ATLAS Missing Energy Signatures and DM Effective Field Theories

Transcription

1 ATLAS Missing Energy Signatures and DM Effective Field Theories Theoretical Perspectives on New Physics at the Intensity Frontier, Victoria, Canada James D Pearce, University of Victoria Sept 11, / 4

2 OUTLINE 1. DM Effective Field Theories EFT vs UV complete Regions of validity EFT operators. DM Detection methods 3. ATLAS monojet analysis Signature Selection Background estimate EFT Limits 4. Validity of DM EFT Issue of large momentum transfer ATLAS Strategy 5. Summary 6. Auxiliary Material / 4

3 WHAT WE KNOW ABOUT DARK MATTER 1. It s neutral under electric charge, since it does not produce photons,. 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 massive particle (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 / 4

4 FROM UV COMPLETE TO EFT (I) UV complete Theory Effective Theory By Taylor expanding the SM-DM propagator around the momentum transfer and only keeping the leading order we get an effective coupling constant: ( ( )) 1 = Q Q tr M M tr Q 4 + O tr 1 M M 4 M This approximation is only valid if Q tr < M otherwise all other terms in the expansion (UV complete theory) must be considered. 4 / 4

5 FROM UV COMPLETE TO EFT (II) Once the mediator has been integrated out we no longer talk about the parameter M, instead we replace it with Λ (or M ), which parameterizes the energy scale of the EFT. Λ = M/ g χ g q, where g χ and g q are the couplings of the mediator to the DM and quark fields. Given Q tr < M Perturbation theory requires g χ g q < (4π) Kinematics imposes Q tr > m χ So we can say: Λ > Q tr gχg q > Q tr 4π > mχ π Typically this is the region where EFTs are considered valid. 5 / 4

6 CONTACT INTERACTION OPERATORS arxiv: Name Operator Coefficient D1 χχ qq m q /Λ 3 D χγ 5 χ qq im q /Λ 3 D3 χχ qγ 5 q im q /Λ 3 D4 χγ 5 χ qγ 5 q m q /Λ 3 D5 χγ µ χ qγ µ q 1/Λ D6 χγ µ γ 5 χ qγ µ q 1/Λ D7 χγ µ χ qγ µ γ 5 q 1/Λ D8 χγ µ γ 5 χ qγ µ γ 5 q 1/Λ D9 χσ µν χ qσ µν q 1/Λ D χσ µν γ 5 χ qσ αβ q i/λ D11 χχg µν G µν α s /4Λ 3 D1 χγ 5 χg µν G µν iα s /4Λ 3 D13 χχg Gµν µν iα s /4Λ 3 D14 χγ 5 χg Gµν µν α s /4Λ 3 The theory is then characterized by an effective Lagrangian L eff : L eff = c i O i Where c i 1 Λ d 4 and O i is an effective operator which is some Lorentz invariant combination of the SM and DM (χ) fields. Place limits on a representative set: D1 (scalar), D5 (vector), D8 (axial-vector), D9 (tensor) and D11 (couples to gluons) 6 / 4

7 DETECTION METHODS Collider Direct detection Indirect detection Experiments: ATLAS CMS D0 CDF...and many more Experiments: XENON0 CDMS SIMPLE CoGent IceCube Picasso COUPP Experiments: Fermi-LAT PAMELA AMS-0 WMAP Planck 7 / 4

8 COLLIDER SIGNATURE Require 1 or high-p T ISR (Initial State Radiation) objects. (jet/γ/w/z) Large momentum imbalance in the transverse plan (E miss T ) Zero high-p T leptons ATLAS-CONF / 4

9 BACKGROUNDS u Z u g g u Z(νν) + jet(s) Irreducible Data-driven estimate Dominant background: 50-70% W(lν)/Z(ll) + jet(s) Lepton(s) not reconstructed/misidentified For W: 46-9%, Z: < 1% Multijet mis-measured jet Contribution 1% Diboson, t t single top Monte Carlo estimate Combined 1% Non-Collision Beam halo, cosmic muons Contribution 1% 9 / 4

10 T INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL SIGNAL REGION SELECTION [Events/GeV] miss dn/de Data / BG 5 data 01 ATLAS Preliminary Total BG Z ( ) + jets 4-1 W ( l ) + jets Ldt=.5fb Multi-jet Non-collision BG Z ( ll ) + jets 3 s = 8 TeV Dibosons tt + single top ADD n=, M =3 TeV (x5) D D5 M=80GeV, M =670GeV (x5) =1TeV, * G ~ + ~ q/ ~ g, M ~ M ~ ~= q/ g G ev (x5) miss ET [GeV] Orange dashed line indicates hypothetical DM signal ( 5) Selection: Trigger: E miss T > 80 GeV At least one primary vetex Lead jet: p T > 10 GeV, η < lepton veto: e, µ Multijet suppression: φ(e miss T, jet ) > 0.5 jet veto: N jet SR: E miss T >150 GeV Scan in E miss T for excess above background / 4

11 EW BACKGROUND ESTIMATE 1. Select data events in CR: NCR Data. Remove (non-ew) backgrounds in CR: (NCR Data Nbkg CR ) 3. Factor out EW backgrounds in CR: 1 F EW = NMC CR All EW 4. Transfer from lepton phase space to SR: TF = NMC SR NCR MC N MC CR Master equation: NSR est = (NData CR Nbkg CR ) (1 F EW) TF There are four CRs that can be used to estimate SR backgrounds: 11 / 4

12 ENERGY SCALE LIMITS arxiv: [GeV] * Suppression scale M 500 Operator D11, SR3, 90%CL Expected limit (± 1 ± exp ) Observed limit (± 1 theory ) Thermal relic ATLAS Preliminary s=8 TeV -1 Ldt =.5 fb effective theory not valid WIMP mass m [GeV] 3 Limits are taken from SR3 (jet p T > 350 GeV and E miss T > 350 GeV). Λ (M = Λ) below observed line are excluded. Green line indicates the Λ values at which WIMPs of a given mass would result in the required relic abundance. The shaded grey regions indicate where the effective field theory approach breaks down. 1 / 4

13 ] ] INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL WIMP-NUCLEON SCATTERING LIMITS WIMP Nucleon cross section [ cm ATLAS 1 s = 7 TeV, 4.7 fb, 90%CL XENON0 01 D1: qq j(χχ) Dirac CDMSII low energy D5: qq j(χχ) Dirac CoGeNT 0 D11: gg j(χχ) Dirac D5: CDF qq j(χχ) 1 σ Dirac theory 1 Spin independent 3 WIMP mass m χ [ GeV ] WIMP nucleon cross section [ cm ATLAS SIMPLE 011 Picasso 01 D8: CDF qq j(χχ) Dirac D8: CMS qq j(χχ) Dirac 1 1 s = 7 TeV, 4.7 fb, 90%CL D8: qq j(χχ) Dirac D9: qq j(χχ) Dirac 1 σ theory Spin dependent 3 WIMP mass m χ [ GeV ] Cross sections above observed are excluded. Assumption is that DM interacts with SM particles solely by a given operator Spin Independent operators: D1, D5, D11 Spin Dependent operators: D8, D9 13 / 4

14 WIMP ANNIHILATION LIMITS / s] 3 Annihilation rate < v> for qq [cm ATLAS 1-1 s = 7 TeV, 4.7 fb, 95%CL ( Fermi-LAT dsphs ( ) bb ) Majorana D5: qq ( ) Dirac D8: qq ( ) Dirac -1 theory Thermal relic value WIMP mass m [ GeV ] Comparison with FERMI-LAT is possible through our EFT 3 The results can also be interpreted in terms of limits on WIMPs annihilating to light quarks All limits shown here assume 0% branching fractions of WIMPs annihilating to quarks Below GeV for D5 and 70 GeV for D8 the ATLAS limits are below the values needed for WIMPs to make up the DM relic abundance 14 / 4

15 MOMENTUM TRANSFER AT THE LHC arxiv: Now lets revisit our assumption that Q tr < M. Setting g χ g q = 1 the truncation to the lowest-dimensional operator of the EFT expansion is accurate only if Q tr < Λ. What fraction of events pass this condition? R tot Λ σ Q tr <Λ σ = Where 0.5 < p T < 1TeV and η <. p max T p min dp T dη T p max T p min T dp T dη d σ dp T dη d σ dp T dη Qtr <Λ 15 / 4

16 REGIONS OF VALIDITY D5 s 8 TeV 500GeV pt 1 TeV, Η 4 D5 s 8 TeV 500GeV pt 1 TeV, Η GeV R tot 75 R tot 50 GeV 3 R tot R tot 5 R tot mdm R4 Π tot 50 mdm Π 1 3 m DM GeV 1 3 m DM GeV Even only requiring % of the events to pass significantly reduces the phase space. Highest fraction of EFT-valid events fall in the low mass region, where LHC bounds are the most competitive. EFT-valid region highly dependent upon value of g χ g q. 16 / 4

17 LIMITS RE-EVALUATED GeV Qtr 4Π Qtr Qtr ATLAS limit D mdm mdm GeV mdm GeV Qtr 4Π Qtr Qtr ATLAS limit D mdm mdm GeV mdm mdm Π Limits can be rescaled with R tot Λ, taking into account the dimension of the operator: Λ > [R tot Λ (m χ)] 1/[(d 4)] Λ expt For maximal couplings, g χ g q = (4π), bounds are essentially the same. For couplings g χ g q 1 previous ATLAS bounds are over estimated. 17 / 4

18 SUMMARY EFTs allow us to search for WIMPs in a model-independent way as well as compare results from different experiments and signatures. The monojet searches at the LHC are competitive and complementary to direct and indirect detection experiments. However, the large momentum transfer at the LHC reduces the phase space in which EFTs can be reliably used. 18 / 4

19 Auxiliary slides 19 / 4

20 EVIDENCE FOR DARK MATTER (I) Galactic Rotation Curves Strong Gravitational Lensing Galactic rotation curves show stars orbit at the same speeds This implies mass density of galaxies is uniform. Image of Abell 1689 cluster as observed by the hubble telescope The mass of galaxies is not enough to account for the strong gravitational lensing. 0 / 4

21 EVIDENCE FOR DARK MATTER (II) Weak Gravitational Lensing Cosmic Microwave Background Two galaxy clusters colliding. The pink shows the x-ray emissions. Blue shows unseen mass as measured with weak gravitational lensing techniques. Anisotropies in the CMB are due to acoustic oscillations in the early universe. Angular scales of the oscillations reveal the different effects of baryonic matter and DM. 1 / 4

22 RELIC ABUNDANCE AND THE WIMP MIRACLE 1. DM and SM particles are in thermal (chemical) equilibrium.. Universe expands and cools; DM production drops exponentially ( e mχ/t ). 3. Energy drops below DM production threshold; DM abundance remains constant ( Freeze out ). We are left with a relic abundance of DM: Ω χ 1 σv m χ g χ 4 / 4

23 Cross sections above observed are excluded. Assumption is that DM interacts with SM particles solely by a given operator 3 / 4 INTRO DM EFT DETECTION MONOJET ANALYSIS EFT VALIDITY SUMMARY AUXILIARY MATERIAL WIMP-NUCLEON SCATTERING LIMITS ] χ-nucleon Cross Section [cm CMS Preliminary s = 8 TeV -1 L dt = 19.5 fb Spin Independent 1 CMS 01 Vector CMS 011 Vector CDF 01 XENON0 01 COUPP 01 SIMPLE 01 CoGeNT 011 CDMSII 011 CDMSII 0 M χ (χγ χ)(qγ µ Λ µ q) 3 [GeV/c ] ] χ-nucleon Cross Section [cm CMS Preliminary s = 8 TeV -1 L dt = 19.5 fb 1 (χγ γ µ Spin Dependent χ)(qγ 5 Λ CMS 01 Axial Vector CMS 011 Axial Vector CDF 01 SIMPLE 01 CDMSII 011 COUPP Super-K W W + - IceCube W W µ γ q) 5 M χ 3 [GeV/c ]

24 CMS-PAS-EXO WIMP-NUCLEON SCATTERING LIMITS ] χ-nucleon Cross Section [cm CMS Preliminary s = 8 TeV -1 L dt = 19.5 fb -44 Spin Independent CMS 01 Vector CMS 011 Vector CDF 01 XENON0 01 COUPP 01 SIMPLE 01 CoGeNT 011 CDMSII 011 CDMSII 0 M χ (χγ χ)(qγ µ Λ µ q) 3 [GeV/c ] 90% CL limit on Λ [GeV] CMS Preliminary s = 8 TeV -1 L dt = 19.5 fb -1 m χ=500 GeV/c, Γ=M/3 m χ=500 GeV/c, Γ=M/ m χ=500 GeV/c, Γ=M/8π m χ=50 GeV/c, Γ=M/3 m χ=50 GeV/c, Γ=M/ m χ=50 GeV/c, Γ=M/8π µ (χγ χ)(qγ q) µ Λ 1 Mediator Mass M [TeV/c ] CMS (01) limits for D5 (vector) operator Light mediator model is studied to see how limits change with mediator mass, WIMP mass and decay width. 4 / 4