Minimal SUGRA Model and Collider Signals

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by  R. Arnowitt

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MINIMAL SUGRA MODEL AND COLLIDER SIGNALS
R. ARNOWITT,† BHASKAR DUTTA,∗ T. KAMON† AND V. KHOTILOVICH†
†Department of Physics, Texas A&M University, College Station, TX 77807, USA
∗Department of Physics, University of Regina, Regina, Saskatchewan S4S 0A2, Canada
5
0
0 The SUSY signals in the dominant stau-neutralino coannihilation region at a 500(800) GeV linear
2 collider are investigated. The region is consistent with the WMAP measurement of the cold dark
matterrelicdensityaswellasallothercurrentexperimentalboundswithinthemSUGRAframework.
n Thesignalsarecharacterized byanexistence of verylow-energytau leptons inthefinal state dueto
a small mass difference between τ˜1 and χ˜01 (5-15 GeV). We study the accuracy of the mass difference
J measurementwitha1◦ activemasktoreduceahugeSMtwo-photonbackground.

2

1 Introduction 1000
2
v A=0, m> 0
2 The recent measurement of cold dark mat- GeV] GeV] ta0nb =40
110 tweirth(CtDhMe )Hrigelgics dmeansssitybofruonmdWanMdAtPh1eablon→g 800 14 GeV 00cc˜˜[500 21 17 GeV 00cc˜˜[800 21 20 GeV
sγ constraint have restricted the parameter 1 1 1
1 ]
4 space significantly2 within the framework of eV
0 minimal supergravity (mSUGRA) model.3,4 [G 600 b→sg am<11×10-10
/ m0
h Oneprominentparameterspaceistheregion
-p wherethemassdifference(∆M)betweenthe 400 ˜t1˜t1[800 GeV]
p lighter stau (τ˜1) and the lightest neutralino
:he (feχ˜r01e)nciseaablloouwte5d-1t5heGτ˜e1Vt.oTchoiasnsnmihailllamteaisns dthife- ˜t1˜t1[50d0a Grke Vm]atter amllco˜0w> medt˜
v early universe along with the χ˜0 in order 200
i 1 200 400 600 800 1000
X to produce the current amount of the CDM
m [GeV]
r (χ˜01). The coannihilation region has a large 1/2
a extension for m up to 1-1.5 TeV, and can Figure1. Allowedregioninthem0-m1/2 planefrom
1/2 the relic density constraint for tanβ = 40, A0 = 0
be explored at the LHC. The main difficulty,
andµ>0. Thedetailsareprovidedintext.
however, in probing this region is to detect
very low-energy taus in the final state of the
SUSY events due to the small ∆M value. the electroweak scale; and the sign of µ, the
In this paper, we report a feasibility Higgsmixingparameterinthesuperpotential
study of measuring the small mass difference (Wµ =µH1H2).
in this τ˜1-χ˜01 coannihilation region at a 500 Figure 1 is anexample ofthe allowedre-
GeV linear collider (LC). gion in the m0-m1/2 plane for tanβ = 40
with A0 = 0 and µ > 0. The most impor-
tantexperimentalresults for limiting the pa-
2 mSUGRA Parameter Space
rameter space are: (1) The light Higgs mass
The mSUGRA model depends on only four bound (pink lines in the figure) from LEP:5
parameters and one sign. These are m0 (the Mh >114GeV;(2)The b→s+γ branching
universalsoftbreakingmassattheGUTscale ratio (brick red region):6 2×10−4 <B(B →
MG);m1/2 (theuniversalgauginosoftbreak- Xsγ) < 4.5×10−4; (3) Previous CDM (χ˜01)
ingmassatMG);A0 (theuniversalcubicsoft density bounds of 0.07<Ωχ˜01h2 <0.21 (yel-
breakingmassatMG);tanβ =hH2i/hH1iat low band) from balloon flights (Boomerang,
For Publisher’s use
Maxima, Dasi, etc.) and the 2σ bound of
Table1. Masses(inGeV)ofSUSYparticlesinthree
0.095 < Ωχ˜01h2 < 0.129 (blue band) from representativescenariosof∆M form1/2 =360GeV,
WMAP1; (4) The bound on the lightest tanβ=40,µ>0,andA0=0.
cmhuaornginmoamgnaestsi:c7mχ˜±1om>en1t0a4nGomeVa;ly(5()ligPhotssbilbulee MC m0 Mχ˜02 Mτ˜1 Mχ˜01 ∆M
Pt.
region to be excluded if δa >11×10−10).8
µ
1 205 274.2 147.2 142.5 4.7
ItisstrikingtolearnthatonlytwoSUSY
2 210 274.2 152.0 142.5 9.5
productionprocessescan be studied at a 500
GeV LC: τ˜+τ˜− and χ˜0χ˜0. The kinematical 3 220 274.3 161.6 142.6 19.0
1 1 2 1
reaches via the τ˜+τ˜− and χ˜0χ˜0 production
1 1 2 1
arealsoshowninFig.1. Themaximumreach
in m along the coannihilation band can
1/2
be expected via e+e− → τ˜1+τ˜1− → (τ+χ˜01)+ TBa(bτle2.τhSU)2SiYnfabn)dfoSrMpoplraoridzuacttioionnfocrroeslsecstercotniobnesa(mσs·
(τ−χ˜01). of (→e−)= 0.9(RH).
P −
We use the hadronic final state of tau
SUSY Pt. 1. χ˜0χ˜0 0.43
(τh )sinceithaslargerbranchingratios. Due τ˜+1τ˜−2 28.25
to the small ∆M value, the taus in the final 1 1
SUSY Pt. 2. χ˜0χ˜0 0.39
statesarelowenergyandhencehardertode- 1 2
τ˜+τ˜− 25.85
tect. 1 1
SUSY Pt. 3. χ˜0χ˜0 0.38
1 2
τ˜+τ˜− 22.95
1 1
3 SUSY Signals at 500 GeV LC
SM (four fermion process) 7.84
In order to optimize the event selection cuts,
we choose three points of m0 = 205,210 and
220 GeV for m = 360 GeV, tanβ = 40,
1/2
µ > 0, and A0 = 0. The SUSY masses ISAJET9 to generate SUSY events; WPHACT10
givenbyISAJET9aresummarizedinTable1. for SM backgrounds; TAUOLA11 for tau de-
There are two major Standard Model (SM) cay;aLCdetectorsimulation2toreconstruct
background processes: (i) four-fermion final jets with JADE algorithm.12 In our calcula-
state ν¯ντ+τ− arising from processes such as tion, beamstrahlung and bremsstrahlung are
diboson(WW,ZZ)production,and(ii)two- included in both ISAJET and WPHACT.
photon processes e+e− → γ∗γ∗ + e+e− → Theacceptednumberofsignalandback-
τ+τ− (or qq¯) + e+e− where the final state ground events are summarized in Tables 4
e+e− pair are at a small angle to the beam and 5. It should be noted that the number
pipe and the qq jets fake a τ+τ− pair. of SM γγ events with the forward electrons
The production cross-sections for SUSY just below 3◦ are 11400. The acceptances
(ISAJET) and SM four-fermion processes for τ˜+τ˜− events are 11.2%, 5.9%, and 0.86%
1 1
(WPHACT10)arelistedinTable2fora500GeV for ∆M= 19, 9.5, and 4.7 GeV, respectively
LC. We choose with right handed (RH) po- with 1◦mask. The acceptance drops fast as
larized electron beams to enhance the τ˜+τ˜− ∆M goes below 5 GeV. For example, 0.23%
1 1
events over the χ˜01χ˜02 and SM four-fermion for ∆M= 3.8 GeV (m0 = 204 GeV). We see
events. the robust discovery significance for the sig-
In Table 3, we summarize the event se- nal events for ∆M> 5 GeV with 1◦ mask in
∼
lection criteria for the RH case. The Monte Table6. Weconcludethatthemaskisessen-
Carlo (MC) events are generated, simulated tial to detect SUSY events in this region of
and analyzed using the following programs: parameter space.
For Publisher’s use
Table3. EventselectioncriteriafortheRH( = 0.9)case.
P −
Variable(s) Cuts
N (E >3 GeV) 2
jet jet
τ ID 1, 3 tracks
h
Jet acceptance |cos(θ )|<0.65
jet
−0.6<cos[θ(j2,pvis)]<0.6
Missing p (/p ) > 5 GeV
T T
Acoplanarity >40◦
Veto on EM clusters No EM cluster in 5.8◦ <θ <28◦ with E >2 GeV
or electrons No electrons within θ >28◦ with p >1.5 GeV
T
Beam mask (1◦(or 2◦) - 5.8◦) No EM cluster with E >100 GeV
Tfba−b1lefo4r. tNhuemRbHercaosfeS.USYevents expected with500 TSUabSlYe 6d.isScoigvneirfiycaunsicneg(1N◦Sm/√asNk.B) with 500 fb−1 for
Process ∆M = 4.7 9.5 19 Process (RH) ∆M= 4.7 9.5 19
χ˜02χ˜01 15 26 29 τ˜+τ˜− 10 63 101
τ˜+τ˜− 122 786 1283
Table 5. Number of SM events expected with 500
fb−1. calculatetheχ2 ofthefits. Heretheχ2 value
SM four-fermion 129 is calculated as χ2 = Ni− jCjFij 2
SM γγ 2-5.8◦ Mask 248 i(cid:18) Pσi (cid:19)
P
1-5.8◦ Mask 2 whereNi isthenumberofeventsini-thMeff
bin of the 500 fb−1 sample, C Fj is the cor-
j i
responding value for the template “j” where
4 Measurement of Stau Neutralino j is for SM, τ˜+τ˜− or χ˜0χ˜0 processes. C is a
1 1 1 2 j
Mass Difference normalization parameter and a free variable
except for the SM process. This is because
Since ∆M is small, it needs to be measured we should be able to measure the SM events
with a very good accuracy. We choose the very well before we discover SUSY events.
invariant mass Meff ≡ M(j1,j2,E/) of two We scanthe rangeofm0 = 203-220GeV
τ-jets and missing energy as a key discrimi- andplot the ∆χ2 ≡χ2−χ2 in Fig. 3. The
min
nator. We generate high statistics MC sam- ∆χ2 value is minimum for the template for
plesforthe SMandvariousSUSYevents(by m0 = 210 GeV. We find that 1σ in the ∆χ2
changingthem0 value)andpreparethetem- corresponds to 9.5±1 GeV, where the true
plates of the Meff distributions for the SM, value of ∆M for the Point 2 is 9.53 GeV.
χ˜0χ˜0, and τ˜+τ˜− events. We repeat the same study for different
1 2 1 1
WethengeneratetheMCsamplesequiv- stau masses i.e. for different ∆M values and
alentto 500 fb−1 of luminosity for particular twodifferentbeammaskdesigns(1◦ and2◦).
∆M values and fit them with the template For ∆M ∼ 5 GeV, a beam mask of 1◦ is
functions. Forexample,inFig.2weshowthe crucial. The accuracy of mass determination
fitting of the 500 fb−1 MC samples for Point for is summarized in Table 7, showing the
2 with the templates for m0 = 210 GeV and uncertainties are at a level of 10%.
For Publisher’s use
10
ents90 mfitt=in2g1 0m t0e=m2p10la ‘tdesata’ with 9
Ev80 0 c~ 0c~ 0
of ~t+1~t-2 8
ber 70 S1M1 7
Num456000 NNc 2((/~~tcn+01.~t~cdc-02.o)f)m . bine 7d 61 7460..84.1 ––8 31/ 069..866 cc22)/n.d.f.-(min456
30 1 1 3
N(SM) 377.6 (fixed) D M(true) = 9.53
20 2
10 1
0 02 4 6 8 10 12 14 16 18 20
0 50 100 150 200 250 D M
M(j+j+Emiss) [GeV]
1 2
Figure 3. χ2 (defined in the text) for Point 2 as a
Figure 2. Meff ( M(j1,j2,E/)) distributions for a functionof∆M.
500 fb−1 MC sa≡mples for SUSY (m0 = 210 GeV)
andSMevents, beingfitted to thetemplates form0
=210GeV.
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