Non-perturbative beyond the Standard Model physics Enrico Rinaldi - - PowerPoint PPT Presentation

Non-perturbative beyond the Standard Model physics

Enrico Rinaldi

YITP, Kyoto, July 23 2015 Numerical approaches to the holographic principle, quantum gravity and cosmology

This research was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and supported by the LLNL LDRD “Illuminating the Dark Universe with PetaFlops Supercomputing” 13-ERD-023. Computing support comes from the LLNL Institutional Computing Grand Challenge program. LLNL-PRES-669543

Numerical approaches to the holographic principle, quantum gravity and cosmology

• “Numerical approaches”: study systems at strong

coupling and investigate non-perturbative physics

• “Cosmology”: indicates presence of dark matter

and physics beyond the Standard Model

Numerical approaches to the holographic principle, quantum gravity and cosmology

• “Numerical approaches”: study systems at strong

coupling and investigate non-perturbative physics

• “Cosmology”: indicates presence of dark matter

and physics beyond the Standard Model

Numerical approaches to the holographic principle, quantum gravity and cosmology

• Lawrence Livermore National Lab. is starting to investigate

the holographic principle (Thanks to Masanori and Kostas!)

• Great workshop to help connecting different communities.

Thanks to all the organizers!

Dark Matter

• Gravitational effects of DM show up in CMB,

lensing and other large scale phenomena

• direct Standard Model interactions are needed for

production in the early Universe

• Direct detection and Collider experiments rely on

SM interactions, but they are suppressed

• Strong exclusion bounds push theorists to explore

a wider landscape of models for DM

Outline

• Part I
• Lattice Field Theory methods for searches of

composite dark matter particles

• Part II
• Lattice Field Theory methods for searches of

axion-like dark matter particles

Outline

• Part I
• Lattice Field Theory methods for searches of

composite dark matter particles

• Part II
• Lattice Field Theory methods for searches of

axion-like dark matter particles

• Part III
• Lattice Field Theory methods for composite Higgs models

Part I

• Features of strongly-coupled composite dark

matter

• Focus on Stealth Dark Matter model with rich

phenomenology

• GOAL: Lower bounds on composite dark matter

using lattice field theory simulations

[LSD collab., Phys. Rev. D89 (2014) 094508] [LSD collab., arxiv:1503.04203] [LSD collab., arxiv:1503.04205]

based on work with Lattice Strong Dynamics collaboration

Strongly-coupled composite dark matter

• Dark matter is a composite
• bject of a new sector
• Composite object is

electroweak neutral

• Constituents can have

electroweak charges

• Dark matter is stable thanks

to a global symmetry (like baryon number)

Strongly-coupled composite dark matter

• Dark matter is a composite
• bject of a new sector
• Composite object is

electroweak neutral

• Constituents can have

electroweak charges

• Dark matter is stable thanks

to a global symmetry (like baryon number)

Akin to a technibaryon

Strongly-coupled composite dark matter

• Dark matter is a composite
• bject of a new sector
• Composite object is

electroweak neutral

• Constituents can have

electroweak charges

• Dark matter is stable thanks

to a global symmetry (like baryon number)

Akin to a technibaryon Suppressed interactions with SM

Strongly-coupled composite dark matter

• Dark matter is a composite
• bject of a new sector
• Composite object is

electroweak neutral

• Constituents can have

electroweak charges

• Dark matter is stable thanks

to a global symmetry (like baryon number)

Akin to a technibaryon Suppressed interactions with SM Mechanisms to provide

• bserved relic abundance

Strongly-coupled composite dark matter

• Dark matter is a composite
• bject of a new sector
• Composite object is

electroweak neutral

• Constituents can have

electroweak charges

• Dark matter is stable thanks

to a global symmetry (like baryon number)

Akin to a technibaryon Suppressed interactions with SM Mechanisms to provide

• bserved relic abundance

Guaranteed in many models

What do we have in mind?

• In general we think about a new strongly-coupled gauge

sector “like” QCD with a plethora of composite states in the spectrum: all mass scales are technically natural

• Dark fermions have dark color and also have electroweak

charges

• Depending on the model, dark fermions have electroweak

breaking masses (chiral), electroweak preserving masses (vector) or a mixture

• A global symmetry of the theory naturally stabilizes the

dark baryonic composite states (e.g. dark neutron)

“Stealth Dark Matter” model

• Let’s focus on a SU(N) dark gauge

sector with N=4

• Let dark fermions have current/chiral

masses together with vector-like masses

• Let dark fermions masses to be at

the dark confinement scale

• Assign electroweak charges to dark

fermions

• The symmetry group is U(4)xU(4)

and with generic masses it breaks down to U(1) (dark baryon number)

[LSD collab., arxiv:1503.04203]

“Stealth Dark Matter” model

• Let’s focus on a SU(N) dark gauge

sector with N=4

• Let dark fermions have current/chiral

masses together with vector-like masses

• Let dark fermions masses to be at

the dark confinement scale

• Assign electroweak charges to dark

fermions

• The symmetry group is U(4)xU(4)

and with generic masses it breaks down to U(1) (dark baryon number)

[LSD collab., arxiv:1503.04203]

lightest baryon is a spin=0 boson

“Stealth Dark Matter” model

• Let’s focus on a SU(N) dark gauge

sector with N=4

• Let dark fermions have current/chiral

masses together with vector-like masses

• Let dark fermions masses to be at

the dark confinement scale

• Assign electroweak charges to dark

fermions

• The symmetry group is U(4)xU(4)

and with generic masses it breaks down to U(1) (dark baryon number)

[LSD collab., arxiv:1503.04203]

lightest baryon is a spin=0 boson avoid issues with charged dark mesons

“Stealth Dark Matter” model

• Let’s focus on a SU(N) dark gauge

sector with N=4

• Let dark fermions have current/chiral

masses together with vector-like masses

• Let dark fermions masses to be at

the dark confinement scale

• Assign electroweak charges to dark

fermions

• The symmetry group is U(4)xU(4)

and with generic masses it breaks down to U(1) (dark baryon number)

[LSD collab., arxiv:1503.04203]

lightest baryon is a spin=0 boson avoid issues with charged dark mesons lighter masses are more strongly constrained by collider bounds

“Stealth Dark Matter” model

• Let’s focus on a SU(N) dark gauge

sector with N=4

• Let dark fermions have current/chiral

masses together with vector-like masses

• Let dark fermions masses to be at

the dark confinement scale

• Assign electroweak charges to dark

fermions

• The symmetry group is U(4)xU(4)

and with generic masses it breaks down to U(1) (dark baryon number)

[LSD collab., arxiv:1503.04203]

lightest baryon is a spin=0 boson avoid issues with charged dark mesons lighter masses are more strongly constrained by collider bounds allow SM interactions necessary for DM production and detection

“Stealth Dark Matter” model

• Let’s focus on a SU(N) dark gauge

sector with N=4

• Let dark fermions have current/chiral

masses together with vector-like masses

• Let dark fermions masses to be at

the dark confinement scale

• Assign electroweak charges to dark

fermions

• The symmetry group is U(4)xU(4)

and with generic masses it breaks down to U(1) (dark baryon number)

[LSD collab., arxiv:1503.04203]

lightest baryon is a spin=0 boson avoid issues with charged dark mesons lighter masses are more strongly constrained by collider bounds allow SM interactions necessary for DM production and detection the only stable particle is the lightest baryon

“Stealth Dark Matter” model

• The field content of the model

consists in 8 Weyl fermions

• Dark fermions interact with the SM

Higgs and obtain current/chiral masses

• Introduce vector-like masses for

dark fermions that do not break EW symmetry

• Diagonalizing in the mass

eigenbasis gives 4 Dirac fermions

• Assume custodial SU(2) symmetry

arising when u ↔ d

Field SU(N)D (SU(2)L, Y )

Q F1 = F u

1

F d

1

!

N (2, 0) +1/2 −1/2

!

F2 = F u

2

F d

2

!

N (2, 0) +1/2 −1/2

!

F u

3

N (1, +1/2) +1/2 F d

3

N (1, −1/2) −1/2 F u

4

N (1, +1/2) +1/2 F d

4

N (1, −1/2) −1/2

[LSD collab., arxiv:1503.04203]

“Stealth Dark Matter” model

• The field content of the model

consists in 8 Weyl fermions

• Dark fermions interact with the SM

Higgs and obtain current/chiral masses

• Introduce vector-like masses for

dark fermions that do not break EW symmetry

• Diagonalizing in the mass

eigenbasis gives 4 Dirac fermions

• Assume custodial SU(2) symmetry

arising when u ↔ d

Field SU(N)D (SU(2)L, Y )

Q F1 = F u

1

F d

1

!

N (2, 0) +1/2 −1/2

!

F2 = F u

2

F d

2

!

N (2, 0) +1/2 −1/2

!

F u

3

N (1, +1/2) +1/2 F d

3

N (1, −1/2) −1/2 F u

4

N (1, +1/2) +1/2 F d

4

N (1, −1/2) −1/2

[LSD collab., arxiv:1503.04203]

“Stealth Dark Matter” model

• The field content of the model

consists in 8 Weyl fermions

• Dark fermions interact with the SM

Higgs and obtain current/chiral masses

• Introduce vector-like masses for

dark fermions that do not break EW symmetry

• Diagonalizing in the mass

eigenbasis gives 4 Dirac fermions

• Assume custodial SU(2) symmetry

arising when u ↔ d

Field SU(N)D (SU(2)L, Y )

Q F1 = F u

1

F d

1

!

N (2, 0) +1/2 −1/2

!

F2 = F u

2

F d

2

!

N (2, 0) +1/2 −1/2

!

F u

3

N (1, +1/2) +1/2 F d

3

N (1, −1/2) −1/2 F u

4

N (1, +1/2) +1/2 F d

4

N (1, −1/2) −1/2

L ⊃ + yu

14✏ijF i 1HjF d 4 + yd 14F1 · H†F u 4

− yd

23✏ijF i 2HjF d 3 − yu 23F2 · H†F u 3 + h.c.

[LSD collab., arxiv:1503.04203]

“Stealth Dark Matter” model

• The field content of the model

consists in 8 Weyl fermions

• Dark fermions interact with the SM

Higgs and obtain current/chiral masses

• Introduce vector-like masses for

dark fermions that do not break EW symmetry

• Diagonalizing in the mass

eigenbasis gives 4 Dirac fermions

• Assume custodial SU(2) symmetry

arising when u ↔ d

Field SU(N)D (SU(2)L, Y )

Q F1 = F u

1

F d

1

!

N (2, 0) +1/2 −1/2

!

F2 = F u

2

F d

2

!

N (2, 0) +1/2 −1/2

!

F u

3

N (1, +1/2) +1/2 F d

3

N (1, −1/2) −1/2 F u

4

N (1, +1/2) +1/2 F d

4

N (1, −1/2) −1/2

L ⊃ + yu

14✏ijF i 1HjF d 4 + yd 14F1 · H†F u 4

− yd

23✏ijF i 2HjF d 3 − yu 23F2 · H†F u 3 + h.c.

L ⊃ M12✏ijF i

1F j 2 − M u 34F u 3 F d 4 + M d 34F d 3 F u 4 + h.c.

[LSD collab., arxiv:1503.04203]

“Stealth Dark Matter” model

• The field content of the model

consists in 8 Weyl fermions

• Dark fermions interact with the SM

Higgs and obtain current/chiral masses

• Introduce vector-like masses for

dark fermions that do not break EW symmetry

• Diagonalizing in the mass

eigenbasis gives 4 Dirac fermions

• Assume custodial SU(2) symmetry

arising when u ↔ d

Field SU(N)D (SU(2)L, Y )

Q F1 = F u

1

F d

1

!

N (2, 0) +1/2 −1/2

!

F2 = F u

2

F d

2

!

N (2, 0) +1/2 −1/2

!

F u

3

N (1, +1/2) +1/2 F d

3

N (1, −1/2) −1/2 F u

4

N (1, +1/2) +1/2 F d

4

N (1, −1/2) −1/2

L ⊃ + yu

14✏ijF i 1HjF d 4 + yd 14F1 · H†F u 4

− yd

23✏ijF i 2HjF d 3 − yu 23F2 · H†F u 3 + h.c.

L ⊃ M12✏ijF i

1F j 2 − M u 34F u 3 F d 4 + M d 34F d 3 F u 4 + h.c.

[LSD collab., arxiv:1503.04203]

yu

14 = yd 14

yu

23 = yd 23

M u

34 = M d 34

Colliders

SUSY Stealth LSP heavier superpartners scalar baryon baryon excited resonances Collider searches dominated by light meson production and decay. Missing energy signals largely absent!

ρ Πs

Plot by G. Kribs

Stealth DM at colliders

VS.

Colliders

SUSY Stealth LSP heavier superpartners scalar baryon baryon excited resonances Collider searches dominated by light meson production and decay. Missing energy signals largely absent!

ρ Πs

Plot by G. Kribs

• Signatures are not dominated by missing energy: DM is not the

lightest particle! The interactions are suppressed (form factors)

Stealth DM at colliders

VS.

Colliders

SUSY Stealth LSP heavier superpartners scalar baryon baryon excited resonances Collider searches dominated by light meson production and decay. Missing energy signals largely absent!

ρ Πs

Plot by G. Kribs

• Signatures are not dominated by missing energy: DM is not the

lightest particle! The interactions are suppressed (form factors)

• Light meson production and decay give interesting signatures:

the model can be constrained by collider limits

Stealth DM at colliders

VS.

Lattice Stealth DM

• Non-perturbative lattice

calculations of the spectrum confirm that lightest baryon has spin zero

• The ratio of pseudoscalar

(PS) to vector (V) is used as probe for different dark fermion masses

• The meson to baryon mass

ratio allows us to translate LEPII bounds on charged meson to LEP bounds on composite bosonic dark matter

0.50 0.55 0.60 0.65 0.70 0.75 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 mPSêmv aM

spin 0 spin 1 spin 2 PS V

[LSD collab., Phys. Rev. D89 (2014) 094508]

• Study systematic effects

due to lattice discretization and finite volume due to the relative unfamiliar nature of the system

Lattice Stealth DM

• Non-perturbative lattice

calculations of the spectrum confirm that lightest baryon has spin zero

• The ratio of pseudoscalar

(PS) to vector (V) is used as probe for different dark fermion masses

• The meson to baryon mass

ratio allows us to translate LEPII bounds on charged meson to LEP bounds on composite bosonic dark matter

0.50 0.55 0.60 0.65 0.70 0.75 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 mPSêmv aM

spin 0 spin 1 spin 2 PS V

[LSD collab., Phys. Rev. D89 (2014) 094508]

• Study systematic effects

due to lattice discretization and finite volume due to the relative unfamiliar nature of the system baryons

Lattice Stealth DM

• Non-perturbative lattice

calculations of the spectrum confirm that lightest baryon has spin zero

• The ratio of pseudoscalar

(PS) to vector (V) is used as probe for different dark fermion masses

• The meson to baryon mass

ratio allows us to translate LEPII bounds on charged meson to LEP bounds on composite bosonic dark matter

0.50 0.55 0.60 0.65 0.70 0.75 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 mPSêmv aM

spin 0 spin 1 spin 2 PS V

[LSD collab., Phys. Rev. D89 (2014) 094508]

• Study systematic effects

due to lattice discretization and finite volume due to the relative unfamiliar nature of the system baryons mesons

Lattice Stealth DM

• Non-perturbative lattice

calculations of the spectrum confirm that lightest baryon has spin zero

• The ratio of pseudoscalar

(PS) to vector (V) is used as probe for different dark fermion masses

• The meson to baryon mass

ratio allows us to translate LEPII bounds on charged meson to LEP bounds on composite bosonic dark matter

0.50 0.55 0.60 0.65 0.70 0.75 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 mPSêmv aM

spin 0 spin 1 spin 2 PS V

[LSD collab., Phys. Rev. D89 (2014) 094508]

• Study systematic effects

due to lattice discretization and finite volume due to the relative unfamiliar nature of the system baryons mesons

• dimension 4 ➥ Higgs exchange
• dimension 5 ➥ magnetic dipole
• dimension 6 ➥ charge radius
• dimension 7 ➥ polarizability

“How dark is Stealth DM?”

Interactions of dark fermions with Higgs + Interactions of dark baryon with photon through form factors

(¯ χσµνχ)Fµν Λdark

(¯ χχ)vµ∂νF µν Λ2

dark

(¯ χχ)FµνF µν Λ3

dark

hf ¯ f

[LSD collab., arxiv:1503.04203] [LSD collab., arxiv:1503.04205]

• dimension 4 ➥ Higgs exchange
• dimension 5 ➥ magnetic dipole
• dimension 6 ➥ charge radius
• dimension 7 ➥ polarizability

“How dark is Stealth DM?”

Interactions of dark fermions with Higgs + Interactions of dark baryon with photon through form factors

(¯ χσµνχ)Fµν Λdark

(¯ χχ)vµ∂νF µν Λ2

dark

(¯ χχ)FµνF µν Λ3

dark

hf ¯ f

spin 0

[LSD collab., arxiv:1503.04203] [LSD collab., arxiv:1503.04205]

• dimension 4 ➥ Higgs exchange
• dimension 5 ➥ magnetic dipole
• dimension 6 ➥ charge radius
• dimension 7 ➥ polarizability

“How dark is Stealth DM?”

Interactions of dark fermions with Higgs + Interactions of dark baryon with photon through form factors

(¯ χσµνχ)Fµν Λdark

(¯ χχ)vµ∂νF µν Λ2

dark

(¯ χχ)FµνF µν Λ3

dark

hf ¯ f

spin 0 custodial SU(2)

[LSD collab., arxiv:1503.04203] [LSD collab., arxiv:1503.04205]

• dimension 4 ➥ Higgs exchange
• dimension 5 ➥ magnetic dipole
• dimension 6 ➥ charge radius
• dimension 7 ➥ polarizability

“How dark is Stealth DM?”

Interactions of dark fermions with Higgs + Interactions of dark baryon with photon through form factors

(¯ χσµνχ)Fµν Λdark

(¯ χχ)vµ∂νF µν Λ2

dark

(¯ χχ)FµνF µν Λ3

dark

hf ¯ f

spin 0 custodial SU(2)

[LSD collab., arxiv:1503.04203] [LSD collab., arxiv:1503.04205]

Computing polarizability

χ χ

Nucleus Nucleus

p p0 k k0 ` ` − q k + `

q = k0 − k = p − p0

cF e2 m3

• χ?χF µ↵F ⌫

↵vµv⌫

Computing polarizability

χ χ

Nucleus Nucleus

p p0 k k0 ` ` − q k + `

q = k0 − k = p − p0

Lattice

cF e2 m3

• χ?χF µ↵F ⌫

↵vµv⌫

Computing polarizability

χ χ

Nucleus Nucleus

p p0 k k0 ` ` − q k + `

q = k0 − k = p − p0

Lattice Nuclear Physics

cF e2 m3

• χ?χF µ↵F ⌫

↵vµv⌫

• Background field method:

response of neutral baryon to external electric field

• Measure the shift of the

baryon mass as a function

• f

Lattice: Polarizability of DM

[LSD collab., arxiv:1503.04203] [Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) 094505 and Phys. Rev. D81 (2010) 054502]

0.000 0.005 0.010 0.015 0.020 0.025 0.030

E

0.89 0.90 0.91 0.92 0.93

E0

SU(4)

0.00 0.01 0.02 0.03 0.04

E

0.61 0.62 0.63 0.64 0.65 0.66 0.67

E0

SU(3)

0.00 0.01 0.02 0.03 0.04

E

−0.35 −0.30 −0.25 −0.20 −0.15 −0.10 −0.05 0.00 0.05

Zr

SU(3)

EB EB Zr E

EB,4c = mB + 2CF |E|2 + O

• E4

EB,3c = mB + ✓ 2CF − µB2 8m3

B

◆ |E|2 + O

• E4

Zr = EµB(E) 2m2

B

E E

precise lattice results

323x64 quenched lattices (large volume)

• ne lattice spacing and two masses (matched)

40 sources on 200 independent configurations multi-exponential fits with 3 states for the baryon

• Background field method:

response of neutral baryon to external electric field

• Measure the shift of the

baryon mass as a function

• f

Lattice: Polarizability of DM

[LSD collab., arxiv:1503.04203] [Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) 094505 and Phys. Rev. D81 (2010) 054502]

0.000 0.005 0.010 0.015 0.020 0.025 0.030

E

0.89 0.90 0.91 0.92 0.93

E0

SU(4)

0.00 0.01 0.02 0.03 0.04

E

0.61 0.62 0.63 0.64 0.65 0.66 0.67

E0

SU(3)

0.00 0.01 0.02 0.03 0.04

E

−0.35 −0.30 −0.25 −0.20 −0.15 −0.10 −0.05 0.00 0.05

Zr

SU(3)

EB EB Zr E

EB,4c = mB + 2CF |E|2 + O

• E4

EB,3c = mB + ✓ 2CF − µB2 8m3

B

◆ |E|2 + O

• E4

Zr = EµB(E) 2m2

B

E E

precise lattice results

323x64 quenched lattices (large volume)

• ne lattice spacing and two masses (matched)

40 sources on 200 independent configurations multi-exponential fits with 3 states for the baryon

• Background field method:

response of neutral baryon to external electric field

• Measure the shift of the

baryon mass as a function

• f

Lattice: Polarizability of DM

[LSD collab., arxiv:1503.04203] [Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) 094505 and Phys. Rev. D81 (2010) 054502]

0.000 0.005 0.010 0.015 0.020 0.025 0.030

E

0.89 0.90 0.91 0.92 0.93

E0

SU(4)

0.00 0.01 0.02 0.03 0.04

E

0.61 0.62 0.63 0.64 0.65 0.66 0.67

E0

SU(3)

0.00 0.01 0.02 0.03 0.04

E

−0.35 −0.30 −0.25 −0.20 −0.15 −0.10 −0.05 0.00 0.05

Zr

SU(3)

EB EB Zr E

EB,4c = mB + 2CF |E|2 + O

• E4

EB,3c = mB + ✓ 2CF − µB2 8m3

B

◆ |E|2 + O

• E4

Zr = EµB(E) 2m2

B

E E

precise lattice results

323x64 quenched lattices (large volume)

• ne lattice spacing and two masses (matched)

40 sources on 200 independent configurations multi-exponential fits with 3 states for the baryon

• Background field method:

response of neutral baryon to external electric field

• Measure the shift of the

baryon mass as a function

• f

Lattice: Polarizability of DM

[LSD collab., arxiv:1503.04203] [Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) 094505 and Phys. Rev. D81 (2010) 054502]

0.000 0.005 0.010 0.015 0.020 0.025 0.030

E

0.89 0.90 0.91 0.92 0.93

E0

SU(4)

0.00 0.01 0.02 0.03 0.04

E

0.61 0.62 0.63 0.64 0.65 0.66 0.67

E0

SU(3)

0.00 0.01 0.02 0.03 0.04

E

−0.35 −0.30 −0.25 −0.20 −0.15 −0.10 −0.05 0.00 0.05

Zr

SU(3)

EB EB Zr E

EB,4c = mB + 2CF |E|2 + O

• E4

EB,3c = mB + ✓ 2CF − µB2 8m3

B

◆ |E|2 + O

• E4

Zr = EµB(E) 2m2

B

E E

precise lattice results

323x64 quenched lattices (large volume)

• ne lattice spacing and two masses (matched)

40 sources on 200 independent configurations multi-exponential fits with 3 states for the baryon

• it is hard to extract the momentum

dependence of this nuclear form factor

• similarities with the double-beta decay

nuclear matrix element could suggest large uncertainties ~ orders of magnitude

• to asses the impact of uncertainties on

the total cross section we start from naive dimensional analysis

• we allow a “magnitude” factor to

change from 0.3 to 3

γ γ A A A M M OM

M A

F

f A

F ∼ 3 Z2 α M A F

R f A

F

= hA|F µνFµν|Ai

σ ' µ2

nχ

πA2 *

• cF e2

m3

χ

f A

F

• 2+

Nuclear: Rayleigh scattering

[Weiner & Yavin, Phys. Rev. D86 (2012) 075021] [Frandsen et al., JCAP 1210 (2012) 033] [Pospelov & Veldhuis, Phys. Lett. B480 (2000) 181] [Ovanesyan & Vecchi, arxiv:1410.0601]

• it is hard to extract the momentum

dependence of this nuclear form factor

• similarities with the double-beta decay

nuclear matrix element could suggest large uncertainties ~ orders of magnitude

• to asses the impact of uncertainties on

the total cross section we start from naive dimensional analysis

• we allow a “magnitude” factor to

change from 0.3 to 3

γ γ A A A M M OM

M A

F

f A

F ∼ 3 Z2 α M A F

R f A

F

= hA|F µνFµν|Ai

σ ' µ2

nχ

πA2 *

• cF e2

m3

χ

f A

F

• 2+

Nuclear: Rayleigh scattering

[Weiner & Yavin, Phys. Rev. D86 (2012) 075021] [Frandsen et al., JCAP 1210 (2012) 033] [Pospelov & Veldhuis, Phys. Lett. B480 (2000) 181] [Ovanesyan & Vecchi, arxiv:1410.0601]

• it is hard to extract the momentum

dependence of this nuclear form factor

• similarities with the double-beta decay

nuclear matrix element could suggest large uncertainties ~ orders of magnitude

• to asses the impact of uncertainties on

the total cross section we start from naive dimensional analysis

• we allow a “magnitude” factor to

change from 0.3 to 3

γ γ A A A M M OM

M A

F

f A

F ∼ 3 Z2 α M A F

R f A

F

= hA|F µνFµν|Ai

σ ' µ2

nχ

πA2 *

• cF e2

m3

χ

f A

F

• 2+

Nuclear: Rayleigh scattering

[Weiner & Yavin, Phys. Rev. D86 (2012) 075021] [Frandsen et al., JCAP 1210 (2012) 033] [Pospelov & Veldhuis, Phys. Lett. B480 (2000) 181] [Ovanesyan & Vecchi, arxiv:1410.0601]

Stealth DM polarizability

[LSD collab., arxiv:1503.04203]

• ×-

×- ×- ×- ×- ×- ×- ()

• ()

σnucleon(Z, A) = Z4 A2 144πα4µ2

nχ(M A F )2

m6

χR2

[cF ]2

Stealth DM polarizability

[LSD collab., arxiv:1503.04203]

• ×-

×- ×- ×- ×- ×- ×- ()

• ()

LUX exclusion bound for spin- independent cross section

σnucleon(Z, A) = Z4 A2 144πα4µ2

nχ(M A F )2

m6

χR2

[cF ]2

Stealth DM polarizability

[LSD collab., arxiv:1503.04203]

• ×-

×- ×- ×- ×- ×- ×- ()

• ()

LUX exclusion bound for spin- independent cross section Coherent neutrino scattering background

σnucleon(Z, A) = Z4 A2 144πα4µ2

nχ(M A F )2

m6

χR2

[cF ]2

Stealth DM polarizability

[LSD collab., arxiv:1503.04203]

• ×-

×- ×- ×- ×- ×- ×- ()

• ()

LUX exclusion bound for spin- independent cross section Coherent neutrino scattering background LEPII bound on charged mesons

σnucleon(Z, A) = Z4 A2 144πα4µ2

nχ(M A F )2

m6

χR2

[cF ]2

Stealth DM polarizability

[LSD collab., arxiv:1503.04203]

lowest allowed direct detection cross-section for composite dark matter theories with EW charged constituents

• ×-

×- ×- ×- ×- ×- ×- ()

• ()

LUX exclusion bound for spin- independent cross section Coherent neutrino scattering background LEPII bound on charged mesons

σnucleon(Z, A) = Z4 A2 144πα4µ2

nχ(M A F )2

m6

χR2

[cF ]2

Stealth DM polarizability

1 10 100 1000 104 10 14 10 13 10 12 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 WIMP Mass GeV c2 WIMP nucleon cross section pb

8B

Neutrinos A t m

• s

p h e r i c a n d D S N B N e u t r i n

• s

7Be

Neutrinos

C O H E R E NT N E U TR IN O S C A T T E R I N G COHERENT NEU TR I NO S C AT T E R IN G C O H E R E N T N EU TRI NO SCATTERING

CDMS II Ge (2009) Xenon100 (2012)

CRESST CoGeNT (2012) CDMS Si (2013)

E D E L W E I S S ( 2 1 1 )

DAMA

SIMPLE (2012) ZEPLIN-III (2012) COUPP (2012) LUX (2013) D A M I C ( 2 1 2 ) C D M S l i t e ( 2 1 3 )

[from arxiv:1307.5458]

Stealth DM polarizability

Direct detection signal is below the neutrino coherent scattering background for MB>1TeV

1 10 100 1000 104 10 14 10 13 10 12 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 WIMP Mass GeV c2 WIMP nucleon cross section pb

8B

Neutrinos A t m

• s

p h e r i c a n d D S N B N e u t r i n

• s

7Be

Neutrinos

C O H E R E NT N E U TR IN O S C A T T E R I N G COHERENT NEU TR I NO S C AT T E R IN G C O H E R E N T N EU TRI NO SCATTERING

CDMS II Ge (2009) Xenon100 (2012)

CRESST CoGeNT (2012) CDMS Si (2013)

E D E L W E I S S ( 2 1 1 )

DAMA

SIMPLE (2012) ZEPLIN-III (2012) COUPP (2012) LUX (2013) D A M I C ( 2 1 2 ) C D M S l i t e ( 2 1 3 )

[from arxiv:1307.5458]

Concluding remarks

• Composite dark matter is a viable interesting

possibility with rich phenomenology

• Lattice methods can help in calculating direct

detection cross sections and production rates at

• colliders. Direct phenomenological relevance.
• Dark matter constituents can carry electroweak

charges and still the stable composites are currently undetectable. Stealth cross section.

Part II

• General features of axions as a solution of the

Strong CP problem

• Current physical constraints on axion models’

parameters based on dark matter interpretation

• GOAL: Lower bound on the axion mass using

lattice QCD as input to axion cosmology

based on work with Evan Berkowitz and Michael Buchoff

[Berkowitz, Buchoff, Rinaldi, arxiv:1505.07455, PRD]

Axion dark matter

• Axions were originally proposed to deal

with the Strong CP Problem

• They also form a plausible DM

candidate

• The axion energy density requires

non-perturbative QCD input

• Being sought in ADMX (LLNL, UW) &

CAST-IAXO (CERN) with large discovery potential in the next few years

• Requiring Ωa ≤ ΩCDM yields a lower

bound on the axion mass today

Ωtot = 1.000(7) PDG 2014

[Preskill, Wise & Wilczek, Phys Lett B 120 (1983) 127-132] [Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791]

Axion dark matter

• Axions were originally proposed to deal

with the Strong CP Problem

• They also form a plausible DM

candidate

• The axion energy density requires

non-perturbative QCD input

• Being sought in ADMX (LLNL, UW) &

CAST-IAXO (CERN) with large discovery potential in the next few years

• Requiring Ωa ≤ ΩCDM yields a lower

bound on the axion mass today

Ωtot = 1.000(7) PDG 2014

[Preskill, Wise & Wilczek, Phys Lett B 120 (1983) 127-132]

Lattice Field Theory Methods

[Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791]

“Strong CP” problem

• QCD has a parameter, θ
• Controls QCD CP violation
• Topological
• θ can take any value in (-π,π]

Q = 1 32⇡2 Z d4x ✏µνρσFµνFρσ ∈ Z

LQCD 3 ✓ 1 32⇡2 ✏µνρσFµνFρσ eiS ∝ eiQθ

“Strong CP” problem

• QCD has a parameter, θ
• Controls QCD CP violation
• Topological
• θ can take any value in (-π,π]
• Neutron EDM ≲ 3 10-26 e cm
• ⟹ |θ| ≲ 10-10

Q = 1 32⇡2 Z d4x ✏µνρσFµνFρσ ∈ Z

LQCD 3 ✓ 1 32⇡2 ✏µνρσFµνFρσ

[Baker et al., PRL 97, 131801 (2006) / hep-ex/0602020]

eiS ∝ eiQθ

“Strong CP” problem

• QCD has a parameter, θ
• Controls QCD CP violation
• Topological
• θ can take any value in (-π,π]
• Neutron EDM ≲ 3 10-26 e cm
• ⟹ |θ| ≲ 10-10

Q = 1 32⇡2 Z d4x ✏µνρσFµνFρσ ∈ Z

LQCD 3 ✓ 1 32⇡2 ✏µνρσFµνFρσ

[Baker et al., PRL 97, 131801 (2006) / hep-ex/0602020]

eiS ∝ eiQθ

Why is θ so small?

m2

af 2 a = ∂2F

∂θ2

• θ=0

Axions as a solution

• Couple to topological charge
• Otherwise have shift symmetry
• Amenable to effective theory treatment
• Axion mass from instantons effects

[Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791]

a → a + α Veff ⇠ cos (θ + chai)

Laxions = 1 2 (@µa)2 + ✓ a fa + ✓ ◆ 1 32⇡2 ✏µνρσFµνFρσ

m2

af 2 a = ∂2F

∂θ2

• θ=0

Axions as a solution

• Couple to topological charge
• Otherwise have shift symmetry
• Amenable to effective theory treatment
• Axion mass from instantons effects

[Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791]

a → a + α

QCD Topological Susceptibility

Veff ⇠ cos (θ + chai)

Laxions = 1 2 (@µa)2 + ✓ a fa + ✓ ◆ 1 32⇡2 ✏µνρσFµνFρσ

Current axion constraints

[ADMX Website]

Current axion constraints

Over-closure constraint on axion mass

[ADMX Website]

Current axion constraints

Over-closure constraint on axion mass

[ADMX Website]

• Two main models for light axions

predict axion coupling to photons

[KSVZ & DFSZ]

• ma (fa) is the only free parameter
• experiments look for a→γγ transitions
• parameter space bound by

astrophysical and cosmological constrains

The over-closure bound

High temperature arguments imply χ vanishes as T→∞

Sketches kindly provided by E. Berkowitz

The over-closure bound

High temperature arguments imply χ vanishes as T→∞

Sketches kindly provided by E. Berkowitz

m2

af 2 a = χ

The over-closure bound

High temperature arguments imply χ vanishes as T→∞ Universe cools as it expands

Sketches kindly provided by E. Berkowitz

m2

af 2 a = χ

The over-closure bound

High temperature arguments imply χ vanishes as T→∞ Universe cools as it expands Axions feel their mass when 3H ~ ma

H: Hubble constant

Sketches kindly provided by E. Berkowitz

m2

af 2 a = χ

The over-closure bound

High temperature arguments imply χ vanishes as T→∞ Universe cools as it expands Axions feel their mass when 3H ~ ma

H: Hubble constant

Sketches kindly provided by E. Berkowitz

m2

af 2 a = χ

T1 ≈ 5.5 Tc

Axions feel their mass when 3H ~ ma T1 ≈ 5.5 Tc from models

Sketches kindly provided by E. Berkowitz

The over-closure bound

Axions feel their mass when 3H ~ ma T1 ≈ 5.5 Tc from models Axions continue to get heavier until the QCD phase transition

Sketches kindly provided by E. Berkowitz

The over-closure bound

Axions feel their mass when 3H ~ ma T1 ≈ 5.5 Tc from models Axions continue to get heavier until the QCD phase transition

ρ(t)R3 ma(t) = # axions in a fixed comoving volume

Sketches kindly provided by E. Berkowitz

The over-closure bound

Axions feel their mass when 3H ~ ma T1 ≈ 5.5 Tc from models Axions continue to get heavier until the QCD phase transition

ρ(t)R3 ma(t) = # axions in a fixed comoving volume

Sketches kindly provided by E. Berkowitz

energy density per co-moving volume is NOT invariant because the mass changes with time!

The over-closure bound

State-of-the-art bound

• Value of ρ when oscillations start

given by FRW equations, EOM and ma(T)

• χPT today yields
• ma(T) is provided by models.

ρ ρc < ΩCDM = 0.12

[Wantz & Shellard, arXiv:0910.1066] Note: assume PQ-symmetry is intact during inflation

State-of-the-art bound

• Value of ρ when oscillations start

given by FRW equations, EOM and ma(T)

• χPT today yields
• ma(T) is provided by models.

ρ ρc < ΩCDM = 0.12

[Wantz & Shellard, arXiv:0910.1066] Note: assume PQ-symmetry is intact during inflation

State-of-the-art bound

• Value of ρ when oscillations start

given by FRW equations, EOM and ma(T)

• χPT today yields
• ma(T) is provided by models.

ρ ρc < ΩCDM = 0.12

[Wantz & Shellard, arXiv:0910.1066] Note: assume PQ-symmetry is intact during inflation

State-of-the-art bound

• Value of ρ when oscillations start

given by FRW equations, EOM and ma(T)

• χPT today yields
• ma(T) is provided by models.

ρ ρc < ΩCDM = 0.12

[Wantz & Shellard, arXiv:0910.1066]

fa ≤ (2.8 ± 2) 1011 GeV ma ≥ 21 ± 2 μeV

Note: assume PQ-symmetry is intact during inflation

State-of-the-art bound

• Value of ρ when oscillations start

given by FRW equations, EOM and ma(T)

• χPT today yields
• ma(T) is provided by models.

ρ ρc < ΩCDM = 0.12

[Wantz & Shellard, arXiv:0910.1066]

fa ≤ (2.8 ± 2) 1011 GeV ma ≥ 21 ± 2 μeV ( ± uncontrolled systematic)

Note: assume PQ-symmetry is intact during inflation

State-of-the-art bound

[Wantz & Shellard, arXiv:0910.1066] [ADMX Website]

Wantz & Shellard IILM

State-of-the-art bound

[Wantz & Shellard, arXiv:0910.1066] [ADMX Website]

Wantz & Shellard IILM

State-of-the-art bound

[Wantz & Shellard, arXiv:0910.1066]

systematic uncertainty?

[ADMX Website]

Wantz & Shellard IILM

Reliance on models is unnecessary: we can calculate ma2fa2 from lattice QCD

State-of-the-art bound

[Wantz & Shellard, arXiv:0910.1066]

systematic uncertainty?

[ADMX Website]

Lattice results

• 1.2

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2. 2.1 2.2 2.3 2.4 2.5 0.15 0.2 0.25 0.3 0.35 0.4 0.45 T/Tc 1/4/Tc

Definition of Q N Globally fit integer

• 64
• 80
• 96
• 144

χ = lim

V →∞

⌦ Q2↵ V

Lattice results

• 1.2

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2. 2.1 2.2 2.3 2.4 2.5 0.15 0.2 0.25 0.3 0.35 0.4 0.45 T/Tc 1/4/Tc

Definition of Q N Globally fit integer

• 64
• 80
• 96
• 144
• previous calculations stop at T/Tc = 1.3 [arxiv:hep-lat/0203013]
• high precision data and careful systematic study

χ = lim

V →∞

⌦ Q2↵ V

Model and extrapolation

• 1.

2. 3. 4. 5. 6. 0. 0.1 0.2 0.3 0.4 0.5 T/Tc 1/4/Tc

N DIGM fit + statistical error

• 64

Systematic fitting error

• 80
• 96
• 144

χ T 4

c

= C (T/Tc)n

Model and extrapolation

• 1.

2. 3. 4. 5. 6. 0. 0.1 0.2 0.3 0.4 0.5 T/Tc 1/4/Tc

N DIGM fit + statistical error

• 64

Systematic fitting error

• 80
• 96
• 144

χ T 4

c

= C (T/Tc)n

• asymptotic large-T susceptibility in the DIGM model

[Gross&Yaffe, RevModPhys.53.43]

• fits lattice data of 𝜓 remarkably well for all temperatures

Axion oscillations

5 10 15 20 25 30 10-10 10-8 10-6 10-4 T/Tc /Tc4

DIGM fit 9H2 fa

2/Tc4, fa=1010 GeV

9H2 fa

2/Tc4, fa=1011 GeV

9H2 fa

2/Tc4, fa=1012 GeV

fa [GeV]

1010 1011 1012

9H2f 2

a = m2 af 2 a = χ

Axion oscillations

5 10 15 20 25 30 10-10 10-8 10-6 10-4 T/Tc /Tc4

DIGM fit 9H2 fa

2/Tc4, fa=1010 GeV

9H2 fa

2/Tc4, fa=1011 GeV

9H2 fa

2/Tc4, fa=1012 GeV

fa [GeV]

1010 1011 1012

T1(fa=1010)

9H2f 2

a = m2 af 2 a = χ

Axion oscillations

5 10 15 20 25 30 10-10 10-8 10-6 10-4 T/Tc /Tc4

DIGM fit 9H2 fa

2/Tc4, fa=1010 GeV

9H2 fa

2/Tc4, fa=1011 GeV

9H2 fa

2/Tc4, fa=1012 GeV

fa [GeV]

1010 1011 1012

T1(fa=1010) T1(fa=1011)

9H2f 2

a = m2 af 2 a = χ

Axion oscillations

5 10 15 20 25 30 10-10 10-8 10-6 10-4 T/Tc /Tc4

DIGM fit 9H2 fa

2/Tc4, fa=1010 GeV

9H2 fa

2/Tc4, fa=1011 GeV

9H2 fa

2/Tc4, fa=1012 GeV

fa [GeV]

1010 1011 1012

T1(fa=1010) T1(fa=1011) T1(fa=1012)

9H2f 2

a = m2 af 2 a = χ

Axion oscillations

109 1010 1011 1012 1013 10 20 30 40 fa [GeV] T1/Tc

T1 Uncertainty

Axion energy density

ρ(t)R3 ma(t) = # axions in a fixed comoving volume

Axion energy density

ρ(Tγ) = ρ(T1)ma(Tγ) ma(T1) ✓ R(T1) R(Tγ) ◆3 Tγ = 2.73K

Axion energy density

ρ(Tγ) = ρ(T1)ma(Tγ) ma(T1) ✓ R(T1) R(Tγ) ◆3 Tγ = 2.73K T1 = T1(fa) ma(T1) = √χ fa

Axion energy density

ρ(Tγ) = ρ(T1)ma(Tγ) ma(T1) ✓ R(T1) R(Tγ) ◆3 Tγ = 2.73K ma(Tγ) = 1 fa √mumd mu + md fπmπ

from χPT

T1 = T1(fa) ma(T1) = √χ fa

Axion energy density

ρ(Tγ) = ρ(T1)ma(Tγ) ma(T1) ✓ R(T1) R(Tγ) ◆3 Tγ = 2.73K ma(Tγ) = 1 fa √mumd mu + md fπmπ

from χPT

R(T)

from cosmology

T1 = T1(fa) ma(T1) = √χ fa

Axion energy density

ρ(Tγ) = ρ(T1)ma(Tγ) ma(T1) ✓ R(T1) R(Tγ) ◆3 Tγ = 2.73K ma(Tγ) = 1 fa √mumd mu + md fπmπ

from χPT

R(T)

from cosmology

T1 = T1(fa) ma(T1) = √χ fa

θ1 random: PQ breaks after inflation

ρ(T1) = 1 2m2

af 2 aθ2 1

Axion energy density

ρ(Tγ) = ρ(T1)ma(Tγ) ma(T1) ✓ R(T1) R(Tγ) ◆3 Tγ = 2.73K ma(Tγ) = 1 fa √mumd mu + md fπmπ

from χPT

R(T)

from cosmology

T1 = T1(fa) ma(T1) = √χ fa

⌦ θ2

1

↵ = π2 3

θ1 random: PQ breaks after inflation

ρ(T1) = 1 2m2

af 2 aθ2 1

Axion energy density

ρ(Tγ) = ρ(T1)ma(Tγ) ma(T1) ✓ R(T1) R(Tγ) ◆3 Tγ = 2.73K ma(Tγ) = 1 fa √mumd mu + md fπmπ

from χPT

R(T)

from cosmology

T1 = T1(fa) ma(T1) = √χ fa

Rely on our lattice calculation

⌦ θ2

1

↵ = π2 3

θ1 random: PQ breaks after inflation

ρ(T1) = 1 2m2

af 2 aθ2 1

Lattice lower bound

control systematics of the non-perturbative physics through lattice methods be able to derive the bound from first-principle results

[ADMX Website] [Berkowitz, Buchoff, Rinaldi, arxiv:1505.07455, PRD]

Lattice lower bound

control systematics of the non-perturbative physics through lattice methods be able to derive the bound from first-principle results

Lattice SU(3) Pure Glue fa < (4.10±0.04) 1011 GeV ma > (14.6±0.1) μeV

[ADMX Website] [Berkowitz, Buchoff, Rinaldi, arxiv:1505.07455, PRD]

Conclusion remarks

• Peccei-Quinn symmetry:
• cleans up the Strong CP problem
• provides a plausible, largely unconstrained DM

candidate: the axion.

• Axion searches will probe interesting parameter space

soon:

• lattice QCD can provide important non-perturbative

input for calculating the axion energy density

• DIGM fits outstandingly to SU(3) YM data at high

temperature.

• First steps toward a full QCD non-perturbative lower bound

for the axion mass have been taken