A Warped Solution to the Strong CP Problem Don Bunk Pheno 5/10 - PowerPoint PPT Presentation

A Warped Solution to the Strong CP Problem Don Bunk Pheno 5/10 Work done with Dr. Jay Hubisz at Syracuse University arXiv:1002.3160

Outline • The Strong CP problem and the Axion • Warped model • An Axion candidate for the Strong CP problem • Phenomenology and constraints for Warped axion model

The Strong CP problem QCD violates CP: ¯ θ where 32 π 2 TrG µ ν ˜ ¯ θ = θ − arg | M q | L QCD,CP = G µ ν Leading to a non-zero dipole moment for the neutron: γ π + π + n n p d n = 3 . 2 · 10 − 10 ¯ θ ecm < 6 . 3 · 10 − 26 ecm θ | < 10 − 10 ? This is the Strong CP problem. Why is | ¯

The Axion 2 hints to a resolution: 1) The QCD vacuum energy is minimized at ¯ θ = 0 hence if was a dynamical field it would relax to zero. ¯ θ 2) The theta term is actually a total derivative � G µ ν � ¯ G µ ν ˜ ∼ ¯ θ∂ µ J µ θ Tr If was a field this would be the coupling from a ¯ θ spontaneously broken global symmetry U (1) P Q L = a ( x ) ∂ µ J µ P Q f P Q

RS Space � 2 ( η µ ν dx µ dx ν − dz 2 ) � R ds 2 = z φ ( x, z ) 1 1 R ′ ∼ R ∼ TeV M pl R z Randall, Sundrum hep-ph/9905221

RS Space � 2 ( η µ ν dx µ dx ν − dz 2 ) � R ds 2 = z B N ∈ U (1) 5 D 1 1 R ′ ∼ R ∼ TeV M pl R z ‘Bulk’ B µ = 0 B µ = 0 Choi hep-ph/0308024 Gripaios 0803.0497, 0704.3981, hep-ph/0611278

The Setup Starting point: U(1) gauge field ( not ! ) U (1) P Q � − 1 � 4 B MN B MN − 1 � d 5 x √ g 2 G ( B N ) 2 S = � 1 � For and a massless B µ | R,R ′ = 0 | R,R ′ = 0 ∂ z z B 5 mode survives: �� � � − 1 � µ ν B ( n ) µ ν + 1 + 1 4 B ( n ) 2 m ( n )2 B ( n ) µ B ( n ) µ 2 ∂ µ B 5 ∂ µ B 5 d 4 x � S eff = n =1 A residual subgroup remains that is global from the 4D perspective B 5 → B 5 + ∂ 5 β

Adding Fermions � d 5 x √ g � ¯ / Ψ + m ¯ � S ferm = Ψ iD ΨΨ To produce a chiral theory we need appropriate BC � χ � For example for Ψ 5 D = ¯ ψ Choosing ψ | R = ψ | R ′ = 0 � χ (0) � χ ( n ) � � Yields � Ψ 5 D = + ¯ ψ ( n ) 0 n =1

Coupling to G · ˜ G Introduce fermions that are charged under SM and : U (1) 5 D � z � � dz ′ B 5 ( x, z ′ ) Ψ ′ ( z, x ) Ψ ( z, x ) ≡ exp iq z 0 So that for , Ψ ′ → e iq β ( z 0 ) Ψ ′ B 5 → B 5 + ∂ z β ( z ) Because of the chiral zero mode this symmetry is anomalous and produces the coupling: 1 B 5 A ⊃ B 5 G · ˜ L = G f P Q √ R With f P Qeff = √ 2 R ′ g 5 D

Suppressing higher dimensional operators In general, higher dimensional operators can displace the axion from its CP-conserving value: � g n � a O n +4 + c QCD G · ˜ L ax ⊃ G M n f P Q P l QCD and For c QCD � G · ˜ G � ∼ Λ 4 O ∼ µ � 4 � M P l � n � Λ QCD g n � 10 − 10 µ µ Typically but in this case µ ∼ f P Q ∼ 10 9 − 12 GeV µ ∼ TeV

Axion bounds In general we need 10 9 GeV ≤ f P Q ≤ 10 12 GeV bound is from ‘Misalignment production’ 10 12 GeV contributing to the energy density of the universe Ω mis h 2 ∼ f P Q 10 9 GeV lower bound is from stellar cooling 1 Luminosity ∼ f 2 P Q

Stellar Cooling Typical interactions are suppressed by f P Q γ photon-axion B 5 γ γ B 5 e − Compton e − e − N N B 5 Bremsstrahlung π N N

Adding gravitational fluctuations � 2 ( e − 2 F η µ ν dx µ dx ν + h µ ν dx µ dx ν − (1 + 2 F ) 2 dz 2 ) � R ds 2 = z Effective vertices from integrating out the Radion: ψ ψ χ χ F m rad ∼ O (100 GeV ) ψ ′ ψ ′ χ ′ χ ′ ∀ χ , χ ′ , ψ , ψ ′

Stellar Cooling For the sun Primakoff-like processes dominate (0) (0) B 5 B 5 e − (0) (0) B 5 (0) B 5 e − B 5 γ (0) B 5 γ e − e − γ e − e − e − e − γ A conservative limit is given by L A < . 2 L ⊙ L γ ≈ 10 33 erg For Sun s L B 5 � 10 23 erg Warped model s

Supernova type II Collapse Bremsstrahlung-like dominate (0) B 5 (0) (0) B 5 B 5 N (0) N N N N B 5 (0) B 5 N (0) B 5 π π π N N N N N N Here the constraint is on neutrino burst duration. SN 1987A: (15 M ⊙ ) L ν ≈ 10 53 erg Experiment: s L B 5 � 10 40 erg Warped model: s

Radion Phenomenology m 3 1 Γ ( r → B 5 B 5 ) = r R ′ 2 192 π For light radions this decay dominates the width: Γ tot ≈ Γ ( r → B 5 B 5 ) And decreases photon branching ratio: Br ( r → γγ ) → 1 10 Br ( r → γγ ) This is a significant modification since is otherwise γγ the most promising channel for the radion at the LHC.

Conclusion • Presented a U(1) gauge model in RS space • Provides an axion candidate • Naturally suppresses dangerous Planck- scale operators • Evades known constraints