Flavour Physics Martin Bauer, Mainz in Randall-Sundrum Models with - PowerPoint PPT Presentation

Flavour Physics Martin Bauer, Mainz in Randall-Sundrum Models with S.Casagrande, U.Haisch, F.Goertz M.Neubert and T.Pfoh based on arxiv:0807.4537

1 Motivation 2 The minimal Randall-Sundrum (RS) model 3 Flavour Observables 4 Summary & Conclusion

Motivation M Pl • The Hierarchy problem Why is the Higgs mass so much lighter than the Planck scale? f H H H = − | λ f | 2 � � ⇒ ∆ m 2 m 2 f + . . . 8 π 2 LHC

Motivation M Pl • The Hierarchy problem Why is the Higgs mass so much lighter than the Planck scale? f H H H = − | λ f | 2 � � ⇒ ∆ m 2 m 2 f + . . . 8 π 2 LHC s e l c i t r a p M S

Motivation H e r M Pl m e o m n a s y t • The Hierarchy problem e b r e s ! Why is the Higgs mass so much lighter than the Planck scale? f H H H = − | λ f | 2 � � ⇒ ∆ m 2 m 2 f + . . . 8 π 2 LHC s e l c i t r a p M S

Motivation H e r M Pl m e o m n a s y t • The Hierarchy problem e b r e s ! Why is the Higgs mass so much lighter than the Planck scale? f H H H = − | λ f | 2 � � ⇒ ∆ m 2 m 2 f + . . . 8 π 2 LHC • The flavour puzzle Why are the masses of elementary particles so different? s e l c i t r Hamburger fisher boat Queen Mary II a ← → p M up quark top quark S ← →

Geometry Ultraviolet Infrared brane brane S 1 /Z 2 0 φ π d s 2 = e − 2 σ η µν d x ν d x µ − r 2 d φ 2 , σ = kr | φ |

Geometry UV brane IR brane Λ UV ≈ M Pl Λ IR ≈ 1TeV 0 φ π d s 2 = e − 2 σ η µν d x ν d x µ − r 2 d φ 2 ⇒ Λ IR = e − krπ Λ UV

Geometry UV brane IR brane Λ UV ≈ M Pl Λ IR ≈ 1TeV Higgs, Yukawas 0 φ π d s 2 = e − 2 σ η µν d x ν d x µ − r 2 d φ 2 ⇒ Λ IR = e − krπ Λ UV ǫ = Λ IR ≡ e − krπ = M W ≈ 10 − 16 , L = − ln ǫ ≈ 37 Λ UV M Pl ✦ Solves Hierarchy problem due to redshifted Planck mass

Gauge sector UV brane IR brane SU (3) C × SU (2) L × U (1) Y SU (3) C × U (1) EM Higgs, Yukawas 0 φ π Gauge fields are 5D fields (so-called “bulk fields”) Since the extra dimension is compact they are decom- posed into 4D Kaluza-Klein (KK) modes, analogue to QM fields in a potential well

Gauge sector g (1) UV brane IR brane g Higgs, W, Z Yukawas 0 φ π Non flat profiles of KK modes lead d s g (1) to non-diagonal overlap integrals √ √ with fermions and potentially large g s L g s L flavour changing neutral currents s (FCNC’s). d

Fermion sector F ( c q 3 > 0) t R u , d F ( c Q 3 > − 1 / 2) s , c � t L � Q 3 = b L F ( c q 1 < − 1 / 2) 0 φ π d s g (1) Order one parameters c q i control √ √ localization of fermions in the g s L g s L bulk. s d

Fermion sector F ( c q 3 > 0) t R u , d F ( c Q 3 > − 1 / 2) s , c � t L � Q 3 = b L F ( c q 1 < − 1 / 2) 0 φ π F ( c Q 1 ) F ( c s ) d s g (1) 9 parameters c q i chosen in a way √ √ to satisfy 8 conditions g s L g s L { m q i , V us , V cs } . s d F ( c Q 2 ) F ( c d )

Fermion sector - RS GIM The parameters which control the masses of the light quarks suppress potentially dangerous FCNC’s : RS-GIM. F ( c Q 1 ) v h 2 F ( c Q 1 ) Y (5 D ) m d ∼ √ F ( c d ) d � H � Y d v 2 Y eff √ ∼ d F ( c d ) F ( c Q 1 ) F ( c s ) g 2 d s s L F ( c Q 1 ) F ( c d ) F ( c Q 2 ) F ( c s ) g (1) M 2 √ √ KK g s L g s L ∼ g 2 2 m d m s s L s M 2 � 2 � d vY (5 D ) F ( c Q 2 ) F ( c d ) KK d

Flavour Structure • Yukawa matrices ( Y d ) ij can be chosen to be anarchic and of order one: d ) ij ≡ F ( c Q i )( Y d ) (5 D ) ( Y eff F ( c d j ) ij • Hierarchical masses and mixings can be generated by relying on order one parameters only: m q i = O (1) v √ F ( c Q i ) F ( c q i ) 2 F 3 ( c Q 2 ) λ = O (1) F ( c Q 1 ) ρ, ¯ ¯ η = O (1) , F ( c Q 2 ) , A = O (1) F 2 ( c Q 2 ) F ( c Q 3 )

Flavour Structure • Yukawa matrices ( Y d ) ij can be chosen to be anarchic and of order one: d ) ij ≡ F ( c Q i )( Y d ) (5 D ) ( Y eff F ( c d j ) ij • Hierarchical masses and mixings can be generated by relying on order one parameters only: m q i = O (1) v √ F ( c Q i ) F ( c q i ) 2 F 3 ( c Q 2 ) λ = O (1) F ( c Q 1 ) ρ, ¯ ¯ η = O (1) , F ( c Q 2 ) , A = O (1) F 2 ( c Q 2 ) F ( c Q 3 ) ✦ Provides explanation for flavour puzzle!

Flavour in RS � ¯ � � ¯ 1 � L SM + Q i Q j Q i Q j 10 5 Λ 2 CP ✟ ✟ UV 10 4 Λ UV [TeV] 10 3 10 2 10 1 c → u s → d b → d b → s ∆ m s , A s D − ¯ ∆ m K , ǫ K ∆ m d , sin 2 β D SL

Meson Mixing: Neutral Kaons Generically | ǫ K | by a factor O (50) enhanced with respect to | ǫ K | exp = (2 . 23 ± 0 . 01) × 10 − 3 . 3000 randomly chosen RS points with | Y q | < 3 reproducing quark 10 2 masses and CKM parameters with 10 1 χ 2 /dof < 11 . 5 / 10 corresponding 1 to 68% CL 10 � 1 Without Z → b ¯ b constraint 10 � 2 � Ε K � With Z → b ¯ b constraint at 95% CL 10 � 3 Satisfying 95% CL | ǫ K | ∈ [1 . 3 , 3 . 3] · 10 − 3 10 � 4 10 � 5 10 � 6 10 � 7 2 4 6 8 10 M KK � TeV �

Meson Mixing: Neutral D Mesons Very large effects possible in D − ¯ D mixing, including large CP violation. Prediction might be testable at LHCb 12 ) ∗ = � ¯ ( M D D |H ∆ C =2 eff , RS | D � 0.08 = | M D 12 | e 2 iφ D 0.06 D RS � ps � 1 � Experimentally favoured region at 68% CL 0.04 Experimentally favoured region at 95% CL consistent with quark masses, CKM pa- � M 12 rameters, and 95% CL limit 0.02 | ǫ K | ∈ [1 . 3 , 3 . 3] · 10 3 0.00 � 50 0 50 � D � ° �

Meson Mixing: B s Sector In RS model significant corrections to semileptonic CP asymmetry A s SL and S ΨΦ = sin(2 | β s | − 2 φ B s ) consistent with | ǫ K | can arise SL = Γ( ¯ B s → ℓ + X ) − Γ( ¯ B s → ℓ − X ) A s Γ( ¯ B s → ℓ + X ) + Γ( ¯ B s → ℓ + X ) 300 = Im Γ s 12 M 12 200 100 s � SM SM: A s SL = 2 · 10 − 5 , S Ψ φ = 0 . 04 s �� A SL 0 � Experimentally favoured region at 68% CL A SL � 100 Experimentally favoured region at 95% CL � 200 consistent with quark masses, CKM parameters, 95% CL limit � 300 | ǫ K | ∈ [1 . 3 , 3 . 3] · 10 3 � 1.0 � 0.5 0.0 0.5 1.0 S ΨΦ

Flavour in RS RS results for 10 5 m (1) = 3 TeV CP ✟ g ✟ 10 4 Λ UV [TeV] 10 3 10 2 10 1 c → u s → d b → d b → s ∆ m s , A s D − ¯ ∆ m K , ǫ K ∆ m d , sin 2 β D SL

Flavour in RS RS results for 10 5 m (1) = 3 TeV CP ✟ g ✟ ✦ 10 4 ✦ ✪ Λ UV [TeV] 10 3 ✦ 10 2 10 1 c → u s → d b → d b → s ∆ m s , A s D − ¯ ∆ m K , ǫ K ∆ m d , sin 2 β D SL

Summary and Conclusion • Warped extra dimensions offer compelling geometrical explanation of gauge and fermion hierarchy problem, mysteries left unexplained in SM • Flavour-changing tree-level transitions of K and B s mesons particularly interesting as their sensitivity to KK scale extends beyond LHC reach. • Flavour-anarchy models need tuning to survive constraints from CP- violation in kaon sector, which calls for additional flavour structure