1, 2, 3) and the CP-odd HiggsAi(i = 1, 2) can be obtained by h1

h2h3

= Sij

H1

H2

SR

,

(a1a2

)= Pij

(A

SI

), (2.26)

where the matrix Sij can diagonalize the mass matrix M2S′ , and the matrix Pij can diago-

nalize the mass matrix M2P .

– 4 –

2.2 The electroweakino sector of NMSSM and scNMSSM

In the NMSSM, there are five neutralinos χ0i (i = 1, 2, 3, 4, 5), which are the mixture of

B (bino), W 3 (wino), H0d , H

0u (higgsino) and S (singlino). In the gauge-eigenstate basis

ψ0 = (B, W 3, H0d , H

0u, S), the neutralino mass matrix takes the form [15]

Mχ0 =

M1 0 −cβsWmZ sβsWmZ 0

0 M2 cβcwmz −sβcWmZ 0

−cβsWmZ cβcwmz 0 −µ −λvdsβsWmZ −sβcWmZ −µ 0 −λvu

0 0 −λvd −λvu 2κvs

(2.27)

where sβ = sinβ, cβ = cosβ, sW = sinθW , cW = cosθW . To get the mass eigenstates, onecan diagonalize the neutralino mass matrix Mχ0

N∗Mχ0N−1 = MDχ0 = diag(mχ0

1,mχ0

2,mχ0

3,mχ0

4,mχ0

5) (2.28)

where MDχ0 means the diagonal mass matrix, and the order of eigenvalues is mχ0

1< mχ0

2<

mχ03< mχ0

4< mχ0

5. Meanwhile, one can get the mass eigenstates

χ01

χ02

χ03

χ04

χ05

= Nij

B

W 0

Hd

Hu

S

(2.29)

In the scNMSSM, bino and wino were constrained to be very heavy, because of thehigh mass bounds of gluino and the universal gaugino mass at GUT scale, thus they canbe decoupled from the light sector. Then the following relations for the Nij can be can befound [17]:

Ni3 : Ni4 : Ni5 =

[mχ0

i

µsβ − cβ

]:

[mχ0

i

µcβ − sβ

]:µ−mχ0

i

λv(2.30)

We assume the lightest neutralino χ01 is the lightest supersymmetric particle (LSP) and

makes up of the cosmic dark matter. If the LSP χ01 satisfies N2

15 > 0.5, we call it singlet-dominated. And the coupling of such an LSP with the CP-even Higgs bosons is given by[17]

Chiχ01χ

01

=√

2λ[Si1N15(N13cβ−N14sβ)+Si2N15(N14cβ +N13sβ)+Si3N15(N13N14−κ

λN2

15)]

(2.31)In the singlet-dominated-LSP scenario, taking N11 = N12 = 0, the mass of LSP can be

written as mχ01≈Mχ0,SS = 2κvs. And from eq.(2.27), eq.(2.13) and eq.(2.25), one can find

the sum rule [18]:

M2χ0,SS

= 4κ2v2s = M2S,SRSR +

1

3M2P,SISI −

4

3vuvd(

λ2Aλµ

+ κ) (2.32)

– 5 –

In the case that h1 singlet-like, tanβ sizable, λ, κ and Aλ not too large, this equation canbecome

m2χ01≈ m2

h1 +1

3m2a1 (2.33)

The Chargino sector in the NMSSM is very similar to neutralino sector. The chargedHiggsino H+

u , H−d (with mass scale around µ) and the charged gaugino W± (with mass

scale M2) can also mixed respectively, forming two couples of physical chargino χ±1 , χ±2 . In

the gauge-eigenstate basis (W±, H±u,d), the chargino mass matrix is given by [15]

Mχ± =

(M2

√2cβmW√

2sβmW µ

). (2.34)

To obtain the chargino mass eigenstates, one can use two unitary matrix to diagonalize thechargino mass matrix

U∗Mχ±V−1 = MD

χ± = diag(mχ±1,mχ±2

) (2.35)

where MDχ± means the diagonal mass matrix, and the order of eigenvalues is mχ±1

< mχ±2.

Meanwhile, we can get the mass eigenstates(χ+1

χ+2

)= Vij

(W+

H+u

),

(χ−1χ−2

)= Uij

(W−

H−d

). (2.36)

In the scNMSSM, since M2 � µ, χ±1 can be higgsino-dominated, with mass around µ.With χ0

1 singlino-dominated, χ02,3 can be higgsino-dominated, with masses nearly degenerate

also around µ, and withN223+N2

24 > 0.5. Then with µ not large, smaller than other sparticlemass, the nearly-degenerate χ±1 and χ0

2,3 can be called the next-to-lightest SUSY particles(NLSPs). In this work, we will focus on the detection of the higgsino-dominated NLSPs(χ±1 and χ0

2,3) in the scNMSSM.

3 The Light Higgs-dominated NLSPs in scNMSSM

In this work, we use the scan result in our former work about scNMSSM [7], but onlyconsider the surviving samples with singlino-dominated χ0

1 (|N15|2 > 0.5) as the LSP,and impose the SUSY search constraints with CheckMATE [19]. We did the scan with theprogram NMSSMTools-5.4.1 [20], and considered the constraints there, including theoreticalconstraints of vacuum stability and Landau pole, experimental constraints of Higgs data,muon g-2, B physics, dark matter relic density and direct searches, etc. We also useHiggsBounds-5.1.1beta [21] to constrain the Higgs sector (with h2 as the SM-like Higgsand 123 < mh2 < 127 GeV), and SModelS-v1.1.1 [22] to to constrain the SUSY particles.The scanned spaces of the parameters are:

0 < M0 < 500 GeV, 0 < M1/2 < 2 TeV, |A0| < 10 TeV,

100 < µ < 200 GeV, 1 < tanβ < 30, 0.3 < λ < 0.7,

0 < κ < 0.7, |Aλ| < 10 TeV, |Aκ| < 10 TeV . (3.1)

– 6 –

Since in scNMSSM the bino and wino are heavy because of the high bounds of gluinomass, and the χ0

1 LSP is singlino-dominated in our samples, the neutralino and charginoNLSPs (χ±1 and χ0

2,3) are Higgsino dominated in this work. In the following, we focus on theHiggsino-dominated NLSPs in the scNMSSM, considering the constraints from the recentsearch results at the LHC Run I and Run II, and possibility of discovery at the HL-LHCin the future.

3.1 Constraints from the recent search results at the LHC

Unlike colored particles, the production rates of electroweakinos are very low at the LHC.But they can mainly decay to leptons plus E/T , and the SM backgrounds in these leptonschannels are relatively cleaner than jet channels at the LHC. In recent years, Atlas andCMS collaborations have released several search results with the LHC Run-I & Run-II datain such channels as 2`+E/T [23], 3`+E/T [24, 25] , 2γ+E/T [26] and Higgs+E/T [27]. In theiranalyses, they considered simple models, where purely higgsino or wino NLSP produced inpair, each decaying to χ0

1 plus h, Z, or W± in 100%.In this work, we use these result to constrain our specific surviving samples in scN-

MSSM. We consider the production and decay of χ+1 χ−1 , χ

±1 χ

02,3 and χ0

2,3χ02,3 at the LHC,

using CheckMATE 2.0.26 [19] to impose these constraints.Firstly, We use MadGraph5_aMC@NLO 2.6.6[28] to generate three types tree level process

at 8 TeV and 13 TeV:

pp→ χ+1 χ−1 , pp→ χ±1 χ

02,3 , pp→ χ0

2,3χ02,3 . (3.2)

Since the cross sections by the MadGraph are at tree level, we multiply them by a NLO K-factor calculated with the Prospino2 [29]. Then, we use the PYTHIA 8.2 [30] to deal withparticle decay, parton showering, and hardronization, use Delphes 3.4.1 [31] to simulatethe detector response, and use the anti-kT algorithm [32] for jet clustering.

After the simulation, we can get a ‘.root’ file. We use the CheckMATE2 to read this ‘.root’file. Then, we apply the same cuts in signal regions of the CMS and ATLAS experimentsat 8 TeV and 13 TeV, by using analysis cards which have been implement in CheckMATE2.At the last step, with the CheckMATE2 we get a r-value for each samples, which is definedas

r ≡ S − 1.96∆S

S95Exp.

(3.3)

where S is the total number of expected signal events, ∆S is the uncertainty of S, andS95Exp. is the experimentally measured 95% confidence limit of signal events number. So, a

model can be considered excluded at 95% confidence level, if r ≥ 1. If the r ≥ 1 in onlyone signal region, the model can also be excluded. We can get rmax, the maximal value ofr in different signal regions. The model is excluded if rmax ≥ 1.

In Fig.1, we show the production cross sections of χ+1 χ

02, χ

+1 χ

03, χ

−1 χ

02, χ

−1 χ

03, χ

+1 χ−1 ,

χ02χ

03, χ0

2χ02 and χ0

3χ03 at the 14 TeV LHC.

• The relation between the cross sections and the masses of final states is clear shown inall of these plots, that is, the masses of final states particles are heavier, its production

– 7 –

120 140 160 180 200

mχ±1[GeV]

140

160

180

200

220

mχ

0 2[G

eV]

400 600 800 1000 1200 1400

σ(pp→ χ+1 χ

02)[fb]

250 500 750 1000 1250 1500

σ(pp→ χ+1 χ

02)[fb]

100

200

300

400

500

600

700

800

900

1000

σ(pp→

χ− 1χ

0 2)[

fb]

130 140 150 160 170 180 190µ[GeV]

120 140 160 180 200

mχ±1[GeV]

140

160

180

200

220

240

260

mχ

0 3[G

eV]

200 400 600 800 1000

σ(pp→ χ+1 χ

03)[fb]

0 200 400 600 800 1000 1200

σ(pp→ χ+1 χ

03)[fb]

0

100

200

300

400

500

600

700

σ(pp→

χ− 1χ

0 3)[

fb]

130 140 150 160 170 180 190µ[GeV]

120 140 160 180 200

mχ±1[GeV]

120

130

140

150

160

170

180

190

200

µ[G

eV]

400 600 800 1000 1200 1400 1600

σ(pp→ χ+1 χ−1 )[fb]

140 160 180 200 220

mχ02[GeV]

140

160

180

200

220

240

260

mχ

0 3[G

eV]

100 200 300 400 500 600

σ(pp→ χ02χ

03)[fb]

140 160 180 200 220

mχ02[GeV]

−0.25

−0.20

−0.15

−0.10

−0.05

0.00

|N23|2−|N

24|2

1 2 3 4

σ(pp→ χ02χ

02)[fb]

140 160 180 200 220 240 260

mχ03[GeV]

−0.30

−0.25

−0.20

−0.15

−0.10

−0.05

0.00

|N33|2−|N

34|2

1 2 3 4 5

σ(pp→ χ03χ

03)[fb]

Figure 1. The cross sections of the surviving samples at 14 TeV LHC are showed in these plots.Upper Panel: The first and third plots show that in plane of mχ0

i− mχ±

1, the colors indicate

the cross section σ(pp → χ+1 χ

0i ), where i = 2, 3 for first and third plot respectively. The second

and fourth plot show that in plane of σ(pp → χ−1 χ

0i ) − σ(pp → χ+

1 χ0i ), the colors indicate the

values of µ which approximate to the masses of χ±1 and χ0

i , where i = 2, 3 for second and fourthplot respectively. Lower Panel: The first plot shows that in plane of µ −mχ±

1, where the colors

indicate the cross section σ(pp→ χ+1 χ

−1 ). The second plot shows that in plane of mχ0

3−mχ0

2, where

the colors indicate the cross section σ(pp → χ02χ

03). The rest of two plots show that in plane of

(|Ni3|2 − |Ni4|2) − mχ0i, the colors indicate the cross section σ(pp → χ0

i χ0i ), where i = 2 for the

third plot and i = 3 for the fourth plot.

cross section is lower, because that the phases space is suppressed by the mass of finalstate.

• From the second and fourth plots in the upper panel, the production cross sectionof χ+

1 χ0i is about 2 times of χ−1 χ

0i , for both i = 2 and 3. The Feynman Amplitudes

of the productions of χ+1 χ

0i and χ−1 χ

0i are the same, and the production of χ+

1 χ0i or

χ−1 χ0i need the initial state to be ud or du, respectively. So, the reason is that the

LHC is proton-proton collider, and the proton is a bound state of uud, so the partondistribution functions (PDF) for up quark is more than down quark, that leads to alinear relation of 2 times.

• From the third and fourth plots in lower panel, we can see that the production crosssection of χ0

2χ02 (i = 2 or 3) is very small, only a few fb. The reason is that the squarks

are very heavy, so σ(pp→ χ0i χ

0i ) mainly contribute from s channel through Z boson

– 8 –

resonance. The coupling of Z − χ0i − χ0

j is given by

CZχ0i χ

0j

=− i

2(g1sW + g2cW )(N∗j3Ni3 −N∗j4Ni4)(γµPL)

+i

2(g1sW + g2cW )(N∗i3Nj3 −N∗i4Nj4)(γµ PR) (3.4)

where the matrix N is neutralino mixing matrix. And we can see that if (|Ni3|2 −|Ni4|2) ≈ 0, then σ(pp→ χ0

i χ0i ) ≈ 0.

After using CheckMATE to checking our surviving samples, we notice that most of thesamples excluded are by the CMS analysis in multilepton final states at 13 TeV LHC with35.9 fb−1 data [24]. We checked that the relevant mechanism is χ±1 χ

02 produced and each

decaying to 2 body. Since the sleptons are heavier, the χ±1 and χ02 mainly decay to the χ0

1

LSP plus a W , or Z, or Higgs boson. The most effective process excluding the samples arepp→ χ±1 (W±χ0

1)χ02(Zχ

01) and pp→ χ±1 (W±χ0

1)χ02(h2χ

01).

The searching strategy for these two process is three or more leptons plus large E/Tin the final state. The CMS searches related to our process included the following signalregions (SR) SR-A, SR-C and SR-F

• SR-A: events with three light leptons (e or µ), two of which forming an opposite signsame-flavor (OSSF) pair. The SR-A is divided into 44 bins, according to the invariantmass of OSSF pairM``, the third lepton’s transverse massMT and the missing energyE/T .

• SR-C: events with two light leptons (e or µ) forming an OSSF pair, and one τhcandidate. The SR-C is divided into 18 bins, according to the invariant mass M``,the two-lepton ‘stransverse mass’ MT2(`1, `2) [33] instead of MT on the off-Z regions,and the E/T . The MT2 is defined as:

MT2 = minE/T1+E/T2=E/T

[max

{MT (~p `1

T1 , E/T1),MT (~p `1T2 , E/T2)

}], (3.5)

where the E/T1 and E/T2 stand for the missing transverse energy for the two leptonsrespectively. And it’s used to suppressed the SM background, since the large tt

background is at low MT2.

• SR-F: events with one electron or muon plus two τh candidates. SR-F is divided into12 bins, according to M``, MT2(`, τ1) and the E/T .

In Fig.2, we show the branching ratios of χ+1 on the plane of mχ0

1vs mχ+

1. We can

see that, the chargino χ+1 decay to χ0

1 plus a W boson in 100%: when the mass differencebetween χ+

1 and χ01 is greater than mW , the W boson is a real one; while when the mass

difference is insufficient, the W boson is a virtual one, that is, the decay is a three-bodydecay χ±1 → `νχ0

1. The low mass difference is negative for us to search for the SUSYparticles, since the leptons coming form a virtual W boson are very soft and hard to detect.

The main decay modes of neutralino χ0i (i = 2, 3) are to a χ0

1 plus a Z boson or a Higgsboson. In Fig.3, we show the branching ratios of the neutralinos χ0

i on the plane of mχ01vs

– 9 –

120 140 160 180 200

mχ±1[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ±1−mχ0

1= mW

0.0 0.2 0.4 0.6 0.8 1.0

Br(χ+1 → χ0

1W+)

120 140 160 180 200

mχ±1[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ±1−mχ0

1= mW

0.0 0.2 0.4 0.6 0.8 1.0

Br(χ+1 → χ0

1W+∗)

Figure 2. The samples in the mχ01versus mχ+

1plane, where colors indicate the branching ratios of

the chargino χ+1 to χ0

1 plus W boson. In the left panel, the W boson is a real one and the decay isreal two-body decay; while in the right panel the W boson is a virtual one and the decay is virtualthree-body decay.

140 160 180 200 220

mχ02[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ02−mχ0

1= mZ

mχ02−mχ0

1= mh2

0.0 0.2 0.4 0.6 0.8

Br(χ02 → χ0

1Z)

140 160 180 200 220

mχ02[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ02−mχ0

1= mZ

mχ02−mχ0

1= mh2

0.0 0.2 0.4 0.6 0.8

Br(χ02 → χ0

1Z∗)

140 160 180 200 220

mχ02[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ02−mχ0

1= mZ

mχ02−mχ0

1= mh2

0.0 0.2 0.4 0.6 0.8

Br(χ02 → χ0

1h1)

140 160 180 200 220

mχ02[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ02−mχ0

1= mZ

mχ02−mχ0

1= mh2

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Br(χ02 → χ0

1h2)

140 160 180 200 220 240 260

mχ03[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ03−mχ0

1= mZ

mχ03−mχ0

1= mh2

0.0 0.2 0.4 0.6 0.8

Br(χ03 → χ0

1Z)

140 160 180 200 220 240 260

mχ03[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ03−mχ0

1= mZ

mχ03−mχ0

1= mh2

0.0 0.1 0.2 0.3 0.4 0.5

Br(χ03 → χ0

1Z∗)

140 160 180 200 220 240 260

mχ03[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ03−mχ0

1= mZ

mχ03−mχ0

1= mh2

0.2 0.4 0.6 0.8 1.0

Br(χ03 → χ0

1h1)

140 160 180 200 220 240 260

mχ03[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ03−mχ0

1= mZ

mχ03−mχ0

1= mh2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Br(χ03 → χ0

1h2)

Figure 3. The samples in the mχ01versus mχ0

iplanes (upper i = 2, lower i = 3). From left to the

right, colors indicate the branching ratios Br(χ0i → χ0

1Z), Br(χ0i → χ0

1Z∗) (Z∗ means a virtual Z

boson), Br(χ0i → χ0

1h1) and Br(χ0i → χ0

1h2), respectively. The dash line and the dotted line meansthat the mass difference, mχ+

1−mχ0

1, equal to mZ and mh2 respectively.

mχ0i, where i = 2, 3. In these plots, we use the dash line, mχ+

1−mχ0

1= mZ , and the dotted

line, mχ+1−mχ0

1= mh2 , divided the plane into 3 parts.

• Case I: In the region mχ+1−mχ0

1< mZ , the neutralino χ0

i can only decay to χ01 plus

a virtual Z boson or a light Higgs boson h1. And we can see from the second andthird plots on the upper panel, the χ0

2 mainly decay to a virtual Z boson plus a χ01,

with only a small fraction to the light Higgs boson h1 plus χ01. On the contrary, the

second and third plots on the lower panel show that the χ03 mainly decay to the light

Higgs boson h1.

– 10 –

• Case II: In the region mZ ≤ mχ+1−mχ0

1< mh2 , the neutralino χ0

i can decay to χ01

plus a real Z boson or a light Higgs boson h1. As showed in the first and third plotson the upper panel, the χ0

2 mainly decay to a real Z boson with χ01. While according

to the first and third plots on the lower panel, the χ03 mainly decay to a light Higgs

boson h1 plus a LSP.

• Case III: In the region mχ+1−mχ0

1≥ mh2 , the neutralino χ0

i can decay to χ01 plus

a 125 GeV SM-like Higgs boson h2, which is showed in the fourth plot (upper andlower panels).

In the channel χ0i → χ0

1Z (i = 2, 3), like the χ±1 → W±χ01, when the mass difference is

insufficient the Z boson becomes a virtual one, which make it hard to detect. In the channelχ0i → χ0

1H (i = 2, 3), where the Higgs boson can be h1 or h2 and h2 is the SM-like one.Both h1 and h2 mainly decay to bb, thus the tt background is sizable at the LHC. In the casethat Higgs decay to WW, ZZ, or ττ, and W or Z decays leptonically, it might contributionto the multilepton final state. Since the light Higgs h1 is highly singlet-dominated, theχ0i → χ0

1h1 is very hard to contribute to the multilepton signal regions. Thus only theχ0i → χ0

1h2 can contribute to the multilepton signal regions visibly.It is worth to mention that, when the heavier neutralinos decay to the χ0

1 LSP, the χ02

and χ03 behave differently. Especially in the case II, χ0

2 prefers to decay to a Z boson plusχ01, Br(χ0

2 → χ01Z) > Br(χ0

2 → χ01h1); while χ0

3 tends to decay to a light Higgs boson h1plus χ0

1, Br(χ03 → χ0

1Z) < Br(χ03 → χ0

1h1). The couplings Ch1χ02χ

01and Ch1χ0

3χ01can be

written down as

Ch1χ02χ

01∼ λ (N14N23 +N13N24)S13√

2−√

2κN15N25S13 (3.6)

Ch1χ03χ

01∼ λ (N14N33 +N13N34)S13√

2−√

2κN15N35S13 (3.7)

where the N11, N12, N21, N22, N31 and N32 was set to 0 since the wino and bino are veryheavy and decoupled in the scNMSSM, and the S11 and S12 was set to 0 since |S13| �|S11|, |S12|. λ/

√2 � 1 and

√2κ � 1, so the couplings Ch1χ0

2χ01and Ch1χ0

2χ01are both very

small and roughly the same. While the couplings CZχ02χ

01and CZχ0

3χ01can be different from

each other according to eq.(3.4), which can be approximated to

CZχ02χ

01∼ g2cW

(N13N23 −N14N24) (3.8)

CZχ03χ

01∼ g2cW

(N13N33 −N14N34) (3.9)

where the g2/cW ∼ 1. When the two terms in eq.(3.8) or eq.(3.9) have different sign, anddo not cancel with each other, the couplings CZχ0

i χ01can be much larger than Ch1χ0

i χ01;

otherwise the cancel between the two terms can make CZχ0i χ

01smaller than Ch1χ0

3χ01. For

some surviving samples, CZχ03χ

01have the cancellation between the two terms, and that

leads to small Br(χ03 → χ0

1Z) and large Br(χ03 → χ0

1h1). Six benchmark points are listedin the Table 1.

– 11 –

Table 1. Masses and branching ratios for 6 benchmark points in the scNMSSM. The signal signif-icances in the last line are calculated with the luminosity of 300 fb−1, and with similar analysis ofmulti-lepton final state as in Ref. [24].

P1 P2 P3 P4 P5 P6mχ±1

(GeV) 183 173 175 189 175 187mχ0

1(GeV) 120 119 103 108 82 92

mχ02(GeV) 200 187 200 209 202 206

mχ03(GeV) 216 200 214 216 212 209

Br(χ+1 → χ0

1W ) 0% 0% 0% 100% 100% 100%Br(χ+

1 → χ01W∗) 100% 100% 100% 0% 0% 0%

Br(χ02 → χ0

1Z) 0% 0% 90% 93% 94% 95%Br(χ0

2 → χ01Z∗) 80% 65% 0% 0% 0% 0%

Br(χ02 → χ0

1h1) 20% 35% 10% 7% 6% 5%Br(χ0

2 → χ01h2) 0% 0% 0% 0% 0% 0%

Br(χ03 → χ0

1Z) 1% 0% 1% 13% 13% 38%Br(χ0

3 → χ01Z∗) 0% 0% 0% 0% 0% 0%

Br(χ03 → χ0

1h1) 99% 100% 99% 87% 33% 62%Br(χ0

3 → χ01h2) 0% 0% 0% 0% 54% 0%

ss = S/√B@300fb−1 (σ) 3.1 2.9 2.1 3.8 10.8 8.8

3.2 Possibility of discovery at the HL-LHC in the future

In this part, we investigate the possibility of detect electrowekinos in the future High Lumi-nosity LHC (HL-LHC). We adopt the same analysis of multilepton final state by CMS [24],only increasing the integrate luminosity from 35.9 fb−1 to 300 fb−1, to see the possibilityof discovery in the future. And we evaluate the signal significance by

ss = S/√B (3.10)

where S and B are the number of events from signal and background process respectively.In the Fig.4, we show ss on the planes of mχ0

1versus mχ±1

, mχ02and mχ0

3respectively.

We can see that most of the samples can be checked at 5σ level when the mass differencebetween LSP χ0

1 and NLSPs χ±1 , χ02,3 is sufficient. However, there are still some samples

can not be checked at level above 3 or 5 sigma. The main reasons is that the mass spectrais compacted, so that the leptons from the decay of NLSPs are very soft. Because PT cuthas to be very large at the LHC due to the large background, detecting soft particles is noteasy. Combining with Fig.2 and 3, we can learn the following facts:

• If χ±1 or χ0i (i = 2, 3) decays to a virtual vector boson, the area over the dash line in

all the planes, the signal significance is less than 5σ, and it is hard to check at theLHC with 300 fb−1 data.

• If χ±1 or χ02 decays to a real vector boson, the area between the dash and dotted line

in left and middle the planes, the signal significance can be larger than 5σ, and it iseasy to check at the LHC with 300 fb−1 data.

– 12 –

120 140 160 180 200

mχ±1[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ±1−mχ0

1= mW

0 3 5 7S/√B@300fb−1

140 160 180 200 220

mχ02[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ02−mχ0

1= mZ

mχ02−mχ0

1= mh2

0 3 5 7S/√B@300fb−1

140 160 180 200 220 240 260

mχ03[GeV]

40

60

80

100

120

140

mχ

0 1[G

eV]

mχ03−mχ0

1= mZ

mχ03−mχ0

1= mh2

0 3 5 7S/√B@300fb−1

Figure 4. The samples in the mχ01versus mχ±

1(left), mχ0

1versus mχ0

2(middle), mχ0

1versus mχ0

3

(right) planes. The colors indicates the signal significance, where red represents ss < 3σ, greenrepresents 3σ < ss < 5σ, and gray represents 5σ < ss. In the left plane, the dash line indicates themass difference equal to mW , mχ±

1−mχ0

1= mW . In the middle and right planes, the dash line and

dotted line indicate the mass difference equal to mZ and mh2respectively, that is, mχ0

i−mχ0

1= mZ

and mχ0i−mχ0

1= mh2 , where i = 2, 3 for the middle and right planes respectively.

40 60 80 100 120 140

mχ01[GeV]

0

50

100

150

200

250

300

ma

1[G

eV]

2mχ01

= ma1

2mχ01

= mh2

2mχ01

= mZ

0 3 5 7S/√B@300fb−1

Figure 5. The samples in the ma1 versus mχ01plane. The color convention is the same as in Fig.4.

The dash, dotted and dash dotted lines indicate 2mχ01, equal to ma1 , mh2 , and mZ respectively.

• The χ03 decay to a light Higgs h1, the area between the dash and dotted line in the

right plane, the signal significance is less than 5σ for some samples. The reason isthat the decay width of light Higgs h1 has been constrained by many experiments, soit’s hard to detect it.

• If χ0i (i = 2, 3) decays to a SM-Like Higgs, the area under the dotted line in middle

and right planes, it is also have ss > 5σ for most samples.

For the samples with insufficient mass difference between the NLSPs and the LSP, theintegrate luminosity at 300 fb−1 is not enough. So we also tried to increase the luminosityto 3000 fb−1, the result is that almost all samples can be checked with ss > 5 at 3000 fb−1.

– 13 –

In Fig.5, we show ss on the planes of mχ01versus ma1 . We can see that there are mainly

two mechanisms for dark matter annihilation: the a1 funnel where 2mχ01' ma1 , and the

h2/Z funnel where 2mχ01' mh2 or 2mχ0

1' mZ . Unfortunately, searching for the NLSPs is

helpless to distinguish these two mechanisms.

4 Conclusions

In this work, we have discussed the light higgsino-dominated NLSPs in the scNMSSM,which is also called the non-universal Higgs mass (NUHM) version of the NMSSM. Weuse the scenario of singlino-dominated χ0

1 and SM-like h2 in the scan result in our formerwork on scNMSSM, where we considered the constraints including theoretical constraintsof vacuum stability and Landau pole, experimental constraints of Higgs data, muon g-2,B physics, dark matter relic density and direct searches, etc. In our scenario, the binoand wino are heavy because the high mass bound of gluino and the unification of gauginomasses at GUT scale. Thus the χ±1 and χ0

2,3 are higgsino-dominated and mass-degeneratedNLSPs.

We first investigate the constraints to these light higgsino-dominated NLSPs, includingsearching for SUSY particle at the LHC Run-I and Run-II. We use Monte Carlo to do thedetailed simulations to add these constraints from search SUSY particles at LHC. Then wediscuss the possibility of discovering the higgsino-dominated NLSPs at the HL-LHC in thefuture. We use the same analysis by increasing the integrate luminosity to 300 fb−1 and3000 fb−1.

Finally, we come to the following conclusions regarding the higgsino-dominated 100 ∼200 GeV NLSPs in scNMSSM or NUHM-NMSSM:

• Among the search results for electrowekinos, the ‘multi-lepton final state’ constrainour scenario most, and can exclude some of our samples. While up to now, the searchresults by Atlas and CMS with Run I and Run II data at the LHC can still not excludethe light higgsino-dominated NLSPs of 100 ∼ 200 GeV.

• When the mass difference with χ01 is smaller than mh2 , χ0

2 and χ03 have different

preference on decaying to Z/Z∗ or h1.

• The best channels to detect the NLSPs are though the real two-body decay χ±1 → χ01W

and χ02,3 → χ0

1Z/h2. When the mass difference is sufficient, most of the samples canbe checked at 5 σ level with future 300 fb−1 data at the LHC. While with 3000 fb−1

data at the LHC, nearly all of the samples can be checked at 5σ level even if the massdifference is insufficient.

• The a1 funnel and the h2/Z funnel are the mainly two mechanisms for the singlino-dominated LSP annihilation, which can not be distinguished by searching for NLSPs.

– 14 –

Acknowledgments

We thank Yuanfang Yue, Yang Zhang and Liangliang Shang for useful discussions. Thiswork was supported by the National Natural Science Foundation of China (NNSFC) undergrant Nos. 11605123, 11547103, 11547310.

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