Scholarly article on topic 'Closing up a light stop window in natural SUSY at LHC'

Closing up a light stop window in natural SUSY at LHC Academic research paper on "Physical sciences"

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Abstract of research paper on Physical sciences, author of scientific article — Archil Kobakhidze, Ning Liu, Lei Wu, Jin Min Yang, Mengchao Zhang

Abstract Top squark (stop) plays a key role in the radiative stability of the Higgs boson mass in supersymmetry (SUSY). In this work, we use the LHC Run-1 data to determine the lower mass limit of the right-handed stop in a natural SUSY scenario, where the higgsinos χ ˜ 1 , 2 0 and χ ˜ 1 ± are light and nearly degenerate. We find that the stop mass has been excluded up to 430 GeV for m χ ˜ 1 0 ≲ 250  GeV and to 540 GeV for m χ ˜ 1 0 ≃ 100  GeV by the Run-1 SUSY searches for 2 b + E T miss and 1 ℓ + jets + E T miss , respectively. In a small strip of parameter space with m χ ˜ 1 0 ≳ 190  GeV , the stop mass can still be as light as 210 GeV and compatible with the Higgs mass measurement and the monojet bound. The 14 TeV LHC with a luminosity of 20  fb − 1 can further cover such a light stop window by monojet and 2 b + E T miss searches and push the lower bound of the stop mass to 710 GeV. We also explore the potential to use the Higgs golden ratio, D γ γ = σ ( p p → h → γ γ ) / σ ( p p → h → Z Z ⁎ → 4 ℓ ± ) , as a complementary probe for the light and compressed stop. If this golden ratio can be measured at percent level at the high luminosity LHC (HL-LHC) or future e + e − colliders, the light stop can be excluded for most of the currently allowed parameter region.

Academic research paper on topic "Closing up a light stop window in natural SUSY at LHC"

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Physics Letters B

www.elsevier.com/locate/physletb

Closing up a light stop window in natural SUSY at LHC

Archil Kobakhidzeb, Ning Liu3 *, Lei Wu° *, Jin Min Yangc d, Mengchao Zhang

a Institution of Theoretical Physics, Henan Normal University, Xinxiang 453007, China

b AfiC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Sydney, NSW2006, Australia c Department of Physics, Tohoku University, Sendai 980-8578, Japan d Institute of Theoretical Physics, Academia Sinica, Beijing 100190, China

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Received 30 November 2015 Received in revised form 18 January 2016 Accepted 1 February 2016 Available online 4 February 2016 Editor: J. Hisano

Top squark (stop) plays a key role in the radiative stability of the Higgs boson mass in supersymmetry (SUSY). In this work, we use the LHC Run-1 data to determine the lower mass limit of the right-handed stop in a natural SUSY scenario, where the higgsinos x0 2 and x± are light and nearly degenerate. We find that the stop mass has been excluded up to 430 GeV for mx 0 < 250 GeV and to 540 GeV for mx0 —

100 GeV by the Run-1 SUSY searches for 2b + E^ and 11 + jets + E^, respectively. In a small strip of parameter space with mx0 > 190 GeV, the stop mass can still be as light as 210 GeV and compatible

with the Higgs mass measurement and the monojet bound. The 14 TeV LHC with a luminosity of 20 fb-1 can further cover such a light stop window by monojet and 2b + Em'ss searches and push the lower bound of the stop mass to 710 GeV. We also explore the potential to use the Higgs golden ratio, Drr = a(pp — h — YY)/°(pp — h — ZZ* — 4i±), as a complementary probe for the light and compressed stop. If this golden ratio can be measured at percent level at the high luminosity LHC (HL-LHC) or future e+e- colliders, the light stop can be excluded for most of the currently allowed parameter region.

© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

1. Introduction

Weak scale supersymmetry is a leading candidate for solving the naturalness problem of the Standard Model, i.e. explaining the radiative stability of the hierarchy between the electroweak scale and high energy scales, such as Planck mass. In the minimal super-symmetric standard model (MSSM), the minimization condition of the Higgs potential is given by [1]

(m2Hd + ) - (m2Hu + ) tan2 p

tan2 p - 1

where mHd and mHu

"2 denote the weak scale soft SUSY breaking masses of the Higgs fields, tan p = vu /vd and // is the higgsino mass parameter. £u and £d arise from the radiative corrections to the tree level Higgs potential, which include the contributions from various particles and sparticles with sizeable Yukawa and/or gauge couplings to the Higgs sector. Explicit forms for the £u and £d are given in the Appendix of Ref. [2]. Obviously, in order to

get the observed value of MZ without finely tuned cancellations in Eq. (1), each term on the right-hand side should be comparable in magnitude. This then suggests that the electroweak fine-tuning of MZ can be quantified by A-,,1

^ewW = (M 2/2)/maxi |Ci |.

Here, Chu = ~m2Hu tan2 p/(tan2 p - 1), CHi = m2Hi/(tan2 p - 1) and

Cn = -fi2. Also, CZu(i) = (i)(tan2 P)/(tanp -1) and C^d(i) = £d(i)/(tanp -1), where i labels the various loop contributions to Zu and Zd. So an upper bound on A-, > 10% from naturalness considerations implies that the higgsino mass parameter f must be of the order of ~ 100-200 GeV. Hence, to probe the SUSY naturalness at LHC, the most essential task is to search for light higgsi-nos. However, due to the low (percent level) signal-to-background ratio, detecting the pair production of these nearly degenerate hig-gsinos through monojet(-like) or vector boson fusion events seems challenging at LHC [5-7].

* Corresponding authors.

E-mail addresses: wlln@mail.ustc.edu.cn (N. Liu), wuleihep@gmail.com (L. Wu), mczhang@itp.ac.cn (M. Zhang).

1 The Barbieri and Guidice (BG) measure in Ref. [3] is applicable to a theory with

several independent effective theory parameters. But for a more fundamental theory, BG measure often leads to over-estimates of fine tuning [4].

http://dx.doi.org/10.1016/j.physletb.2016.02.003

0370-2693/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

Besides higgsinos, the stops usually strongly relate with the naturalness, which can contribute to A—, at one-loop level and favor the stop mass not to be too heavy2 [8]. In addition, there are other good theoretical motivations of considering a light stop. For example, in some popular grand unification models, supersymme-try breaking is usually assumed to transmit to the visible sector at a certain high energy scale, and then Yukawa contributions to the renormalization group evolution tend to reduce stop masses more than other squark masses. Another one is that the chiral mixing for certain flavor squarks is proportional to the mass of the corresponding quark, and is therefore more sizable for stops. Such a mixing will further reduce the mass of the lighter stop. Moreover, we note that a light stop is phenomenologically needed by the electroweak baryogenesis [10]. Given these, the searches for pair/single production of stop are also important to understand the naturalness and to test supersymmetric models at LHC [11-13].

So far, experimental searches for stops at LHC Run-1 have resulted in bounds on stop masses of a few hundred GeV [14-24]. The present search strategies of the direct stop pair production mainly depend on the mass splitting between the stop and the lightest supersymmetric partner (LSP). For example, when Amt _xo ^ mt, the top quark from stop decay can be quit energetic as compared with the top quarks in the tt background. Therefore, certain endpoint observables, like MT 2, can be used to efficiently reduce the tt background [15,17,18,23,24]. Contrary to this, in the compressed region, where Am~t^_xo ^ mt, the kinematics of the top quarks from stop decay are similar to those in the top pair production and the standard search strategies often suffer from a poor sensitivity. For this case, one way is to compare the top pair production cross section measurement with the theoretical prediction, which can rule out stop masses below ~ 180 GeV for a light neutralino LSP [16,25,26]. Another way is to use a high momentum jet recoiling against t^t* system to produce the large Em'ss and anti-correlation between Em'ss and the recoil jet transverse vectors [27-29]. Furthermore, if Am~t ~o ^ mt, the stop

decay will be dominated by the four-body channel fj ^ bf f x0 or the two-body loop channel fi ^ cx0 [30-33]. But due to the small mass difference, the decay products of the stop are usually too soft to be observed. Thus the single high pT hard jet from the ISR/FSR (with the heavy quark tagging) is used to tag these compressed stop events [34-37]. At the same time, many theoretical studies have been devoted to improving the LHC sensitivity to the stop searches in some special kinematical regions [38] and to constraining the light stops in various theoretical frameworks [39].

Besides the sparticle mass splitting, the assumption on the branching ratios of stop and the nature of neutralinos can significantly affect the sensitivity of the LHC direct searches. For examples, if M1,2 ^ the left-handed stop decay f 1 ^ tx0 2 is enhanced by the large top quark Yukawa coupling. Also, due to the SU(2) symmetry and nearly degenerate higgsinos (x0 2 and

X±), the left-handed sbottom decay b 1 ^ tx- inevitably mimics the stop signals t1 ^ tx0 2. The combined null results of the stop and sbottom searches have excluded a left-handed stop below about 600 GeV in natural SUSY scenario [40-43]. On the other hand, since the right-handed stop has no SU(2) gauge symmetry link with the sbottom sector, sbottoms can be decoupled and will not necessarily contribute to the stop events. Thus, the LHC direct search constraints on the right-handed stop will become weaker, and may still allow stop mass around the weak scale.

2 In some supersymmetric models, such as Ref. [9], the bound on the stop mass from naturalness can be weakened due to the cancellation between stop loop and other sparticle loops.

In this work, we use the LHC Run-1 data to determine the lower mass limit of the right-handed stop in a natural SUSY scenario, where the higgsinos x0 2 and x± are light and nearly degenerate in mass (2 GeV < Am < 5 GeV). Then we investigate the prospect of closing up the currently allowed light right-handed stop mass region through the direct searches for 2b + Em'ss, 1£ + jets + Em'ss and monojet events at 14 TeV LHC. Apart from the direct searches, one may also utilize indirect observations to constrain the light stops. Namely, the light stops can significantly affect the loop processes gg ^ h and h ^ yy. With the upgrade of LHC, the Higgs couplings with the gauge bosons will be measured with much higher experimental accuracy than the current measurements and may be used to indirectly constrain our scenario. We also explore the potential of the Higgs golden ratio Drr = ff(pp ^ h ^ yy)/a(PP ^ h ^ ZZ* ^ 4£±) [44] as a complementary probe for the light stop scenario.

2. Calculations, results and discussion

Considering the higgsinos and stops are closely related to the naturalness problem, we scan the following region of the MSSM parameter space:

100 GeV < ^ < 300 GeV , 100 GeV < mtR < 1 TeV,

1.5 TeV < 3 TeV , 1 TeV < At < 3 TeV,

5 < tan / < 50. (3)

As our study is performed in a simplified phenomenological MSSM, we abandon the relation M1 : M2 : M3 = 1 : 2 : 7 inspired the gaugino mass unification3 and assume M1 = M2 = 2 TeV at the weak scale for simplicity. Such a condition leads to the nearly degenerate higgsinos (with the mass splitting around 2-5 GeV). Besides, in order to avoid introducing too much fine-tuning, we take M3 = 1.5 TeV, which usually contributes to the Higgs mass at two-loop level. The sleptons and the first two generations of squarks in natural SUSY are supposed to be heavy to avoid the SUSY flavor and CP problems, which are all fixed at 3 TeV. We also assume mA = 1 TeV, Ab = 0 and mf = 2 TeV. Such a setup will make our lighter stop tf1 dominated by the right-handed component, and also provide the correct Higgs mass. In our scan we consider the following constraints:

2.1. Indirect constraints

(1) We choose the light CP-even Higgs boson as the SM-like Higgs boson and require its mass in the range of 123-127 GeV. We use the package of FeynHiggs-2.11.2 [46] to calculate the Higgs mass.4 Besides, a light stop with the large mixing trilinear parameter At needed by the Higgs mass often leads to a global vacuum where charge and color are broken [49,50]. We impose the constraint of the metastability of the vacuum state by requiring | At | < 2.67 /M2 + M? + MA cos2 / [50].

V Q 3L tR A

3 Note that one possible way to relax the naturalness problem is to choose a suitable boundary condition of gaugino masses at the GUT scale, such as M2 : M3 ~ 5 : 1 in Ref. [45].

4 In general, different packages may give a different Higgs mass prediction. It is known from the MSSM that spectrum generators performing a DR calculation (such as Suspect [47]) can agree quite well, while sizable differences to the OS calculation of FeynHiggs exist. The differences are assumed to arise from the missing electroweak corrections and momentum dependence at two-loop level as well as from the dominant three-loop corrections. These are the effects that underlie the often-quoted estimate of a few GeV uncertainty for the SM-like Higgs mass in the MSSM [48].

1 I— 10

Table 1

The signals of the LHC stop direct searches and the corresponding sources in the natural SUSY.

Amf „ (GeV)

Fig. 1. Dependence of the stop decay branching ratio on the mass splitting Amf]_xo.

(2) Since the light stop and higgsinos can contribute to the B-physics observables, we require our samples to satisfy the bound of B ^ Xsy at 2a level. We use the package of SuperIsov3.3 [51] to implement this constraint.

(3) As known, in the natural MSSM, the thermal relic density of the light higgsino-like neutralino dark matter is typically low because of the large annihilation rate in the early universe. In order to provide the required relic density, several alternative ways have been proposed [52-54], such as choosing the axion-higgsino admixture as the dark matter [55]. However, if the naturalness requirement is relaxed, the heavy higgsino-like neutralino with a mass about 1 TeV can solely produce the correct relic density in the MSSM [56]. So we require the thermal relic density of the neutralino dark matter is below the 2a upper limit of the Planck value [57]. We use the package of MicrOmega v2.4 [58] to calculate the relic density.

We have also verified using HiggsBounds-4.2.1 [59] and Higgs-Signals-1.4.0 [60] packages that the samples allowed by the above constraints are also consistent with the Higgs data from LEP, Teva-tron and LHC.

In Fig. 1, we show the dependence of the stop decay branching ratios on the mass splitting Am-ti_x) in our scenario. The branching ratios are calculated by the package of SDECAY [61]. We can see that a heavy right-handed stop decays to bx+ with Br ~ 50% and tx) 2 with Br ~ 25%, 25%. This is because the partial decay width r(f1 ^ bx+) and r(it1 ^ tx)2) are both proportional to y2 (yt is the top quark Yukawa coupling) [31]. Other decay modes f1 ^ tx) 4 are kinematically forbidden because the bino and wino mass is assumed to be decoupled in our calculations. For mb + mW < Amt _xo < mt, the dominant decay process t1 x1

is still f1 ^ bx+ because it has a much larger phase space than the three-body decay channel f1 ^ bWX0. Further, if Am^_xo < mb + mW, the four-body decay process f1 ^ bf f'x) and the loop decay channel f1 ^ cx) are extremely suppressed (except for the region where f1 ^ bx+ is kinematically forbidden), as shown in Fig. 1. The reason is that our stop is predominantly right-handed and the neutralino x) is higgsino-like, so that the decay width of f1 ^ cx) is heavily reduced because of tiny tL, R — CL mixing and of the gaugino-higgsino nature of neutralinos [3)]. The decay f1 ^ bf f 'x) is also suppressed due to the small phase space (note

LHC stop direct searches Sources in natural SUSY

i + jets + Emiss [15,23] pp ^ t1t1 (t1 ^ tx°2)

2b + E™ss [19] pp ^ t1t1 (t1 ^ bx+)

jet + E™ss [14] pp ^ jet + t1t1 (t1 ^ bx+, bff'x)2, cx)2)

that the neutralinos xx) 2 and the chargino are nearly degenerate higgsinos).

2.2. Direct constraints

In our scenario, due to M12 ^ //, the higgsinos x± and x)2 are nearly degenerate so that their decay products are too soft to be tagged at LHC. Such a feature can change the conventional LHC signatures in some certain stop decay channels. For example, the stop pair production followed by the dominant decay f1 ^ bxx+ will appear as 2b + Em'ss. So in our study, we consider the following relevant LHC direct search constraints at .Js = 8 TeV:

(1) The ATLAS search for stop/sbottom pair production in final states with missing transverse momentum and two b-jets [19].

(2) The ATLAS and CMS search for stop pair production in final states with one isolated lepton, jets, and missing transverse momentum [15,23].

(3) The ATLAS search for pair-produced stops decaying to charm quark or in compressed supersymmetric scenarios [14].

In Table 1, we summarize the signals of the above direct searches and the corresponding source of each signal in our scenario. We use the packages CheckMATE-1.2.1 [62] and MadAnalysis 5-1.1.12 [63] to recast the above ATLAS analyses (1)-(3) and CMS analysis (2), respectively. We calculate the NLO + NLL cross section of the stop pair production by using NLL-fast package [64] with the CTEQ6.6M PDFs [65]. The parton level signal events are generated by the package MadGraph5 [66] and are showered and hadronized by the package PYTHIA [67]. The detector simulation effects are implemented with the tuned package Delphes [68], which is included in CheckMATE-1.2.1 and MadAnalysis 5-1.1.12. The jets are clustered with the anti-kt algorithm [69] by the package FastJet [7)]. Finally, we define the ratio r = max(Nsj/$95%) for each experimental search. Here Ns,' is the number of the signal events for the i-th signal region and So9b5s%,i is the corresponding observed 95% C.L. upper limit. The max is over all the signal regions for each search. If r > 1, we conclude that such a point is excluded at 95% C.L.

2.3. Results

In Fig. 2, we plot the exclusion limits of the direct searches for the stop pair in the plane of m-t1 versus LSP mass at 8 TeV LHC with L = 2) fb—1. The green crosses represent the samples allowed by the current indirect and direct constraints. Since the moderate or heavy right-handed stop dominantly decays to bx+ and tx® 2, which produces 2b + Emiss and tt + Erl"ss signatures respectively, we can see that the searches for 2b + Emiss and H + jets + Emiss events give strong bounds on the stop mass in the

region with Am? _x) > mt. For example, when x ~ D) (25)) GeV,

the stop mass has been excluded up to about 54) (43)) GeV by H + jets + Efss (2b + Efss). If the stop mass is close to the LSP mass, the b-jets from the stop decay f1 ^ bx+/bf f x) 2 or c-jets from f1 ^ cx) 2 become soft. Then the monojet search will be a

8 TeV 20 fb"1 14TeV20fb"1

1-1-,-1-,-1-,-1-,-1-,-1-,-1-< | ■ i —,-1—,-1—,-1—,-1—,—|—,—r

100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 Hf, (GeV) mj, (GeV)

Fig. 2. Regions excluded by the direct searches for the stop pair at 8 TeV run (left panel) and extrapolation to the 14 TeV run (right panel) with L = 20 fb-1. For 1l + jets + Ems and 2b + Ems, the region below each curve is the excluded region. For the monojet search, the region to the left of the curve is its excluded region. The green crosses represent the samples allowed by the current indirect and direct constraints. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

m I, (GeV)

Fig. 3. Constraints of the Higgs golden ratio Dyy = o(ppp — h — YY)/a(pp — h — ZZ* — 4l±) on the light stop shown in the left panel of Fig. 2. The colormap represents the mass difference between the stop and the LSP.

sensitive probe for this region and can exclude the stop mass up to 150 GeV for f — 100 GeV. While in a small strip of parameter space with mx0 > 190 GeV, the stop mass can still be as light as 210 GeV and compatible with all the current bounds. As mentioned in [71], the higher energy will improve the sensitivity of the monojet searches for a mass splitting below 100 GeV. So, we regenerate the corresponding signals and backgrounds, and extrapolate our analyses to 14 TeV LHC by taking the same cut values and the definitions of the signal regions as those at 8 TeV LHC.5 Then, we can see that such a narrow region for a light stop can be further covered by the constraints of monojet and 2b + EmT iss with 20 fb-1 of data. At the same time, the lower bound of the stop mass will be pushed up to about 660 GeV for m~0 < 330 GeV

and 710 GeV for m~ 0 ~ 100 GeV by 2b + Efss and 1l + jets + Efss searches, respectively.

On the other hand, with more data collected at the LHC, the precision measurement of Higgs couplings can be used as indirect probes of light new particles [72]. In natural SUSY, the stops may significantly change the loop processes gg — h and h — YY. However, the signal strength measurement of pp — h — YY suffers from some theoretical uncertainties [73]. To solve this problem, a high-precision Higgs observable Dyy that can be measured at percent level was constructed by using the ratio of the Higgs golden channel signal strengths [44],

D yy = f(pp — h — YY)/f(pp — h — ZZ* — 4l±).

5 Here we conservatively estimate the exclusion limits at 14 TeV LHC. The optimization of the cut values and the signal regions may further improve our results.

In Fig. 3, we present the constraints of the Higgs golden ratio Dyy on the light stop window shown in Fig. 2. It can be seen that the stop with mass m^ — mt can significantly reduce the value of Dyy by about 18% because such a light stop will cancel with the contribution of W-loop in the decay of h — yy. While with the increase of the stop mass, the contribution of the stop loop can change the sign and constructively interfere with the W-loop. On the other hand, since the decay width of h — yy also depends on the tri-

linear parameter At and tan p [74], some of our samples can make Dyy very close to 1. Therefore, if the golden ratio Dyy can be measured at 1% level (as discussed in [44]) at the HL-LHC or future e+e- colliders, most of our light stop region allowed by 8 TeV LHC can be excluded.

3. Conclusions

In this work we used the LHC Run-1 data to constrain the right-handed stop in a natural SUSY scenario, where the higgsinos x02 and x± are light (f — 100-300 GeV) and nearly degenerate. For m^ ^ mt, we found that the stop mass is excluded up to about 540 (430) GeV for f — 100 (250) GeV by the 8 TeV LHC direct searches in 1l + jets + E^ (2b + ET"ss) channel. However, in a small strip of parameter space with mx0 > 190 GeV, the stop mass can still be as light as 210 GeV and compatible with the bounds from the Higgs mass and the current monojet searches. We have extrapolated our analyses to 14 TeV LHC and found that such a light stop mass window can be further covered by the monojet and 2b + Em'ss searches. The lower bound of the stop mass will be pushed up to about 710 GeV. We also found that the precision measurement of the Higgs golden ratio DYY = a(pp — h — YY)/a(pp — h — ZZ* — 4l±) at percent level can exclude most of our light stop region and thus play a complementary role in probing the light stop.

Acknowledgements

We thank Manuel Drees and Jong Song Kim for helpful discussions. This work is partly supported by the Australian Research Council, 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, by the Startup Foundation for Doctors of Henan Normal University under contract No. 11112, and the Joint Funds of the National Natural Science Foundation of China (U1404113).

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