Strongly Coupled Physics and the Strong CP problem Anson Hook - PowerPoint PPT Presentation

Strongly Coupled Physics and the Strong CP problem Anson Hook Stanford Anson Hook - hep-ph/1411.3325 + work in progress w/ S. Dimopoulos, G. Marques-Tavares, J. Huang

Classical Strong CP problem Neutron contains an up quark and two down quarks h Neutron i 6 2 � 1 + D 3 � 3 i 6 U � 1 D � 3

Classical Strong CP problem Electric Dipole moment d n = qx h i 6 2 � 1 + D 3 � 3 i 6 U � 1 D � 3

Expected Dipole moment √ | d n | ≈ ex 1 − cos θ √ ≈ 10 − 14 e 1 − cos θ cm D θ U D

Expected Dipole moment • Dimensional analysis suggests d n ∼ 10 � 14 e cm • Observed bound is | d n | < 2 . 9 × 10 − 26 e cm

Classical Strong CP problem × θ < 10 − 12 D θ U D

Quantum Strong CP problem g 2 G µ ⌫ + Y u HQu c + Y d H † Qd c 32 π 2 θ G µ ⌫ ˜ L � Neutron EDM can be calculated · − | d n | = 3 . 2 × 10 − 16 ( θ + arg det Y u Y d ) e cm Quantum calculation × θ + arg det Y u Y d ≡ θ < 10 − 10

Axion solution ! ! ! g 2 G µ ⌫ + 1 32 π 2 ( θ � a ) G µ ⌫ ˜ 2 ∂ µ a ∂ µ a L � f a V ( a ) Axion dynamically sets the neutron EDM to 0 θ f a a ⌘ 0 2 | d n | = 3 . 2 ⇥ 10 − 16 ( θ � h a 0 2 π f a i ) e cm f a

Massless up quark h i a U ! e i ↵ U U ! e i ↵ U θ ! θ + 2 α No invariant to construct EDM out of Must vanish | | ⇥ 1 m u m d | d n | = 3 . 2 ⇥ 10 − 16 ( θ + arg det Y u Y d ) 1 . 6 MeV e cm ( m u + m d ) m u ! 0 ) d n ! 0

Massless up quark solution h i a U ! e i ↵ U U ! e i ↵ U θ ! θ + 2 α • In the IR ! h UU i 6 = 0 • Anomalous symmetry is spontaneously broken • Looks like axion solution

Massless up quark m 2 � 2 + f ( η 0 � f η 0 θ ) η 0 � f η 0 θ η 0 � L IR = 2 • η ’ boson obtains a vev which removes θ from the IR • η ’ acts as the axion

Lattice input • Progress cannot not be made without lattice input • Sum rules at lowest order in mass • Higher order terms in chiral Lagrangian can fake an up quark mass • Need lattice input to determine the size of higher dimensional operators / mass of the up quark

Status of the massless up quark m u = 2 . 3 +0 . 7 − 0 . 5 MeV Massless up quark solution ruled out J. Beringer et al. (Particle Data Group) (2012). "PDGLive Particle Summary 'Quarks (u, d, s, c, b, t, b', t', Free)'"

Generalized massless up quark solution • 40 years since it was invented • Why throw away a good idea? • Simplest generalization of the massless up quark solution

Generalized massless up quark solution • Before confinement there is a massless quark • There is a sector which confines • After confinement, the vev of the η ’ boson removes θ from the IR

Generalized massless up quark This is the simplest generalized massless up quark solution Z 2 SM 0 SM SU (3) 0 SU (2) 0 SU (2) W SU (3) c B B c W θ θ SU (3) F SU (3) 0 F

Symmetry explanation Anomalous symmetry renders sum of angles unphysical and difference physical Discrete symmetry results in the difference being zero Z 2 SM 0 SM SU (3) 0 SU (2) 0 SU (2) W SU (3) c B B c W θ θ SU (3) F SU (3) 0 F

Symmetry explanation B → Be i α θ → θ + 2 α θ → θ + 2 α B → Be i α Z 2 SM 0 SM SU (3) 0 SU (2) 0 SU (2) W SU (3) c B B c W θ θ SU (3) F SU (3) 0 F

Constraints What are the constraints on this model? Z 2 SM 0 SM SU (3) 0 SU (2) 0 SU (2) W SU (3) c B B c W θ θ SU (3) F SU (3) 0 F

Constraints • We do not see a mirror sector • The mirror sector must have larger masses • The Higgs vev in the other sector must be much larger than ours! • For the sake of plotting results, set it to 10 14 GeV

RG evolution 3.0 h H 0 i = 10 14 GeV 2.0 ! 1.5 g QCD 0 ) g QCD 1.0 g QCD 1000 10 7 10 11 10 19 10 15 Μ H GeV L

RG evolution 3.0 h H 0 i = 10 14 GeV 2.0 1.5 g QCD SM 0 SM 1.0 SU (3) 0 SU (2) 0 SU (2) W SU (3) c B B c W θ θ SU (3) F SU (3) 0 F 1000 10 7 10 11 10 19 10 15 Μ H GeV L

RG evolution 3.0 h H 0 i = 10 14 GeV 2.0 1.5 SM g QCD SU (3) 0 SU (2) W SU (3) c B B c 1.0 θ θ SU (3) F 1000 10 7 10 11 10 19 10 15 Μ H GeV L

RG evolution 3.0 h H 0 i = 10 14 GeV 2.0 1.5 g QCD 1.0 SM SU (2) W SU (3) c 0 SU (3) F 1000 10 7 10 11 10 19 10 15 Μ H GeV L

Higher dimensional operators ! g 2 HH † G + H 0 H 0 † G 0 ˜ G ˜ G 0 M 2 M 2 32 π 2 pl pl Solutions to the strong CP problem strongly constrained by higher dimensional operators h i θ = H 0 H 0 † � HH † h H 0 i 2 10 38 GeV 2 < 10 � 10 ⇡ M 2 � � p H 0 . 10 14 GeV

Collider Observables • Observable signatures come from the pseudo-goldstone bosons SM SU (3) 0 SU (2) W SU (3) c B B c θ θ SU (3) F

Collider Observables • Observable signatures come from the pseudo-goldstone bosons • Color octet scalars • Obtain a 1-loop mass from gauge boson loops • Like charged pions, quadratic divergence cut off by rho mesons π 0 ≈ 9 α s m 2 4 π m 2 ρ 0

Collider Observables 1 ¥ 10 4 5000 1000 m p ' H GeV L 500 100 50 10 10 10 10 11 10 12 10 13 10 14 10 15 < H' > H GeV L

Collider Observables 1 ¥ 10 4 5000 1000 m p ' H GeV L 500 100 50 Maximum mass for lightest new Maximum mass for lightest new particles is 2 TeV! particles is 2 TeV! 10 10 10 10 11 10 12 10 13 10 14 10 15 < H' > H GeV L

Collider Observables G B π 0 B B G Pions decay through the anomaly into a pair of gluons

Collider Observables G G π 0 π 0 G G

Collider bounds 8 TeV [pb] CMS Top squark pair production ~ '' σ Observed limit ( t qq) λ → 10 312 4 jet event with a Expected 1 ± σ Expected 2 ± σ pair of resonances -1 Low-mass search (12.4 fb ) (a) 1 -1 (b) High-mass search (19.4 fb ) New CMS result : hep-ex / 1412.7706 -1 10 8 TeV, 19.4 fb -1 (b) (a) -2 10 200 300 400 500 600 700 800 900 1000 M [GeV] ~ t

Collider bounds 8 TeV 100 [pb] CMS Top squark pair production ~ '' σ Observed limit ( t qq) λ → 10 312 4 jet event with a 10 Expected 1 ± σ Expected 2 ± σ pair of resonances -1 Low-mass search (12.4 fb ) (a) 1 1 -1 (b) High-mass search (19.4 fb ) New CMS result : hep-ex / 1412.7706 -1 10 0.1 8 TeV, 19.4 fb -1 (b) (a) -2 10 0.01 200 400 600 800 1000 200 300 400 500 600 700 800 900 1000 M [GeV] ~ t

Massless up quark summary • A strong CP problem solution which is predicted to be observable at low energies • Simple confining gauge group SU(3) with 3 flavors with the 3 flavors gauged under • another SU(3) Depending on hypercharge assignments, heavier • resonances may decay into photons and be seen before the lighter pseudo-goldstones

a 750 GeV axion • What if the axion was heavy enough to be seen at the LHC? • e.g. 750 GeV decays into photons • Need to add an additional source of mass for the axion that does not ruin the solution to the strong CP problem • Necessarily involves new confining gauge groups • New confining gauge group is REQUIRED to have exactly the same theta angle as us

A too simple model Z 2 SM 0 SM SU (3) 0 SU (2) 0 SU (2) W SU (3) c c W θ θ SU (3) F SU (3) 0 F axion

a LHC visible axion • To fit a potential 750 GeV bump • f a ~ TeV • Confinement scale ~ TeV • Three main issues to address • Such a low f a introduces a fine tuning worse than what we are trying to solve • Why is f a and the confinement scale around the same scale • Why is this scale at a TeV?

Model Z 2 SU (3) 0 SU (3) c c θ θ ψ , ψ c SU (3) a θ 0 χ , χ c

Model Z 2 Confinement of SU(3) a gives the axion as a goldstone boson SU (3) 0 SU (3) c c 2 singlet goldstone bosons θ θ ψ , ψ c U (1) axion U (1) ⌘ 0 SU (3) a ψ , ψ c 1 1 θ 0 χ , χ c -9 1 χ , χ c

Model Z 2 Before confinement of mirror color : SU(3) a has 10 flavors and is conformal SU (3) 0 SU (3) c c θ θ After confinement of mirror color : SU(3) a has 1 flavors ψ , ψ c and confines Confinement of mirror color SU (3) a causes confinement of θ 0 axion gauge group! χ , χ c

A 750 GeV axion • The 750 GeV excess could be the axion • Success of implementation requires strong dynamics • Conformal/Confining window of SU gauge groups is important • Product gauge group CFTs/confinement needs to be understood better

Conclusion • Strong CP problem typically involves strongly coupled groups • Lattice input can be critical • Generalized massless up quark solution • SU(3) with 3 flavors with flavor gauged • a 750 GeV axion • Confining/Conformal window needs to be well understood for both single and product gauge groups