Searching for Stoponium Along with the Higgs Boson

Vernon Barger*

Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA

Muneyuki Ishida†

Department of Physics, School of Science and Engineering, Meisei University, Hino, Tokyo 191-8506, Japan

Wai-Yee Keung‡

Department of Physics, University of Illinois, Chicago, Illinois 60680, USA(Received 11 October 2011; published 23 February 2012)

Stoponium, a bound state of the top squark and its antiparticle in a supersymmetric model, may be

found in the ongoing Higgs searches at the LHC. Its WW and ZZ detection ratios relative to the standard

model Higgs boson can be more than unity from the WW� threshold to the two Higgs threshold. The ��

channel is equally promising. Some regions of the stoponium mass below 150 GeV are already being

probed by the ATLAS and CMS experiments.

DOI: 10.1103/PhysRevLett.108.081804 PACS numbers: 14.80.Ly, 12.60.Jv, 13.85.Rm

Discovery of a Higgs boson h0 is a top priority of LHCexperiments, as is the search for the supersymmetry whichis an attractive candidate for physics beyond the standardmodel (SM). Here we make the observation that there is apossibility of finding supersymmetry in the LHC search forthe Higgs boson.

The top squark ~t1, a scalar superpartner of the top quark,is expected to have the lightest mass of all the squarks [1]and may plausibly be lighter than the top quark. If the massdifference between ~t1 and the lightest supersymmetricparticle neutralino ~N1 is small and the tree-level decays~t1 ! t ~N1 and ~t1 ! b ~C1 (where ~C1 is the lightest chargino)are not kinematically allowed, the ~t1 becomes long-livedand ~t�1~t1 will form a bound state called stoponium. Thisexpectation is supported by the result [2] that the partialwidth of ~t1 ! c ~N1 occurring at loop level is negligiblysmall compared with the binding energy of the stoponium,a few GeV.

The possibility of stoponium discovery at hadron col-liders was considered long ago [3,4]. Its production via ggfusion and its decays are quite similar to the heavy quark-onium of the fourth generation quarks [5]. The productionamplitude is proportional to the wave function at the origin,and so the S-wave JPC ¼ 0þþ bound state, denoted here as~�, is expected to have the largest production cross section.Detection of stoponium is complementary to the detec-

tion of the top squark. Actually, current LHC data alreadygive a strong limit on the light top squark mass [6] by

considering the possible decay channels of ~tL ! ~bLW� and

~tL ! t ~N1. For the parameter space where these decaymodes are kinematically forbidden and the top squark islong-lived, as required for stoponium existence, this con-straint does not apply. The top squark decays to a charmquark and lightest supersymmetric particle neutralino atloop level, and this decay mode is notoriously difficult to

be identified, because of hadronic effects and the smallphase space. In this parameter region, stoponium detectionmay be the best way to search for supersymmetry.In this Letter, we refine the calculation of the production

and decays of the ~� appropriate to the LHC experiments at7 TeV (LHC7) and consider the possibility of finding the ~�in the ongoing LHC Higgs searches. Related work can befound in Ref. [7], and more recently in Ref. [8], at treelevel, and the NLO radiative corrections are considered inRefs. [9,10]. We demonstrate that ~� could be found in theSM Higgs search in the �� and W�W� channels at LHC7.Stoponium can be distinguished from a Higgs boson bydifferences in decay branching fractions.Stoponium production cross section.—The production

cross section of stoponium ~� in hadron colliders is mainlyvia gg fusion, similarly to the production of a Higgs bosonh0. The cross sections are proportional to the respectivepartial decay widths to gg. The production cross section ofh0 has been calculated in next-to-next-to-leading order(NNLO) [11], and by using this result [12] we can directlyestimate the production cross section of ~� as

�ðpp ! ~�XÞ ¼ �ðpp ! h0XÞ �ð~� ! ggÞ�ðh0 ! ggÞ : (1)

By using the �ð~� ! ggÞ partial width given later and�ðh0 ! ggÞ of the SM, we can predict �ðpp ! ~�XÞ.The result is compared with the SM Higgs production inFig. 1.The production of ~� exceeds that of the SMHiggs boson

of the same mass mh0 ¼ m~� for m~� < 230 GeV. This isbecause the ~� production from gg fusion has an amplitudefrom the four-point coupling at tree level, while h0 pro-duction is governed by the one-loop diagram of the topquark. Our prediction of �ðgg ! ~�Þ in Fig. 1 includes the

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�25% uncertainty associated with the theoretical uncer-tainty on �ðgg ! h0Þ.

Stoponium decay.—For the ~� decay channels ~� ! AB,we consider AB ¼ gg, ��, Z�, WþW�, ZZ, b �b, t�t, andh0h0. Their partial widths are given by the formula

�ð~� ! ABÞ

¼ 3

32�2ð1þ �ABÞ2pðm2

~�;m2A;m

2BÞ

m~�

jRð0Þj2m2

~�

X jMj2;

(2)

where M represent the free ~t1~t�1 ! AB amplitude, p is the

momentum of particle A (or B) in the c.m. system, andRð0Þis the radial wave function of stoponium at the origin. Thetotal width �tot

~� is the sum of these partial widths. Here weomit the lightest supersymmetric particle neutralino chan-nel AB ¼ ~N1

~N1, which is a suppressed decay mode [7,8].All the relevant formulas are given in the previous works[4,7,8], so we briefly explain here our method and theselection of parameters.

In calculations of the amplitude M ¼ Mð~t1~t�1 ! ABÞ,the mass of the lighter Higgs h0 is fixed to

mh0 ¼ 125 GeV, and a maximal mixing �~t ¼ �=4 be-tween the two top squarks ~tL and ~tR is taken. The valueof tan� ¼ vu=vd, the ratio of vacuum expectation valuesof the two Higgs doublets in supersymmetry, is taken to be10, and the Higgs mixing angle � is also fixed from thetree-level formula, tan2� ¼ f½ðm2

A þM2ZÞ=ðm2

A �M2Z��

tan2�g, with the choice mA ¼ 800 GeV, for whichtan� ¼ �0:103 [13].The contributions from the heavier Higgs H0 and the

heavier top squark ~t2 to the amplitudes are neglected underthe assumption that they are heavy. Amplitudes of t� , u�channel ~t or ~b exchanges are neglected except for the ~t1exchange in the h0h0 channel. Then, all the amplitudes aredescribed by the contact four-point interaction and/orthe s-channel h0 amplitudes when they contribute. TheFeynman diagrams of our analysis are shown in Fig. 2.For the gg decay of ~�, we include the radiative correc-

tions at NNLO by using the K factor from Higgs produc-tion [14]. For decay to ��, special attention is givento Ref. [9], since this branching fraction is larger thanthat of the Higgs boson for which a strong cancellation

between top-quark and W loops occurs. We use the Rð1Þ ¼�ð~� ! ��Þ=�ð~� ! hadronsÞ at NLO in Ref. [9], equating

their �ð~� ! hadronsÞ to our �ð~� ! ggÞ. Multiplying Rð1Þby our �ð~� ! ggÞ, we obtain �ð~� ! ��Þ. The off-shellWW�ðZZ�Þ channels in the low-mass ~� case are treated byfollowing Ref. [17].The gg partial decay width of ~� is proportional [5] to

½jRð0Þj=m~��2. We use the nonrelativistic quark model withthe Wisconsin potential, where a potential term in theintermediate range is added to the Cornell potential, toobtain the value of jRð0Þj [5,18]. The binding energy, afew GeV, is much smaller than m~t1 , and the stoponium

mass m~� is well approximated by 2m~t1 .

With these simplifications, the results depend only upontwo quantities: m~� and the h0~t1~t

�1 coupling �h0~t1~t

�1, denoted

asm~t1�2 in our previous work [4]. The �h0~t1~t�1is determined

by a dimensionless parameter [19]. In our illustrations,we consider two values of , ¼ 3 and �1, which corre-spond to the strong and weak h0~t1~t

�1 coupling, respectively.

The m~� is taken as a free parameter varying a wide

FIG. 1 (color online). The production cross section of ~�½pb�from gg fusion (solid blue line), �ðgg ! ~�Þ½pb�, compared withthat of the SM Higgs boson with the same mass mh0 ¼ m~� (solidred line). The overall theoretical uncertainties [11] are denotedby dotted lines.

FIG. 2. Dominant generic diagrams of ~� decay. Thin dashed lines with arrows represent the initial ~t1~t�1 of ~�, and two wavy lines

represent the final states �XX. Diagram (a) is taken into account in �XX ¼ gg; ��; Z�, diagram (b) in �XX ¼ �bb, and diagrams (a) and (b)in �XX ¼ WW;ZZ, while all three diagrams contribute to �XX ¼ h0h0.

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range: 135 GeV<m~� < 300 GeV. Below 135 GeV, themixing between ~� and h0 (with mh0 taken to be 125 GeVhere) may be important, although this mixing can behandled if necessary.

The decay branching fractions of ~� are given in Fig. 3. In

the case of ¼ 3 [larger �h0~t1~t�1ð¼ 396Þ GeV case], the

branching fractions ofWW, ZZ, h0h0, b �b, and t�t are larger

than those for ¼ �1 [smaller �h0~t1~t�1ð¼ 169Þ GeV case]

because of larger contributions from the s-channel h0

diagram. WW, ZZ, and h0h0 branching fractions become

even larger in the ¼ 10 case, where WW is dominant in2mW <m~� < 2mh0 . In the ¼ �1 case, the decay ampli-tude to h0h0 vanishes when m ~� ’ 370 GeV because of adestructive interference among the four-point interaction,t-, u-channel ~t1 exchange and the s-channel h0 diagrams.The existence of this cancellation has not been previouslynoted in the literature.The total width of ~� in the mass range m~� ¼

135–250 GeV is fairly small, �tot~� � 2–7 MeV, and in the

mass range m~� ¼ 260–300 GeV, it is at most �40 MeVfor the ¼ 3 case. Thus a ~� resonance would be observed

150 200 250 30010 4

0.001

0.01

0.1

1

3

hh

WW

ZZ

gg

Z

bb

150 200 250 30010 4

0.001

0.01

0.1

1

1

hh

WW

ZZ

gg

Z

bb

FIG. 3 (color online). Decay branching fractions of ~� versus m~�ðGeVÞ for ¼ 3 and �1. mh0 is taken to be 125 GeV.

150 200 250 3000.01

0.1

1

10

100

3

WW

ZZ

150 200 250 3000.01

0.1

1

10

100

1

WW

ZZ

FIG. 4 (color online). ~� DR to the SM Higgs boson h0 of Eq. (3) for the �XX ¼ WþW� (solid blue line), ZZ (dashed green line), and�� (solid black line) final states for ¼ 3 and �1 versus m~�ðGeVÞ.

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with the width of the experimental resolution. At m ~� >2mW , the �ð~� ! WWÞ partial width is negligibly smallcompared with �ðh0 ! WWÞ, and thus ~� production viavector boson (WW, ZZ) fusion is negligible at the LHC.

The ZZ toWW ratio of the ~� decay branching fraction ispredicted to be 0.32–0.36 (for ¼ 3) in the mass range200 GeV<m~� < 300 GeV, as compared with 0.36–0.44of the SM h0 in the same mass range. This ratio can beused to check if an observed resonance is actually stopo-nium or not.

Stoponium detection compared to the SM Higgsboson.—Next, we consider the detection of ~� in WþW�,ZZ, and �� channels. The ~� search can be made inconjunction with the Higgs search. The properties of h0

at the LHC are well known, so we use them as benchmarksof the search for ~�.

The ~� detection ratio (DR) to h0 in the �XX channel isdefined [20] by

DR � �~�!gg�~�! �XX=�tot~�

�h0!gg�h0! �XX=�toth0; (3)

where �XX ¼ WþW�, ZZ, and ��. The DR are plottedversusm~� ¼ mh0 in Fig. 4 for the two cases ¼ 3 and�1.

In the case of ¼ 3 (the large �h0~t1~t�1case), the ~� to h0

detection ratio is relatively large in both the WW and ZZchannels. The ratio is more than 0.5 in the mass range160<m~� < 250 GeV between the WW threshold and theh0h0 threshold. For m~� < 190 GeV, the ratio is nearlyunity. Even in the ¼ �1 case, the detection ratio is largein the 160<m~� < 250 GeV mass range.

The cross section of a putative Higgs-boson signal,relative to the standard model cross section, as a functionof the assumed Higgs-boson mass, is widely used by theexperimental groups to determine the allowed and ex-cluded regions of mh0 . By use of the DR in Fig. 4, wecan determine the allowed region of m ~� from the presentLHC data. Figure 5 shows the 95% confidence level upperlimits on Higgs-like ~� signals decaying into �XX versusm~�

for �XX ¼ WW;ZZ (ATLAS [21]) and �� (ATLAS [22]).For ¼ 3, m~� is excluded by the ATLAS data over

some ranges ofm~�, while for the ¼ �1 no regions ofm~�

are yet excluded. Similar results are found from the CMSdata [23].

The ~� search is also applicable to the Tevatron data. TheCDF and D0 experiments excluded the SM Higgs bosonwith mass 158 GeV<mh0 < 175 GeV from the data ofWW and ZZ channels. The same data exclude ~� in the ¼ 3 case in the mass range 160 GeV<m~� < 177 GeV.

The �� final state is very promising for ~� detection,because the ~� to h0 detection ratio is generally very largein all the mass range of m~�, as shown in Fig. 4. From the�� data of ATLAS, some regions of stoponium mass in135<m~� < 150 GeV are already excluded in both thecases of . The dependence of DR in �� is small below

the WW threshold, because the partial widths of all theallowed two-body final states are independent of . Form~� > 150 GeV, the �� signal of h0 is too small to bedetected, but the data in this region can determine theexistence of ~�.Concluding remarks.—We have investigated the possibil-

ity of finding stoponium ~� at LHC7. In the optimistic case ofthe stoponium mass and coupling, ~� will be discovered inthe WW, ZZ, and �� channels in the search for the SMHiggs boson h0. The detection rates can be comparable tothat of the SM h0, in the mass region m~� � 160 GeV up to2mh0 as shown in Fig. 4. The �� search channel is particu-larly promising, since the ~� detection ratio to h0 is verylarge (more than 3) in all mass regions. Some regions ofstoponium mass below 150 GeV are already excluded in awide range of supersymmetry parameters from the presentATLAS �� data. The h0h0 decay of ~� is another possiblemode for discovery, especially for large .M. I. is very grateful to the members of the phenome-

nology institute of University of Wisconsin–Madison forhospitalities. This work was supported in part by the U.S.

136 138 140 142 144 146 148 150

0.2

0.5

1.

2.

5.

10.

ATLAS

150 200 250 300

0.2

0.5

1.

2.

5.

10.

ATLAS WW

FIG. 5 (color online). The 95% confidence level upper limitsof ð1=DRÞ � ½�exp=�ðgg ! h0 ! �XXÞ�. This is the signal of a

boson decaying into �XX relative to the stoponium cross section½�ðgg ! ~� ! �XXÞ ¼ �ðgg ! h0 ! �XXÞ � DR� for �XX ¼WW (ATLAS [21]) and �� (ATLAS [22]) data. The cases ¼ 3 (solid blue line) and �1 (solid green line) are shown.Similar results for the SM Higgs boson are also given (thin solidred curve).

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Department of Energy under Grants No. DE-FG02-95ER40896 and No. DE-FG02-84ER40173, in part byKAKENHI [2274015, Grant-in-Aid for Young Scientists(B)], and in part by a grant as Special Researcher of MeiseiUniversity.

*barger@wisc.edu†Present address: Department of Physics, University ofWisconsin–Madison, Madison, WI 53706, USA.mishida@wisc.edu‡keung@uic.edu

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055.[12] In the approximation that the gg ! ~� interaction is

essentially pointlike, the QCD radiative corrections tothe tree level gg ! h0 and gg ! ~� should be nearlyequal, so we can use the tree-level result for �ð ~� ! ggÞ=�ðh0 ! ggÞ.

[13] This formula should be applied with a limit � ! �� �2 as

mA ! 1.[14] We use central values of the K factor of Higgs production

in NNLO given in Fig. 8 of Ref. [15]: For mh0 ¼100–300 GeV, K ¼ 2:0–2:3. This value is about 10%larger than the K factor of the Higgs boson decayinginto gg in NNLO given in Ref. [16] but within theuncertainty of the choice of the renormalization scale.So we simply assume that they are equal and adopt thevalue in Ref. [15]. Here we also note that the K factor for~� production is calculated in NLO [10] as K ’ 1:4 inm~� ¼ 200–600 GeV, which is, contradictorily with ourargument [12], 25% smaller than the value K ’ 1:9 in theNLO calculation for h0 given in Ref. [15].

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[19] �h0~t1~t�1

includes a term proportional to ð� sin�þm6At cos�Þ � MW , where is the Higgsino mass termin the superpotential andm6At is a soft breaking parameterof the trilinear scalar interaction [4].

[20] V. D. Barger and R. J. N. Phillips, Collider Physics(Westview, Boulder, CO, 1991), updated edition.

[21] ATLAS Collaboration, in Proceedings of SUSY2011at FNAL, 2011, Report No. ATLAS-CONF-2011-163(unpublished).

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[23] CMS Collaboration, ‘‘Search for the Higgs BosonDecaying to W þW in the Fully Leptonic Final State,’’CMS physics result, 18 August, 2011, for the analysisCMS-HIG-11-014 on the CMS public Web site.

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