☆ KK parity relaxes the constraints from EWPT ⇒ 1/R > 300 GeV (5D on S^1/Z 2 ) testable @colliders Appelquist, Cheng & Dobrescu (2001) ☆ KK parity naturally predicts a candidate of dark matter “lightest KK particle (LKP)” like a LSP in SUSY w/ R-parity ∵ 1st KK modes are always produced in pairs 2: # of generations from anomaly cancellation (6D) Dobrescu & Poppitz (2001) Witten anomaly: ( ) ( ) ( ) ( ) Π = − = ⇒ = SU 2 N 2 N 2 0 mod6 n 0 mod3 + − 6 g W 3: Proton stability by Lorentz subgroup (6D) Appelquist, Dobrescu, Ponton & Yee (2001) ⊂ 2 Z T Z 8 2
Decays & products of 1 st KK modes (5D on S^1/Z 2 ) Dominant transition Rare transition (Q,L): SU(2) L doublet (q,l): SU(2) L singlet LKP
Discovery reach for 5D UED in Q 1 Q 1 -> 4l + missing energy Excluded by CDF
Gauge-Higgs Unification “LHC Signals for Coset Electroweak Gauge Bosons in Warped/Composite PGB Higgs Models” K. Agashe, A. Azatov, T. Han, Y. Li, Z-G. Si & L. Zhu PRD81 096002 (2010)
Gauge-Higgs unification A y A μ Identified with ⇔ Higgs in the SM Mass term is forbidden Higher dimensional by the gauge symmetry Lorentz invariance Higher dimensional gauge symmetry Higgs potential is generated @1-loop and finite due to the higher dim. gauge symmetry ↓ EW scale is stabilized
Gauge symmetry breaking: ( ) ( ) → ⊇ × by an orbifold (ex. S^1/Z 2 ) G H SU 2 U 1 Parity assignments of gauge sector H subgroup ( ) ( ) ( ) − = ∂ = H H H A y A y A y 0 Only even mode has µ µ µ ⇔ y ( ) ( ) ( ) − = − = a massless mode H H H A y A y A y 0 y y y SU(2) x U(1) H G/H coset A : Gauge fields µ ( ) ( ) ( ) − = − = Higgs G H G H G H G H A : A y A y A y 0 µ µ µ ⇔ y ( ) ( ) ( ) − = ∂ = G H G H G H A y A y A y 0 y y y y Model independent new fields G H A µ ⇒ SU(2) doublet coset gauge boson partner of Higgs
( ) vs ± ± → → 1 pp W t pp W t C C
( ) vs ± ± → → 1 pp W t pp W t C C We focus on the low mass region of M ( ) 1 ∵ our goal is to explore the t reach of discover of W C
Dominant channels of W C production & its decay b b ( ) ( ) ( ) → → ( ) 1 1 1 W 1 bg W t bt t ( ) t C 1 t C ( ) g 1 t + → ν + 1:3 2 5 b W l jets ( ) ( ) ( ) 2 ( ) ( ) ( ) → × → ≈ × 2 = 1 1 Br W t b Br t bW 90% 50% 22.5% C ( ) → ν + 2: bbWtH Z l 7 jets bW ( ) ( ) ( ) ( ) ( ) ( ) ( ) → 1 → × → × → × → 1 1 1 t 2 Br W t b Br t bW Br t tH tZ , ( ) C tH tZ ( ) ≈ × × 2 = 2 90% 50% 45% ( ) ( ) → ν + 3: btH Z tH Z l 9 jets ( ) ( ) ( ) 2 ( ) ( ) ( ) → × → ≈ × 2 = 1 1 Br W t b Br t tH tZ , 90% 50% 22.5% C
= 14 s TeV
(3 events) (5 events) (15 events) = 14 s TeV
Higgsless Models “Collider Phenomenology of the Higgsless Models” A. Birkedal, K. Matchev & M. Perelstein, PRL94 191803 (2005)
Higgsless model??? In extra dimensions, the gauge symmetry can be broken by BCs ⇒ New possibility SU(2) x U(1) -> U(1) em by BCs without a Higgs boson??? Immediate question: How unitarizes W/Z scattering amplitudes without Higgs???
(Warped) Model Csaki, Grojean, Pilo & Terning (2003) = − η µ ν + AdS 5 on an interval 2 2 ky 2 ds e dx dx dy µν SU(2) L x SU(2) R x U(1) B-L → U(1) em SU(2) L x U(1) B-L SU(2) L x SU(2) R ↓ ↓ U(1) y SU(2) D ± = R A 0 − = µ La Ra A A 0 µ µ ′ − = R 3 0 g B g A ( ) µ µ 5 5 ∂ + = La Ra ( ) A A 0 µ µ ′ 5 ∂ + = R 3 g B g A 0 µ µ 5 5 5 Planck TeV
± → ± W Z W Z L L L L W W W W W W W W Z Z Z Z Z Z 4 2 2 E E M ( ) ( ) ( ) ( ) = + + + 4 2 0 n A O A A A E M n 2 M M E n n
± → ± W Z W Z L L L L W W W W W W W W Z Z Z Z Z Z W W W ( ) W n W ( ) n W Z Z Z Z 4 2 2 E E M ( ) ( ) ( ) ( ) = + + + 4 2 0 n A O A A A E M n 2 M M E n n
Necessary conditions for unitarity ( ) ( ) ∑ 2 = + ← = 2 4 O g g g E 0 ( ) WWZZ WWZ n WZW n ( )( ) 4 M − + + 2 2 2 2 Z 2 g g M M g WWZZ WWZ W Z WWZ 2 M W ( ) 2 − 2 2 ( ) ( ) M M ( ) ∑ 2 ( ) 2 = − ← = Z W n 2 O g 3 M E 0 ( ) ( ) ± n ( ) 2 W WZW n M n ± W These sum rules are automatically satisfied by higher dimensional gauge invariance This sum rule can be satisfied 2 g M by only the 1 st KK mode ≤ WWZ Z g ( ) ( ) 1 1 WZW in a good approximation 3 M M ± W W
for ≤ 0.04 g 2 ( ) g M 1 ( ) WZW ≤ 1 WWZ Z g ( ) ( ) ( ) ≥ WZV 1 1 M 700 GeV CDF 3 M M ± ± W W W ( ) 1 Check this rule by measuring and g M ( ) 1 ± WZW (Independent of model-building details) W ( ) “gold-plated” ± ± → → l ν + 1 W W Z 3 events l ± q q W ± ( ) ± ν W ± 1 W L L l + Z Z L q ′ q ′′ l − L
for ≤ 0.04 g 2 ( ) g M 1 ( ) WZW ≤ 1 WWZ Z g ( ) ( ) ( ) ≥ WZV 1 1 M 700 GeV CDF 3 M M ± ± W W W ( ) 1 Check this rule by measuring and g M ( ) 1 ± WZW (Independent of model-building details) W ( ) “gold-plated” ± ± → → l ν + 1 W W Z 3 events l ± q q W ± ( ) ± ν W ± 1 W L L l + Z Z L q ′ q ′′ l − L
for ≤ 0.04 g 2 ( ) g M 1 ( ) WZW ≤ 1 WWZ Z g ( ) ( ) ( ) ≥ WZV 1 1 M 700 GeV CDF 3 M M ± ± W W W ( ) 1 Check this rule by measuring and g M ( ) 1 ± WZW (Independent of model-building details) W ( ) 1 production ( ) “gold-plated” W ± ± → → l ν + 1 W W Z 3 cross sections events @LHC l ± q q W ± ( ) ± ν W ± 1 W L L l + Z Z L q ′ q ′′ l − L
# of events in the 2jet + 3l + ν channel Discovery reach (10 events) 550 GeV (1 TeV) requires 10 (60) fb^-1 for 1-2 year
Higgs “Kaluza-Klein Effects on Higgs Physics in Universal Extra Dimensions” F.J. Petriello, JHEP05 (2002) 003 “Gauge-Higgs Unification at the CERN LHC” N. Maru & N. Okada, PRD77 (2008) 055010 “Higgs Production from Gluon Fusion in Warped Extra Dimensions” A. Azatov, M. Toharia & L. Zhu, arXiv:1006.5939
Discovery Mode
Discovery Mode 2γ decay is a promising mode for m H < 140GeV and well studied
gg -> H - > γγ g γ H ( ) n t ( ) n t ( ) n W g γ t W , Model y g m , information t W , n
GHU (5D SU(3)) Maru & Okada (2007) periodic m h = 120 GeV anti-periodic 14% deviation @m 1 = 1 TeV SM n t = 1 n t = 3 n t = 5 ← 1st KK mass
UED (5D) Additive 1/R = 500 GeV 1/R = 750 GeV 1/R = 1 TeV SM 1/R = 1.25 TeV, 1.5 TeV Petriello, JHEP05 (2002) 003
RS with Bulk Higgs × : 1/R’ = 5 TeV ＋ : 1/R’ = 2 TeV △ : 1/R’ = 1.5 TeV mH = 120GeV σ σ RS RS → → γγ > < gg h h 1, 1 σ σ SM SM → → γγ gg h h Azatov, Toharia & Zhu, 1006.5939
RS with Brane Higgs × : 1/R’ = 5 TeV ＋ : 1/R’ = 2 TeV △ : 1/R’ = 1.5 TeV mH = 120GeV Sign cannot be predicted Azatov, Toharia & Zhu, 1006.5939
Radion “Graviscalars from Higher-Dimensional Metrics and Curvature-Higgs Mixing” G.F. Giudice, R. Rattazzi & J.D. Wells “Radion Phenomenology on Realistic Warped Space Models” C. Csaki, J. Hubisz & S.J. Lee, PRD76 (2007) 125015
Radion is a scalar perturbation of the metric which cannot be gauged away ( ) ( ) − + = η − + 2 2 ky F 2 2 ds e 1 2 F dy µν ( ) 2 ( ) ( ) R ( ) ( ) ′ = − η µ ν − + = < < = − 2 2 F 2 1 e dx dx 1 2 F dz R 1/ k z R TeV µν z 1 ∫ = − δ 5 MN S d x gT g radion MN Radion-Matter 2 interaction 2 ( ) ( ) 1 z ∫ = µ − 5 55 d x g r x T 2 T g µ ′ Λ 55 R r 4D ( ) 2 2 canonically 2 r x 1 R z z 6 ( ) ( ) ( ) = = Λ ≡ ≈ F z x , r x , TeV ′ ′ ′ normalized Λ r R R R R 6 r radion r(x) Localized on TeV brane
Coupling to the SM fermions ( ) m m ( ) ( ) − ψ ψ ψ ψ , , c c r others r t b Λ Λ L R UV UV IR IR L R L r r Coupling to massive gauge bosons (W, Z) 2 2 3 M 2 3 M 1 ( ) ( ) ′ µ ′ µ − + + − + 2 2 W Z 1 log kR M rW W 1 log kR M rZ Z µ µ Λ Λ Λ Λ W Z 2 2 r r r r 1-loop Coupling to massless gauge bosons (γ, g) effects ( ) ( ) ( ) − πα τ + τ 0 0 1 4 α r ∑ ( ) UV IR − + − κ τ µν b F F F ( ) µν ′ Λ π i i i 4log kR 8 i r Brane kinetic term Trace anomaly
Branching fraction of the radion Λ r = 2 TeV Bulk RS1 RS1
Branching fraction of Higgs
Branching fraction of the radion Very similar behavior to Higgs boson (Λ r ⇔ v), but Br(r -> gg) can be enhanced by comparing to Br(H -> gg) by a factor “10” due to the radion coupling through the trace anomaly Λ r = 2 TeV Bulk RS1 RS1
Ratio of gg -> r - > γγ/gg -> H - > γγ SM Bulk RS1 RS1
Summary Now, “Extra Dimensions” as an alternative to solution to the hierarchy problem is no longer alternative KK particles with TeV mass These give rise to various collider signatures@LHC!! Let Let us us ex expec ect tha that t the n the news ews of discovery o of ex extr tra di dimen ensions will c ll com ome soon oon!! !!
Backup
KK Gluon “The Bulk RS KK-gluon at the LHC” B. Lillie, L. Randall & L-T. Wang, JHEP09 (2007) 074 “CERN LHC Signals from Warped Extra Dimensions” K. Agashe, A. Belyaev, T. Krupovnicas, G. Perez & J. Virzi PRD77 (2008) 015003
Bulk SM in RS KK gluons and (right-handed) top Higgs are localized on IR brane ↓ KK gluons strongly couple to top t R 1 st ,2 nd generations KK gluons b R (t, b) L 0 mode graviton Planck TeV
Wave function of 1 st KK gluon ( ) ( ) 1 1 m m ( ) ( ) πφ πφ πφ χ φ ∝ + α 1 k k k e J e Y e 1 1 k k
Coupling of 1 st KK gluon to zero mode fermion UV IR localized localized g ( ) 1 ( ) − 1 + π 3 2 ffA O kr π c g 0.8 kr SM c Q 3L t R
Cross section for production of 1 st KK gluon
Branching ratio of 1 st KK gluon
( ) → 1 Invariant mass distribution of g tt
pp → jet + missing energy Vacavant & Hinchliffe (2001)
Spin sum of polarization tensors ∑ ( ) ( ) ( ) = e k s e , k s , P k µν αβ µναβ s ( ) 1 ( ) = η η + η η − η η P k µναβ µα νβ µβ να µν αβ 2 1 2 2 + η + η + k k k k µν µ ν αβ α β 2 2 6 m m n n ( ) 1 − η + η + η + η k k k k k k k k µα ν β νβ µ α µβ ν α να µ β 2 2 m n
Anomaly cancellation Arkani-Hamed, Cheng, Dobrescu & Hall (2000) Dobrescu & Poppitz (2001) 6D Anomaly = One-loop Square diagram ⇒ Q ⇔ U, D ( ) ( ) SU(3) C ∑ ∑ − a b c d a b c d ⇒ Tr T T T T Tr T T T T Opposite + − chirality N+ = N- Gravitational ⇒ 4 possibilities Q + , U - , D - , L - , E + , N + & (+ ⇔ -) Q + , U - , D - , L + , E - , N- & (+ ⇔ -)
SU(2) W x U(1) Y sector SU(2) W x U(1) Y anomalies cannot be canceled by the SM matter, but GS mechanism helps [SU(2) W ]^4, [U(1) Y ]^4, [SU(2) W ]^2[SU(3) C ]^2, [SU(3) C ]^2[U(1) Y ]^2, [SU(2) W ]^2[U(1) Y ]^2 [SU(2) W ]^3 = 0 (identically), [SU(3) C ]^3U(1) Y = 0 (per generation) Global anomaly Π 6 (G): nontrivial if G= SU(3), SU(2), G 2 Π 6 [SU(3)]: trivial ∵ SU(3) C is vector-like SU(2) L : N(2 + ) - N(2 - ) = 0 mod 6 → n g [N(2 + ) - N(2 - )] = 0 mod 6 ⇒ n g = 0 mod 3 [ ∵ N(Q)=3, N(L)=1]
Reducible anomalies ( ) ( ) 1 2 1 2 2 1 ( ) ( ) ( ) 3 = + − = − + = SU 3 U (1) A Q A U A D A 3 0 6 3 3 6 3 3 ( ) ( ) 1 4 1 2 4 1 1 ( ) ( ) ( ) ( ) ( ) 2 2 = − − = − − = − SU 3 U 1 C Q C U C D C 3 C 3 36 9 9 36 9 9 2 × + + 6 16 3 3 2 1 136 243 95 ( ) 4 = + + + + = = U 1 1 4 4 4 4 6 3 3 2 216 54 1 1 ( ) ( ) ( ) ( ) ( ) ( ) 2 2 = = = SU 3 SU 2 C 3 C 2 C 3 C 2 2 2 3 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) or 2 2 = ± = − SU 2 U 1 C 2 C 2 C 2 C 2 36 4 3 6 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) or 2 2 2 2 = ± = SU 2 SU 2 3 C 2 C 2 2 C 2 C 2
Discovery significance of gg -> r - > γγ ( ) τ = 0 0 EM ( ) τ = 0 0 3 ( ) ( ) τ = τ 0 1 2 3 3 ( ) ( ) τ = τ 0 1 3 3
Discovery significance of gg -> r -> ZZ -> 4l ( ) τ = 0 0 EM ( ) τ = 0 0 3 ( ) ( ) τ = τ 0 1 2 3 3 ( ) ( ) τ = τ 0 1 3 3
Sum Rules ( ) ∑ ( ) 2 ( ) = + ← = n 4 2 0 g g g A WWZZ WWZ WZV n ( ) 2 − 2 2 ( ) ( ) M M ( )( ) 4 M ∑ ( ) 2 ( ) 2 ( ) ± − + + = − Z W ← = n n 2 2 2 2 2 Z 2 g g M M g g 3 M A 0 ( ) WWZZ WWZ W Z WWZ WZV W 2 ( ) 2 M ± n M n W W ( ) ∑ ( ) 2 = + + i 2 2 g g g g γ WWWW WWZ WW WWV i ( ) ( ) ∑ ( ) 2 2 = + i 2 2 2 0 4 g M 3 g M g M WWWW W WWZ Z WWV i i
× : 1/R’ = 5 TeV ＋ : 1/R’ = 2 TeV △ : 1/R’ = 1.5 TeV Azatov, Toharia & Zhu, 1006.5939
Angular dependences of gg -> G(V,S) -> t tbar
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