Cosmology and Dark Matter at the LHC

0.22 MB·English

by  Richard Arnowitt

February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
1
7
0
0
Cosmology and Dark Matter at the LHC
2

n RichardArnowitt,1 AdamAurisano,1 BhaskarDutta,1 TerukiKamon,1
a
NikolayKolev,2 PaulSimeon,1 DavidToback1 andPeterWagner1
J
1 Department of Physics, Texas A&M University,College Station, TX 77843-4242,
8
USA

2Department of Physics, Universityof Regina, Regina, SK S4S 0A2, Canada
1
v
3
WeexaminethequestionofwhetherneutralinosproducedattheLHCcanbe
5
showntobetheparticlesmakinguptheastronomicallyobserveddarkmatter.
0
IftheWIMP alllowedregionliesintheSUGRAcoannihilation region,thena
1
strongsignalforthiswouldbetheunexpectedneardegeneracyofthestauand
0 neutralinoi.e.,amassdifference∆M ≃(5−15)GeV.ForthemSUGRAmodel
7
we show such a small mass difference can be measured at the LHC usingthe
0 signal3τ+jet+Emiss.Twoobservables,oppositesignminuslikesignpairsand
/ T
h the peak of the ττ mass distribution allows the simultaneous determination
p of ∆M to 15% and the gluino mass Mg˜ to be 6% at the benchmark point of
- Mg˜=850GeV,A0=0,µ>0with30fb−1.With10fb−1,∆Mcanbedetermined
p to22%andonecanprobetheparameterspaceuptom1/2=700GeVwith100
e fb−1.
h
:
v
i 1. Introduction
X
Supersymmetry (SUSY) offers the possibility of solving a number of the-
r
a oretical problems of the Standard Model (SM). Thus the cancelations im-
plied by the bose-fermi symmetry resolves the gauge hierarchy problem,
allowing one to consider models at energies all the way up to the GUT
or Planck scale. Further, using the SUSY SM particle spectrum with one
pair of Higgs doublets. (pairs of Higgs doublets are needed on theoretical
grounds to cancel anomalies and on phenomenological grounds to give rise
tobothuanddquarkmasses)the renormalizationgroupequations(RGE)
show that grand unification of the SM gauge coupling constants occurs at
M ≃ 1016 GeV opening up the possibility of SUSY GUT models. How-
G
ever,none ofthis canactually occur unless a naturalway ofspontaneously
breaking SUSY occurs, and this very difficult to do with global supersym-
metry. The problem was resolvedby promoting supersymmetry to a gauge
symmetry, supergravity (SUGRA),1 where spontaneous breaking of super-
February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
2
symmetry can easily occur. One can then build SUGRA GUT models2,3
with gravityplaying a key role in the construction. A positive consequence
of this promotionwasthat the RGE then show that the breakingof super-
symmetry at the GUT scale naturally leads to the required SU(2)×U(1)
breaking at the electroweak scale, thus incorporating all the successes of
the SM, without any prior assumptions of negative (mass)2 terms.
In spite of the theoretical successes of SUGRA GUTs, there has been
noexperimentalevidenceforitsvalidityexceptfortheverificationofgrand
unification(whichhasinfactwithstoodthe testoftime foroveradecade).
However,oneexpectsSUSYparticlestobecopiouslyproducedattheLHC.
Further, models with R parity invariance predict the lightest neutralino
χ˜0 to be a candidate for the astronomically observed dark matter (DM)
1
and models exist4 consistent with the amount of dark matter observed
by WMAP,5 and being searched for in the Milky Way by dark matter
detectors. Thus it is possible to build models that both cover the entire
energy range from the electroweak scale to the GUT scale and go back in
time to ∼ 10−7 seconds after the Big Bang when the current relic dark
matter was created.
Thequestionthenarisescanweverifyifthedarkmatterparticlesinthe
galaxy is the neutralino expected to be produced at the LHC? In principle
this is doable.Thus assuming the DM detectors eventually detect the dark
matter particle, they will measure the mass and cross sections, and these
can be compared with those measured at the LHC. However, this may
take a long time to achieve. More immediately, can we look for a signal at
the LHC that is reasonably direct consequence of the assumption that the
neutralino is the astronomical DM particle and in this way experimentally
unifyparticlephenomenawithearlyuniversecosmology?Toinvestigatethis
questionitisnecessarytochooseaspecificSUSYmodel,andforsimplicity
we consider here the minimal mSUGRA (though a similar analysis could
be done for a wide range of other SUGRA models).
2. The mSUGRA model
The mSUGRA model depends on four soft breaking parameters and one
sign. These are; m (the universal gaugino soft breaking mass at M );
1/2 G
m (theuniversalscalarsoftbreakingmassatM );A (theuniversalcubic
0 G 0
soft breaking mass at M ); tanβ =< H > / < H > at the electroweak
G 2 1
scale (where < H > gives rise to u quark masses and < H > to d quark
2 1
masses); and the sign of µ parameter (where µ appears in the quadratic
part of the superpotential W(2) =µH H ).
1 2
February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
3
2
(cid:170) ~ (cid:186)
(cid:171) (cid:70)10 (cid:187)
(cid:171) (cid:187)
(cid:171) (cid:187) e(cid:16)(cid:507)M / 20 (cid:14)
(cid:171) (cid:187)
~
(cid:171) (cid:87) (cid:187)
1
(cid:171) (cid:187)
(cid:172) (cid:188)
2
(cid:170) (cid:186)
(cid:171) (cid:187)
(cid:171) (cid:187)
(cid:171) (cid:187)
(cid:171) (cid:187)
(cid:171) (cid:187)
(cid:171) (cid:187)
(cid:172) (cid:188)
Fig. 1. The feynman diagrams for annihilation of neutralino dark matter in the early
universe
Currentexperimentaldatasignificantlyconstrainstheseparameters.the
main accelerator constraints are: The Higgs mass m > 114 GeV;6 the
H
lightest chargino mass Mχ˜±1 > 104 GeV; the b → sγ branching ratio 2.2
×10−4 < Br(b → sγ) < 4.5×10−4;7 and the muon g-2 anomaly8 which
nowdeviatesfromtheSMpredictionby3.4σ.Theastronomicalconstraint
istheWMAPdeterminationoftheamountofdarkmatterandweusehere
a 2 σ range:5
0.094<Ωχ˜01h2 <0.129. (1)
The WMAP constraint limits the parameter space to three main regions
arisingfrom the diagramsof Fig.1. (1) The stau-neutralino(τ˜ −χ˜0) coan-
1 1
nihilation region. Here m is small and m ≤ 1.5 TeV. (2)The focus
0 1/2
region where the neutralino has a large Higgsino component. Here m is
1/2
small and m ≥1 TeV. (3) The funnel region where annihilation proceeds
0
throughheavyHiggs bosons which havebecome relativelylight. Here both
m and m are large.
0 1/2
(Inadditionthereisasmallbulkregion)Notethatakeyelementinthe
coannihilation region is the Boltzman factor from the annihilation in the
early universe at kT ∼ 20 GeV: exp[−∆M/20] where ∆M = Mτ˜1 −Mχ˜01.
Thus significant coannihilation occurs provided ∆M ≤ 20 GeV.
February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
4 1000
A=0, m> 0
0
tanb =40
800 GeV GeV GeV
4 7 0
1 1 2
1 1 1
]
V
e
[G 600 b→sg am<11×10-10
0
m
400
mc˜0> mt˜
200
200 400 600 800 1000
m [GeV]
1/2
Fig.2. Allowedparameterspacefortanβ =40withA0=0andµ>0.
Fig.3. SUSYproductionanddecaychannels
The accelerator constraints further restrict the parameter space and if
the muon g-2 anomaly maintains, µ > 0 is prefereed and there remains
mainly the coannihilation region. This is illustrated in Fig.2 which shows
the allowed narrow coannihilation band (for the case tanβ = 40, A = 0,
0
µ>0) where ∆M =(5−15) GeV and m ≤800 GeV. (There is a small
1/2
focus region for small m and m > 1 TeV since the b → sγ constraint
1/2 0
ceases to opperate at m >1 TeV.)
0
Thecoannihilationbandisnarrow(∆M =5−15GeV)duetotheBoltz-
manfactorinFig.1,therangein∆M correspondingtotheallowedWMAP
range for Ωχ˜01h2. The dashed verticle lines are possible Higgs masses.
February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
5
One may ask two questions; (1) Can such a small stau-neutralino mass
difference (5-15 GeV) arise in mSUGRA, i.e. one would naturally expect
theseSUSYparticlestobehundredsofGeVapartand(2)Cansuchasmall
massdifferencebemeasuredattheLHC?Iftheanswerstoboththeseques-
tions are affirmative,the observationof sucha smallmass difference would
be a strong indication that the neutralino is the astronomicalDM particle
since itis the cosmologicalconstraintonthe amountofDMthat forcesthe
near mass degeneracy with the stau, and it is the accelerator constraints
that suggests that the coannihilation region is the allowed region.
3. Can ∆M be Small in SUGRA models?
At the GUT scale m governs the gaugino masses, while m the slepton
1/2 0
masses. Thus, at M one would not expect any degeneracies between the
G
two classes of particles. However, at the electroweak scale the RGE can
modifythis result.Toseeanalyticallythispossibility,considerthelightest
selectron e˜c which at the electroweak scale has mass
m2 =m2+0.15m2 +(37GeV)2 (2)
e˜c 0 1/2
while the χ˜0 has mass
1
m2 =0.16m2 (3)
χ˜01 1/2
The numerical accident that the coefficients of m2 is nearly the same for
1/2
bothcasesallowsaneardegeneracy.Thusform =0,thee˜c andχ˜0become
0 1
degenerate at m =(370-400) GeV. For larger m , the near degeneracy
1/2 1/2
is maintained by increasing m , so that one can get the narrow corridor in
0
the m -m plane seen in Fig.2. Actually the case of the stau τ˜ is more
0 1/2 1
complicated since the large t-quark mass causes left-right mixing in the
stau mass matrix and results in the τ˜ being the lightest slepton (not the
1
selectron). However, a result similar to Eqs. (1,2) occurs, with a τ˜ −χ˜0
1 1
coannihilation corridor resulting.
We note that the results of Eqs.(1,2) depend only on the U(1) gauge
group and so coannihilation can occur even if there were non-universal
scalar mass soft-breaking or non-universal gaugino mass soft breaking at
M .Thus,coannihilationcanoccurinawideclassofSUGRAmodels,and
G
is not just a feature of mSUGRA.
February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
6
4. Coannihilation signal at the LHC
At the LHC, the major SUSY production processes are gluinos (g˜) and
squarks (q˜) e.g., p+p→g˜+q˜. These then decay into lighter SUSY parti-
cles andFig.3showsa majordecayscheme.The finalstatesinvolvetwoχ˜0
1
giving rise to missing transverse energy ET ) and four τ’s, two from the
miss
g˜ and two from the q˜decay chain for the example of Fig 3. In the coanni-
hilation region,two of the taus are high energy (“hard” taus) coming from
the χ˜02 → ττ˜1 decay (since Mχ˜02 ≃ 2Mτ˜1) while two are low energy (“soft”
taus) coming from the τ˜ →τ +χ˜0 decay since ∆M is small. The signal is
1 1
thus Emiss+ jets +τ’s, which should be observable at the LHC detectors.
T
22 22
11..88 D M = 9 GeV 11..88 D M = 20 GeV
11..66 M~g = 850 GeV 11..66 M~g = 850 GeV
V)V) V)V)
ee11..44 ee11..44
GG GG
5 5 11..22 5 5 11..22
11 11

-1-1·· b b 11 Opposite-Signed Pairs -1-1·· b b 11
s / (fs / (f00..88 Like-Signed Pairs s / (fs / (f00..88
airair00..66 airair00..66
PP PP
00..44 00..44
00..22 00..22
00 5500 110000 115500 220000 225500 330000 00 5500 110000 115500 220000 225500 330000
IInnvvaarriiaanntttt tt MMaassss ((GGeeVV)) IInnvvaarriiaanntttt tt MMaassss ((GGeeVV))
Fig.4. Numberoftaupairsasafunctionofinvariantττmass.ThedifferenceNOS-NLS
cancels formass≥100GeVeliminatingbackground events
As seen above we expect two pairs of taus, each pair containing one
soft and one hard tau from each χ˜0 decay. Since χ˜0 is neutral, each pair
2 2
should be of opposite sign(while SM and SUSY backgrounds, jets faking
taus will have equal number of like sign as opposite sign events). Thus
one can suppress backgrounds statistically by considering the number of
oppsite sign events N minus the like sign events N . The four τ final
OS LS
state has the smallest background but the acceptance and efficiency for
reconstructing all four taus is low. Thus to implement the above ideas we
consider here the three τ final state of which two are hard and one is soft.
(The two τ final state with higher acceptance but larger backgrounds was
discussed in,9 and an analysis of the coannhilation signal at the ILC was
February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
7
given in.10
We label three taus by their transverse energies with ET > ET > ET
1 2 3
andformthe pairs13 and23.For signalevents one ofthe two pairsshould
be coming from a χ˜0 decay and have opposite sign(OS) while the other is
2
notcorrelated.Therearetwomeasurablesthatcanbeformed.Thenumber
N andthemassofthe pairM.TosimulatethedataweuseISAJET7.6411
and PGS detector simulator.12 Events are chosenwith Emiss and 1 jet and
T
three taus with visible momenta pvis > 40 GeV, pvis > 40 GeV, pvis > 20
T T T
GeV.Weassumeherethatitispossibletoreconstructtauswithpvis aslow
T
as20GeV.StandardModelbackgroundisreducedbyrequiringEjet1 >100
T
GeV,Emiss >100GeVwithtevatronresults,Ejet1+Emiss >400GeV.We
T T T
also assume rate of a jet faking a τ (fj→τ) to be fj→τ = 1% (with a 20%
error in fj→τ) consistent with Tevatron results.
Fig 4. shows the number of events as a function of the ττ mass for
gluino mass M =850 GeV and ∆M =9 GeV and 20 GeV. One sees that
g˜
the difference N −N cancels out as expected for ττ mass ≥100 GeV
OS LS
(consistent with the fact that the signal events are expected to lie below
100 GeV).
Fig.5showsthebehaviorofNOS−LS asafunctionof∆M andMg˜.The
centralblacklineisfortheassumed1%.rateforjets fakingaτ,theshaded
region around it is for a 20% uncertainty in fj→τ. One sees that provided
this uncertainty is not large, it produces only a small effect.
333
M~g = 850 GeV D M = 9 GeV
111000
222...555
888 1% Fake Rate
-1/ fbNOS-LS 666 -1 / fbNOS-LS 222 1% Fake Rate
444 111...555
222 20% Error on 111 20% Error on
Fake Rate Fake Rate
000
000 555 111000 111555 222000 222555 333000 777555000 888000000 888555000 999000000 999555000
D M (GeV) Gluino Mass (GeV)
Fig.5. NOS−LS asfunctionof∆M (leftgraph)andasafunctionofMg˜(rightgraph).
The central black line assumes a 1% fake rate, the shaded area representing the 20%
errorinthefakerate
February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
8
Figs 4 and 5 show two important features. First, NOS−LS increases
with ∆M(since the τ acceptance increases) and NOS−LS decreases with
M (since the productioncrosssectionofgluinosandsquarksdecreasewith
g˜
Mg˜). Second, from Fig.4 one sees that NOS−LS forms a peaked distribu-
tion.9,13 The ditau peak position Mpeak increases with both ∆M and M .
ττ g˜
This allows us to use the two measurables NOS−LS and Mτpτeak to deter-
mine both∆M andM .Fig.6showsthis determinationforthe benchmark
g˜
caseof ∆M=9GeV,M =850GeV, A =0andtanβ=40.Plottedthere are
g˜ 0
constantvalues ofNOS−LS andconstantvalues ofMτpτeak in the ∆M−Mg˜
plane which exhibit the above dependance of these quantities on ∆M and
M . With luminosity of 30 fb−1 one determines ∆M and M with the
g˜ g˜
following accuracy:
δ∆M/∆M ≃15%; δM /M =6% (4)
g˜ g˜
Fig.7showshowtheaccuracyofthemeasurementchangeswithluminosity.
Oneseesthatevenwith10fb−1(whichshouldbeavailableattheLHCafter
about two years running)one could determine ∆M to within 22%, which
should be sufficient to know whether one is in the SUGRA coannihilation
region.
950
Constant # of
V)900 OS-LS Counts
e
Mass (G850 MLD M~g= =3= 0 89 5f Gb0 -e1GVeV
o
n
ui
Gl800 Constant Mt t
750
5 10 15 20
D M (GeV)
Fig. 6. Simultaneous determination of ∆M and Mg˜. The three lines plot constant
NOS−LS and Mτpτeak (central value and 1σ deviation) in the Mg˜-∆M plane for the
benchmarkpointof∆M=9GeVandMg˜=850GeV assuming30fb−1 luminosity
February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
9
D M = 9 GeV
25 M~g = 850 GeV
Simultaneous Measurement
y
nt 20
ai
ert
nc 15 D M
U
nt
e
erc 10
P
M~g
5
0
10 20 30 40 50 60
Luminosity (fb-1)
Fig.7. Uncertaintyinthedeterminationof∆M andMg˜ asafunctionofluminosity.
5. Conclusions
We have examined here the question of how one might show that the χ˜0
1
particleproducedattheLHCistheastronomicallyobserveddarkmatter.If
∆M,thestau-neutralinomassdifferenceliesinthecoannihilationregionof
theSUGRAm -m planewhere∆M =(5−15)GeV,thiswouldbestrong
0 1/2
indication that the neutralino is the dark matter particle as otherwise the
massdifferencewouldnotnaturallybesosmall.Wesawhowitwaspossible
tomeasuresuchasmallmassdifferenceattheLHCforthemSUGRAmodel
usingasignalofEmiss+1jet+3τ,andsimultaneouslydeterminethegluino
T
mass M , provided it is possible at the LHC to reconstruct taus with pvis
g˜ T
as low as 20 GeV. With 30 fb−1 one could then determine ∆M with 15%
accuracyandM with6%,atourbenchmarkpointof∆M=9GeV,M =850
g˜ g˜
GeV, tanβ = 40, and A =0. Even with only 10fb−1 one would determine
0
∆M to within 25%accuracy,sufficienttolearnwhether the signalisin the
coannihilation region.
While the analysis done here was within the framework of mSUGRA,
similar analyses can be done for other SUGRA models provided the pro-
ductionofneutralinosisnotsuppressed.However,thedeterminationofM
g˜
doesdepend onthe mSUGRA universalityofthe gauginomassesatM to
G
relate Mχ˜02 to Mg˜. Thus a model independent method of determining Mg˜
wouldallowone to to test the questionofgauginouniversality.However,it
may not be easy to directly measure M at the LHC for high tanβ in the
g˜
coannihilation region due to the large number of low energy taus, and the
February2,2008 8:23 WSPC-ProceedingsTrimSize:9inx6in idm06v1
10
ILC would require a very high energy option to see the gluino.
Asmentionedabove,onecanalsomeasure∆M usingthesignalEmiss+
T
2 jets+2τ.9 This signal has higher acceptance but larger backgrounds.
There, with 10 fb−1 one finds that one can measure ∆M with 18% er-
ror at the benchmark point assuming a separate measurement of M with
g˜
5% error has been made. While we have fixed our benchmark point at
M = 850 GeV(i.e. m =360 GeV), higher gluino mass would require
g˜ 1/2
more luminosity to see the signal. One finds that with 100 fb−1 one can
probe m at the LHC up to ∼700 GeV (i.e., M up to ≃1.6 TeV).
1/2 g˜
Finally,itis interesting tocomparewith possiblemeasurementsof∆M
at the ILC. If we implement a very forward calorimeter to reduce the two
γ background, ∆M can be determined with 10% error at the benchmark
point.10 Thusinthecoannihilationregion,thedeterminationof∆M atthe
LHC is not significantly worse than at the ILC.
6. Acknowledgement
ThisworkwassupportedinpartbyDOEgrantDE-FG02-95ER40917,NSG
grant DMS 0216275 and the Texas A&M Graduate Merit fellowship pro-
gram.
References
1. D.Z. Freedman, P. Van Niewenhuisen, and S. Ferrara, Phys. Rev. D13, 1980
(1729);S.DeserandB.Zumino,Phys.Lett.B65,369(1976);Phys.Lett.B65,
1976 (369).
2. A.H.Chamseddine,R.Arnowitt,andP.Nath,Phys.Rev.Lett49,1982(970).
3. R. Barbieri, S. Ferrara, and C.A. Savoy, Phys. Lett. B119, 343 (1982); L.
Hall, J. Lykken, and S. Weinberg,Phys. Rev. D27, 1983 (2359); P. Nath, R.
Arnowitt,andA.H.Chamseddine,Nucl.Phys.B227,121(1983);Forareview,
see P. Nilles, Phys.Rept. 100, 1984 (1).
4. J. Ellis, K. Olive, Y. Santoso, and V. Spanos, Phys. Lett. B176, 565 (2003);
R. Arnowitt, B. Dutta, and B. Hu, hep-ph/0310103; H. Baer, C. Balazs, A.
Belyaev,T.Krupovnickas,and X.Tata, JHEP 0306, 2003 (054); B.Lahanas
and D.V. Nanopoulos, Phys. Lett. 568, 2003 (55); U. Chattopadhyay, A.
Corsetti,andP.Nath,Phys.Rev.D68,((2)003)035005;E.BaltzandP.Gon-
dolo, JHEP 0410 (2004) 052; B. C. Allanach and C. G. Lester, Phys. Rev.
D73,2006(015013);A.Djouadi,M.Drees,andJ-L.Kneur,JHEP0603,2006
(033).
5. WMAP Collaboration, D.N. Spergel et al., Astrophys. J. Suppl. 148, 2003
(175).
6. ALEPH, DELPHI, L3, OPAL Collaborations, G. Abbiendi et al. (The LEP
WorkingGroupforHiggsBoson Searches),Phys.Lett.B565(2003) 61;Par-
ticle Data Group, S. Eidelman et al.,Phys. Lett. 592, 2004 (1).