Flavor in the scalar sector of Warped Extra Dimensions a by Manuel Toharia (University of Maryland) at the University of Virginia, Dec. 2, 2009 a Based on PRD80:03506( 09) A.Azatov, M.T., L.Zhu PRD80:0370( 09) A.Azatov, M.T., L.Zhu
Outline Introduction Flavor Anarchy Radion Pheno and Flavor Higgs FCNC s Conclusions
Introduction Warped Extra Dimension s double motivation Address Planck-TeV hierarchy [Randall,Sundrum](RS) Bulk SM with Fermion localization: Flavor hierarchies [Davoudiasl,Hewett,Rizzo];[P omarol,gherghetta];[n eubert,grossman];... RS Metric Background : ds 2 = e 2ky η µν dx µ dx ν dy 2 Exponential factor warps down mass scales graviton localized near y = 0 Boundary (Planck or UV brane) Higgs localized near the other Boundary (TeV or IR brane)
Gravity Sector Planck TeV g 0 ΜΝ Φ g n ΜΝ RS Metric Background : ds 2 = e 2ky η µν dx µ dx ν dy 2
Matter in the Bulk Planck Higgs TeV c o A o Μ, G o Μ t o u o A n Μ, G n Μ Precision Electroweak Constraints M KK > 3 TeV [Agashe,Delgado,May,Sundrum](03);[Agashe,Contino(06)]; [Carena,Ponton,Santiago,Wagner(06)(07)]; [Contino,DaRold,Pomarol(07)]..
S = Fermion localization: Flavor! d 4 xdy [ i ( g QΓ A D A Q D A QΓ A Q ) + i (ŪΓ A D A U D A ŪΓ A U ) 2 2 +c Q k QQ c u k ŪU + ( Y QHU + h.c. )] Massless Fermion mode profiles Q 0 L(y) e (/2 c Q)ky UR(y) 0 e (/2 c u)ky In flat ED, SEVERE flavor problem M KK > 00 5000 TeV [Delgado,P omarol,quiros] Much milder in Warped case M KK > 5 40 TeV [Csaki,Falkowski,Weiler]; [Agashe,Azatov,Zhu]
Planck Higgs TeV c o t o A o Μ, G o Μ u o A n Μ, G n Μ
Flavor Anarchy Fermion profiles Let f i = Ψ i (y TeV ) Ψ i (y) e (/2 c i)ky ( profile at the TeV brane) SMALL hierarchy in c i s LARGE hierachy in f i s Fermion mass matrix from Y ij HQ i U j 5D Yukawa Y ij m ij = v 2 f QiY ij f uj anarchic and O() Mass matrices still hierachical f Q f u f Q f u2 f Q f u3 m u f Q2 f u f Q2 f u2 f Q2 f u3 f Q3 f u f Q3 f u2 f Q3 f u3 ǫ 4 ǫ 3 ǫ 2 ǫ 3 ǫ 2 ǫ ǫ 2 ǫ
Diagonalize mass matrices: U Qu m u W u = m diag u U Qd m d W d = m diag d SM Fermion physical masses hierarchical m ui v f Qi f ui f Q f Q f Q2 f Q3 f U Qd,U Qu Q f f Q2 Q2 f Q3 W u f u f u2 f u f u2 f u f u3 f u f u3 f u2 f u3 f u2 f u3 f Q f Q3 W d f Q2 f Q3 f d f d2 f d f d2 f d f d3 f d f d3 f d2 f d3 f d2 f d3
SM CKM matrix V CKM = U Q u U Qd = λ λ 3 λ λ 2 U Q u U Qd λ λ 3 λ λ 2 λ 3 λ 2 λ 3 λ 2 W u m u m c λ m u m t λ 3 m u m m c c λ m t λ 2 W d m d m s λ m d m b λ 3 m d m s λ m s m b λ 2 m u m t λ 3 m c m t λ 2 m d m b λ 3 m s m b λ 2 with λ.22 cabibbo angle
The Radion and its interactions In the RS model [Randall,Sundrum,( 98)] the background metric g o AB is defined by ds 2 = e 2σ η µν dx µ dx ν dy 2 = R2 z 2 ( ηµν dx µ dx ν dz 2) with σ(y) = ky (and R = /k). Hierarchy created between the two boundaries at y = 0 and y = πr 0 (z = R and z = R ). The linear metric perturbations h AB (x,y) can be reduced to ds 2 = ( e 2σ η µν + [ e 2σ h TT µν (x,y) η µν r(x) ]) dx µ dx ν + ( + 2e 2σ r(x) ) dy 2 (the graviscalar r(x) is massless. A stabilization mechanism providing it with mass is assumed for example[golberger,wise( 99)])
Ex. RS - Matter on the brane S int (r) = Λ r dx 4 T µ µ φ 0 (x) Higgs H γ Gluon W,Z f α 8π Higgs-like couplings! [ ] α s φ 0 F 8π /2 (τ i )/2 b 3 G µν G µν Λ i r [ ] e 2 i NcF i φ 0 i (τ i ) (b 2 + b Y ) F µν F µν Λ r φ 0 i MV 2 V α V α Λ r φ 0 m f ff Λ r α s 8π α 8π [ ] F /2 (τ i )/2 i [ ] e 2 i NcF i i (τ i ) i H v M2 V V α V α H v m f ff H v G µνg µν H v F µνf µν
Radion Production vs. Higgs production 0 2 0 0 0 σ (pb) 0 0 2 0 3 LHC 0 4 0 5 0 6 gg fusion WW,ZZ fusion Wφ Zφ qq, gg > tt φ Tevatron Run2 0 7 200 400 600 800 000 m φ (GeV) K.Cheung ( 00)(Λ φ = TeV) (CMS TDR)
Radion Branchings vs. Higgs Branchings 0. gg bb ZZ WW Br Φ XX 0.0 0.00 ΓΓ hh tt Ξ 0 0 4 0 5 BULK FIELDS RS 00 200 300 400 500 600 m Φ Branchings of the radion vs. its mass m φ Branchings of Higgs vs. its mass (from CMS TDR)
LHC REACH in (m φ Λ φ )
Radion couplings to 5D fermions family of bulk fermions and a Brane Higgs: [Csaki,Hubisz,Lee(07)] φ 0 Λ r (c U + c Q )m u ūu 5D Computation involved. Simple exlanation, L dependence m u (L) Y v(l)f Q (L)f u (L) Y v(l)e ( c Q c U )kl m o e (c U+c Q )k Radion can be understood as a fluctuation of the radius L. k(l + δl) kl + φ Λ r The linear radion fluctuation in the mass term is m u (L + δl) = m u (kl) φ Λ r (c U + c Q ) m o e (c U+c Q )kl = m u (kl) φ Λ r (c U + c Q ) m u
We extend to 3 families and allow for bulk Higgs (localized towards IR brane) A.Azatov,M.T.,L.Zhu PRD80;0370( 09) φ 0 (c i Q + c j D Λ ) mij d r d i Ld j R + h.c φ 0 Λ r dl (c Q m d + m d c D )d R m d not in the diagonal physical basis; c Q,D are NON-DEGENERATE diagonal matrices. tree-level FCNC s! Diagonalize fermion mass matrix means here [ (U Q d c Q U Qd ) m d diag + m d diag (W d c DW d ) φ 0 Λ r d phys L ] d phys R
In the physical basis we obtain the estimate: L rfv = Λ r a d ij m d i md j φ 0 d i L d j R + h.c. a d ij (c Q + c D ) (c Q c Q2 )λ ms m d G(c Qi )λ 3 mb m d (c D c D2 ) λ md m s (c Q2 + c D2 ) (c Q2 2 )λ2 mb m s F(c Di ) λ 3 md m b (c D2 c D3 ) λ 2 ms m b ( 2 + c D 3 ) where we have taken c Q3 = (IR localized) and λ 0.22. 2 F and G are O(.) 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 C 4 = a ds a sd m d m s m 2 φ Λ2 r K K mixing and ǫ K put tight bounds Radion interaction scale r GeV 25 000 20 000 5 000 0 000 5000 a ds 0.03 a ds 0.2 a ds 0.5 0 0 20 50 00 200 500 Radion mass m r GeV 25 000 20 000 5 000 0 000 5000 M KKG MPl R GeV Figure : Bounds in m φ Λ r plane from ǫ K. [A.Azatov,M.T.,L.Zhu] Bounds on lighter radion even stronger [Ponton,Davoudiasl]
Tree level Higgs FCNC s Effective Theory Approach [Buchmuller,Wyler(86)], [delaguila,perez-victoria,santiago(00)] [Agashe,Contino(09)] Consider in 4D effective action, Dim 6 operators (down sector): λ ij H 2 Λ 2 HQ L i D Rj Corrections to mass matrix ( ) v4 2 v 4 y ij + λ ij Λ 2 Correction to Higgs Yukawa couplings ( ) v4 2 h y ij + 3λ ij Λ 2 2 Q L i D Rj
Tree level Higgs FCNC s Effective Theory Approach [Buchmuller,Wyler(86)], [delaguila,perez-victoria,santiago(00)] [Agashe,Contino(09)] Consider in 4D effective action, Dim 6 operators (down sector): λ ij H 2 Λ 2 HQ L i D Rj k D ij H 2 Λ 2 D R i /D Rj k Q ij H 2 Λ 2 Q L i /Q Lj Corrections to mass matrix (also from canonical normalization) ( ) ( ) ( ) v4 2 v 4 y ij + λ ij Q Λ 2 Li D Rj δ ij /2 + kij D v4 2 D Λ 2 Ri /D Rj δ ij /2 + k Q v4 2 ij Q Λ 2 Li /Q Lj Correction to Higgs Yukawa couplings ) h 2 ( Q Li D Rj 2kij D ( y ij + 3λ ij v 2 4 Λ 2 v ) h 2 ( D Λ 2 Ri /D Rj 2k Q ij v 4 Λ 2 ) h 2 Q Li /Q Lj
Higgs Couplings Q and U 5d fermions Q = Q L + Q R and U = U L + U R Bulk Higgs d 5 x Y H QU Y HQ L U R + Y 2 HQ R U L with Y = Y 2 Brane Higgs dx 4 Y HQ L U R + Y 2 HQ R U L with Y Y 2
Higgs FCNC s in RS [Casagrande et.al.(08); Blanke et.al.(09); Buras et.al.(09)] H H H Y Y q L D R q L Y H H q L d R Y Y d R Q L d R m d SM v f Q Y f d ( f 2 Q Y d SM f Q Y f d ( 2f 2 Q Y 2 v 2 M 2 KK Y 2 v 2 M 2 KK ) fd 2 Y 2 v 2 MKK 2 ) 2fd 2 Y 2 v 2 MKK 2 m d SM Y d SMv m d SM Y 2 v 2 M 2 KK ( f 2 Q + f 2 d)
Higgs FCNC s in RS [Agashe, Contino(09); Azatov,M.T.,Zhu(09)] H H H H Y Y Y 2 Y q L d R q L D R D L Q R Q L d R m d SM v f Q Y f d ( Y Y 2 v 2 M 2 KK ( YSM d f Q Y f d 3 Y ) Y 2 v 2 MKK 2 m d SM Y d SMv m d SM 2 Y Y 2 v 2 M 2 KK )
Define : Tree-level Higgs FCNC s! m d L HFV = a d i md j ij H v d i Ld j 4 2 R + h.c. Solve perturbatively in (Y v 4 /M KK ): λ ms a d ij δ ij Ȳ 2 v4 2 m d MKK 2 λ λ 3 mb m d md m s λ 2 mb m s λ 3 md m b λ 2 ms m b a u ij δ ij Ȳ 2 v 2 4 M 2 KK λ λ m c m u λ 3 m t m u mu m c λ 2 m t m c λ 3 mu m t λ 2 mc m t
Tree level HIGGS exchange will induce s L d R s R d L with coefficient C 4 = a ds a sd m d m s m 2 h v2 4 K K mixing and ǫ K put tight bounds 20 000 FCNC Preferred Y 5 D, 3 20 000 75 quantile FCNC Preferred Y 5 D 2, 6 5 000 5 000 Estimate Higgs exchange MKKG 0 000 75 quantile Estimate Higgs exchange KK gluon exchange MKKG 0 000 25 quantile 5000 25 quantile 5000 KK gluon exchange Disfavored from FCNC s 0 00 50 200 300 500 700 000 m h Disfavored from FCNC s 0 00 50 200 300 500 700 000 m h Figure 2: Bounds from ǫ K in(m h -M KK )plane from Higgs exchange
8000 LHC Reach for t ch 7000 6000 Median MKKG 5000 4000 3000 2000 Y 5 D, 4 Median Y 5 D 3, 3 Observable at LHC 000 00 0 20 30 40 50 60 70 Figure 3: LHC observability t ch in the plane (m h,m KKG ). m h (using [Aguilar Saavedra,Branco(00)] study)
200 50 N of points per bin 50 00 50 N of points per bin 00 50 0 0.5 0.6 0.7 0.8 0.9.0 a bb 0 0.5 0.6 0.7 0.8 0.9.0 a tt Figure 4: Distribution of a tt and a bb, in our numerical scan, with a fixed KK scale of R = 500 GeV (KK gluon mass M KKG = 2.45R ) and for 5D Yukawas Y ij 5D [0.3, 3].
h bb h WW Br h XX 0. 0.0 0.00 h ΤΤ h gg h bs h ΓΓ h ZZ h tc h tt RS SM 0 4 00 50 200 300 500 700 000 m h Figure 5: Higgs Branchings, for (KKG 3.5TeV) Ȳ 3 and /R = 500 GeV.
Outlook Maybe LHC discovers just one (or two) scalar(s) and that s IT. Is it the SM Higgs? (or a 2 Higgs doublet model?) or is it the radion of RS? (or radion plus a Higgs?) Probing couplings to fermions important (and hard). Higgs production may be significantly enhanced (work in progress) Probing the size of the Flavor structure also important. Flavor at LHC? (t ch, (h,φ) t c, (h,φ) µτ.. ) Linear Collider? Muon Collider? Higgs-radion mixing..
Backup Calculation Down quark Action with a Bulk Higgs, in RS: S = d 4 xdz [ i ( g QΓ A D A Q D A QΓ A Q ) + i (ŪΓ A D A U D A ŪΓ A U ) 2 2 + c Q R QQ + c U R ŪU + ( Y QHU + h.c. )] Decompose Q = Q L Q R mixed KK expansion: and D = D L D R Q L (x,z) = q L (z)q L (x) +... Q R (x,z) = q R (z)d R (x) +... D L (x,z) = d L (z)q L (x) +... D R (x,z) = d R (z)d R (x) +... and perform a
Mixed profile equations m d q L q R + c q + 2 q R + z m d q R + q L + c q 2 q L + z m d d L d R + c d + 2 d R + z m d d R + d L + c d 2 d L + z ( ) R v(z)y d d R = 0 z ( ) R v(z)y d d L = 0 z ( ) R v(z)yd q R = 0 z ( R z Massaging them we arrive at: R ( m d = R 4 md dz z ( d L 2 + q 4 R 2 ) + Rv(z) z 5 R ) v(z)y d q L = 0 ) (Y d d R ql Y d q R d L) 4D Higgs Yukawa is : y d 4 = R 5 R R dz h(z) z 5 (Y d d R q L + Y d q R d L)
Misalignement between 4D fermion mass matrix and Yukawas! R ( ) d = R 4 md dz z ( d L 2 + q 4 R 2 ) 2Yd Rv(z) q z 5 R d L. R
Higgs Production - work in progress H glu glu coupling: top quark and KK tower Even if top Yukawa reduced, extra KK tops render the coupling SM-like light quarks and KK tower If shifts in the light quarks yukawa is δ, the KK tower contributes by (δ) Overall coupling becomes + 5δ wrt SM contribution.