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

• The Hierarchy problem

Why is the Higgs mass so much lighter than the Planck scale? ⇒ ∆m2

H = − |λf |2 8π2

• m2

f + . . .

• H

H f MPl LHC

Motivation

• The Hierarchy problem

Why is the Higgs mass so much lighter than the Planck scale? ⇒ ∆m2

H = − |λf |2 8π2

• m2

f + . . .

• H

H f MPl LHC S M p a r t i c l e s

Motivation

• The Hierarchy problem

Why is the Higgs mass so much lighter than the Planck scale? ⇒ ∆m2

H = − |λf |2 8π2

• m2

f + . . .

• H

H f MPl LHC S M p a r t i c l e s H e r e m a y b e m

• n

s t e r s !

Motivation

• The Hierarchy problem

Why is the Higgs mass so much lighter than the Planck scale? ⇒ ∆m2

H = − |λf |2 8π2

• m2

f + . . .

• H

H f

• The flavour puzzle

Why are the masses of elementary particles so different? Hamburger fisher boat ← → Queen Mary II up quark ← → top quark MPl LHC S M p a r t i c l e s H e r e m a y b e m

• n

s t e r s !

Geometry

ds2 = e−2σηµνdxνdxµ − r2dφ2 , σ = kr|φ| Ultraviolet brane Infrared brane φ π S1/Z2

Geometry

ds2 = e−2σηµνdxνdxµ − r2dφ2 ⇒ ΛIR = e−krπΛUV ΛUV ≈ MPl ΛIR ≈ 1TeV UV brane IR brane φ π

Geometry

ds2 = e−2σηµνdxνdxµ − r2dφ2 ⇒ ΛIR = e−krπΛUV ǫ = ΛIR ΛUV ≡ e−krπ = MW MPl ≈ 10−16, L = − ln ǫ ≈ 37

✦ Solves Hierarchy problem due to redshifted Planck mass

ΛUV ≈ MPl ΛIR ≈ 1TeV UV brane IR brane φ π Higgs, Yukawas

Gauge sector

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 SU(3)C × U(1)EM SU(3)C × SU(2)L × U(1)Y UV brane IR brane φ π Higgs, Yukawas

Gauge sector

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

Fermion sector

Order one parameters cqi control localization of fermions in the bulk. g(1) gs √ L gs √ L d s s d φ π s, c u, d Q3 =

• tL

bL

• tR

F(cq1 < −1/2) F(cQ3 > −1/2) F(cq3 > 0)

Fermion sector

9 parameters cqi chosen in a way to satisfy 8 conditions {mqi, Vus, Vcs}. g(1) gs √ L gs √ L d s s d F(cQ1) F(cQ2) F(cd) F(cs) φ π s, c u, d Q3 =

• tL

bL

• tR

F(cq1 < −1/2) F(cQ3 > −1/2) F(cq3 > 0)

Fermion sector - RS GIM

g2

s L

M 2

KK

F(cQ1)F(cd)F(cQ2)F(cs) ∼ g2

s

M 2

KK

L 2mdms

• vY (5D)

d

2 g(1) gs √ L gs √ L d s s d F(cQ1) F(cQ2) F(cd) F(cs) The parameters which control the masses of the light quarks suppress potentially dangerous FCNC’s : RS-GIM. md ∼ v √ 2 F(cQ1) Y (5D)

d

F(cd) ∼ v √ 2 Y eff

d

h F(cQ1) F(cd) Yd H

Flavour Structure

• Yukawa matrices (Yd)ij can be chosen to be anarchic and of order one:

(Y eff

d )ij ≡ F(cQi)(Yd)(5D) ij

F(cdj)

• Hierarchical masses and mixings can be generated by relying on order
• ne parameters only:

mqi = O(1) v √ 2 F(cQi)F(cqi) ¯ ρ, ¯ η = O(1) , λ = O(1)F(cQ1) F(cQ2) , A = O(1) F 3(cQ2) F 2(cQ2)F(cQ3)

Flavour Structure

• Yukawa matrices (Yd)ij can be chosen to be anarchic and of order one:

(Y eff

d )ij ≡ F(cQi)(Yd)(5D) ij

F(cdj)

• Hierarchical masses and mixings can be generated by relying on order
• ne parameters only:

mqi = O(1) v √ 2 F(cQi)F(cqi) ¯ ρ, ¯ η = O(1) , λ = O(1)F(cQ1) F(cQ2) , A = O(1) F 3(cQ2) F 2(cQ2)F(cQ3)

✦ Provides explanation for flavour puzzle!

Flavour in RS

101 102 103 104 105 ΛUV [TeV] ✟ ✟ CP s → d ∆mK, ǫK b → d ∆md, sin 2β b → s ∆ms, As

SL

c → u D − ¯ D LSM + 1 Λ2

UV

¯ QiQj ¯ QiQj

Meson Mixing: Neutral Kaons

Generically |ǫK| by a factor O(50) enhanced with respect to |ǫK|exp = (2.23 ± 0.01) × 10−3.

2 4 6 8 10 107 106 105 104 103 102 101 1 101 102 MKK TeV ΕK

3000 randomly chosen RS points with |Yq| < 3 reproducing quark masses and CKM parameters with χ2/dof < 11.5/10 corresponding to 68% CL Without Z → b¯ b constraint With Z → b¯ b constraint at 95% CL Satisfying 95% CL |ǫK| ∈ [1.3, 3.3] · 10−3

Meson Mixing: Neutral D Mesons

Very large effects possible in D − ¯ D mixing, including large CP violation. Prediction might be testable at LHCb

50 50 0.00 0.02 0.04 0.06 0.08 D ° M12

D RS ps1

(M D

12)∗ = ¯

D|H∆C=2

eff,RS |D

= |M D

12|e2iφD Experimentally favoured region at 68% CL Experimentally favoured region at 95% CL consistent with quark masses, CKM pa- rameters, and 95% CL limit |ǫK| ∈ [1.3, 3.3] · 103

Meson Mixing: Bs Sector

In RS model significant corrections to semileptonic CP asymmetry As

SL and

SΨΦ = sin(2|βs| − 2φBs) consistent with |ǫK| can arise

• 1.0

0.5 0.0 0.5 1.0 300 200 100 100 200 300 SΨΦ ASL

s ASL s SM

As

SL = Γ( ¯

Bs → ℓ+X) − Γ( ¯ Bs → ℓ−X) Γ( ¯ Bs → ℓ+X) + Γ( ¯ Bs → ℓ+X) = Im Γs

12

M12

SM: As

SL = 2 · 10−5, SΨφ = 0.04

Experimentally favoured region at 68% CL Experimentally favoured region at 95% CL consistent with quark masses, CKM parameters, 95% CL limit |ǫK| ∈ [1.3, 3.3] · 103

Flavour in RS

101 102 103 104 105 ΛUV [TeV] ✟ ✟ CP s → d ∆mK, ǫK b → d ∆md, sin 2β b → s ∆ms, As

SL

c → u D − ¯ D RS results for m(1)

g

= 3 TeV

Flavour in RS

101 102 103 104 105 ΛUV [TeV]

✪

✟ ✟ CP s → d ∆mK, ǫK

✦

b → d ∆md, sin 2β

✦

b → s ∆ms, As

SL

✦

c → u D − ¯ D RS results for m(1)

g

= 3 TeV

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 Bs

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