UED review Modifying the UED mass spectrum Electroweak precision constraints on sUED and nUED Conclusions Electroweak constraints on non-minimal UED and split UED Thomas Flacke Universität Würzburg TF , C. Pasold, arXiv:1109.xxxx Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Modifying the UED mass spectrum Electroweak precision constraints on sUED and nUED Conclusions Outline • UED review • Modifying the UED mass spectrum ◦ Motivation ◦ non-minimal UED (nUED) ◦ split UED (sUED) • Electroweak precision constraints on sUED and nUED • Conclusions and Outlook Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Modifying the UED mass spectrum Basics Electroweak precision constraints on sUED and nUED UED pheno review Conclusions UED: The basic setup • UED models are models with flat, compact extra dimensions in which all fields propagate. 5D and 6D: [Appelquist, Cheng, Dobrescu,(2001)] see [Dobrescu, Ponton (2004/05), Cacciapaglia et al. , Oda et al. (2010)] for further 6D compactifications. • The Standard Model (SM) particles are identified with the lowest-lying modes of the respective Kaluza-Klein (KK) towers. • Here, we focus on one extra dimension: Compactification on S 1 / Z 2 allows for boundary conditions on the fermion and gauge fields such that ◦ half of the fermion zero mode is projected out ⇒ massless chiral fermions ◦ A ( 0 ) is projected out ⇒ no additional massless scalar 5 • The presence of orbifold fixed points breaks 5D translational invariance. ⇒ KK-number conservation is violated, but a discrete Z 2 parity (KK-parity) remains. ⇒ The lightest KK mode (LKP) is stable. Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Modifying the UED mass spectrum Basics Electroweak precision constraints on sUED and nUED UED pheno review Conclusions the UED action • UED action S UED , bulk = S g + S H + S f , with Z − 1 1 1 ff MN G AMN − MN W IMN − d 5 x G A W I B MN B MN S g = , 4 ˆ g 2 4 ˆ g 2 4 ˆ g 2 3 2 Y Z n λ ( H † H ) 2 o d 5 x ( D M H ) † ( D M H ) + ˆ µ 2 H † H − ˆ S H = , Z n “ ”o d 5 x i ψγ M D M ψ + λ E LEH + ˆ ˆ λ U QU ˜ H + ˆ S f = λ D QDH + h.c. . Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Modifying the UED mass spectrum Basics Electroweak precision constraints on sUED and nUED UED pheno review Conclusions the MUED spectrum [Cheng, Matchev, Schmaltz, PRD 66 (2002) 036005, hep-ph/0204342] Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Modifying the UED mass spectrum Basics Electroweak precision constraints on sUED and nUED UED pheno review Conclusions (M)UED pheno review Phenomenological constraints on the compactification scale R − 1 • Lower bounds: ◦ FCNCs [Buras, Weiler et al. (2003); Weiler, Haisch (2007)] R − 1 � 650 ( 330 ) GeV at 95 % (99%) cl. ◦ Electroweak Precision Constraints [Appelquist, Yee (2002); Gogoladze, Macesanu (2006)] R − 1 � 650 ( 300 ) GeV for m H = 115 ( 800 ) GeV at 95 % cl. ◦ no detection of KK-modes at LHC, yet [see plenary talk of Nojiri] R − 1 � 500 GeV at 95 % cl. • Upper bound: ◦ preventing over closure of the Universe by B ( 1 ) dark matter R − 1 � 1 . 5 TeV [Servant, Tait (2002); Matchev, Kong (2005); Burnell, Kribs (2005); Belanger et al. (2010)] UED vs. SUSY at LHC [Barr et al. (2004); Datta, Kong, Matchev (2005); Kane et al. (2005) and many more ] Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Motivation Modifying the UED mass spectrum nUED Electroweak precision constraints on sUED and nUED sUED Conclusions Relevance of the detailed mass spectrum I: LHC phenomenology The KK mass spectrum determines decay channels, decay rates and final state jet/lepton energies at LHC. [Cheng, Matchev, Schmaltz, PRD 66 (2002) 056006, hep-ph/0205314] Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Motivation Modifying the UED mass spectrum nUED Electroweak precision constraints on sUED and nUED sUED Conclusions Relevance of the detailed mass spectrum II: Dark Matter relic density 0.5 a0) (1) " annihilation (tree; w/o FS level 2) 0.45 a1) " (1) annihilation (1 ! loop; w/o FS level 2) b0) Coannihilation (tree; w/o FS level 2) 0.4 b1) Coannihilation (1 ! loop; w/o FS level 2) c0) Coannihilation (tree; w/ FS level 2) 0.35 c1) Coannihilation (1 ! loop; w/ FS level 2) 0.3 a1 ! h 2 0.25 0.2 b0 a0 b1 c0 0.15 WMAP 0.1 c1 0.05 m h = 120 GeV, # R = 20 0 400 600 800 1000 1200 1400 1600 R ! 1 (GeV) Left: Relic density for γ ( 1 ) dark matter in MUED including coannihila- Right: Relic density for W 3 ( 1 ) dark matter including coannihilation tion effects of first and second KK modes [Belanger et al. (2010)] effects with first KK modes and different mass degeneracies [Arrenberg, Kong (2008)]. Realization of W 3 ( 1 ) dark matter, see [TF , Menon, Phalen (2008)] Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Motivation Modifying the UED mass spectrum nUED Electroweak precision constraints on sUED and nUED sUED Conclusions UED as an effective field theory • UED is a five dimensional model ⇒ non-renormalizable. • It should be considered as an effective field theory with a cutoff Λ . • Naive dimensional analysis (NDA) result: Λ ∼ 50 / R . This cutoff is low! • Bounds from unitarity imply Λ ∼ O ( 10 ) [Chivukula, Dicus, He (2001)] • Underlying assumption in MUED: all boundary localized terms vanish at the cutoff Λ and are only induced at lower energies via RG running. Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Motivation Modifying the UED mass spectrum nUED Electroweak precision constraints on sUED and nUED sUED Conclusions How much do we really know about the UED mass spectrum? Taking the effective field theory approach to UED seriously, we should include all operators which are allowed by all symmetries. These are 1. Bulk mass terms for fermions (dimension 4 operators), 2. kinetic and mass terms at the orbifold fixed points (dimension 5; radiatively induced in MUED), 3. bulk or boundary localized interactions (dimension 6 or higher) The former two modify the free field equations and thereby the spectrum and the KK wave functions. Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Motivation Modifying the UED mass spectrum nUED Electroweak precision constraints on sUED and nUED sUED Conclusions Boundary localized terms for fermions Concerning boundary localized kinetic terms (BLKTs), today we focus on fermions. [Csaki,Hubisz,Meade(2001);Aguila, Perez-Victoria, Santiago(2003)] For gauge boson BLKTs, see [Carena, Tait, Wagner(2002); TF , Menon, Phalen(2009)] The fermion Lagrangian including BLKTs (“non-minimal UED”) has the form: » i Z Z – “ ” d 5 x Ψ Γ M D M Ψ − D M Ψ Γ M Ψ S = + L BLKT 2 M S 1 / Z 2 with » „ « „ «– y − π R y + π R i Ψ h / L BLKT = a h δ + δ D Ψ h , 2 2 where h = R , L represents the chirality and Γ M is defined as ( γ µ , i γ 5 ) . We choose left-handed BLKTs (right-handed BLKTs are treated analogously). Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Motivation Modifying the UED mass spectrum nUED Electroweak precision constraints on sUED and nUED sUED Conclusions Variation of the free action, leads to conditions ∂ Ψ L + ∂ 5 Ψ R − 1 » δ ( y − π R 2 ) + δ ( y + π R – π R 0 = i / i / δ Ψ L : 2 Ψ R | 2 2 + a L 2 ) ∂ Ψ L , − π R ∂ Ψ R − ∂ 5 Ψ L + 1 π R 0 = i / 2 δ Ψ R : 2 Ψ L | 2 . − π R We perform the KK decomposition with the ansatz ∞ ∞ X Ψ ( n ) R ( x ) f ( n ) X Ψ ( n ) L ( x ) f ( n ) Ψ R ( x , y ) = R ( y ) ; Ψ L ( x , y ) = L ( y ) , n = 0 n = 0 to obtain KK zero modes even numbered KK-modes odd numbered KK-modes f ( 0 ) f ( n ) f ( n ) 1 √ ( y ) = − N cos ( m n y ) ( y ) = ( y ) = N sin ( m n y ) L L L 2 a L + π R f ( 0 ) f ( n ) f ( n ) R ( y ) = 0 R ( y ) = N sin ( m n y ) R ( y ) = N cos ( m n y ) tan ( π R cot ( π R 2 m n ) = − a L m n m 0 = 0 2 m n ) = a L m n The analogous results for right-handed BLKTs are obtained by L ↔ R . Thomas Flacke Electroweak constraints on non-minimal UED and split UED
UED review Motivation Modifying the UED mass spectrum nUED Electroweak precision constraints on sUED and nUED sUED Conclusions nUED Fermion Mass Spectrum m n R 4 Excluded � LKP � 3 2 1 Excluded a L � 10 � 5 � Π 0 5 10 R 2 Masses of the first three fermion KK modes in the presence of BLKTs. [D. Gerstenlauer, Diploma Thesis, Würzburg (2011)] Thomas Flacke Electroweak constraints on non-minimal UED and split UED
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