Probing natural SUSY from stop pair production at the LHC
Abstract
We consider the natural supersymmetry scenario in the framework of the parity conserving minimal supersymmetric standard model (called natural MSSM) and examine the observability of stop pair production at the LHC. We first scan the parameters of this scenario under various experimental constraints, including the SMlike Higgs boson mass, the indirect limits from precision electroweak data and Bdecays. Then in the allowed parameter space we study the stop pair production at the LHC followed by the stop decay into a top quark plus a lightest neutralino or into a bottom quark plus a chargino. From detailed Monte Carlo simulations of the signals and backgrounds, we find the two decay modes are complementary to each other in probing the stop pair production, and the LHC with TeV and 100 luminosity is capable of discovering the stop predicted in natural MSSM up to 450 GeV. If no excess events were observed at the LHC, the 95% C.L. exclusion limits of the stop masses can reach around 537 GeV.
pacs:
14.80.Da,14.80.Ly,12.60.JvI Introduction
Although the standard model (SM) has been successful in describing the existing experimental data, it is suffering from the hierarchy problem and new physics based on certain symmetry is widely expected to appear at TeV scale to stabilize the electroweak hierarchy against radiative corrections. This belief was further strengthened by the recent discovery of the Higgs boson at the Large Hadron Collider (LHC) with its mass determined around 125 GeV ATLASCMS1112 (). This mass value agrees well with the prediction of low energy supersymmetry (SUSY), which is so far the most promising new physics candidate.
In SUSY, all known bosons and fermions have their supersymmetric partners, and the scalar top quarks (called stop with ), as the top quark partners, can modify the property of the SM Higgs boson by exactly canceling out the dangerous quadratic divergence of the top quark loop. Obviously, the experimental determination of the stop properties is crucial to unravel the nature of supersymmetry in protecting the Higgs mass at the weak scale and thus solving the hierarchy problem. In fact, such activities have been carried out extensively at the hadronic colliders such as the LHC and the Tevatron stoplhc (); gluinomediated (); stoptev (), but in contrast with the strong mass bounds (about 1 TeV) on the gluino and the first generation squarks susylhc (), a relatively light stop (say about 300 GeV) can not be excluded. Nevertheless, it should be mentioned that the recently measured Higgs boson mass around 125 GeV may give some indications for the stop sectorhiggsmass (); 125higgscmssm (); cao125Higgs (). In the popular MSSM with moderate and large , the Higgs mass is given by higgsmass ()
(1) 
where , and is the average stop mass scale defined by . This expression indicates that, for the heavier stop around 1 TeV as discussed above, the lighter stop must be heavier than about 200 GeV and must be larger than 1.5 TeV in order to push the Higgs mass up to 125 GeV cao125Higgs (). About these constraints, one should keep in mind that they are independent of the decay modes of , but on the other hand, they may be greatly weakened if there exists additional contribution to the Higgs mass cao125Higgs (); 125higgsnmssm ().
On the theoretical side, there are good reasons to consider at least one stop significantly lighter than other squarks with a mass around several hundred GeV. Firstly, in some popular grand unification models, supersymmetry 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. Secondly, 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. Thirdly, in the MSSM the minimization conditions of its Higgs potential imply mz ()
(2) 
where and represent the weak scale soft SUSY breaking masses of the Higgs fields, is the higgsino mass parameter, . and arise from the radiative corrections to the Higgs potential and the dominant contribution to the is given by
(3) 
These two equations indicate that, if the individual terms on the right hand side of Eq. (2) are comparable in magnitude so that the observed value of is obtained without resorting to large cancelations, the natural values of and should be around 100 GeV and several hundred GeV respectively. Numerically, the requirement of (or ) leads to upper bounded by about 500 GeV (or 1.5 TeV) sigmamstop (). Moreover, we note that a light stop is also phenomenologically needed by the electroweak baryogenesis baryogenesis () and may be welcomed by the dark matter physics coan (). In the MSSM, although the gluino contribute to at the oneloop level and to at twoloop level, the corrections are proportional to and can be greatly enhanced by the large gluino massnaturalsusyRS1 (). In order to the keep the naturalness, we expect to be lighter than about 3 TeV for TeV. However, since the current results of searching for the supersymmetry indicate that a gluino with mass about 1 TeV can safely avoid the LHC constraints, we require 1 TeV 3 TeV in our calculation.
Motivated by the theoretical preference and the results of the LHC search for SUSY, recently the natural MSSM scenario attracted broad attention naturalsusyRS1 (); naturalsusy1 (); naturalsusy2 (); naturalsusy3 (); naturalsusy4 (), which focuses on the following parameter space of the MSSM naturalsusyRS1 (); naturalsusy3 ():

1 TeV 34 TeV to escape the LHC constraint and at same time to avoid spoiling color symmetry; while the electroweakino masses may still be at subTeV scale;

as suggested by the relation and Eq.(2);

TeV to provide a decoupling solution to the SUSY flavor and CP problems.
Since the stop are relatively light and sensitive to probing this scenario, there have been recently many theoretical studies on the collider signatures of the light directly produced stop in the parity conserving and violating MSSMstopth (). For example, by using the top tagging technique, the sensitivity of stop searches were studied in the hadronic, semileptonic and dileptonic channelstoptagging1 (); toptagging2 (); toptagging3 (); toptagging4 (). In order to suppress the dileptonic top backgrounds, the authors in Ref.baiy () explore some new kinematic observables developed from to improve the sensitivity of the stop searches. For the small mass splitting between stop and top, it is pointed that the rapidity difference and spin correlation of the daughter products from stops decay can be helpful to discover the signalhanz (). When the stop mass is close to the lightest supersymmetric particle mass, the monojet signature from production is expected to be useful in detecting the stopdrees (). If the stop mass is degenerate with the sum of the masses of its decay products, the searches based on missing transverse energy ( or ) have significant reach for stop masses above 175 GeVmet (). When the parity is violated, the decay modes of the stop will be very different from the ones in parity conserving MSSM, such as stop decaying to dilepton and trilepton final statesrpv (). We also noted that the constrains on the light stop in the natural SUSY have been discussed by using the results from sparticles searches at the LHC, and indicated that they were mild and can be safely avoided currentlynaturalsusyRS1 (); naturalsusy3 (); naturalsusy4 (); yan ().
In this work, we investigate the potential of the LHC in probing the lighter stop predicted by the natural MSSM with parity, which is based on some considerations: (i) Most of the studies of the stop searches have been carried out under some assumptions at the LHC in a model independent way or in simplified models. It will be meaningful to explore what might happen in a realistic model like MSSM under the current available experimental constraints; (ii) Due to the parity conservation, there will be sizeable missing energy appearing in the sparticles productions and decays, which can be easily identified in the LHC data; (iii) One interesting phenomenological feature of the natural MSSM with parity is that both the lightest neutralino and the lighter chargino are Higgsinolike, and consequently always decays dominantly into and with , which can greatly simplify the analysis of the detection at the LHC.
For this purpose, we first scan the parameter space of the natural MSSM by considering various constraints in Sec. II. Then in Sec. III we discuss the observability of through the direct stop pair production in the allowed parameter space by performing the Monte Carlo simulations for the channel and the channel . We will present their corresponding sensitivities for 8 TeV LHC and for 14 TeV LHC respectively. Finally in Sec. IV, we summarize the conclusions obtained in this work.
Ii Scan over the parameter space
Motivated by the natural MSSM, we scan the parameter space of the MSSM as follows:
(4) 
For other unimportant parameters, we fix all the soft breaking parameters in the slepton sector and the first two generation sector at 10 TeV, and we assume , and (inspired by the grand unification relation). In our scan, we consider following constraints:

We require the SMlike Higgs mass within the range GeV. We use the code FeynHiggs2.8.6 feynhiggs () to calculate the mass and the code HiggsBounds3.8.0 higgsbounds () to consider the experimental constraints on the Higgs sector of the natural MSSM.

Since the natural MSSM has important implications in Bphysics naturalsusyb (), we use the code susyflavor v2.0 susyflavor () to consider the constraints from the processes and .

We consider indirect constraints from the precision electroweak observables such as , , and . We use our own code for such calculation rb ().

We require the thermal relic density of the lightest neutralino (as the dark matter candidate) is below the WMAP value wmap (). We use the code MicrOmega v2.4 micromega () to calculate the density.
After analyzing the surviving samples, we find they have two characters. One is that the Higgs mass of GeV requires GeV and there is a rather strong correlation between and the ratio , as shown in Fig.1. Here we further clarify that, if and are at subTeV scale, the minimum of will be enhanced to about 300 GeV cao125Higgs (). The other feature is that for most cases, the values of are significantly smaller than so that the lightest neutralino is higgsinolike. Fig.2 indicates that the surviving samples lie within two isolated regions. We checked that the lightest neutralino is binolike in the left region and higgsinolike in the right region. Here the bino(higgsino)like means it is still a mixed state but the dominant component is bino(higgsino). For the light neutralino dark matter(binolike), the main annihilation channel is through exchanging Z boson. The annihilation cross section is roughly proportional to . When the neutralino mass is about 50GeV60GeV, the annihilation cross section may be very large, so the relic density will be less than 0.1. When the neutralino becomes heavier(60GeV90GeV, neutralino is still binolike), the annihilation cross section will drop. The relic density becomes large and even exceeds the WMAP value, and these samples are excluded. This is the reason for the gap between 60GeV90GeV. When the neutralino goes on becoming heavy(90 GeV), the dominant component of the neutralino will be higgsino. The coupling between neutralino and Higgs gets important and annihilation rate goes up, then the relic density drops.
About the natural MSSM, we have two comments. One is that in this scenario the diphoton signal of the SMlike Higgs boson can hardly be enhanced to satisfy the requirement of the LHC data. This is because in the framework of the MSSM, there are only two cases which can enhance the diphoton rate, i.e. the small scenario smallalpha (); diphotonnmssm () and the light scenario higgsmass (); lightstau (), and in each case a large is needed. In the Ref.hooper (), the authors pointed that the light stop with large couplings to Higgs boson in the SM+stop model can improve the SM fitting to the LHC and Tevatron data by enhancing and suppressing . However, we should note that it does not mean that the diphoton production rate can reach the measurement of the LHC in a concrete MSSM model since the reduction of is usually much stronger than the enhancement of for large values of djouadi (). The other is that recently the ATLAS collaboration searched for the gluinomediated stop pair production followed by the decay , which set a lower bound gluinomediated (). This conclusion is not applicable to the our calculations since we take the gluino mass to be larger than 1TeV in the allowed parameters space of the natural SUSY.
Iii Observability of stop pair production at the LHC
In this section we discuss the LHC potential of discovering the stop through the direct stop pair production in the natural MSSM at TeV. In Fig.3 we show the production rate at the next leading order for the surviving samples. In getting this figure we used the package Prospino2.1 prospino () and the parton distribution function CTEQ6.6m cteq () with the renormalization scale and factorization scale setting to . This figure indicates that the maximal values of the cross section reach 5.5 pb and 25.7 pb for the LHC with TeV and TeV respectively, and with the increase of the stop mass, the production rates drop rapidly.
In Fig.4 we present various decay branching ratios of which are obtained by using the package SDECAY sdecay (). This figure indicates that for where the decay channel does not open up, decays into with a ratio of , and as the stop becomes heavier, the branching ratios for and may still be around . In contrast, the branching ratios for decays into and are usually less than .
In the following we perform detailed Monte Carlo simulations to investigate the observability of the direct stop pair production at the LHC. We concentrate on the semileptonic analysis with the btagging efficiency 40%, where the signal is consisted of four jets(at least one bjet), one lepton ( or ), and missing transverse energy. We first consider the process
(5) 
From the ATLAS search for the signal stoplhc (), we can see that the dominant SM background after the and cuts is dileptonic channel with one lost lepton and two additional jets from initial state radiation to fake the hadronic . Another backgrounds include semileptonic channel, dileptonic channel with one from top decay misidentified as a jet, jets and . Here we emphasize that the background becomes important for a heavy stop and should be considered in estimating the significance. In our calculation, we normalize the signal and the background to their NLO values prospino (); topnlo (), and simulate the signal and backgrounds by MadGraph5 mad5 () interfaced with PYTHIA pythia () and Delphes delphes () to carry out the parton shower and fast detector simulation. We use the anti algorithm antikt () with the distance parameter to cluster jets and the MLM scheme mlm () to match our matrix element with parton shower. We checked that the shapes of the matched 1,2,3 partons are very similar, and for simplicity, we take 2 jets samples in our calculations. In our calculations, since we employ the the variable defined in Ref.baiy (), we checked our results with theirs for the same parameters at TeV and found they were consistent with each other.
In Fig.5, we show the distributions of , the transverse mass defined in stoplhc () and for the backgrounds and our benchmark point GeV and GeV with TeV (similar results are found for TeV). This figure indicates that most events of jj and semileptonic backgrounds are characterized by GeV and GeV, and most events of the dileptonic backgrounds are characterized by , while a significant fraction of the signal may have larger , and . Fig.5 also indicates that the distributions of the background are quite similar to the signal and are difficult to be suppressed. Fortunately, the production rate of is much smaller than the one of .
cut (GeV)  cut (GeV)  cut (GeV)  (8TeV)  (14TeV) 

150      1.26  4.05 
150  150    2.75  7.91 
150  150  173  3.11  8.60 
In Table I, we present the significance of our benchmark point for 100 luminosity with TeV and 14 TeV respectively by sequentially imposing the cuts on , and . It can be seen that, for the given reference point, the cut GeV can greatly enhance the significance and GeV further improves the significance by about for TeV and for TeV to reach 3.11 and 8.60 respectively.
Therefore, for our simulations in the allowed parameters space, we take the following events selection criteria:

One isolated electron or muon that passes the following requirements;

Electrons GeV and without ;

Muon: GeV and ;

Events are rejected if they contain a second lepton candidate with GeV;


Four or more reconstructed jets with and .

150GeV, 150GeV, 173GeV.
where the basic cuts about and on leptons and jets are from the ATLAS reportstoplhc (). In order to improve the signal sensitivity, we increase the values of ATLAS cut from 100 GeV to 150 GeV to further suppress the semileptonic background and use the new cut 173 GeV to reduce the dileptonic background in our calculations.
In Fig.6 we show the significance of the surviving samples with GeV. This figure indicates that the largest significance can be reached at GeV where the significance is about 1.5 for TeV with 20 luminosity and 8.5 for TeV with 100 luminosity, and with the increase of the stop mass, the significance drop by one half for GeV mainly due to the reduction of the production rate. Our results are not as optimistic as those in toptagging1 (); toptagging2 (); baiy () because we have taken into account the branch ratio of . Fig.6 also indicates that there are two branches for the significance in the mass region 320 GeV 600 GeV. We checked that the upper branch corresponds to high branching ratio of , which varies from to and results in a large signal rate, while the lower branch corresponds to a small ratio due to the competition of the decay mode with and .
Above analysis implies that, in order to fully explore the parameter space of the natural MSSM in stop detection, the decay mode should also be considered. So we next consider the process
(6) 
Same as in Fig.5, we show the distributions of the three variables in Fig.7 for the benchmark point GeV, GeV and GeV. Compared with the distribution in Fig.5, one can see that more signal events have lower values of and low , due to the relatively light . Fig.7 also indicates the variable is helpless in suppressing the dileptonic events and any cut on may hurt the signal greatly.
In Fig.8, we show the significance of the surviving samples for the process in Eq.(6). In order to keep more signal events, here we relax the cuts of and used for the process in Eq.(5) as follows:
(7) 
From this figure, one can learn that, due to the large stop pair production rate, the significance for GeV may reach 7 for TeV with 20 luminosity and 64 for TeV with 100 luminosity, but for GeV, the maximum value drops to 1.5 and 10 respectively.
Finally, we summary the significance of the direct stop pair production with the above two decay modes of for GeV and 100 luminosity. The results are displayed in Fig.9 where only the maximal significance under each cut is shown. This figure indicates that, for 400GeV, detecting the stop pair production through the chargino decay is more effective, while for the neutralino decay is more effective. This figure also indicates that the LHC can discover predicated in nature MSSM up to . If no excess events were observed at the LHC, the 95% C.L. exclusion limits of the stop masses can go up to around 537 GeV no matter what decay modes of the stop in the natural MSSM.
Iv conclusion
In this work we studied the direct stop pair production at the LHC in the natural MSSM. We scanned over the corresponding parameter space by considering various experimental constraints and then in the allowed parameter space we examined the observability of the direct stop pair production at the LHC through the semileptonic analysis. We focused on the following two channels
and performed detailed Monte Carlo simulations about the signals and backgrounds. We found that for the second channel is better while for the first channel is better. We also found that the LHC with and luminosity is capable of discovering predicated in nature MSSM up to . If no excess events were observed at the LHC, the 95% C.L. exclusion limits of the stop masses can reach around 537 GeV in the natural MSSM.
Note Added
Very recently, the ATLAS collaboration reported the result of the direct searching for the stop pair production base on of dataatlasstop (). We validated our simulation by reproducing the ATLAS exclusion limit according to the assumptions and cuts in the report as follows:

One isolated electron or muon passing ‘tight’ selection criteria;

Electrons GeV and ;

Muon: GeV and .


Four or more jets with and 80, 60, 40 and 25 GeV, and at least one jet to be identified as a bjet;

,where is the minimum azimuthal separation between the two highest jets and the missing transverse momentum direction;

The jetjet pair having invariant mass 60 GeV and the smallest is selected to form the hadronically decaying boson. The mass is reconstructed including a third jet closest in to the hadronic boson momentum vector and 130 GeV 205 GeV is required;

150 GeV, 7 GeV and 120 GeV;

Events are rejected if they contain additional leptons passing looser selection criteria. Here we treat the looser selection criteria as 15 GeV.

The branch ratio of is assumed to be 100%.
In Fig.10, we display the expected exclusion limit from our simulation. Considering the differences between the fast simulation and full detector simulation, we can see that our result is consistent with the ATLAS exclusion limit within the reasonable error range. We also expect our result can be improved by the simultaneous fits method used by ATLAS for five signal regions and three control regions, however, which is beyond the scope of our simulation. It should be noted that the above stop masses limits can be avoided in our study, since the stop decays with a mixture of the branching ratios.
Acknowledgement
Lei Wu thanks Xerxes Tata, Zijun Xu and Qiang Li for helpful discussion about the natural SUSY and MG/ME, and appreciates the organizers and lecturers at the KIAS school on MadGraph for LHC physics simulation (Oct. 2429, 2011, KIAS, Soul). This work was supported in part by the National Natural Science Foundation of China (NNSFC) under grant Nos. 10821504, 11135003, 10775039, 11075045, by Specialized Research Fund for the Doctoral Program of Higher Education with grant No. 20104104110001, and by the Project of Knowledge Innovation Program (PKIP) of Chinese Academy of Sciences under grant No. KJCX2.YW.W10.
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