vicTheoryWorkshop

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


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


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


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


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


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

http://arxiv.org/abs/1008.1783


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


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

https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2012-147/


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


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


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


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

http://arxiv.org/abs/arXiv:1210.4491


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(→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



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


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


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

http://xxx.tau.ac.il/abs/1402.1275v1


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


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


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


Auxiliary slides

19 / 24


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


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


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



]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


-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

http://arxiv.org/abs/1304.4279



]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


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


-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

http://cds.cern.ch/record/1525585?ln=en

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