Top-squark in natural SUSY under current LHC run-2 data

Abstract

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

We utilize the recent LHC-13 TeV data to study the lower mass bound on the top-squark (stop) in natural supersymmetry. We recast the LHC sparticle inclusive search of [InlineEquation not available: see fulltext.]1)[InlineEquation not available: see fulltext.] with ...... variable, the direct stop pair search (1-lepton channel and all-hadronic channel) and the monojet analyses. We find that these searches are complementary depending on stop and higgsino masses: for a heavy stop the all-hadronic stop pair search provides the strongest bound, for an intermediate stop the inclusive SUSY analysis with ...... variable is most efficient, while for a compressed stop-higgsino scenario the monojet search plays the key role. Finally, the lower mass bound on a stop is: (1) 320 GeV for compressed stop-higgsino scenario (mass splitting less than 20 GeV); (2) 765 (860) GeV for higgsinos lighter than 300 (100) GeV.

Eur. Phys. J. C (2017) 77:93DOI 10.1140/epjc/s10052-017-4662-7

Regular Article - Theoretical Physics

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Web End = Top-squark in natural SUSY under current LHC run-2 data

Chengcheng Han3,a, Jie Ren4,b, Lei Wu1,2,c, Jin Min Yang5,d, Mengchao Zhang6,e

1 Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu 210023, China

2 ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia

3 Kavli IPMU (WPI), UTIAS, University of Tokyo, Kashiwa 277-8583, Japan

4 Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China

5 Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

6 Center for Theoretical Physics and Universe, Institute for Basic Science (IBS), Taejon 34051, Korea Received: 27 October 2016 / Accepted: 16 January 2017 / Published online: 11 February 2017 The Author(s) 2017. This article is published with open access at Springerlink.com

Abstract We utilize the recent LHC-13 TeV data to study the lower mass bound on the top-squark (stop) in natural supersymmetry. We recast the LHC sparticle inclusive search of (1)jets+ /

ET with T variable, the direct stop pair search (1-lepton channel and all-hadronic channel) and the monojet analyses. We nd that these searches are complementary depending on stop and higgsino masses: for a heavy stop the all-hadronic stop pair search provides the strongest bound, for an intermediate stop the inclusive SUSY analysis with T variable is most efcient, while for a compressed stophiggsino scenario the monojet search plays the key role. Finally, the lower mass bound on a stop is: (1) 320 GeV for compressed stophiggsino scenario (mass splitting less than20 GeV); (2) 765 (860) GeV for higgsinos lighter than 300 (100) GeV.

1 Introduction

The discovery of the Higgs boson is a great triumph for the Standard Model (SM). However, the SM Higgs mass is quadratically sensitive to the cutoff scale (usually taken as GUT or Planck scale) via radiative corrections because of the lack of symmetry protection. This renders the SM with mh 125 GeV rather unnatural. A well-known theory

for solving such a naturalness problem is supersymmetry.

Among various supersymmetric models, natural super-symmetry (NSUSY) is a well-motivated framework [13], which consists of a small set of sparticles that closely relate to

a e-mail: mailto:[email protected]

Web End [email protected]

b e-mail: mailto:[email protected]

Web End [email protected]

c e-mail: mailto:[email protected]

Web End [email protected]

d e-mail: mailto:[email protected]

Web End [email protected]

e e-mail: mailto:[email protected]

Web End [email protected]

the naturalness, such as higgsinos, stop, and gluino. This can be understood by the minimization of the Higgs potential [4],

M2Z

2 =

(m2Hd + d) (m2Hu + u) tan2 tan2 1

2

(m2Hu + u) 2, (1)

where is the higgsino mass parameter in the superpotential and contributes to MZ at tree level, tan vu/vd 1

is assumed in the last approximate equality, m2Hd and m2Hu

denote the soft SUSY breaking masses of the Higgs elds at weak scale, and u and d arise from the radiative corrections to the Higgs potential. Due to the large top Yukawa couplings, u is dominated by the stop at 1-loop level, while the gluino contributes to u via the corrections to the stop mass. Other contributions from the rst two generation squarks and sleptons to MZ are negligibly small. Therefore, the requirement of getting the correct value of MZ without ne-tuning will give upper bounds on the masses of higgsinos, stops, and gluino [5,6]. In the past few years, much work has been devoted to the searches for the stop at the LHC in NSUSY [722].

With the recent 15 fb1 dataset at the LHC run-2, the

stop and gluino masses are respectively excluded up to 1

TeV [23] and 1.8 TeV [24], while the electroweakinos below0.41 TeV can also be covered for different decay channels [25]. But these limits are obtained in the simplied models [2628] and sensitively depend on the assumptions of the nature of the lighest supersymmetric partner (LSP), the branching ratios of heavier sparticles and the mass splitting between heavier sparticles and the LSP. Therefore, it is necessary to examine the current LHC run-2 coverage of NSUSY and assess the ne-tuning extent. In this work, we utilize the recent results of the LHC run-2 inclusive sparticle searches and direct stop pair searches to constrain the stop mass in

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93 Page 2 of 6 Eur. Phys. J. C (2017) 77 :93

NSUSY. We compare their sensitivities and nd that they are complementary in probing NSUSY. We will also evaluate the electroweak ne-tuning measure in the allowed parameter space of NSUSY and comment on the prospect for covering the low ne-tuning parameter space of NSUSY at HL-LHC.

2 Constraints on stop in NSUSY

In MSSM, the stop mass matrix in the weak-basis (tL, tR) is given by

M2t = [parenleftBigg]

m2tL mt Xt

mt Xt m2tR [parenrightBigg]

f CR = g2Vi1 cos t + yt Vi2 sin t, (13)

with yt = 2mt /(v sin ) and yb = 2mb/(v cos )

being the Yukawa couplings of top and bottom quarks. The mixing matrices of the neutralinos Ni j and charginos Ui j,

Vi j are dened in [29]. In NSUSY, M1,2 , one has

V11, U11, N11,12,21,22 0, V12 sgn(), U12 1 and

N13,14,23 = N24 1/2. So,

1 and

01,2 are higgsino-like and nearly degenerate.1 The left-handed stop will mainly decay to t

01,2 when the phase space is accessible and tan is small. The couplings of the right-handed stop with

01,2

and

with

m2tL = m2Q3L + m2t + m2Z [parenleftbigg]

1 are proportional to yt, and the branching ratios of

t1 t 01,2 and t1 b +1 are about 25 and 50%, respec

tively.

To address the lower mass limit of the stop in NSUSY, we can focus on a right-handed stop. This is because the left-handed stop is linked with the left-handed sbottom by the SU(2) symmetry. Then the left-handed sbottom decay channel b1 t

, (2)

1

2

2

3 sin2 W [parenrightbigg]

cos 2 , (3)

2

3m2Z sin2 W cos 2 , (4)

Xt = At cot . (5) Here m2Q3L and m2U3R are the soft-breaking mass parameters

for the third generation left-handed squark doublet Q3L and the right-handed stop3R, respectively. At is the stop soft-

breaking trilinear parameter. The weak eigenstates tL,R can be rotated to the mass eigenstates t1,2 by a unitary transfor

mation,

[parenleftbigg]

t1

t2

m2tR = m2U3R + m2t +

[parenrightbigg] = [parenleftbigg]

cos t sin t sin t cos t

[parenrightbigg][parenleftbigg]

tL

tR

. (6)

After diagonalizing the mass matrix, see Eq. (2), we can have the stop masses m

t1,2 and the mixing angle t (/2 t

/2),

m

t1,2 =

1

2

1 can mimics the left-handed stop signals

t1 t 01,2 since 01,2 and +1 are higgsino-like and degener

ate in NSUSY. This enhances the LHC limit on a left-handed stop, which is stronger than the limit on a right-handed stop [15,20].

Now we examine the constraints on the NSUSY scenario that consists of a right-handed stop and higgsinos. We scan the parameter space in the ranges

100 GeV 600 GeV,

100 GeV m Q3L,3R 2.5 TeV,1 TeV At 3 TeV, 5 tan 50. (14)

The lower limit on the higgsino mass is motivated by the LEP searches for electroweakinos. We require the stop mixing angle | sin t|2 > 0.5 to obtain a right-handed stop t1.

Since the gluino contributes to the naturalness measure in Eq. (15) at 2-loop level, a low ne-tuning allows the gluino with a mass up to several TeV, which is possibly beyond the reach of LHC. So we assume the gluino mass parameter to be M3 = 2 TeV in our scan. Since the electroweak gauginos,

heavy Higgs bosons, the sleptons, the rst two generations of squarks and the right-handed sbottom are not strongly related to the naturalness, we decouple their contributions by xing M1 = M2 = m A = m

m2tL + m2tR [radicalbigg][parenleftBig]m2tL m2tR[parenrightBig]2 + 4m2tX2t

[bracketrightBigg]

, (7)

tan 2t =

2mt Xt

m2tL m2tR

. (8)

The decays of stop are determined by the interactions between stop and neutralinos/charginos, which are given by

Lt1 b

+i = t1 b( f CL PL + f CR PR)

+i + h.c.,

= m q1,2 = m DR = 2 TeV at the

0i = t1t( f NL PL + f NR PR)

0i + h.c., (9)

where PL/R = (1 5)/2 and

f NL = [bracketleftbigg]

g22 Ni2 +

g132 Ni1[bracketrightbigg]

cos t yt Ni4 sin t (10)

f NR =

22

3 g1Ni1 sin t yt Ni4 cos t, (11) f CL = ybUi2 cos t, (12)

weak scale.

In our scan, we impose the following indirect constraints:

Higgs mass We require that the lighter CP-even Higgs

boson be the SM-like Higgs boson with a mass in the

1 The detection of such light higgsinos through a monojet (or a monojet-like case) may be challenging at the LHC [3034].

Lt1t

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Eur. Phys. J. C (2017) 77 :93 Page 3 of 6 93

range of 1252 GeV, which is calculated by the package

FeynHiggs-2.11.2 [35,36].2

Vacuum stability We impose the constraint of metasta

bility of the vacuum state by requiring |At| [lessorsimilar] 2.67

M2Q3L + M2tR + M2A cos2 [38], because the large tri-linear parameter At can potentially lead to a global vacuum where charge and color are broken [3840].

Low-energy observables We require our samples to sat

isfy the bound of B Xs at 2 range, which is imple

mented by the package of SuperIso v3.3 [41,42].

Dark matter detection We require the thermal relic den

sity of the neutralino dark matter h2 to be below the 2 upper limit of 2015 Planck value [43]3 and the LUX WS2014-16 [47]. The results for the spin-independent neutralinoproton scattering cross section SIp is rescaled by a factor of h2/ P Lh2. We use the package of

MicrOmega v2.4 [48] to calculate h2 and SIp .

Besides, the LHC run-2 experiments have covered a wide parameter space of the MSSM. We list the relevant LHC experimental analyses for our scenario:

From ATLAS, Stop, 0 lepton + (b)jets + /

ET , 13.3 fb1 [49], Stop, 1 lepton + (b)jets + /

ET , stop, 13.3 fb1 [50], Stop, 2 leptons + (b)jets + /

ET , stop, 13.3 fb1 [51], Sbottom, 2 b-tagged jets + /

ET , 3.2 fb1 [52], Compressed Spectrum, 1 jet + /

ET , 3.2 fb1 [53].

From CMS, Inclusive, 0 lepton + [greaterorequalslant] 1 jets + /

ET + T , 12.9 fb1

[54]

Inclusive, 0 lepton + [greaterorequalslant] 1 jets + /

Table 1 The LHC Run-2 analyses used in our study

ATLAS CMS

1 lepton + (b)jets + /

ET [50] 0 lepton +([greaterorequalslant]1)jets + /

ET + T [54]

1 jet + /

ET [53] 0 lepton + (b)jets + /

ET [23]

It should be mentioned that the higgsinos

1 and

02 have

the small mass difference with the LSP

01 in NSUSY. Then

the decay products of

1 and

02 are too soft to be tagged at the LHC. So, the stop decays can be categorized into two topologies: 2b+ /

ET . Among the current ATLAS searches for the stop, the all-hadronic nal state channel has a better sensitivity than those with leptons in the high stop mass region (m

t1 > 800 GeV) because of the application of boosted top technique. Similar results are obtained by the

CMS Collaboration. With the decrease of the mass splitting m

t1 01 , the sensitivity of the conventional stop searches

for the energetic top quark in the nal states become poor. In particular, if m

t1 01 mt, the stop decay will be dominated by the four-body channel t1 bf f

01 [59,60] or the two-body loop channel t1 c

01 [6165]. Then the decay products of the stop are usually very soft so that a high pT hard jet from the ISR/FSR is needed to tag these compressed stop events, such as the ATLAS monojet analysis listed above. Note that the very recent CMS monojet with the soft lepton pair analysis of the compressed electroweakinos can exclude the wino-like chargino mass m

1 up to 175 GeV for a mass difference of 7.5 GeV with respect to the LSP.

However, this limit is not applicable to our scenario because the cross section of the higgsino pair production is 1/4 of the wino pair. On the other hand, both ATLAS and CMS experiments have performed the inclusive SUSY searches for nal states with (generally untagged) jets and a large amount of /

ET , which can also be used to derive limits on the parameter space in various simplied models. In our study, we reinterpret the recent CMS analysis of 0lepton + ([greaterorequalslant]1)jets + /

ET .

ET and t t+ /

ET + MT2, 12.9 fb1

[55]

Inclusive, 0 lepton + [greaterorequalslant] 1 jets + /

ET + HmissT, 12.9

fb1 [56]

Stop, 0 lepton + (b)jets + /

ET , 12.9 fb1 [23],

Stop, 1 lepton + (b)jets + /

ET , 12.9 fb1 [57], Compressed Spectrum, 1 jet + soft lepton pair + /

ET , 12.9 fb1 [58].

2 The prediction of the SM-like Higgs mass depends on the spectrum generators. The differences arise from the choice of the renormalization scheme and the higher order correction calculations. These effects often lead to a few GeV uncertainty for the SM-like Higgs mass in the MSSM [37].

3 The thermal relic density of the light higgsino-like neutralino dark matter is typically low as a result of the large annihilation rate in the early Universe. One possible way to produce the correct relic density is introducing the mixed axionhiggsino dark matter [44,45]. However, if the naturalness requirement is relaxed, the heavy higgsino-like neutralino with a mass 12 TeV can solely produce the correct relic

density in the MSSM [46].

This strategy is built around the use of the kinematic variable T , which is constructed from jet-based quantities to provide strong discriminating power between sources of genuine and misreconstructed

pmissT. Such a variable can highly suppress multijet background, and is suitable for early searches at 13

TeV LHC. Based on the above considerations, we use four LHC experimental analyses to constrain the parameter space of NSUSY, which are listed in Table 1.

In our Monte Carlo simulations, we use MadGraph5_a MC@NLO [66] to generate the parton level signal events, which are showered and hadronized by the package PYTHIA [67]. The detector simulation effects are implemented with the package Delphes [68]. The jets are clustered with the anti-kt algorithm [69] by the package FastJet [70].

The cross section of the stop pair production at 13 TeV

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93 Page 4 of 6 Eur. Phys. J. C (2017) 77 :93

3162 F(m2t1,2)

y2t g2Z f 2t A2t 8g2Z(14 23 xW ) tm2t2 m2t1 [bracketrightBigg](16)

where the form factor F(m2) = m2 [parenleftBig]

log m2Q2 1[parenrightBig]

with the

optimized scale Q2 = mt1mt2 , yt is the top quark Yukawa coupling and t = (m2tL m2tR)/2 + M2Z cos 2(14 23 xW ),

xW sin2 W . In this gure the triangles, squares, and bullets

represent the samples that have the electroweak ne-tuning 4 < EW < 10, 10 < EW < 30 and 30 < EW < 300, respectively. In our parameter space, the low ne-tuning 4 < EW < 10 requires the higgsino mass [lessorsimilar] 200 GeV and the stop mass 0.4 TeV [lessorsimilar] mt1 [lessorsimilar] 1.3 TeV. It can be seen that 70%

of such a parameter space can be covered by the current LHC Run-2 SUSY searches. A lighter stop mass (m

t1 [lessorsimilar] 0.4 TeV) requires a large trilinear parameter At to satisfy the Higgs mass constraint, which leads to a large value of EW.

Besides, from Fig. 1 it can be seen that the ATLAS monojet search produces a strong exclusion limit in the low stop mass region, which excludes the stop mass up to 320 GeV for m

01 = 300 GeV. This is because when the stop mass is

close to the LSP mass, the b-jets from the stop decay t1

b

+1/bf f

01,2 or c-jets from t1 c

01,2 are too soft to be identied. Then the monojet search is very sensitive in the low stop region.

In the moderate or heavy stop region, the stop dominantly decays to b

+1 and t

01,2, which produce 2b + EmissT and

t t+EmissT signatures, respectively. The CMS inclusive search

with T shows a better sensitivity than the 0/1-lepton stop searches in most of parameter space. But we also note that the exclusion limit of the CMS 0-lepton stop search is slightly stronger than the CMS inclusive search because of the application of top tagging technique in ATLAS analysis. Finally, we conclude that the stop mass can be excluded up to 765 (850) GeV for m

01 < 300 (m 01 = 100) GeV by the cur

rent LHC Run-2 experiments. Such limits are much stronger than the LHC run-1 limits on NSUSY, which excluded a stop below 600 GeV [15,16,18,20].

It should be mention that when the stop and LSP mass splitting m

t1 01 mt, the kinematics of the top quarks

from stop decay are similar to those in the top pair production so that the above LHC searches for stop pair have the poor sensitivity. With the help of an additional high momentum jet recoiling against stop pair system, one can utilize the observable RM /

600

30 < < 300 10 < < 30

4 < 10

uu(t1,2) =

1 jet + (CMS, 13 TeV, 12.9 fb ) Monojet (ATLAS, 13 TeV, 3.2 fb )

1 lepton stop (ATLAS, 13 TeV, 13.2 fb ) Hadronic stop (CMS, 13 TeV, 12.9 fb )

500

400

m (GeV)

~ 300

200

100 100 350 600 850 1100 1350 1600 1850

mt (GeV)

~

Fig. 1 Scatter plots on the plane of mt1 versus m

01 . All samples satisfy the constraints of the Higgs mass, vacuum stability, B Xs , and dark

matter detections. The exclusion limits of the LHC SUSY searches in Table 1 are recast. The triangles (gray), squares (cyan) and bullets (red) represent the samples that have the electroweak ne-tuning EW < 10, 10 < EW < 30 and 30 < EW < 300, respectively

LHC are calculated by NLL-fast package [7175] with the CTEQ6.6M PDFs [76]. We impose the ATLAS monojet constraint with MadAnalysis 5-1.1.12 [7779]. The ATLAS 1-lepton stop and the CMS 0-lepton stop analyses are implemented within the CheckMATE framework [80,81]. But as mentioned above, we only focus on the heavy stop mass range (m

t1 > 500 GeV) for the CMS 0-lepton analyses because of the improved sensitivity by application of the top tagging technique. Besides, the higgsinos

1 and

01,2 are nearly degenerate in NSUSY. The stop decay t b

+1 gives the same topology as the sbottom decay b b

01. So we can determine the exclusion limit on the stop by using the cross section upper limit of the sbottom pair production reported from the CMS inclusive search with T .

In Fig. 1, we project the samples allowed by the Higgs mass, vacuum stability, B Xs and dark matter detections

on the plane of m

t1 versus m 01 . To quantitatively evaluate

the naturalness, we use the electroweak ne-tuning measure EW4 [82]; we have

EW maxi|Ci|/(M2Z/2), (15) where C = 2, CHu = m2Hu tan2 /(tan2 1), CHd =

m2Hd /(tan2 1), C u(i) = u(i)(tan2 )/(tan 1), and

C d(i) = d(i)/(tan 1) with i labeling the various loop

contributions by u and d. The one-loop stop contributions u(t1,2) are given by [83].

4 The Barbieri and Guidice (BG) measure in Ref. [5] is applicable to a theory with several independent effective theory parameters. But for a more fundamental theory, the BG measure often leads to an overestimate of ne-tuning [82].

ET /pT ( jI SR) to extend the reach of stop to about 800 GeV at 13 TeV LHC with L = 3000 fb1

[84]. Besides, the VBF production of the stop pair was also proposed to detect such a compressed stop region, which can cover the stop mass to about 300 GeV because of the

123

Eur. Phys. J. C (2017) 77 :93 Page 5 of 6 93

large systematical uncertainty [85]. In NSUSY, when both decay channels t1 t

01 and t1 b

+1 are allowed, search for the asymmetric nal states t( t

01)t( b

1) can

provide a complementary way to probing stop at the LHC. With the variable topness to suppress t t background, such

an asymmetric stop search has a comparable sensitivity with the symmetric stop searches at the HL-LHC [86]. Therefore, together with conventional LHC search strategies, we can expect that the future high luminosity LHC is able to probe the stop and higgsino mass up to 1.5 and 0.6 TeV, respectively [87]. At that time, most of the NSUSY parameter space with EW < 30 can be covered [87,88].

3 Conclusions

In this paper, we examined the lower mass limit of the stop in natural supersymmetry (NSUSY) by using the recent LHC-13 TeV data. We recast the LHC SUSY inclusive search for (1)jets + /

ET events with T variable, the direct stop pair searches (1-lepton channel and all-hadronic channel) and the monojet analyses. We found that the inclusive SUSY analysis with T is complementary to the direct stop pair analyses in probing NSUSY. The current LHC data can exclude the stop up to 765 (860) GeV for m

01 < 300 (m 01 = 100) GeV.

While in the compressed region ( m

t1 01 20 GeV), the

stop mass can be still light as 320 GeV. About 70% of the NSUSY parameter space with EW < 10 can be covered by the current LHC Run-2 data. The future HL-LHC is expected to push the lower mass limits of the stop and higgsino up to 1.5 and 0.6 TeV, respectively, and cover most NSUSY parameter space with EW < 30.

Acknowledgements This work is partly supported by the Australian Research Council, by the CAS Center for Excellence in Particle Physics (CCEPP), by the National Natural Science Foundation of China (NNSFC) under Grants Nos. 11275057, 11305049, 11375001, 11405047, 11135003, 11275245, by Specialised Research Fund for the Doctoral Program of Higher Education under Grant No.20134104120002. CCH is supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. MCZ is supported by Institute for Basic Science (IBS-R018-D1).

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

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Web End =ons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Funded by SCOAP3.

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