a r X i v :h e p -p h /9712393v 1 16 D e c 1997
Search for the next-to-lightest neutralino
I.Iashvili and A.Kharchilava
Institute of Physics,Georgian Academy of Sciences,6Tamarashvili,380077
Tbilisi,Georgia
1Introduction
The Standard Model (SM),despite its phenomenological successes,is most likely a low energy e?ective theory of matter fermions interacting via gauge bosons.A good candidate for the new physics is the Supersymmetry (SUSY),which in its minimal version introduces a scalar (fermion)partner to each ordinary fermion (boson)with the same couplings.If R -parity is conserved,SUSY particles are produced in pairs and a stable Lightest Supersymmetric Particle (LSP)appears at the end of each sparticle decay chain.Weakly inter-acting LSP escapes detection and masses of sparticles cannot be reconstructed https://www.doczj.com/doc/1b1796973.html,ually,one characterises the SUSY signal signi?cance by an excess of events over the SM background expectation.
SUSY partners of gauge and Higgs bosons mix to form physical states,charginos ?χ±1,2,and neutralinos,?χ01,2,3,4.Depending on a particular SUSY scenario the
decays ?χ02→l +l ??χ
1and/or ?χ02→l ±?l ?→l +l ??χ01can take sizable branching ra-tios.The dilepton invariant mass spectrum in these decays has a speci?c shape with the sharp edge near the kinematical upper limit.In case of three-body
(direct)decays ?χ02→l +l ??χ
1the position of edge is M max l +l ?=M ?χ02
?M ?χ01(1)
and in case of two-body(cascade)decays it is
M max
l+l?=
M?
l
(2)
As discussed in Ref.[1]for?χ±1?χ02Electro-Weak(EW)production,the three-body leptonic decays of?χ02can be used to measure the mass di?erence be-tween?χ02and?χ01.At LHC,however,much higher production cross-sections are expected for strongly interacting gluinos and squarks.If?q(?g)is lighter than?g(?q),it can decay to quark plus neutralino or chargino:?q→q?χ0i/q′?χ±i (?g→qq′?χ0i/qq′?χ±i).Eventually,this source of?χ02is much more proli?c than direct EW production.Therefore,we propose to perform inclusive search for?χ02and to use the speci?c shape of the dilepton mass spectrum as evi-dence for SUSY[2].For the SM background suppression,besides two same-?avour opposite-sign leptons,one can ask an additional signature character-ising SUSY.This can be:missing energy taken away by escaping LSPs,or additional jets coming from gluinos and squarks cascade decays,or an ex-tra high-p T lepton from charginos,neutralinos,sleptons,IVBs,or b-quarks copiously produced in SUSY.Depending on sparticle masses and predomi-nant decay modes one of these extra requirements can turn out to be more advantageous than the others,or to be complementary.
In this paper we discuss the possibility to observe the?χ02in the inclusive
3leptons and3leptons+E miss
T ?nal states with the CMS detector at LHC.
The search strategy for SUSY is to look for a characteristic shape in the dilepton invariant mass spectrum with a sharp edge,rather than just for an event excess over the SM expectations.Such an observation would reveal SUSY through?χ02production,and at the same time would allow to constrain sparticle masses and some of the SUSY model parameters.We also propose a way to resolve the?χ02decay type ambiguity(three-body versus two-body),and a method of slepton mass determination in the?χ02two-body decay chain.
The present analysis is performed within the framework of the minimal Su-persymmetry Model motivated by Supergravity(mSUGRA),where only?ve extra parameters are introduced[3]:m0,the universal scalar mass,m1/2,the universal gaugino mass and A0,the universal trilinear term at GUT scale; tanβ,the ratio of vacuum expectation values of two Higgs?elds;sign(μ), the sign of the Higgsino mass parameter.Once these parameters are speci?ed all sparticle masses and couplings at EW scale are evolved via the renor-malization group equations.In the following we limit ourselves to the set: tanβ=2,A0=0,μ<0and investigate what is the region of(m0,m1/2) parameter space,where the dilepton invariant mass edge is visible[2].
2?χ0
2
production and decay
Within mSUGRA the following relations are valid:
M?χ0
2≈M?χ±1≈2M?χ01≈(0.25÷0.35)M?g≈0.9m1/2(3)
M2?
l L
=m20+0.52m21/2?0.5(1?2sin2θW)m2Z cos2β(4)
M2?
l R
=m20+0.15m21/2?sin2θW m2Z cos2β(5)
The three-body leptonic decays of?χ02dominate below m1/2～200GeV nearly for all values of m0,and there is also a small region at higher m1/2where
these decays are open.In these regions the measurement of M max
l+l?within
mSUGRA allows to get estimate of M?χ0
1(?χ01=LSP),M?χ0
2
,M
?χ±
1
,M?g and
m1/2(c.f.eqs.(1),(3)).At m1/2～200GeV,the modes,?χ02→h?χ01/Z?χ01, become kinematically allowed thus suppressing direct leptonic decays of?χ02. The two-body decays of the?χ02via?l L/R occur mostly at a low values of m0. In these regions the measurement of only the edge position does not provide information on masses unambiguously(c.f.eq.(2)).However,as shown later, by analysing some kinematical distributions,the masses of?χ01,?χ02and of the intermadiate slepton can be determined with a reasonable precision.Therefore, with two-body decays one can constrain m1/2and m0if the information on tanβis available,e.g.,from the Higgs sector of the model.In some regions of parameter space the two-body and three-body leptonic decays coexist or both modes?χ02→l±?l?R and?χ02→l±?l?L are open,leading to a possibile observation of a”double edge”.
At LHC the?χ02is abundantly produced either from gluinos or from squarks over almost the whole(m0,m1/2)plane,as illustrated in Figs.1a,b.Figure 1c shows the?χ02decay branching ratio into leptons(l=μor e).Finally, the?χ02inclusive production cross-section times branching ratio into leptons is shown in Fig.1d.Clearly,one expects quite large rates of opposite-sign same-?avour dileptons from inclusive?χ02production over a large portion of (m0,m1/2).Similarly to the?χ02,the lightest chargino is also copiously produced from strongly interacting sparticles.Moreover,the leptonic decay branching of the?χ±1always exceeds0.1per lepton?avour.For low values of m0,in the regions where decays to sleptons are kinematically allowed,the?χ±1gives a lepton with a probability close to1.Making use of this proli?c production of leptons from?χ±1,as well as from other SUSY sources,the SM background can be suppressed by asking for an additional high-p T lepton.Thus the?χ02
inclusive production can be studied in3lepton and3lepton+E miss
T ?nal
states.
mSUGRA parameters: tan β = 2, A 0 = 0, μ < 0
5001000
1500
2000
200
400
600
8001000
10
-1
1
B (g ~
→ χ~02 + x )
a)
500
1000
1500
2000200
400
600
8001000
10
-1
1
B (u ~
L → χ~0
2 + x )
b)
500
1000
1500
2000
200
400
600
8001000
10
-1
1
B (χ~
02 → l +l - + i n v .)
c)
500
1000
1500
2000200
400
600
8001000
10
-2
10-1110102103σ?B (χ~0
2 → l +l -
+ i n v .), p b
d)
Fig.1.?χ02inclusive production and decay:a)branching ratio B(?
g →?χ02+x),b)B(?u L →?χ02+x),c)B(?
χ02→l +l ?+invisible )and d)?χ02inclusive production cross-section times branching ratio into l +l ?(l =μor e).
3Event simulation and selection
For signal simulation we have generated all mSUGRA processes,using ISAJET
7.14[4].The considered SM sources of background,WZ,t ˉt ,ZZ and Z b ˉb pro-ductions,have been simulated by P YTHIA 5.7[5].The following production
cross-sections have been assumed at LHC energy of
√
account:i)particle bending in a4T magnetic?eld;ii)smearing of lepton momentum according to parameterisation obtained from detailed simulations; iii)90%triggering plus reconstruction e?ciency per lepton within geometrical acceptance|η|<2.4;iv)90%reconstruction e?ciency per charged track with p T>1GeV within|η|<2.4;v)coverage,granularity,main cracks,energy resolution and electronic noise of the calorimetry system;vi)?uctuation of starting point and the spatial development of electromagnetic and hadronic showers by parameterisation of the lateral and longitudinal pro?les.For the high luminosity study,L=1034cm?2s?1,on top of each signal and background events we have superimposed on average15”hard”pile-up events(P YTHIA QCD jet production with?p T>5GeV)?uctuated by Poissonian distribution. In the inclusive3lepton channel we require:1)two opposite-sign,same-?avour leptons(μor e)with p T>10GeV;2)a third”tagging”lepton with p T>15 GeV;3)lepton isolation:if there is no track with p T>2(1.5)GeV within √
?R=
20
40
60
80
050100150
m 0= 200 GeV, m 1/2= 100 GeV L int =20 pb
-1
p 1,2
T > 15 GeV
Isolation p 3T > 15 GeV
a)
10
20
30
0100200300400
m 0= 150 GeV, m 1/2= 700 GeV p 1,2,3
T > 50, 25, 10 GeV Isolation E miss
T > 300 GeV
b)
L int = 105 pb
-1
Fig.2.Expected l +l ?mass spectrum for mSUGRA points:a)m 0=200GeV,m 1/2=100GeV in the inclusive 3lepton ?nal states;b)m 0=150GeV,m 1/2=700
GeV in the 3lepton +E miss T
?nal states.The other mSUGRA parameters are tan β=2,A 0=0and μ<0.The hatched histogram corresponds to the SM back-ground.
the mass scale as well as the production cross-section.
With increasing m 1/2the observation of the ”edge”becomes more di?cult due to a rapid fall of gluino/squark production cross-sections.Here,on the other hand,heavier ?g and ?q provide higher missing transverse energy.Asking E miss T >200(300)GeV rejects most of the SM background whilst retaining a large fraction of signal events.Figure 2b shows the dilepton spectrum for
the mSUGRA point (150GeV,700GeV)in the 3lepton +E miss
T ?nal states.In this region of high m 1/2dileptons are mainly produced through cascade decays of ?χ02through intermediate state sleptons.The third,”tagging”lep-ton,predominantly comes from a ?χ±1produced in association,again from ?g ,?q cascades.
In order to delineate the region of parameter space where the l +l ?edge is vis-ible,the (m 0,m 1/2)plane has been systematically scanned for ?xed tan β=2,A 0=0and μ<0.At least 40signal events in a mass interval >10GeV just below the edge position and a statistical signi?cance S =N S /
√
100
200300400500600700800900
1000100200300400500600700800900
1000
mSUGRA parameters: tan β=2, A 0=0, μ<0
T H E O R Y
E X P E R I M E N T
?h
2
0.4
0.15
.....
.
........................
.... 3 lepton, L int = 104 pb
-1
3 lepton + E miss
T , L int = 105 pb -1
Fig.3.Explorable region of mSUGRA in inclusive 3lepton and 3lepton +E miss T
?nal states with L int =104pb ?1and L int =105pb ?1,respectively.Shaded regions are excluded by theory and/or experiment.The simulated mSUGRA points are shown by circles.The cosmologically preferred region 0.15
critical density of the Universe and h is the Hubble constant scaling factor.In
the 3lepton +E miss
T ?nal states with L int =105pb ?1the reach extends up to
m 1/2～900.A detectable edge is seen as long as σ·B >～10?2
pb (see Fig.1d ).5
?χ02decay type and slepton mass determination
The ?χ02decay type (three-body versus two-body)determination is essential for the interpretation of the observed edge.The p T spectra of leptons from ?χ02(cascade)two-body decays are more asymmetric compared to the three-body ones.To characterise this asymmetry we introduce the variable A =
p max T
?p min T
10
2
10
3
10
4
20406080100
L int =5?103 pb -1
p 1,2
T > 15 GeV Isolation p 3
T > 15 GeV
m 0=100 GeV, m 1/2=150 GeV
Fig.4.l +l ?mass distribution for m 0=100GeV,m 1/2=150GeV,tan β=2,A 0=0and μ<0.The hatched his-togram corresponds to the SM back-ground.
100
200300400500600
70000.10.20.30.40.50.60.70.80.91
3-body decays
“Observed“
Fig.5.Lepton p T -asymmetry distribu-tions in three-and two-body decays of ?χ02with the same position of dilepton invariant mass edge.
this point with L int =5·103pb ?1,superimposed on the SM background,in the inclusive 3lepton ?nal states.An edge is situated at ～52GeV,as expected.To look at the lepton p T -asymmetry distribution,we pick up the lepton pairs with M l +l ?<52GeV.Figure 5(full line)shows the corresponding A spectrum for the selected events.The pronounced asymmetry in p T indicates the cascade nature of ?χ02decays.The dotted histograms are obtained with the assumption that the ”observed”edge is due to direct three-body decays with various M ?χ02,M ?χ01combinations providing M ?χ02?M ?χ01=52GeV.In these cases the asymmetry A distributions peak at zero.
After the decay type is determined a further analysis step is carried out to
extract the masses of involved particles:i)assume M ?χ02
=2M ?χ01,ii)generate samples of ?χ022-body cascade decays for various M ?χ01
(M ?l );note,that the slepton mass is constrained to provide the ”observed”position of an edge
given by eq.(2),iii)the best combination of M ?χ01
,M ?χ02and M ?l is then chosen by means of a χ2-test of the shape of the lepton p T -asymmetry distributions.
This procedure provides the following precisions on masses:δM ?χ01<～
5GeV,δM ?l <～10GeV.The use of the total number of observed events,as well as the dilepton invariant mass spectrum itself in a combined χ2-test would further improve these results.
10
2
103
104
20406080100
M l ~ = 120 GeV
M l ~
= 77 GeV
Fig.6.Predicted l +l ?mass spectra for two values of slepton mass:M ?l =120GeV (full line)and M ?l =77GeV (dashed line);mSUGRA parameters are as in Fig.4.0
20
406080
100120020406080100120140
m 0= 50 GeV, m 1/2= 125 GeV
p 1,2
T > 15 GeV
Isolation p 3T > 15 GeV
L int = 103 pb -1
Fig.7.Expected l +l ?mass spectrum for mSUGRA Point m 0=50GeV,m 1/2=125GeV,tan β=2,A 0=0and μ<0.The hatched histogram corre-sponds to the SM background.
6Double edge
As discussed in section 2,in some regions of the (m 0,m 1/2)plane the di?erent leptonic decay modes of ?χ02can be simultaneously open and observation of ”double edges”is possible if the branching ratios are not too dissimilar.This is the case,for instance,for the mSUGRA point (100GeV,150GeV)discussed in
the previous section.Here,beside the ?χ02→l ±?l ?R →l +l ??χ
1decays,the direct three-body decay mode is also open,though,with a much smaller branching
ratio,B(?χ02→l +l ??χ
1)=0.05.The second edge at M max l +l ?=69GeV seen in Fig.4is thus less spectacular than the one at 52GeV.The p T -asymmetry distribution of dileptons with 55GeV positions and assuming M ?χ02 =2M ?χ01,we obtain two solutions for the slepton mass from equations (1)and (2):M ?l =120GeV and 77GeV.Corresponding dilepton invariant mass spectra for these two solutions are shown in Fig.6.The clear di?erence in the predicted spectra (Fig.6vs.Fig.4)allows to eliminate the M ?l =77GeV solution.At this particular mSUGRA point the use of both edges provides a precision of δM ?χ01,?l <～1GeV.Another example of a ”double edge”is given in Fig.7for the mSUGRA point (50GeV,125GeV).Here the sparticle masses are M ?χ02 =116GeV,M ?χ01=55GeV,M ?l L =110GeV,M ?l R =78GeV and now two two-body decays coexist, with a comparable branching ratios B(?χ02→l ±?l ?L →l +l ??χ 1)=0.037and B(?χ02→l ±?l ?R →l +l ??χ 1)=0.013and their analysis could proceed as indicated above providing a strong constraint on the underlying model. 7Conclusions ?Observation of an edge in the dilepton invariant mass spectrum re?ects production of?χ02and hence establishes existence of SUSY;this observation in some cases is possible with very small statistics and could be the?rst evidence for SUSY at LHC. ?In the inclusive3lepton?nal states,with no great demand on detector performance,a large portion of parameter space,including the cosmologically preferred mSUGRA domain,can be investigated at an integrated luminosity of L int=104pb?1. ?In the inclusive3lepton+E miss T?nal states and with L int=105pb?1most of the region where the?χ02inclusive production cross-section times branching ratio into leptons>～10?2pb can be covered. ?From the observation of characteristic edge(s)and with mSUGRA motivated assumptions,it is possible to determine masses of?χ01and?χ02in case of direct decays and masses of?χ01,?χ02and sleptons in case of cascade decays. Acknowledgements We would like to thank Daniel Denegri for many fruitful discussions and en-couragement,Walter Geist,Tejinder Virdee and John Womersley for useful remarks. References [1]H.Baer,C-h.Chen,F.Paige and X.Tata,Phys.Rev.D50(1994)2148. [2]A.Kharchilava,Search for next-to-lightest neutralino,in:LHCC SUSY Workshop, CERN,October29?30,1996;Copies of transparencies available under http://www.cern.ch/Committees/LHCC/SUSY96.html;CMS Document1996-149; I.Iashvili and A.Kharchilava,CMS NOTE/1997-065. [3]For a review,see e.g.,H.P.Nilles,Phys.Rep.110(1984)1. [4]H.Baer,F.Paige,S.Protopopescu and X.Tata,in:Proceedings of the Workshop on Physics at Current Accelerators and Supercolliders,eds.J.Hewett,A.White and D.Zeppenfeld(Argonne National Laboratory,Argonne,Illinois,1993). [5]T.Sj¨o strand,https://www.doczj.com/doc/1b1796973.html,m.82(1994)74. [6]S.Abdullin,A.Khanov and N.Stepanov,CMS TN/94-180. [7]H.Baer and M.Brhlik,Phys.Rev.D53(1996)597.
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