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INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
ATLAS Missing Energy Signatures and DM EffectiveField Theories
Theoretical Perspectives on New Physics at the Intensity Frontier, Victoria, Canada
James D Pearce,University of Victoria
Sept 11, 2014 1 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
OUTLINE
1. DM Effective Field TheoriesI EFT vs UV completeI Regions of validityI EFT operators
2. DM Detection methods3. ATLAS monojet analysis
I SignatureI SelectionI Background estimateI EFT Limits
4. Validity of DM EFTI Issue of large momentum transferI ATLAS Strategy
5. Summary6. Auxiliary Material
2 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
WHAT WE KNOW ABOUT DARK MATTER
1. It’s neutral under electric charge, since it does not produce photons,2. It’s stable, or at least has a lifetime on cosmological scales,3. It’s non-baryonic, to preserve the success of ΛCDM,4. It has a relic abundance consistent with weak scale mass and
interactions.
These seem to all point us to some sort of weakly interacting massiveparticle (WIMP). We can use an EFT to model what we know about DM,without resorting to any one specific UV complete theory (eg. SUSY,LED, etc.)
3 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
FROM UV COMPLETE TO EFT (I)
UV complete Theory Effective Theory
By Taylor expanding the SM-DM propagator around the momentumtransfer and only keeping the leading order we get an effective couplingconstant:
1Q2
tr−M2 = − 1M2
(1 +
Q2tr
M2 +O(
Q4tr
M4
))≈ − 1
M2
This approximation is only valid if Qtr < M otherwise all other terms inthe expansion (UV complete theory) must be considered.
4 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
FROM UV COMPLETE TO EFT (II)
Once the mediator has been “integrated out” we no longer talk about theparameter M, instead we replace it with Λ (or M∗), which parameterizesthe energy scale of the EFT. Λ = M/
√gχgq, where gχ and gq are thecouplings of the mediator to the DM and quark fields. Given
I Qtr < MI Perturbation theory requires gχgq < (4π)2
I Kinematics imposes Qtr > 2mχ
So we can say:
Λ > Qtr√gχgq> Qtr
4π >mχ2π
Typically this is the region where EFTs are considered valid.
5 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
CONTACT INTERACTION OPERATORS
Name Operator CoefficientD1 χχqq mq/Λ
3
D2 χγ5χqq imq/Λ3
D3 χχqγ5q imq/Λ3
D4 χγ5χqγ5q mq/Λ3
D5 χγµχqγµq 1/Λ2
D6 χγµγ5χqγµq 1/Λ2
D7 χγµχqγµγ5q 1/Λ2
D8 χγµγ5χqγµγ5q 1/Λ2
D9 χσµνχqσµνq 1/Λ2
D10 χσµνγ5χqσαβq i/Λ2
D11 χχGµνGµν αs/4Λ3
D12 χγ5χGµνGµν iαs/4Λ3
D13 χχGµνGµν iαs/4Λ3
D14 χγ5χGµνGµν αs/4Λ3
arXiv:1008.1783
I The theory is thencharacterized by an effectiveLagrangian Leff :
Leff =∑
ciOi
Where ci ∼ 1Λd−4 and Oi is an
effective operator which issome Lorentz invariantcombination of the SM andDM (χ) fields.
I Place limits on arepresentative set: D1 (scalar),D5 (vector), D8 (axial-vector),D9 (tensor) and D11 (couplesto gluons)
6 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
DETECTION METHODSCollider Direct detection Indirect detection
Experiments:I ATLASI CMSI D0I CDF
Experiments:I XENON100I CDMSI SIMPLEI CoGentI IceCubeI PicassoI COUPP
Experiments:I Fermi-LATI PAMELAI AMS-02I WMAPI Planck
...and many more7 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
COLLIDER SIGNATURE
I Require 1 or 2 high-pT ISR (Initial State Radiation) objects.(jet/γ/W/Z)
I Large momentum imbalance in the transverse plan (EmissT )
I Zero high-pT leptons
ATLAS-CONF-2012-1478 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
BACKGROUNDS
u
g
Z
u
ug
Z(νν) + jet(s)I IrreducibleI Data-driven estimateI Dominant background: 50-70%
W(lν)/Z(ll) + jet(s)I Lepton(s) not
reconstructed/misidentifiedI For W: 46-29%, Z: < 1%
MultijetI mis-measured jetI Contribution 1%
Diboson, tt single topI Monte Carlo estimateI Combined ≈1%
Non-CollisionI Beam halo, cosmic muonsI Contribution 1%
9 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
SIGNAL REGION SELECTION
[Eve
nts/
GeV
]Tm
iss
dN/d
E
-110
1
10
210
310
410
510 data 2012Total BG
) + jets Z ( ) + jets l W (
Multi-jetNon-collision BG
ll ) + jetsZ ( Dibosons
+ single toptt=3 TeV (x5)DADD n=2, M
=670GeV (x5)*
D5 M=80GeV, MeV (x5)-4=10
G~=1TeV, M
g~/q~, Mg~/q~ + G~
-1 Ldt=10.5fb
= 8 TeVs
ATLAS Preliminary
[E
vent
s/G
eV]
Tmis
sdN
/dE
-110
1
10
210
310
410
510
[GeV]TmissE
200 400 600 800 1000 1200
Dat
a / B
G
0.51
1.5
I Orange dashed line indicateshypothetical DM signal (×5)
Selection:I Trigger: Emiss
T > 80 GeVI At least one primary vetexI Lead jet: pT > 120 GeV, |η| < 2I lepton veto: e, µI Multijet suppression:
∆φ(EmissT , jet2) > 0.5
I jet veto: Njet ≤ 2I SR: Emiss
T >150 GeVI Scan in Emiss
T for excess abovebackground
10 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
EW BACKGROUND ESTIMATE
1. Select data events in CR: NDataCR
2. Remove (non-EW) backgrounds in CR: (NDataCR −Nbkg
CR )
3. Factor out EW backgrounds in CR: 1− FEW =NMC
CRAll EW∑
NMCCR
4. Transfer from lepton phase space to SR: TF =NMC
SRNMC
CR
Master equation: NestSR = (NData
CR −NbkgCR )× (1− FEW)× TF
There are four CRs that can be used to estimate SR backgrounds:
11 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
ENERGY SCALE LIMITS
[GeV]WIMP mass m210 310
[GeV
]*
Supp
ress
ion
scal
e M
100
150
200
250
300
350
400
450
500 , SR3, 90%CL Operator D11)exp 2± 1 ±Expected limit (
)theory 1±Observed limit (
Thermal relic
PreliminaryATLAS
=8 TeVs-1Ldt = 10.5 fb
not valideffective theory
I Limits are taken from SR3 (jetpT > 350 GeV and Emiss
T > 350GeV).
I Λ (M∗ = Λ) below observed lineare excluded.
I Green line indicates the Λvalues at which WIMPs of agiven mass would result in therequired relic abundance.
I The shaded grey regionsindicate where the effectivefield theory approach breaksdown.
arXiv:1210.4491
12 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
WIMP-NUCLEON SCATTERING LIMITS
[ GeV ]χ
WIMP mass m
1 10210
310
]2
WIM
PN
ucle
on c
ross s
ection [ c
m
4510
4310
4110
3910
3710
3510
3310
3110
2910ATLAS , 90%CL1 = 7 TeV, 4.7 fbs
Spinindependent
XENON100 2012
CDMSII lowenergy
CoGeNT 2010
Dirac)χχ j(→qD5: CDF q
Dirac)χχ j(→qD1: q
Dirac)χχ j(→qD5: q
Dirac)χχ j(→D11: gg
theoryσ1
[ GeV ]χ
WIMP mass m
1 10210
310
]2
WIM
Pn
ucle
on c
ross s
ection [ c
m
4110
4010
3910
3810
3710
3610
3510
ATLAS , 90%CL1 = 7 TeV, 4.7 fbs
Spindependent
SIMPLE 2011
Picasso 2012
Dirac)χχ j(→qD8: CDF q
Dirac)χχ j(→qD8: CMS q
Dirac)χχ j(→qD8: q
Dirac)χχ j(→qD9: q
theoryσ1
I Cross sections above observed are excluded.I Assumption is that DM interacts with SM particles solely by a given
operatorI Spin Independent operators: D1, D5, D11I Spin Dependent operators: D8, D9
13 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
WIMP ANNIHILATION LIMITS
[ GeV ]WIMP mass m1 10 210 310
/ s]
3 q
q [c
m
v> fo
r An
nihi
latio
n ra
te <
-2910
-2810
-2710
-2610
-2510
-2410
-2310
-2210
-2110
-2010
-1910
Thermal relic value
)b bMajorana
) ( Fermi-LAT dSphs (×2
Dirac) (qD5: q
Dirac) (qD8: q
theory-1
ATLAS , 95%CL-1 = 7 TeV, 4.7 fbs
I Comparison with FERMI-LATis possible through our EFT
I The results can also beinterpreted in terms of limitson WIMPs annihilating tolight quarks
I All limits shown here assume100% branching fractions ofWIMPs annihilating to quarks
I Below 10 GeV for D5 and 70GeV for D8 the ATLAS limitsare below the values neededfor WIMPs to make up theDM relic abundance
14 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
MOMENTUM TRANSFER AT THE LHC
Now lets revisit our assumption that Qtr < M. Setting gχgq = 1 thetruncation to the lowest-dimensional operator of the EFT expansion isaccurate only if Qtr < Λ. What fraction of events pass this condition?
RtotΛ ≡
σ|Qtr<Λ
σ =
∫ pmaxT
pminT
dpT∫ 2−2 dη
d2σ
dpTdη
∣∣∣∣∣∣Qtr<Λ∫ pmax
TpminT
dpT∫ 2−2 dη
d2σ
dpTdη
Where 0.5 < pT < 1TeV and |η| < 2.
arXiv:1402.1275
15 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
REGIONS OF VALIDITY
101 102 103
500
1000
1500
2000
2500
3000
mDM @GeVD
L@GeV
D
D5s = 8 TeV
500GeV £ pT £ 1 TeV, ÈΗÈ £ 2
RLtot= 10%
RLtot= 25%
RLtot= 50%
RLtot= 75%
L < 2 mDM
101 102 103
102
103
104
mDM @GeVD
L@GeV
D
D5s = 8 TeV
500GeV £ pT £ 1 TeV, ÈΗÈ £ 2
R4 ΠLtot = 50%
RLtot= 50%
L < mDMH2ΠL
I Even only requiring 10% of the events to pass significantly reducesthe phase space.
I Highest fraction of EFT-valid events fall in the low mass region,where LHC bounds are the most competitive.
I EFT-valid region highly dependent upon value of gχgq.
16 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
LIMITS RE-EVALUATED
10 20 50 100 200 500 1000
200
400
600
800
1000
mDM @GeVD
L@G
eVD
ATLAS limit D5
Qtr<4Π L
Qtr<2 L
Qtr<L L<2mD
M
L<mD
M
L< mDMH2ΠL
10 20 50 100 200 500 10000
100
200
300
400
500
mDM @GeVD
L@G
eVD
ATLAS limit D11
Qtr<4Π L
Qtr<2 L
Qtr<L
L<2m D
M
L<mD
M
L< mDMH2ΠL
Limits can be rescaled with RtotΛ , taking into account the dimension of the
operator:
Λ > [RtotΛ (mχ)]1/[2(d−4)]Λexpt
I For maximal couplings, gχgq = (4π)2, bounds are essentially thesame.
I For couplings gχgq ∼ 1 previous ATLAS bounds are over estimated.17 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
SUMMARY
I EFTs allow us to search for WIMPs in a model-independent way aswell as compare results from different experiments and signatures.
I The monojet searches at the LHC are competitive andcomplementary to direct and indirect detection experiments.
I However, the large momentum transfer at the LHC reduces thephase space in which EFTs can be reliably used.
18 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
Auxiliary slides
19 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
EVIDENCE FOR DARK MATTER (I)Galactic Rotation Curves Strong Gravitational Lensing
I Galactic rotation curves showstars orbit at the same speeds
I This implies mass density ofgalaxies is uniform.
I Image of Abell 1689 cluster asobserved by the hubbletelescope
I The mass of galaxies is notenough to account for thestrong gravitational lensing.
20 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
EVIDENCE FOR DARK MATTER (II)Weak Gravitational Lensing Cosmic Microwave Background
I Two galaxy clusters colliding.I The pink shows the x-ray
emissions.I Blue shows unseen mass as
measured with weakgravitational lensingtechniques.
I Anisotropies in the CMB aredue to acoustic oscillations inthe early universe.
I Angular scales of theoscillations reveal the differenteffects of baryonic matter andDM. 21 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
RELIC ABUNDANCE AND THE “WIMP MIRACLE”
1. DM and SM particles are inthermal (chemical) equilibrium.
2. Universe expands and cools;DM production dropsexponentially (∼ e−mχ/T).
3. Energy drops below DMproduction threshold; DMabundance remains constant(“Freeze out”).
We are left with a relic abundance ofDM:
Ωχ ∝ 1〈σv〉 ∼
m2χ
gχ4
22 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
WIMP-NUCLEON SCATTERING LIMITS
]2 [GeV/cχM1 10 210 310
]2-N
ucle
on C
ross
Sec
tion
[cm
χ
-4610
-4410
-4210
-4010
-3810
-3610
-3410
-3210
-3010
-2810-2710
CMS 2012 VectorCMS 2011 VectorCDF 2012XENON100 2012 COUPP 2012 SIMPLE 2012 CoGeNT 2011CDMSII 2011 CDMSII 2010
CMS Preliminary = 8 TeVs
Spin Independent
-1L dt = 19.5 fb∫
2Λ
q)µγq)(χµ
γχ(
]2 [GeV/cχM1 10 210 310
]2-N
ucle
on C
ross
Sec
tion
[cm
χ-4610
-4410
-4210
-4010
-3810
-3610
-3410
-3210
-3010
-2810
-2710CMS 2012 Axial VectorCMS 2011 Axial VectorCDF 2012
SIMPLE 2012CDMSII 2011COUPP 2012
-
W+Super-K W-W+IceCube W
CMS Preliminary = 8 TeVs
-1L dt = 19.5 fb∫
Spin Dependent
2Λ
q)5
γµγq)(χ5
γµ
γχ(
I Cross sections above observed are excluded.I Assumption is that DM interacts with SM particles solely by a given
operatorI Yellow contours show candidate events from CDMS: arXiv:1304.427923 / 24
INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL
WIMP-NUCLEON SCATTERING LIMITS
]2 [GeV/cχM1 10 210 310
]2-N
ucle
on C
ross
Sec
tion
[cm
χ
-4610
-4410
-4210
-4010
-3810
-3610
-3410
-3210
-3010
-2810-2710
CMS 2012 VectorCMS 2011 VectorCDF 2012XENON100 2012 COUPP 2012 SIMPLE 2012 CoGeNT 2011CDMSII 2011 CDMSII 2010
CMS Preliminary = 8 TeVs
Spin Independent
-1L dt = 19.5 fb∫
2Λ
q)µγq)(χµ
γχ(
]2Mediator Mass M [TeV/c-110 1 10
[GeV
]Λ
90%
CL
limit
on
0
500
1000
1500
2000
2500
3000=M/3Γ, 2=500 GeV/cχm
=M/10Γ, 2=500 GeV/cχm
π=M/8Γ, 2=500 GeV/cχm
=M/3Γ, 2=50 GeV/cχm
=M/10Γ, 2=50 GeV/cχm
π=M/8Γ, 2=50 GeV/cχm
CMS Preliminary = 8 TeVs
-1L dt = 19.5 fb∫
2Λ
q)µγq)(χµγχ(
I CMS (2012) limits for D5 (vector) operatorI Light mediator model is studied to see how limits change with
mediator mass, WIMP mass and decay width.
CMS-PAS-EXO-12-048
24 / 24