JHEP01(2021)161 ) L L − − B B Springer Gev, and Resonance E,F 2 a 500 August 10, 2020 January 26, 2021 : December 12, 2020 U(1) & : November 27, 2020 Symmetry

Home , Qaisar Shafi

JHEP01(2021)161 ) L L − − B B Springer GeV, and resonance e,f 2 A 500 August 10, 2020 January 26, 2021 : December 12, 2020 U(1) & : November 27, 2020 symmetry. This may be tested by : : 1 ˜ τ R 20 , m & and Bin Zhu Received U(1) β Revised d Published Accepted tan Published for SISSA by [email protected] https://doi.org/10.1007/JHEP01(2021)161 , Cem Salih Un resonance solutions are also shown around c 3 H TeV, and also coannihilation processes involving and symmetry and a global 5 . 2 1 L [email protected] H − , resonance solutions with . B Qaisar Shaﬁ, 2 ± 1 ˜ χ b A m U(1) ≈ 0 1 ˜ χ m . 3 . [email protected] , TeV. We identify chargino-neutralino coannihilation processes in the LHC searches.. While the relic density constraint excludes the bino-like Shabbar Raza, 1 − a The Authors. τ & 24 TeV c + .

We consider a class of SUSY models in which the MSSM gauge group is τ 0 , S,P ˜ ν [email protected] → , m ˜ µ A/H , m ˜ e Department of Physics, Chung-AngSeoul University, 06974, Korea E-mail: [email protected] Bartol Research Institute, Department ofUniversity Physics of and Delaware, Astronomy, Newark, DEDepartment 19716, of U.S.A. Physics, Bursa16059 Uludağ Bursa, University, Turkey Department of Physics, Yantai University, Yantai 264005, P.R. China School of Physics, NankaiNo.94 University, Weijin Road, Nankai District,Department Tianjin,China of Physics, Federal UrduScience University and of Technology, Karachi Arts, 75300, Pakistan b c e d a f Open Access Article funded by SCOAP mass region stau, selectron, smuon and sneutrinossolutions are for found masses around around 1 TeV, and 10.5 TeV. TeV In and addition, 1 TeV . Somethe of the neutralino, the model yields quite aThe rich phenomenology LSP depending relic on density the DM constraintabout composition. provides 3 TeV a and 4 lower TeV respectively, bound whichsuch is on testable the as in stop the HL-LHC. near and futurecan gluino collider masses experiments The be of chargino tested mass basedm on lies the between allowed 0.24 TeV decay and channels. about 2.0 We TeV, also which find Abstract: supplemented with aextension gauged introduces only electrically neutraldouble states, the and number the of new states SUSY partners inand effectively the singlino neutralino sector from that a now includes gauge a blino singlet (from superfield. If the DM density is saturated by a LSP Waqas Ahmed, Sparticle spectroscopy and darkextension matter of in MSSM a JHEP01(2021)161 2008.01568 Supersymmetry Phenomenology ArXiv ePrint: We show that all theseas solutions LUX-Zeplin will and be Xenon-nT. tested in future direct detection experimentsKeywords: such DM, it is still possible to realize higgsino, singlino and blino-like DM for various mass scales. JHEP01(2021)161 ] L − 19 B gauge L U(1) − as well as symmetry B 2 L Z − B U(1) (more precisely U(1) breaking is achieved SO(10) 4 symmetry. Among other R SO(10) discusses scanning procedure we present the salient features 3 U(1) 2 symmetry in SUSY models yields L we will present the collider and dark . − gauge boson together with its SUSY with a Higgs field carrying two units 4 5 B 0 symmetry with no anomalies is readily , the center of L 4 Z 6 − L Z B − U(1) B ]. The presence of this unbroken – 1 – U(1) 3 such as this is a major focus of the recent and U(1) 0 symmetry which is precisely ‘matter’ parity. This Z 2 ]. A supersymmetric extension of this scenario yields Z 2 ]. There appears a ]. Our investigation is based on the model proposed in ref. [ 13 18 – – 4 14 gauge symmetry is broken at tree level. A unique renormalizable . The search for 0 L 1 ˜ − 16 B B 2 ]. Turning this into a local 1 U(1) charge leaves unbroken a ), and it is realized as an unbroken symmetry if the R symmetry. A low scale breaking of L − (10) The rest of the paper is organized as follows: in section symmetry coincides with the subgroup of B U(1) 2 of the model including some ofand the various main constraints predictions. we Section have imposed.matter results In of section the model,MSSM. which include Our two conclusions new are dark summarized mark in candidates section not found in the fermion partner planned experiments [ where the superpotential is realized duethings to the the model presence contains diphoton ofpresent resonances a our as global results well for as the new collider. dark matter candidates. We ensures that the lightestviable supersymmetric dark particle matter (LSP) candidate.we is explore Motivated stable the by and lowa the energy if planned consequences neutral, Run-3 of it ata MSSM is the rich supplemented a LHC phenomenology by next [ year, symmetry. The spontaneousof breaking of Z Spin with fields in the tensor representations [ The Standard Model (SM) withsymmetry massless neutrinos [ possesses an accidentalachieved global through the introduction ofleft-right symmetric one models right-handed of neutrino ref.a per [ family, Minimal similar Supersymmetric to Standard the Model [MSSM] supplemented by a 1 Introduction 3 Phenomenological constraints and scanning4 procedure Sparticle spectroscopy and dark5 matter Conclusions Contents 1 Introduction 2 The model JHEP01(2021)161 L L by − and − B (2.1) L L B − ). This B 2 U(1) / and 3 0 0 0 0 2 1 1 1 1 1 1 B R m U(1) × L ) ) SM − ) 1 2 1 6 term is effectively ) ) ) B 1 6 and a R-symmetry G 0) 1) 1 6 0) 1 2 1 2 , 1) 0) − − − , − − ]. The Higgs mecha- L , , , , , , , 1 µ , , 1 , 1 1 3 1 3 1 1 , c 1 3 charge, and develops a , , , , , U(1) 20 c , , 2 , , ˆ e 2 , 1 1 2 2 1 1 1 ν l ˆ , 1 1 R , , , , , c 1 2 , , U(1) ⊗ d , , 1 2 1 6 1 2 2 3 ν ˆ (0 (0 1 3 − ( (1 (0 ( H (0 ¯ ( − ( − Φ SM e ( ( c is responsible for generating are the standard electroweak y U(1) ν G charges, and their VEVs spon- have twice the lepton number, d λ Φ + ], since the H ¯ L Φ c + , ˆ ν − d 23 l ˆ u – u H ˆ B H and u H 21 1 1 1 1 1 3 3 3 3 3 3 ν Φ y SH , lepton number which are singlets under the MSSM gauge + µ B , and Generations only carries a c λ c ¯ Φ are the usual quark and lepton superfields of ˆ d ν S c ˆ q 1 2 e d . Since U(1) ) + – 2 – problem [ ˆ , d u and 2 ∗ ∗ R ∗ R R ∗ R H l ˜ ¯ ˜ c q φ φ 2) S ˜ − ˜ e ν d u d H H ν Φ M µ y − , Spin , l lead also to significant implications for inflationary − + S , c c ¯ ¯ summarizes the quantum numbers of the various su- Φ Φ = 2( d ˆ u ∗ ∗ d u , , ˆ , ∗ q R ∗ R 1 l ¯ ˜ ˜ ˜ L q 0 R R 0 φ φ fields carry non-zero S (Φ c ˜ ˜ e u ν ˜ H H ˜ d u − symmetry. Furthermore, u ˆ ¯ and Spin 0 Φ H B , κS u L q Q y + Φ − B , and = . Table S i has Φ ]. S W v are the Yukawa couplings and the family indices are generally sup- U(1) ¯ h Φ) 25 e µ d u , ˆ l ˆ ˆ ˆ ˆ ˆ ˆ e q ˆ ¯ ˆ d ν u y S Φ Φ ˆ ˆ λ Φ( H H 24 , ν ≡ y , µ instantons. We supplement the gauge symmetry of MSSM with local d Higgs Superfields y Matter Superfields L , u . Chiral superfields and their charges under the local guage symmetry y -symmetry. , where, for simplicity, we ignore the tiny non-perturbative violation of R R SU(2) phenomenology [ they are called as bileptinos.non-zero The VEV superfield after softcan SUSY provide breaking a proportional resolution to toobtained the the as gravitino MSSM mass ( perfields. In addition, pressed for simplicity. Also, MSSM including the right handedHiggs neutrinos superfields. The taneously break the a Majorana mass termsymmetry only for if the right-handed neutrinos. Such terms preserve the where U(1) the symmetry whose spontaneous breaking isnism achieved includes as three described new super ingroup. [ fields The full renormalizable and gauge invariant superpotential can be written as 2 The model The renormalizable superpotential of the MSSMglobal with symmetries, R-parity namely conservation baryon possesses number three Table 1 U(1) JHEP01(2021)161 as are ) (2.9) (2.4) (2.5) (2.6) (2.7) (2.8) (2.3) ˜ , the S † , i, j ˜ ¯ Φ N . 0 ˜ ˜ χ Φ φ,ik ,                     0 T 0 j 0 j m 2 S. d u | ˜ ∗ λ λ , and B h.c. (2.2) 3 6 ˜ 0 ˜ ¯ ˜ ∗ 18 S , R,k φ φ ∗ ∗ j j λv λv | N 0 ˜ S S u ν A 2 0 0 0 2 + N 2 S 1 1 N N ˜ ν ¯ √ √ φ m m H ∗ = R,i ij Y m + v , j j − − ˜ δ ν 2 0 d X X ˜ ¯ (bileptinos) can mix ¯ φ + φ λ φ ˜ = 0 φ H ˜ ¯ φ v BL 2 2 17 ¯ ˜ = = v Φ ˜ , diag χ ˜ | φ φS + ν 1 0 0 ¯ B N 0 φ √ ˜ M d T φ κ BY m m m | g 2 ˜ g ˜ ¯ 0 2 φ W , − H + ˜ and ˜ 0 ¯ φ ST B ¯ m ˜ φ φ v ˜ ¯ = φ A ˜ B, v 1 2 φ Φ c ) as ˜ ¯ ( ˜ ¯ φ φS 16 φ + B 00 0 0 0 , ν BY ˜ g φS + 2 m 8 m N g λ | − 0 2.4 − − φ µ + | = λ d 0 2 φ BB u v , m ¯ 0 φ ˜ c ,..., v B φ φ m v ˜ ν M ST 0 v v λ BL , , YB B 0 0 0 0 0 15 BB + 2 ˜ u B YB + g g T B 0 j 0 j 0 j (singlino), = 1 g g M N 1 2 λ M ˜ − λ λ λ H B , 1 2 2 2 5 8 S − κ λ − ∗ ∗ ∗ + ν,ij d 1 j j j √ s d T 0 u u u H N N N + u v v κA ˜ − λv v λv 2 H , i, j L,j – 3 – + 1 j j j 2 2 0 g j ˜ 1 ν 1 YB g X X X R,j 14 = 2 1 = √ stand for bino, wino, higgsinos, blino, bileptinos √ λ µ g 1 2 ˜ ν λ 1 2 N − ij ∗ − − κ R,i = = = S ˜ ¯ φS ˜ ν T 0 N d ˜ 0 2 ν,ij + 0 s ST u u d v ˜ , 0 B d u 0 v ˜ d m = µ H W v λv 1 λv ˜ and λ 2 H YB 2 g 0 2 H 0 i , m 1 1 g ∗ 0 g R,i 1 2 d + ˜ s √ χ √ A ˜ ¯ 1 2 1 2 φ 13 ν v µ − H − − 2 m , − N λ + ˜ ν,ij λ ˜ φ + u T 2 + d v , = 1 S 0 v 2 2 L,j 0 √ 2 0 0 0 0 0 0 0 0 g ˜ L,j ˜ ν µ B g M 1 2 ˜ ˜ ˜ e ST − λ W 2 1 , − 2 l,ij T 0 , ,S , u ∗ 12 R,i + = ¯ 0 j 0 j 0 j , φ ˜ ˜ d ν m H 0 φ N ˜ 2 v u φ v λ λ λ + v u ˜ ¯ v 1 1 φ , 4 7 1 ∗ L,i ∗ ∗ ∗ 1 j j j g 0 0 0 + BB 0 d BY H ν g M 1 2 m BY g ˜ κM N N N ˜ 1 2 MSSM M H g B matrix and it can be constructed in the basis 0 − − + ˜ − L , j j j L 11 8 0                     X X X = N × ˜ = W = = = = 8 = SB , 0 0 S ˜ ¯ u ˜ φ ˜ B ˜ 0 1 L χ T B ˜ H χ − m After diagonalizing the mass matrix given in eq. ( As stated earlier, even though the chargino sector remains intact, the neutralino sector The relevant soft supersymmetry breaking (SSB) terms are given as follows: is also allowed to mix with the other neutralinos. Thus the neutralino mass matrix be- 0 where and singlino receptively. The LSP neutralino can be written as follows: neutralino mass eigenstates can be obtained as , with where Z comes an where generation indices. is enriched, since thewith fermionic the components MSSM of neutralinos after the symmetry breaking. In addition, the superpartner of JHEP01(2021)161 . ]. L is = = − 2 and B = 0 29 g 22 , , L c ν arising GUT ν ≈ 28 Y deviates λ U(1) M 3 3 g g = GUT SU(2) ]. Note that . Concerning , M L 11 39 , C c − ν B λ , receives the largest 3 ]. SU(3) GeV) [ g U(1) TeV 3 . 42 5 , , , , , , , , all of the SSB parameters 3 3 3 3 2 2 10 41 ≤ ≤ ≤ ≤ ≤ ≤ ≤ = 173 GUT at the low scale. Since we set 0 t 0 0 0 GeV [ d M m 3 µ /m 2 H /m κ /m /m λ µ L 0 κ 0 m λ − L A A ]. Also for simplicity, we set A 1 6= 33 ] generated with SARAH 4.9.0 [ ≤ ≤ ≤ ≤ ≤ ≤ ≤ u 3 3 3 3 2 2 1 H 27 − − − − − − m , 26 – 4 – , , , , , between the right-handed neutrinos and the MSSM c , ν , λ are the MSSM gauge couplings for 20 TeV 60 2 5 TeV 5 TeV 5 TeV 1 corresponds to the gauge coupling for ] by requiring g ≤ ≤ ≤ ≤ ≤ ≤ L via the renormalization group equations (RGEs). 38 0 is determined at the low scale, and values larger than about 2 0 − β – β / 0 c Z B S 1 ν and g 34 v m λ M M tan 2 GUT tan g as a diagonal matrix, with the entries given as M , ≤ ≤ ≤ ≤ ≤ ≤ ], and it is allowed to deviate from the unification point up to about 3 Φ 3 2 1 0 0 4 g . 32 0 . – . With the boundary conditions given at 2 30 3% at the GUT scale, the required separation between the masses of the MSSM κM . Note that d , where 4 . = H L 0 ], but it can shift the Higgs boson mass by 3 − m respectively, while B L ' 40 g = Y One of the important theoretical constraints arises from radiative electroweak symme- We take the Yukawa matrix, We have performed random scans over the following parameter space: can yield Landau pole below the GUT scale [ 33 u , . If a solution does not satisfy this condition within this allowance, SPheno does not = c H 4 ν . 1 try breaking (REWSB) [ m Higgs fields can be generatedtop through quark. the RGEs In with arbitrary our large case, Yukawa coupling radiative for symmetry breaking is also employed for the singlet Higgs field λ 0 Finally, we set thethe top sparticle quark spectrum mass is to notmass its very [ central sensitive to value one ( or two sigma variation in the top quark where guarantees that the solutions are compatibleno with more the than unification condition, and along with the gauge and Yukawa couplings are evolved back to the weak scale. the contributions from thefrom threshold some corrections unknown to breaking mechanisms thecontributions of gauge [ the couplings GUT gauge at group, 3% generate an output for such solutions by default. Hence, the existence of an output file In this package, thethe weak scale unification values scale ofdetermined the by gauge the and requirement Yukawag of couplings the are gauge evolved to couplingU(1) unification, described as like, singlino-like andGUT blino-like scale. LSPs, despite the universal gaugino3 mass term at Phenomenological constraints the andWe scanning have procedure employed SPheno 3.3.3 package [ In addition to bino-dominated LSP, the variety of neutralinos can also result in higgsino- JHEP01(2021)161 , ∼ γ s A (3.7) (3.3) (3.4) (3.5) (3.6) (3.1) (3.2) X m → ∼ s B H ], which ex- , m in the MSSM − 43 µ h + m µ and the LSP, which ] set bounds on the → . , s 4 , . . 63 9 4 B WZ , − , ] − − sector. Another important 62 10 64 10 10 L × ) GeV . × × 350 GeV − 2 TeV 2 87 5 . . . . B 4 3 1 & ˜ µ > q e ≤ ≤ ≤ 11(syst . ) ⇒ 0 ) − ]. Furthermore, we apply the following τ ) 127 GeV µ ± + τν ) sγ 45 ≤ . meson such as the , , m µ ], we consider the following constraints on h − → → 44 61 ]: → m B u b – – 5 – s B ≤ 2 TeV 53 59 B . , 21(stat 100 GeV = ] . 2 BR( 0 52 BR( 47 < BR( ± & 0 1 g e e χ , these decays also bound their masses as ≤ ≤ ≤ 09 ]. . m ± m 9 4 4 123 GeV meson decays yield a strong impact on the MSSM Higgs 46 − − − H based on [ − since the SM predictions are in a good agreement with the 10 10 10 B ) = 125 × × × a and h ( 6 GeV) [ the experimental combination for the Higgs mass reported by the . ) if ]. 99 70 m A b 1 . . we impose the bounds that the LEP2 experiments set on charged ( 2 0 58 , 100 – H 54 & ] — we apply the constraint from the Higgs boson mass to our results as 48 GeV [ is an appropriate state including a strange quark, the results of our analyses are s 300 X & Searches for two and three leptons plus missing energy [ ± H electro-weak production of charged-neutral higgsinoscan decaying be to approximately translated into the following condition [ m Current LHC searches: gluino and first/second generation squark masses The constraints from rare spectrum. The lightestconsistent CP-even with Higgs these boson constraints.decays should come Since be from the the supersymmetric SM-like contributions Higgs to boson these to rare be required to be consistentfollowing with constraints the from measurements B-physics for [ such processes. Thus we employ the Rare B-meson decays: experimental results for the rarewhere decays of Due to an estimated— 2 GeV see theoretical uncertainty e.g. in [ follows the calculation of constraints successively. LEP constraints: sparticle masses ( Higgs boson mass: ATLAS and CMS Collaborations is [ constraint comes from thecludes relic regions abundance where the of charged theour SUSY stable scans, particles such we charged as allow particles only stau [ condition and solutions is stop for satisfied. become which one the In of LSP. scanningMetropolis-Hasting In the the parameter neutralinos algorithm space, is described we the use in LSP our and [ interface, REWSB which employs symmetry, and it constrains the Yukawa couplings in the JHEP01(2021)161 – σ ≥ 14 L [ (3.8) (3.9) ) the − 0 1 B Z − CL limit /g fb 0 ]. Bounds ]. We also CL limit is Z % 70 74 M % CL [ ) respectively. The ) the 95 1 % the 95 1 uncertainty. They are − 1 − exposure [ . σ − ab ) fb 5 y σ ) 95 fb · 1 planes. Grey points satisfy t − µ fb 126 (5 − . 0 1 ˜ t ≤ m ]: 5 TeV 66 ≤ and 0 CL @ 27 TeV (15 ˜ g Z m % M − – 6 – ≤ 1 ˜ t ), 95 (Planck 2018) 1 m 2 − h for the discussion on the phenomenology of neutralino ab ) 4 c CDM ( ) the mass limits for the gluino and stop are about 2.1 TeV ]. All points lying above these upper bounds have been Ω is being constantly updated by comprehensive analyses. The 1 0 − 69 ≤ ] guarantees avoiding possible exclusions on our solutions due Z – exposure and XENONnT with 20 fb in our scan is only for keeping its mass range in the testable era 18 M 67 y 0 114 comes from negative results from the LEP data as . · Z 0 0 t Z M TeV [ ] are also shown. M 4 ]. Similarly at the LHC Run-3 @ 13 TeV (300 ≥ 72 , 74 0 mass. Thus we restrict its range in our scan as , we show plots in the Z 0 71 1 Z M ]. Even though considering its decay modes can lower the mass bound on 65 CL HL-LHC, @ 27 TeV (15 CL limit for gluino mass is about 2.4 TeV, and with 3000 ] that @ 13 TeV (137 can be from 1 to 8 TeV (green points). If we impose the DM constraints, then the In figure We use the current LUX and XENON1T spin-independent (SI) DM cross section with Finally the bound on 73 % % 1 ], setting ˜ t TeV [ for stop mass isdisplay various about bounds 2.4 from TeV High-Luminosity andsearches. (HL) rises and Vertical to High-Energy brown, @ 2.9 TeV 27 blue95 TeV (3000 (HE) and LHC yellow lineshorizontal represent purple, the black and reach cyan for lines the represent for stop the mass reach at for the gluino mass with 5 m lower mass limits ofin gluino [ and stopand rise 0.9 to TeV respectively. 4 TeV and For95 3 the TeV respectively. LHC Run-3, Itabout namely is 2.9 LHC TeV reported [ @ 13-14 TeV (300 the REWSB and theand B-physics LSP constraints. neutralino Red conditions. points2018 form bounds a Green on subset the points of relic greenalso satisfy abundance points of consistent the and the with satisfy mass LSP the the neutralino bounds We Planck within current see dark in matter our direct present detection scans bounds that, presented by the LUX. gluino mass can be between 2.2 to 10 TeV, while 4 Sparticle spectroscopy andIn dark this matter section we arethe focusing constraints on discussed the above. sparticle spectrum consistent with mass bounds and excluded from the plots.of We also XENON1T show with the 2 projectionfor of spin-dependent future cross limits section ofexperiments of already [ DM published set by the current LUX and future LUX-ZEPLIN the current measurements of the Planck satellite [ bounds as a constraint [ The upper bound on of the current and near future experiments. DM searches and relic density: DM in our scenario, we impose the following constraint for the LSP relic density, based on severest bound on 6 17 to the light JHEP01(2021)161 ˜ g ]. m 75 − ˜ q m ) respectively [ 1 uncertainty. They are − σ 5 ab . Moreover if the stop decays 1 − ab ]. If the stop decays to higgsinos, it CL @ 27 TeV(15 76 % ] for a discovery. integrated luminosity due to additional SUSY 1 78 – 7 – − ) and 95 ab 1 − ab displays the results for the squark masses in the 1 can lie in a wide range from 2 to 10 TeV (green), the constraint on ˜ q @ 27 TeV(15 m σ ), 5 1 − ab . Grey points satisfy the REWSB and the LSP neutralino conditions. Green points satisfy the gluino discovery limit is about 11 TeV [ The top right panel of figure As far as future searches at @ 100 TeV proton-proton collider are concerned, with 3000 1 − can be discovered (excluded)through up gluinos to to LSPs, 6 onebackgrounds (7) needs from TeV 30 gluino with pair 3 production [ plane. Even though assumption that the LSP isis formed significantly by extended the in MSSM ourdeviate neutralinos. model, from these Since one limits, the can when neutralino analyzein the sector by the LSP how MSSM neutralino much framework. contains the additional implications states can not included fb @ 14 TeV(3 We see that thesegreen LHC color searches and may some probeabove part nearly mentioned of half limits the of on red the the points probe parameter shown of space in the shown stop the in and plots. gluino On mass the scales other are hand, based on the the Figure 1 the mass bounds andPlanck B-physics 2018 constraints. bounds on Red theconsistent points relic with form the abundance a current of dark subset thedescription matter LSP of direct of neutralino green detection dashed within bounds points horizontal presented and and by vertical satisfy LUX. lines See in text for left the panel. JHEP01(2021)161 0 1 ], @ ˜ χ 62 1 m − − S 1 problem ˜ ν TeV (red − 30 ab 5 m varies from . µ , 1 | 0 1 µ ˜ χ | and . m 1 ± 1 − − ˜ χ ]. The probing scale 1 ˜ e m . The diagonal lines 3 ab 76 m [ 1 TeV are excluded [ ≈ ). As mentioned earlier, , 1 1 0 1 0.2 TeV are allowed since . boson and charged Higgs 0 1 − ˜ χ ˜ 1 χ − 3.7 m m | ∼ , and the correct relic density . W 0 1 − µ ]. However, the existence of a | ˜ χ . 1 ± i ˜ τ ˜ 86 χ m plane show that one can identify – m 24 m . 0 1 ∼ , 83 ˜ 0 χ 0 1 ]. If the mass difference between the 1 ˜ χ ˜ τ m 87 term, since Light Higgsions are required m m − term. We expect that we may avoid little µ − ± 1 d ˜ ± 1 χ ˜ χ GeV [ H m u from 0.1 TeV to about 1.3 TeV (green points); m – 8 – 0 1 500 ˜ χ SH µ m ≥ λ ± i ] with integrated luminosity of ≈ ˜ TeV, in which χ -problem). 1 1 µ 77 ˜ . τ m 1 m . ]. 1 ˜ τ 88 m ] with a relatively light discovery reach is about 16 TeV and 20 TeV thus covering entire . 82 σ – 9 . plane represents our solutions for the stau and LSP neutralino masses. 0 79 0 1 ˜ χ planes. The color coding is the same as in figure stand for the lightest and heaviest charginos respectively. On the other m 0 1 , we present the plots in the ˜ χ 2 − 2 , m 1 TeV). The approximate mass degeneracy between the LSP neutralino and the ˜ τ − 1 integrated luminosity is collected in the collider experiments with 14 TeV center of . m = 1 ] for possible solutions to 0 P 1 1 i ˜ ν term in this model, arises from − 22 & m The In figure In the bottom panel, we see that the MSSM higgsino mass parameter µ symmetry and its spontaneous breaking lead to the domain wall problem in NMSSM ± 1 0.15 TeV to 4 TeV (for green points), and the DM constraint bounds it from below at ˜ χ 3 It is seen thathowever, one a can significant realize portionon of the these relic solutions abundancestau are of mass excluded range the by as LSP theis neutralino. Planck achieved 2018 through The bound the relic stau-neutralino density coannihilation constraint processes. restricts the Interestingly, it is also chargino and LSP neutralinoboson, is then less these than bounds the onm masses the chargino of mass the islightest reduced chargino to those is from one LEP2probed of results up (i.e. the to characteristics about features 1 TeV [ of higgsino-like DM, which can be charginos based on their decaywith modes. a If the suitable chargino is SMwhere allowed particle, to decay then into a thehand, stau solutions if along with the stausbound is are less heavy restrictive, and namely the charginos cannot decay into them, then the mass the coannihilation channels ofconsistent the thermal relic LSP density. neutralino Evenmass with though at appropriate it around is sparticles 2.0 possible TeV,the to the to chargino-neutralino yield realize results coannihilation a the in processes lightestpoints the chargino around for the diagonal line). A recent analyses has revealed new mass bounds on the Z (See [ and represent solutions with degenerate masses of the particles displayed. These plots identify the neutralino mass in this casethe is heavier than 100 GeVhierarchy (see problem eq. [ to address the electroweak fineis tuning also problem. accommodated Indeed, in this Next resolution to to MSSM the (NMSSM) [ In addition to it,100 TeV it collider is the shown 5 model in parameter [ space. ∼ about 2.8 TeV (red). We also note that the solutions with 300 fb mass energy, the squarks canto be about probed 3 TeV up when the tofor integrated 2.7 TeV, luminosity the while reaches squarks this to will 3000 scale be fb isthus, about expected nearly 6.6 to half TeV in raise of the our collisions solutions of 33 will TeV center likely of be mass tested energy, and in near future collider experiments. the relic density of the LSP neutralino (red) shrinks this range to [4, 10] TeV. When the JHEP01(2021)161 0 m planes. The 0 1 ˜ χ ). m 2 − P 1 ˜ ν m and 0 1 ˜ χ m − S 1 ˜ ν m , 0 1 ˜ χ m (also see Point 3 in table − ˜ τ 1 ˜ e m m – 9 – , ∼ 0 1 ˜ χ ˜ µ m m − ≈ 1 . The diagonal lines represent the solutions with degenerate ˜ τ ˜ e ). Such solutions also favor selectron(smuon)-neutralino 1 m ˜ µ m , 0 1 m ˜ χ m ≈ ˜ e − ± 1 m ˜ χ m ], the CMS collaboration interpreted the data in the context of simplified 89 . Plots in the values, which also yield 0 A A dedicated search around these points can generate more points in these regions. In (also with smuon since coannihilation processes, and they canand be identified in the regions with relatively small an analysis [ Figure 2 color coding is themasses same of as the in particles figure displayed. possible in this region that the selectron mass is nearly degenerate with the neutralino mass JHEP01(2021)161 . , 0 1 0 1 ˜ ˜ χ χ 1.0 m m ∼ show − ) 2 = 2 2 P 1 A 3 ν ( m ,H 2 m ) are bounded . The diagonal A,H 3 . Even though 0 1 1 H m ˜ χ m m and = 2 strictly restrict its mass 2 3 , we have red points from planes, and the resonance 0 1 H S 1 ,H ˜ 0 1 χ 2 ν ˜ m χ m ,H ) sneutrino masses versus the m 2 2 P 1 A − ν planes. The color coding is the same ≈ m 3 0 1 2 ˜ χ H A m m m − 3 H and m 0 1 ˜ χ m and – 10 – ) and CP-odd ( 0 1 − ˜ χ can lie in a wide range from a few GeV to about S 1 2 ν , we see red points along the line from m 2 H P 1 A − m ν 2 m H interactions, and such a slepton can be probed up to only m , L 0 1 ˜ χ planes. The color coding is the same as in figure m 0 1 − ˜ SU(2) χ A m m − TeV. The CP-even Higgs boson masses ( 3 3 . H 1 plane shows that m 0 1 . , we show the results for various Higgs resonances with plots in the ˜ χ 3 2 m . The diagonal lines indicate the Higgs resonance solutions for which and A 1 0 1 m − ˜ . Plots in the χ 1 to 1.4 TeV. Similarly, for 2 . m A ∼ 1 − In figure m . 2 S 1 1 ν H lines indicate the Higgsthe resonance solutions for12 TeV which (red points), theas resonance solutions with 3.5 TeV and 6 TeV as seen from the LSP neutralino mass. We seem that along the diagonalto line 1.1 TeV. for Such points indicate sneutrino-neutralino coannihilation processes. m LSP cases. ThisThe bound significant slightly reduction decreases in tothey the do 400 GeV, not bound if participate happens theabout when slepton 290 GeV. the is We slepton are onlyefficiently optimistic is left-handed. that probe right-handed, the the since updates parameter fromour the space results future of for experiments our will the more model. lightest CP-even The ( last two plots of figure Figure 3 as in figure SUSY models such that the sleptons can be probed up to about 450 GeV in the massless JHEP01(2021)161 , ]. 68 ] of and 91 , 70 0 1 ˜ χ 90 m − 2 h Ω , ] bounds, and the 0 1 ). In the bottom-left ˜ χ ] and XENON1T [ ] of XENON1T with 69 m 3.9 , 67 planes. Turquoise points 70 − 68 0 1 ˜ χ TeV. These Higgs bosons SD m 5 σ . − , 2 0 0 1 Z ˜ χ . M m 3 ] and the cyan dashed line represents , exposure, respectively. In the bottom- 2 − y 71 H and · processes. The current LHC analyses SI t m 0 1 σ ˜ χ − m τ ] and XENON1T [ + − τ 67 2 . h Ω → – 11 – , 0 1 ˜ χ m A/H − SD σ , 0 1 ˜ χ m ) constrain them further, − 0 1 ˜ χ SI ] σ m exposure and XENONnT with 20 TeV, if these Higgs bosons decay only into a pair tau-leptons [ 72 2 y 1 · t ≈ & 3 i , 2 ,H display our results with plots in the planes. Turquoise points represent higgsino-type neutralino, brown points H 2 A 4 0 1 m ˜ χ m . Plots in the m − Figure 0 Z ] bounds, and the dashed orange and brown lines show the projection of future limits [ M are bino-type neutralino solutions,represent orange blino-type points neutralino show solutions.lines singlino respectively solutions, In represent and the the red currentdashed top-left LUX points orange [ and panel, brown the lines show solid the black projection of and future red limits [ solutions ( can be constrained furtherresult over in the 69 XENON1T with 2 right plot, the blackthe solid future line LZ is bound the [ current LUX bound [ Figure 4 represent higgsino-type neutralino, brownshow points singlino are bino-type solutions, neutralino andlines solutions, in red the orange points top-right points panel represent indicatepanel, the blino-type DM the relic neutralino solid density black bounds solutions. and given in red The eq. lines ( horizontal respectively represent the current LUX [ JHEP01(2021)161 plot in figure 0 1 versus the LSP ˜ χ 0 Z m M − 2 ]. In the bottom-right h Ω 93 , 92 GeV. Furthermore, the bino-like GeV, the Planck2018 bound within 800 100 . ] and the cyan dashed line represents the 0 1 & ˜ 71 χ exposure, respectively. In the top-right plot, 0 1 m ˜ χ y · m – 12 – t is not very restrictive for the low scale results of 0 TeV. All this discussion, on the other hand, is based Z ). The bottom-right panel shows 5 . 1 3.9 & 0 1 summarize our results for the direct and indirect detection ˜ χ 4 m so barely constraint even by future searches such as XENONnT SI σ ]. In this figure we show only those points which satisfy the direct 72 exposure. Similarly the top-right panel represents the spin-dependent scat- plane. y · 0 1 ˜ χ t . In this respect, the mass of m exposure and XENONnT with 20 0 Z − y As mentioned before, the LSP composition is also important for the possible stop and Even though a significant portion of the solutions are excluded by the DM constraint The top panels of figure uncertainty excludes the solutions with · 2 M t h σ of our model. gluino probe in the current4 and shows future that collider only experiments. higgsino-like and The singlino-like LSP solutions can be consistent with the Another strong impact from thewhose relic mass density is constraint restricted can as on be the observed on assumption the that blinoassumption the LSP is DM dropped, density the isstill saturated solutions be only with available by lower inplot the relic conjunction we LSP abundance see with neutralino. of that other all LSP If form(s) possible neutralino this of types may DM of LSP [ neutralinos can be realized for almost any value LSP solutions mostly yieldcurrent a measurements. relatively This is large because relicprocesses the density, through bino-like which LSP the participates is weak inlowered inconsistent the interactions, by with coannihilation and such the thus processes. itscan In still relic contrast be density to compatible cannot the with be higgsino the adequately DM and constraint bino-like even LSP, if a it singlino weighs LSP as low as about 100 GeV. Ω on the relicdespite density, the its higgsino impact LSP5 differs solutions for with different compositions of DM. For instance, with 20 tering cross-sections versus theconsistent LSP with neutralino current mass. bounds Welike and see DM a that small can all portion be ofalready of our probed excluded parameter solutions by by space are the yielding the future higgsino- relic Lux-Zeplin density analyses. constraint as However, discussed these in solutions the are results shown in the Similarly bino-type solutions are0.5 TeV also to in 1.8 TeV. considerabletween Blino-type numbers 1 solutions and TeV to are with 1.7 relatively masses TeV.solutions small between considerably. We in see We numbers also that withtralino notice current masses that cross and be- blino-type section future solutions indirect are searches small will nucleon probe to neu- our experiments with respect to the LSPwhich neuralino satisfy mass. current Note that direct weWe and plot see only that indirect those in detection solutions our experimental scansalmost most bounds entire of indicated range the solutions above. of are(orange LSP higgsino-type points) neutralino (turquoise are points) mass also covering in between large 100 number GeV ranging to neutralino 2 TeV. mass from Singlino 0.15 TeV solution to 1.7 TeV. the black solid line isfuture the LZ current LUX bound bound [ and [ indirect DM bounds.relic density The bounds horizontal given lines inneutralino in eq. mass. ( the bottom-left panel indicate the DM 2 JHEP01(2021)161 at 2 g inter- L & , point 1 − L 2 B − B g U(1) GeV. Such light 65 . 1 A m -resonance solution (bino-type 2 H ). Since these fields do not couple ¯ φ ) associated with the L ]). This result may slightly strengthen φ, − B 13 g – 4 ), and thus this weakening effect is negligible. – 13 – 1% -funnel (singlino-bileptino mixed neutralino) solu- 3 , point 1 displays H 3 -resonance solutions with higgsino-type neutralino. Point 4 2 , the renormalization group evolution leads to A , even the current LHC results can severely exclude the stop 2 , g GUT 1 g M ) at L L − − B g B g = 2 g In addition to the DM implications, the selected benchmark points also reveal that the Before concluding, we present some benchmark points in two tables. In table It is worth discussing the case when the stop decays into a blino-like neutralino, whose = 1 g CP-odd Higgs bosons can beif consistent they with the belong constraints to employedto in the the our MSSM analyses MSSM only Higgs singletscalar fields Higgs bosons directly, fields the are ( decaysphenomenology strongly of in suppressed. the our SM-like model Therefore, Higgs essentially boson coincide the with into implications the such for MSSM light predictions. the Higgs boson neutralino). Point 2 is antion, example and of Point 3 represents depicts an example of blino-bileptino mixed LSP neutralino. mass spectrum usually includes light CP-odd Higgs bosons as represents chargino-neutralino coannihilation solutions. Pointwith 2 is NLSP a stau. representative solution in Point mass 3 with displays the aninvolving CP-even LSP example and neutralino. where CP-odd sneutrinos, theof Points respectively. selectron higgsino-type 4 All is neutralino. these and points almost 5 In are degenerate table represent also examples the coannihilation scenarios the weak scale (see,the for signal instance, process, eq. but (3.1)the it in stop is [ mass still is beyondHowever, bounded it the at can reach about yield of 3 a the TeV stronger from current impact below LHC from by experiments, the the since HL-LHC Planck results. bound in our model. strength is proportional toactions. the gauge For coupling ( solutions. However, if the model( is constrained by the gauge coupling unification condition along with a Higgs boson.the However, this higgsinos decay and mode is singlino,higgsino proportional which neutralino to the is forms mixing an severely between stop almost restricted signals is stable by mostly state. the frombe the Planck MSSM As followed bound. neutralinos also a and/or for result, blino. the Thus the The gluino the similar missing search discussion at energy can the in LHC the and future collider experiments. its mixing to very smallIf the percentages singlino ( happens toneutralino, be and the a possible LSP, the signalIf stop process does for the the not stop stop have involves decays acoupling decays direct into into to coupling other bino, the neutralinos. to singlino. wino the Hence, orenergy LSP they in blino, are the these collisions. the stable latter If neutralino neutralinos the states stop do and decays not form into the higgsinos, have missing the a latter direct can decay into singlino realize consistent blino-like LSP solutionsof in a higgsino-like small neutralinos, region. it yields Ifone MSSM the recovers decay LSP processes the is composed consisting currentfor mostly of LHC stop future limits signals, experiments. and onforming Even the the though stop LSP the mass neutralino singlino which scales weakens is as the allowed signal well to strength, as the mix the Planck with bound implications the restricts higgsino in Planck bound on the relic abundance of LSP neutralino, even though it is also possible to JHEP01(2021)161 7 11 − − .9 .9 10 10 .5475 × 5661 .43858 × 2204 0 4933 0 − 6 11 − − − . − . 2 1 8 10 − − .5 .6 9107.4 10 10 × × 7348 4131 39 − − 85 . . 2 3 7 − 10 − .1 8694.5 .5 .8 10 10 .401 0.54949 × 0 975 × 3035 3001 − − 4 − − . 075 . 2 . Points 1 and 2 represent chargino-neutralino 2 and all points satisfy the sparticle mass bounds, 3 0 – 14 – 7 10 − − 10 10 µ > × 1014 2208 × − − 60 23 . . 3 3 7 10 − − .5 3047.7 .28 10 10 × 7103 × 126 122 123 125 125 .48214 0.2582 4246 2590 3239 4863 1134 4238 2590 3239 1435 3965 7925 5533 7479 9671 9264 7238 4620 3599 9569 5781 7232 4618 4854 9548 5783 1542 4857 3990 4320.5 8416.9 3998.3 155 0 0.1178 0.101 0.12192 0.119 0.122 1663.8 105.85 73.208 147.44 6347.9 5109.2 3230.8 2038.2 22.357 − 4849.4 4554.5 4827.6 4146.6 4769.5 1.9475 1.759 1.9033 1.6519 1.1389 7.9521 13.699 5.7389 49.984 8.114 3837.2 2637.5 3645.5 4750.8 4560.7 2851.1 1114.2 1178.4 3864.9 2295.2 Point 1 Point 2 Point 3 Point 4 Point 5 0.35373 0.2910 0.4146 0.28002 92 − − 33 − . 4900,5410 3706, 5428 4686, 5377 4510, 6667 4675, 5443 40.2, 2662 6.239, 2662 6.8787,4105 25, 6993 28, 5213 . 2895, 4240 783, 891 1255, 3240 3013, 4103 2846, 3966 2916, 4247 2609, 4971 1268, 3243 8904, 9286 2895, 3984 6787, 7219 4438, 4831 6096, 6443 7865, 7891 7862,7991 7240, 7461 4887,4972 6453, 6666 8874, 9286 8013, 8471 5728, 6792 3701, 4450 5152, 6103 66827, 7844 6701, 7864 7171, 7461 4796, 4971 6375, 6665 8904, 9286 8109, 8471 1108, 3406 786, 2338 1124, 3218 1387, 4225 1085, 4036 3257, 3406 1775,2338 2720, 3219 2487, 4225 3527, 4036 1938, 2058 1189, 1334 1797, 1830 1534, 1643 2225, 2294 1106, 1109 781, 788 1121, 1124 1382, 1388 1083, 1085 5133, 7232 4618, 4682 4854, 5217 7287,9548 5236, 5782 2053, 2821 1038, 2130 1583, 3186 2169,2874 2043, 4260 1 1 5 3 2 2 A H H 2 0 h odd 2 8 6 4 2 2 2 2 2 2 2 even 2 0 1 , , , , , 3 , β , ± , , , , β µ − / ˜ 0 g ± 1 7 0 0 5 0 3 0 1 1 0 1 1 − 1 0 κ 1 1 Z µ M (pb) S A H λ ˜ 1 (pb) ˜ ˜ t ˜ ˜ ˜ ˜ ˜ ˜ , m , m , m H b ˜ τ e ˜ d κ u χ χ χ χ χ v λ L A A 1 4 2 m m ∗ CP CP A M m m m ˜ M m tan m m m . Masses are in units of GeV, m SI ν ˜ m m m m m m ν CDM tan A SD H H κ σ σ Ω m m m m m Table 2 and B-physics constraintscoannihilation described and in stau NLSP section respectively.display examples Point 3 of corresponds CP-even to and selectron CP-odd NLSP. lightest Points sneutrinos 4 respectively. and 5 JHEP01(2021)161 resonance 3 H 9 12 − − .8 .2 and 10 10 2 × H × 4212 9722 0 00 − − . . 2 1 8 10 − − .7 .1 10 10 × × -funnel solution . Point 4 displays an 5360 2478 2 − − 78 A 183 . . 3 3 8 11 − − .7 8841 27.574 .7 10 10 . Points 1 and 2 represent .277 and all points satisfy the sparticle mass bounds, × 861 .13297 0.5898 0.29133 3 × 61 3467 0 – 15 – 0 − 1 96 − − . − . 1 3 µ > 7 10 − − .8 10 10 × × 125 127 122 122 6722 4767 9532 9951 9398 1120 2915 1960 1630 3925 2773 4599 5268 10286 4789 8873 10481 10289 4788 8883 10503 3500.9 1650.1 3093.3 4570.8 2168.0 4718.8 4914.2 4578.2 14.203 6.8025 15.35 51.398 1.3478 1.5042 1.134 1.6519 4644.6 4674.8 4797.7 4263.5 1747.2 0.2946 5697.6 7388.3 9294.2 3507.1 10686 0.4548 0.17831 0.4139 0.59597 4576.6 4100 3464.9 10609 293.37 63182 2.658 1.2881 0.1112 0.11763 0.123 0.1546 Point 1 Point 2 Point 3 Point 4 26 − 43 . 1433,1615 895,1704 1790, 2515 1680, 1681 1941,3026 2406,3185 2657,3338 2420, 4081 3849,6178 4167,6297 4359,6371 5300, 7201 1426,1940 894,4167 1186,4359 1679, 4081 5245,5353 8100,8550 8800, 9274 9010, 9347 3985,5353 2289,3889 4663, 9274 9010, 9347 3325,3463 2272,3885 3468, 3631 3483, 4723 . 2272, 2700 985,1395 1931, 2237 2149, 3196 1106, 1426 669,894 1182, 1187 1493,1539 2924, 4307 6604, 7861 6589, 8209 6806, 7824 5277, 5354 8125, 8551 8785, 9274 8976, 9347 4296, 5164 7856,8107 8203,8638 7817, 7955 6002,10286 4789,5137 4547, 8874 8680, 10481 2 1 4.3512,5185.6 63.397,2813 5.325,2574 32.877,8478 3 5 2 2 H H A 2 0 h odd 2 4 6 8 2 2 2 2 2 2 2 even 2 0 1 , , , , , 3 , β , ± , , , , β µ / ˜ − 0 g 0 1 0 3 0 5 7 0 ± 1 1 0 1 1 − 1 0 κ 1 1 Z µ M (pb) S A H λ ˜ 1 (pb) ˜ ˜ t ˜ ˜ ˜ ˜ ˜ ˜ , m , m , m H b ˜ τ e ˜ d κ u χ χ χ χ χ v λ L A A 2 4 1 m m CP ∗ CP A M m m ˜ m ν M m tan m m m m SI ˜ m m m m m m ν CDM tan A SD H H κ σ σ Ω m m m m m . Masses are in units of GeV, Table 3 and B-physics constraints describedsolutions in respectively, and section point 3example corresponds of to blino-type selectron LSP neutralino. JHEP01(2021)161 − τ + τ → A/H symmetry, the particle content L − B U(1) 325 GeV, which may help in ameliorating ∼ may be tested further by the symmetry groups. In addition to the presence of – 16 – 20 R & β U(1) tan ) associated with the 0 Z and a global L − B U(1) and charged Higgs boson masses, such solutions are still viable. In addition to extended MSSM includes diphoton resonances and additional neutralino states. ± L parameter can take values as low as W − resonance solutions with µ B 2 The LSP composition also affects the possible signal processes and their strengths The sparticle spectrum has interesting implications for the DM searches. The richness The mass spectrum in this region involves staus heavier than about 500 GeV. In this Exploring the collider implications of this class of models reveals that the stop and A in stop andresults gluino from searches. the LHC analyses Despitestrengthen are the the mostly recovered implications richness in for of ourdecays the model, into the blino-like future while neutralino neutralino. it collider may sector, experiments, potentially the especially when current the stop degenerate with the LSP neutralinoget mass. bino-like We DM notice that consistent inhiggsino, with our singlino the present and relic scans blino-like density it DMsolutions is constraint, hard for but can to various it be mass is scalesXenon-nT. tested possible of to in the achieve LSP the neutralino. direct These detection DM searches including LUX-Zeplin and of the neutralino sectorsinglino-like allows and one blino-like to DM.neutralino identify coannihilation higgsino-like and processes. We bino-like haveselectron, In DM, also smuon addition, and as identified, sneutrinos coannihilation well can as processes as be indicated involving realized with stau, above, their chargino- masses around 1 TeV and nearly less than staus, it is also possiblemasses to of realize selectron, about smuons, 1and CP-even TeV and and two CP-odd higher. additional sneutrinos CP-even with Thethe Higgs Higgs bosons spectrum whose masses involvesLHC a can searches. CP-odd be below Higgs 500 boson GeV. Some of imposing the relic density constraintsit yields can a also chargino be mass as as light heavy as as 240 1.5 GeV, TeV although orcontext, so the (chargino-neutralino solutions coannihilation with region). adecay chargino into mass staus, lighter and than since 500 the GeV do mass not difference allow between the the latter chargino and to LSP neutralino is on the gluino and stoprequirement masses that of 4 the TeV and LSP 3 neutralino TeVconstraints respectively comprises the are the gluino found DM and after imposing stop inMSSM the masses the can universe. as Without light thethe as DM little 2.2 TeV and hierarchy problem. 1 TeV respectively. The The chargino masses vary between 0.1–2.6 TeV. In addition, Indeed, the number of neutralinosthe is DM doubled in density comparison is withphenomenology saturated the that by MSSM we a and have LSP assuming explored neutralino, in the this paper. resulting modelgluino yields are quite accessible a in rich future experiments such as HL-LHC. In some cases lower bounds We have discussed a class of SUSYwith models a in gauged which the MSSMa gauge new group neutral is gauge supplemented boson ( of this 5 Conclusions JHEP01(2021)161 ]. ] 96 Phys. (2016) SPIRE , (1976) 8 ]. IN 93 (1982) 237 ][ 37 SPIRE (1974) 275 113 IN ]. in the MSSM and ][ 10 Naturalness and Phys. Rev. D γ Lepton-flavor , (2018) 100 arXiv:1703.00229 SPIRE Phys. Rev. D [ , and Z IN 07 Phys. Rev. Lett. ][ γγ , Phys. Lett. B arXiv:1503.05408 , [ Phys. Rev. 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