Radion flavor in Warped Extra Dimensions. a by Manuel Toharia - PowerPoint PPT Presentation

Radion flavor in Warped Extra Dimensions. a by Manuel Toharia (University of Maryland) at PHENO 2009, Madison, May 2009 a Based on arXiv:0812.2489 A.Azatov, M.T., L.Zhu

Outline • Introduction – Flavor in RS – The radion in RS • radion Flavor • Conclusions

Introduction • Warped Extra Dimensions: One compact extra dimension with warped geometry. • Original setup: Two branes as boundaries and all SM fields on the TeV Brane → RS1. – Towers of KK gravitons – Radion graviscalar • More recent setups: Two branes, Higgs field on TeV brane, SM fields in the “bulk”. – Towers of KK gravitons – Towers of KK SM fields – Radion graviscalar

Flavor anarchy: masses and mixings from fermion localization

The Radion and its interactions In the RS1 model [ Randall,Sundrum, ( ′ 98)] the background metric g o AB is defined by R 2 e − 2 σ η µν dx µ dx ν + dy 2 η µν dx µ dx ν + dz 2 � ds 2 � = = z 2 with σ ( y ) = ky (and R = 1 /k ). Hierarchy created between the ( z = R and z = R ′ ). two boundaries at y = 0 and y = πr 0 The linear metric perturbations h AB ( x, y ) can be reduced to ds 2 = dx µ dx ν + e − 2 σ η µν + e − 2 σ h TT 1 + 2 e 2 σ r ( x ) � � �� � � dy 2 µν ( x, y ) − η µν r ( x ) (the graviscalar r ( x ) is massless. A stabilization mechanism pro- viding it with mass is assumed for example[ Golberger,W ise ( ′ 99)] )

Ex. RS1 - Matter on the brane Higgs H 1 � dx 4 T µ S int ( r ) = µ φ 0 ( x ) Λ r Higgs-like couplings! �� � �� � α s φ 0 α s H G µν G µν v G µν G µν Gluon F 1 / 2 ( τ i ) / 2 − b 3 F 1 / 2 ( τ i ) / 2 8 π Λ r 8 π i i �� � �� � α φ 0 α H i N i F µν F µν e 2 i N i v F µν F µν γ c F i ( τ i ) − ( b 2 + b Y ) e 2 c F i ( τ i ) 8 π Λ r 8 π i i φ 0 H V V α V α M 2 V V α V α W , Z v M 2 Λ r H φ 0 m f ¯ v m f ¯ ff ff f Λ r

Radion Production vs. Higgs production 2 10 1 10 0 10 −1 10 LHC σ (pb) −2 10 −3 10 −4 10 gg fusion −5 10 WW,ZZ fusion Tevatron W φ Run2 Z φ −6 10 − , gg −> tt − φ qq −7 10 200 400 600 800 1000 m φ (GeV) K.Cheung (’00)(Λ φ = 1 TeV) (CMS TDR)

Radion Branchings vs. Higgs Branchings 1 WW gg ZZ 0.1 bb Br � Φ�� XX � 0.01 hh Ξ� 0 ΓΓ tt 0.001 � 4 10 BULK FIELDS RS1 � 5 10 100 200 300 400 500 600 m Φ Branchings of the radion vs. Branchings of Higgs vs. its its mass m φ mass (from CMS TDR)

LHC REACH in ( m φ − Λ φ ) (with Nobu Okada)

Radion couplings to 5D fermions • 1 family of bulk fermions and a Brane Higgs: [Csaki , Hubisz , Lee(07)] φ 0 ( c Q − c U ) m u ¯ uu Λ r Computation slightly involved, but a way to understand it is look at R ′ dependance in fermion mass term: m f ∼ Y v ( R/R ′ ) c Q − c U − 1 ∼ (1 /R ′ ) c Q − c U Radion can be understood as perturbation in the interbrane distance L , or in 1 /R ′ scale in the conformal frame. So we can 1 /R ′ → 1 /R ′ (1 + φ/ Λ r ) write Then include it in mass term and expand linearly in the radion ( c Q − c U ) φ/ Λ r (1 /R ′ ) c Q − c U ⇒ ( c Q − c U ) φ/ Λ r m f

• We extend to 3 families and allow for bulk Higgs (localized towards IR brane) [ A . Azatov , M . T ., L . Zhu (arXiv:0812 . 2489)] φ 0 d ¯ Q − c j D ) m ij d iL d j ( c i R + h.c Λ r φ 0 ¯ d L ( c Q m d − m d c D ) d R Λ r where m d is not in the diagonal physical basis and c Q , D are diagonal matrices. c i Q,D are the fermion bulk parameters for UV fermions BUT | c i Q,D | = 1 / 2 for IR fermions (and c Q > 0 and c D < 0). ⇒ tree-level FCNC’s! Diagonalize fermion mass matrix means here φ 0 d phys ¯ d phys ( U † c Q U ) m d diag − m d diag ( W † c D W ) � � L R Λ r

In the physical basis we obtain the estimate: L HFV = 1 � j φ 0 ¯ L d j a d d i m d i m d R + h.c. ij Λ r G ( c Q i ) λ 3 � �   m b m s ( c Q 1 − c D 1 ) ( c Q 1 − c Q 2 ) λ m d m d   � 2 ) λ 2 � m d m b a d ( c D 1 − c D 2 ) 1 ( c Q 2 − 1 ij ∼ ( c Q 2 − c D 2 )   λ m s m s     � � m d m s F ( c D i ) 1 ( c D 2 − c D 3 ) 1 ( 1 2 − c D 3 ) λ 3 λ 2 m b m b where we have taken c Q 3 = 1 2 (IR localized) and λ ∼ 0 . 22 . F and G are O ( . 1) functions of the c i ’s ⇒ a ds ∼ a sd ∼ 0 . 06

Tree level RADION exchange will induce s L d R s R d L with coefficient 1 ⇒ K − ¯ C 4 = a ds a sd m d m s K mixing and ǫ K put tight bounds m 2 φ Λ 2 r 25000 25000 Radion interaction scale � r � GeV � a ds � 0.5 KKG � � M Pl � R � � GeV � 20000 20000 15000 15000 a ds � 0.12 10000 10000 M 1 5000 5000 a ds � 0.03 0 10 20 50 100 200 500 Radion mass m r � GeV � Figure 1: Bounds in m φ − Λ r plane from ǫ K . Here we have called � | a ds a ∗ a ds ≡ sd | . From [ A . Azatov , M . T ., L . Zhu (arXiv:0812 . 2489)]

Outlook Maybe LHC discovers one or two neutral scalars, and that’s IT. Is it a Higgs? (or a 2 Higgs doublet model?) or is it an RS type scenario? (radion plus a Higgs?) The Radion is Higgs-like but has special signatures: • Very narrow width • Special production process and we have just seen that • Probing the size of FV couplings important. • Without flavor symmetry, m radion > ∼ 20 − 50 GeV • Flavor at LHC? ( r → t c ?) • Higgs-radion mixing?