In Search of Extra Dimensions Hooman Davoudiasl Brookhaven National Laboratory Pheno 10 May 10-12, 2010, University of Wisconsin-Madison
Extra dimensions: 96-year old idea! • G. Nordstr¨ om, 1914: Unify pre-GR gravity and EM in 5D. • Th. Kaluza, 1921: Unify GR and EM in 5D. • O. Klein, 1926: Unify GR and EM with one compact extra dimension.
Extra dimensions in Recent Times • String theory, since the 1980’s. - Quantum gravity. - Consistency requires 10 or 11 dimension. - Extra dimensions compactified near fundamental scale M F ( M P ∼ 10 19 GeV). • Particle Physics, since the 1990’s. - Motivation: the hierarchy, m W /M P ∼ 10 − 17 . - Antoniadis, 1990: TeV − 1 extra dimensions and SUSY breaking. - Weak scale superstrings, Lykken, 1996. - Large Extra Dimensions; Arkani-Hamed, Dimopoulos, Dvali, 1998: m W < ∼ M F . - A Warped Extra Dimension; Randall, Sundrum, 1999: m W ∼ e − kπr c M P ; kπr c ∼ 35. - TeV − 1 Universal Extra Dimensions; Appelquist, Cheng, Dobrescu, 2000. - . . .
Large Extra Dimensions (LED) Arkani-Hamed, Dimopoulos, Dvali, 1998 P ∼ R n M n +2 • n compact extra dimensions, M F ∼ TeV: M 2 F - R < ∼ mm (gravity tests) ⇒ n ≥ 2. • SM localized on a 3-brane (4D). • Gravity propagates in all dimensions. - Gravity “diluted” in extra dimensions. • Graviton Kaluza-Klein (KK) modes. - Quantized momenta in extra dimensions: m KK = j/R ; j = 0 , 1 , 2 , . . . j } h ( − → M P T µν � j ) L = − 1 fm < ∼ R < 2 ≤ n ≤ 6. µν ; ∼ mm; {− →
Key Signals for LED • Missing energy: KK gravitons escape into the “bulk.” e + e − → γ G KK q ¯ q → j G KK ( E / ) ; . . . Missing E signature. Giudice, Rattazzi, Wells 1998 Mirabelli, Perelstein, Peskin, 1998 • Virtual exchange of spin-2 tower. + _ e Han, Lykken, Zhang, 1998 Spin-2 mediated angular distributions. q Σ (n) G Hewett, 1998 _ q e • Black hole production for √ s ≫ M F . Giddings, Thomas, 2001 Dimopoulos, Landsberg, 2001 - Potentially spectacular signals: energetic multi-jets, leptons, . . . . - Under debate. e.g. Meade, Randall, 2007: 2 → 2 quantum gravity effects more likely at the LHC.
LED: Current Bounds and Future Prospects • Collider limits: 1.6 1.6 Jets/ γ + E T / CDF II Jet/ + E γ T Lower Limit (TeV) Lower Limit (TeV) -1 CDF II + E (2.0 fb ) 1.4 1.4 γ T -1 CDF II Jet + E (1.1 fb ) CDF Collaboration (T. Aaltonen et al.), T LEP Combined 1.2 1.2 Phys.Rev.Lett.101:181602,2008 1 1 0.8 0.8 D D M M 0.6 0.6 2 2 2 3 3 4 4 5 5 6 6 [TeV] expected limit Number of Extra Dimensions Number of Extra Dimensions 1.8 observed limit D 1.6 M -1 CDF 2.0 fb limit 1.4 LEP combined limit 1.2 1 D ∅ Collaboration; γ + E / 0.8 D ∅ Note 5729-CONF, 2008 0.6 0.4 -1 DØ, Run II preliminary 2.7 fb 0.2 0 2 3 4 5 6 7 8 Number of Extra Dimensions
• Cosmology and Astrophysics: Arkani-Hamed, Dimopoulos, Dvali, 1998 - Cosmology: Typically T reheat < ∼ 1 GeV for M F ∼ 1 TeV. - SN 1987A, energy loss: M F > ∼ 50 TeV for n = 2. Cullen, Perelstein, 1998 - Neutron star, excess heat from KK-could: M F > ∼ 700(30) TeV, n = 2(3). Hannestad, Raffelt, 2001 & 2003 • 5 σ LHC reach: Dimuon channel Kabachenko, Miagkov, Zenin, ATL-PHYS-2001-012 I. Belotelov et al. , CMS Note 2006/076
Universal Extra Dimensions (UED) Appelquist, Cheng, Dobrescu, 2000 • All SM in TeV − 1 extra dimensions. • Bulk momentum conservation: 4D KK number preserved. - KK particles not singly produced. - Only loop contributions to EW precision data. - Less stringent bounds on 1 /R . • Chiral fermions via Z 2 orbifolds: KK number → KK-parity. • Compactification: Lorentz violation along extra dimensions. - Loops around compact directions: δm KK . Cheng, Matchev, Schmaltz, 2002 - Lightest KK particle (LKP) stable, dark matter candidate. Cheng, Matchev, Schmaltz, 2002 - Can mimic supersymmetry at the LHC!
UED: Current Status and LHC Prospects • EW precision: Hooper and Profumo, Phys.Rept.453:29-115,2007 Flacke, Hooper, March-Russell, 2006 • Tevatron: CDF, Run IB ...99%, - - - 95% m KK > ∼ 280 GeV Lin, 2005 • LHC Prospects: Cheng, Matchev, Schmaltz, Phys.Rev.D66:056006,2002
Warped Models • The Randall-Sundrum (RS) Model Randall, Sundrum, 1999 - 5D warped model of hierarchy, M 5 ∼ M P . • A slice of AdS 5 spacetime. - Negative constant curvature. - Flat boundaries: Planck (UV) and TeV (IR) branes. - Gravity UV-localized, SM on TeV-brane. - AdS/CFT: Dual geometric picture of strong dynamics. Maldacena, 1997 • Metric: ds 2 = η µν dx µ dx ν − dy 2 . e − 2 ky � �� � warp factor - k < ∼ M 5 and y ∈ [0 , πr c ]. • Redshift: e − kr c π � H 5 � ∼ m W ; IR-localized Higgs, � H 5 � ∼ k . - kπr c ≈ 35; hierarchy via exponentiation.
RS Signatures with SM on the Wall • TeV-scale tower of KK gravitons. - KK masses m n = x n ke − kπr c H.D., Hewett, Rizzo, 1999 x n = 3 . 83 , 7 . 02 , . . . e + e − → µ + µ − - Coupling to SM-brane: ∼ TeV − 1 . - KK graviton spin-2 resonances. - Decay into e + e − , γγ , . . . . - Distinct signature. • Stabilized geometry → Radion scalar Goldberger, Wise, 1999 - Typically lighter than KK modes. - Couplings similar to Higgs. - Can mix with Higgs through curvature-scalar coupling. Cs´ aki, Graesser, Kribs, 1999
Tevatron Bounds and LHC Prospects CDF Collaboration (Aaltonen et al. ); di-muon channel Phys.Rev.Lett.102:091805,2009 m G > 921 GeV for k/M P l = 0 . 1 ; 2.3 fb − 1 D0 Collaboration (Abazov et al. ) Phys.Rev.Lett.100:091802,2008 ) (pb) ) (pb) SE Median 68% of SE 95% of SE µ µ µ µ Data → → k/M = 0.01 BR(G* BR(G* -1 -1 10 10 Pl k/M = 0.015 Pl k/M = 0.025 Pl k/M = 0.035 × × Pl σ σ k/M = 0.05 95% C.L. Limits on 95% C.L. Limits on Pl k/M = 0.07 Pl k/M = 0.1 Pl -2 -2 10 10 0 0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1 1 1.2 1.2 1.4 1.4 M M (TeV) (TeV) G* G* ( γγ , e + e − )
• ATLAS: 100 fb − 1 , 3.5 TeV for k/M P ≃ 0 . 1. Allanach et al. , JHEP 0212:039,2002 k =0.01 M 100 100 Pl (TeV) (TeV) + - G e e → ( .B) ∆ σ 90 90 σ .B π π Λ Λ 80 80 20% 70 70 10% 60 60 5% k =0.02 50 50 M Pl 1% 40 40 k =0.03 M 30 30 Pl k =0.05 20 20 M Pl 10 10 Belotelov et al. , CMS Note 2006/104 0 0 0 0 500 500 1000 1000 1500 1500 2000 2000 2500 2500 3000 3000 3500 3500 4000 4000 Graviton Mass (GeV) Graviton Mass (GeV) • CMS: 100 fb − 1 , 4 TeV for k/M P ≃ 0 . 1.
The RS Model with 4D SM (1999) Pros : • Natural Planck-weak hierarchy. • Striking signals. Cons : • Dangerous operators: Large IR cutoff-scales → little hierarchy. • Flavor still a mystery.
SM Flavor from a Warped Bulk • 5D fermion masses, m/k ∼ 1 → localization. Grossman, Neubert, 1999 - UV(IR)-localization (overlap with Higgs) → Light (heavy) fermion. - UV-localization: Large effective cutoff scales. Gherghetta, Pomarol, 2000 ∴ Unwanted light flavor operators suppressed. • Modified KK couplings. - Gauge KK couplings: ( kπr c ≈ 35) UV-brane ( e.g. e , u ): ∼ g/ √ kπr c IR-brane ( e.g. H , t R ): ∼ g √ kπr c 5D Warped Spacetime Planck - Graviton KK couplings in ∼ TeV − 1 : Gauge Field Light fermions: ∼ Yukawa. IR-brane ( e.g. H , t R ): ∼ 1. Light Fermion Gauge fields ( g , γ ): ∼ 1 / ( kπr c ). Higgs Heavy Fermion Graviton th 5 Dimension • Collider Signals: more challenging. - Important production and decay channels suppressed.
Constraints on Warped Hierarchy/Flavor Models • Control δT : 5D custodial G c = SU (2) L × SU (2) R × U (1) X . Agashe, Delgado, May, Sundrum, 2003 • Zb ¯ b : G c × Z 2 Agashe, Contino, Da Rold, Pomarol, 2006 • Gauge KK mass m KK > ∼ 2 − 3 TeV. Carena, Pont´ on, Santiago, Wagner, 2007 • KK gluon exchange contribution to ǫ K : Agashe, Perez, Soni, 2004 Csaki, Falkowski, Weiler, 2008 • m KK > ∼ 20 TeV; O (30%) uncertainty Further 5D flavor structure for m KK ∼ TeV. E.g. Fitzpatrick, Perez, Randall, 2007
Collider Signals and Realistic Bulk Flavor • The basic RS signals need to be revisited. Agashe, Belyaev, Krupovnickas, Perez, Virzi, 2006 • KK gluons: Lillie, Randall, Wang, 2007 - Production from light quark initial states, suppressed. - Decay mostly to t ¯ t , Γ KK ∼ m KK / 6. - Top-polarization (different t L and t R KK gluon couplings) a handle. - LHC reach 3-4 TeV with 100 fb − 1 . • Limits on narrow t ¯ t resonances: 4 3.5 Expected Limit (95% C.L.) ) [pb] CDF Collaboration (T. Aaltonen et al. ) 1 Expected Limit ± σ (995 pb − 1 ) Phys.Rev.D77:051102,2008 t 3 t Observed Limit (95% C.L) → Z’)(Z’ RS KK gluon ( Γ = 0.17M) 2.5 Topcolor Leptophobic Z’ → Sequential Z’ (k =1.3) ⋆ Light t 1 ( SU (2) L × SU (2) R × Z 2 models): 2 p (p σ Upper Limit on 1.5 - Favored by EW data. 1 Carena, Pont´ on, Santiago, Wagner, 2006 0.5 - Larger Γ KK , reduced BR( g 1 → t ¯ t ). 0 500 600 700 800 900 Carena, Medina, Panes, Shah, Wagner, 2008 2 Mass of t t Resonance [Gev/c ]
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