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

Neutron contains an up quark and two down quarks U D D

h 2 3

i 6 1 3 i 6 1 3

• +

Neutron

Classical Strong CP problem

Electric Dipole moment

Classical Strong CP problem

U D D

h 2 3

i 6 1 3 i 6 1 3

• +

dn = qx

Expected Dipole moment

U D D

θ

|dn| ≈ ex √ 1 − cos θ ≈ 10−14 e √ 1 − cos θ cm

Expected Dipole moment

• Dimensional analysis suggests

dn ∼ 1014e cm

• Observed bound is

|dn| < 2.9 × 10−26 e cm

Classical Strong CP problem

× θ < 10−12

U D D

θ

Quantum Strong CP problem

Neutron EDM can be calculated

L g2 32π2 θGµ⌫ ˜ Gµ⌫ + YuHQuc + YdH†Qdc

− · |dn| = 3.2 × 10−16 (θ + arg detYuYd) e cm

Quantum calculation

× θ + arg detYuYd ≡ θ < 10−10

Axion solution

Axion dynamically sets the neutron EDM to 0

⌘ |dn| = 3.2 ⇥ 10−16 (θ h a fa i) e cm

! ! ! L g2 32π2 (θ a fa )Gµ⌫ ˜ Gµ⌫ + 1 2∂µa∂µa

V (a)

a

2

2πfa

θfa

Massless up quark

No invariant to construct EDM out of Must vanish

h i

a

U ! ei↵U U ! ei↵U θ ! θ + 2α

| | ⇥ |dn| = 3.2 ⇥ 10−16 (θ + arg detYuYd) mumd (mu + md) 1 1.6 MeV e cm

mu ! 0 ) dn ! 0

Massless up quark solution

• In the IR

h i

a

U ! ei↵U U ! ei↵U θ ! θ + 2α

• Anomalous symmetry is spontaneously

broken

• Looks like axion solution

! hUUi 6= 0

Massless up quark

• η’ boson obtains a vev which removes θ

from the IR

• η’ acts as the axion

LIR = m2

η0

2

• η0 fη0θ

2 + f(η0 fη0θ)

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

mu = 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

SU(3)c SU(2)W SU(3)F

SM

θ

B B

θ

SM 0

SU(2)0

W

SU(3)0

F

SU(3)0

c

Z2

This is the simplest generalized massless up quark solution

Symmetry explanation

Anomalous symmetry renders sum of angles unphysical and difference physical Discrete symmetry results in the difference being zero

SU(3)c SU(2)W SU(3)F

SM

θ

B B

θ

SM 0

SU(2)0

W

SU(3)0

F

SU(3)0

c

Z2

Symmetry explanation

SU(3)c SU(2)W SU(3)F

SM

θ

B B

θ

SM 0

SU(2)0

W

SU(3)0

F

SU(3)0

c

Z2

B → Beiα B → Beiα

θ → θ + 2α θ → θ + 2α

Constraints

What are the constraints on this model?

SU(3)c SU(2)W SU(3)F

SM

θ

B B

θ

SM 0

SU(2)0

W

SU(3)0

F

SU(3)0

c

Z2

• 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 1014 GeV

Constraints

RG evolution

! gQCD0

1000 107 1011 1015 1019 1.0 2.0 3.0 1.5 Μ HGeVL gQCD

) gQCD

hH0i = 1014 GeV

RG evolution

1000 107 1011 1015 1019 1.0 2.0 3.0 1.5 Μ HGeVL gQCD

hH0i = 1014 GeV

SU(3)c SU(2)W SU(3)F

SM

θ

B B

θ

SM 0

SU(2)0

W

SU(3)0

F

SU(3)0

c

RG evolution

1000 107 1011 1015 1019 1.0 2.0 3.0 1.5 Μ HGeVL gQCD

hH0i = 1014 GeV

SU(3)c SU(2)W SU(3)F

SM

θ

B B

θ

SU(3)0

c

RG evolution

1000 107 1011 1015 1019 1.0 2.0 3.0 1.5 Μ HGeVL gQCD

hH0i = 1014 GeV

SU(3)c SU(2)W SU(3)F

SM

Solutions to the strong CP problem strongly constrained by higher dimensional operators

Higher dimensional

• perators

g2 32π2 HH† M 2

pl

G ˜ G + H0H0† M 2

pl

G0 ˜ G0 !

h i θ = H0H0† HH† M 2

p

⇡ hH0i2 1038GeV2 < 1010

• H0 . 1014 GeV

• Observable signatures come from the

pseudo-goldstone bosons

Collider Observables

SU(3)c SU(2)W SU(3)F

SM

θ

B B

SU(3)0

c

θ

• 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

m2

π0 ≈ 9αs

4π m2

ρ0

Collider Observables

1010 1011 1012 1013 1014 1015 10 50 100 500 1000 5000 1 ¥ 104 <H'> HGeVL mp' HGeVL

Collider Observables

Maximum mass for lightest new particles is 2 TeV!

1010 1011 1012 1013 1014 1015 10 50 100 500 1000 5000 1 ¥ 104 <H'> HGeVL mp' HGeVL

Maximum mass for lightest new particles is 2 TeV!

Collider Observables

Pions decay through the anomaly into a pair of gluons

π0

B B

G G

B

Collider Observables

π0 π0

G G G G

Collider Observables

4 jet event with a pair of resonances

New CMS result : hep-ex / 1412.7706 8 TeV, 19.4 fb-1

[GeV]

t ~

M 200 300 400 500 600 700 800 900 1000 [pb] σ

• 2

10

• 1

10 1 10

Observed limit σ 1 ± Expected σ 2 ± Expected

)

• 1

Low-mass search (12.4 fb )

• 1

High-mass search (19.4 fb

(a) (b)

(b) (a)

8 TeV

CMS

Top squark pair production qq) → t ~ (

312 ''

λ

Collider bounds

4 jet event with a pair of resonances

New CMS result : hep-ex / 1412.7706 8 TeV, 19.4 fb-1

[GeV]

t ~

M 200 300 400 500 600 700 800 900 1000 [pb] σ

• 2

10

• 1

10 1 10

Observed limit σ 1 ± Expected σ 2 ± Expected

)

• 1

Low-mass search (12.4 fb )

• 1

High-mass search (19.4 fb

(a) (b)

(b) (a)

8 TeV

CMS

Top squark pair production qq) → t ~ (

312 ''

λ

200 400 600 800 1000 0.01 0.1 1 10 100

Collider bounds

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

SU(3)c SU(2)W

SU(3)F

SM

θ

Z2

θ

SM 0

SU(2)0

W

SU(3)0

F

SU(3)0

c

axion

• To fit a potential 750 GeV bump
• fa ~ TeV
• Confinement scale ~ TeV
• Three main issues to address
• Such a low fa introduces a fine tuning worse than what we

are trying to solve

• Why is fa and the confinement scale around the same scale
• Why is this scale at a TeV?

a LHC visible axion

Model

SU(3)c

θ

Z2

θ

SU(3)0

c

SU(3)a

ψ, ψc

χ, χc

θ0

Model

SU(3)c

θ

Z2

θ

SU(3)0

c

SU(3)a

ψ, ψc

χ, χc

θ0

Confinement of SU(3)a gives the axion as a goldstone boson 2 singlet goldstone bosons

U(1)axion U(1)⌘0 ψ, ψc 1 1 χ, χc

• 9

1

Model

SU(3)c

θ

Z2

θ

SU(3)0

c

SU(3)a

ψ, ψc

χ, χc

θ0

Before confinement of mirror color : SU(3)a has 10 flavors and is conformal After confinement of mirror color : SU(3)a has 1 flavors and confines Confinement of mirror color causes confinement of axion gauge group!

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