Dark matter & Axions! Javier Redondo (Zaragoza U. & MPP - - PowerPoint PPT Presentation

Dark matter & Axions!

Javier Redondo (Zaragoza U. & MPP Munich)

Overview

• Strong CP problem
• Axions and ALPs
• Axion Dark matter
• Dark matter experiments

Parity and Time reversal

in particle physics (electroweak interactions) P-violation (Wu 56)

R( ¯ K0 → K0) − R(K0 → ¯ K0) R( ¯ K0 → K0) + R(K0 → ¯ K0)

T-violation (CPLEAR 90’s) 60% 40%

... but not in the strong interactions

many theories based on SU(3)c (QCD)

LQCD = −1 4GµνaGµν

a +

X

q

i¯ qγµDµq − ¯ qmq + αs 8π θGµνa e Gµν

a

θ ∈ (−π, π) infinitely versions of QCD... all are P,T violating αs 8π θGµνa e Gµν

a

induces P and T (CP) violation ∝ θ P,T conserving we tend to forget this P,T violating

θ ∼ O(1)

Neutron EDM Most important P, T violating observable dn ∼ θ × O(10−15)e cm

EDM violates P,T

The theta angle of the strong interactions

θ

π −π

• The value of controls P,T violation in QCD

n ¯ n n ¯ n

θ

n ¯ n

Measured today |θ| < 10−10 (strong CP problem)

Roberto Peccei and Helen Quinn 77

any special value?

• QCD vacuum energy is minimum at θ = 0

Energy density (potential) as a function of (Euclidean path integral)

θ t → −ix0

e−

R d4xEV [θ] =

• Z

Dga

µe−SE[ga

µ]−iθ

R d4xE

αs 8π Ga µν e

Gµν

a

• ≤

Z Dga

µe−SE[ga

µ]

• e−iθ

R d4xE

αs 8π Ga µν e

Gµν

a

• ≤

Z Dga

µe−SE[ga

µ] = e−

R d4xV [0]

*we have assumed S_E does not contain P, T violation->Real In the SM, CP-violation in the CKM will propagate (three loops) and shift slightly the minimum of the potential from 0

• Potential is periodic V (θ) = V (θ + 2π)

Z d4xαs 8π Ga

µν e

Gµν

a

= Z d4x∂µKµ = Z dσµKµ = n ∈ Z

The theta-term is a total derivative and its integral a topological index

eiS = eiS+i2π

QCD vacuum energy minimised at CP conservation!!

π −π

n ¯ n

Energy

θ

Measured today |θ| < 10−10 (strong CP problem)

generated by QCD!

• but ... theta is a constant of the SM

beyond the SM ...

π −π

• ... if is dynamical field, relaxes to its minimum

n ¯ n

Energy

θ

Measured today |θ| < 10−10 (strong CP problem will be solved dynamically!)

θ(t, x)

generated by QCD!

• F. Wiczek
• S. Weinberg

a new particle is born ...

π −π

• if is dynamical field

Energy

θ

θ(t, x)

generated by QCD!

Field Excitations around the vacuum are particles

it’s a higgslet!

clears the strong CP problem like my favorite soap

and a new particle is born ... the axion

π −π

• if is dynamical field

Energy

θ

θ(t, x)

generated by QCD!

Field Excitations around the vacuum are particles

it’s a higgslet!

clears the strong CP problem like my favorite soap

and a new scale sets the game, fa

π −π

Energy

generated by QCD!

• kinetic term for requires a new scale

θ

Lθ = αs 8π Gµνa e Gµν

a θ + 1

2(∂µθ)(∂µθ)f 2

a

Lθ = αs 8π Gµνa e Gµν

a

a fa + 1 2(∂µa)(∂µa)

θ = a/fa

And we have our simplest axion model (low energy theory ... of course!)

• Peccei-Quinn global U(1) symmetry, color anomalous + spontaneously broken at

fa

Example: Simple model KSVZ

ENERGY

L ∈ 1 2(∂a)2 + αs 8π G e G a fa

• At energies below , (also PQ scale)

fa

~fa

• At energies below , mixing

ΛQCD

a − η0 − π0 − η − ...

La,I = X

N

cN,a ¯ Nγµγ5N a fa + caγ α 2π Fµν e F µν a fa + ...

nucleons ... photons ... mesons ...

axion mass couplings

ma ' mπfπ fa ⇠ 6meV109GeV fa

~GeV

L = LSM + i ¯ QDQ + 1 2(∂µσ)(∂µσ∗) − (y ¯ QLQRσ + h.c) − λ|σ|4 + µ2|σ|2

σ(x) = ρ(x)ei a(x)

fa

fa = p µ2/2λ

Axion-like particles (ALPs) pseudo Goldstone Bosons

• Global symmetry spontaneously broken
• massless Goldstone Boson @ Low Energy

shift symmetry θ(x) → θ(x) + α

• small symmetry breaking small mass

stringy axions

• Im parts of moduli fields (control sizes)
• O(100) candidates in compactification
• “decay constant” , string scale
• masses from non-perturbative effects
• HE decay constant,

Ms

φ(x) = ρ(x)eiθ(x)

Lkin = 1 2(∂µθ)(∂µθ)f 2

f = hρi

Axions and axion-like particles (ALPs) appear very naturally beyond the SM

Axion couplings at low energy

• From -term, axion mixes with eta’ and the rest of mesons

θ

1 fa

a

η0

Lθ = αs 8π Gµνa e Gµν

a

a fa + 1 2(∂µa)(∂µa)

In our simple axion theory, axion interactions are all generated from so the axion field interations will always be suppressed by 1/fa

θ αs 8π Ga

µν e

Gµν

a

1 fa a 1 fa a 1 fa a hadrons, Photons Leptons (in some models)

Axion couplings at low energy

ma = p Vθθ(θ) 1 fa = pχ 1 fa ' 5.7 meV109GeV fa Mass

1 fa a 1 fa a 1 fa a

The lighter the more weakly interacting

hadrons, Photons Leptons (in some models)

Axion couplings at low energy

ma = p Vθθ(θ) 1 fa = pχ 1 fa ' 5.7 meV109GeV fa Mass

Axion Landscape

Reactors

• Had. dec

PQWW models

fa ∼ vEW

Invisible models

fa vEW

Bounds and hints from astrophysics

Tip of the Red Giant branch (M5)

• Axions emitted from stellar cores accelerate stellar evolution
• Too much cooling is strongly excluded (obs. vs. simulations)
• Some systems improve with additional axion cooling!

White dwarf luminosity function HB stars in globular clusters Neutron Star CAS A

Axion Landscape

Reactors

• Had. dec

Axion Landscape

Reactors

• Had. dec

Excluded

Astro-hints?

• dynamical relaxes to its minimum ...

Axions and dark matter

π −π

time

Coherent oscillations = Cold Dark Matter Axions Energy Oscillation frequency Energy density (harm. oscillator)

θ(t, x)

generated by QCD!

θ(t) = θ0 cos(mat)

ω = ma ρaDM = 1 2m2

af 2 aθ2 0 = 1

2(75MeV)4θ2

Evolution of the axion dark matter field

• We move back to the very early Universe ...
• Assume some random set of initial conditions ...
• Let us see how the field evolves !
• fa is soooooo small, and the relevant momenta sooooo small than we neglect all interactions of the axion
• The evolution of a lonely scalar field

Equations of motion S = Z d4x√−gL = Z d4x√−g ✓fa 2 (∂µθ)(∂µθ) − V (θ) + Lint ◆ = Z d4x√−g ✓1 2(∂µa)(∂µa) − V (a/fa) + Lint ◆ δS = 0 ✓ δL δ(∂µa) ◆

;µ

− δL δa = 0 Scale factor is now R(t) Fourier transform (linear equation) and modes decouple

Field evolution

For simplicity I linearised around a=0

¨ ak + 3H ˙ ak + k2 R2 ak + m2

aak ' 0

∂V ∂a = χ fa sin θ ∼ χ fa θ = m2

aa

¨ a + 3H ˙ a 1 R2 r2a + ∂V ∂a = 0

T µ

ν = (∂µa)(∂νa) − Lδµ ν

Energy density and pressure

ρ = 1 2(˙ a)2 + 1 2(ra)2 + V (a) p = 1 2(˙ a)2 1 2(ra)2 V (a)

0.001 0.01 0.1 1 10 100 1000

• 0.5

0.0 0.5 1.0

a(t) a0 Radiation a frozen ρ = cons ¨ ak + 3H ˙ ak + k2 R2 ak = 0 ρ ∼ ρ0/R(t)4

Relativistic modes

(This corresponds to the wavelength entering the horizon)

¨ ak + 3H ˙ ak + ω2(t)ak = 0

Again a damped oscillator (time-dependent frequency...)

tk ∼ 1 ω = R k

t = 1/H → HR ∼ k

time

0.001 0.01 0.1 1 10 100 1000

• 0.5

0.0 0.5 1.0

a(t) a0 ρ ∼ ρ0/R(t)3 DUST-like Lambda-like ¨ ak + 3H ˙ ak + m2

aak ' 0

(SIMPLIFIED)

ρ = cons

Zero and non-relativistic modes

Again a damped oscillator ω = ma

H ∼ ma t1 = 1 2H ∼ 1 ma

time

Equation of state and speed of sound

Even for NR modes, k/R << ma, the fact that axions and ALPs have non-zero momentum can be important -> field gradients oppose to compression because of the uncertainty principle leading to a “uncertainty pressure”, (sometimes called “quantum pressure” ....)

¨ ak + 3H ˙ ak + (k2/R2 + m2

a)ak ' 0

Why the axion is so COLD ?

k

ρ ∝ 1/R4

ρ ∝ 1/R3 ρ = const. R RH(∝ 1/R)

Modes above are quite suppressed

k ∼ maR

✓R1 R0 ◆3 ∼ ✓T0 T1 ◆3 ∼ ✓ T0 √H1mPl ◆3 ∼ ✓ T0 √mamPl ◆3 ∝ m−3/2

a

• Energy density redshifts as matter, from the onset of oscillations

Energy density

• dilution until today

Smaller mass axions, start oscillating later, and get less diluted ... time

ρa(t)

mat ∼ 1

tosc ∼ 1 ma

ρa(t) ∼ θ2

Iχ

✓ R1 R(t) ◆3 ∝ θ2

Iχm−3/2 a

H(t1) ∼ ma

• with

ρa(t0) ∝ θ2

Im − 6+n

4+n

a

χ ∝ T −n

0.10 0.15 0.20 0.25 0.30 0.00 0.02 0.04 0.06 0.08

• []

χ / []

Effective mass, lattice calculations

Lattice QCD (DWF) 2+1 [Buchoff] (points) IILM [Wantz] DIGA (T>>Tc) [Borsanyi] Lattice QCD 2+1 [Bonati] Lattice QCD 2+1+1 [Borsanyi]

V (θ) = −χ(T) cos θ m2

af 2 a = χ(T)

Lattice QCD: we can compute axion mass At high T (no mesons) we can analytically compute potential (DIGA)

Axion-like particle and axion dark matter

Everything I’ve told you applies to any ALP weakly coupled V = 1 2m2φ2 ρ0

φ ∼ VI(R1/R0)2 = m2 φφ2 I

✓ T0 √mφmPl ◆3 Axions are a bit special because their periodic potential V = χ(1 − cos θ)

Many things :

• production is NON-THERMAL
• the relic density depends on initial condition!
• typical momenta k~H(t1)R(t1) related to Hubble, not T

• Peccei-Quinn symmetry, color anomalous, spontaneously broken at fa

Simple model KSVZ

ENERGY

L ∈ 1 2(∂a)2 + αs 8π G e G a fa

• At energies below (SSB)

fa

~fa

• At energies below , mixing

ΛQCD

a − η0 − π0 − η − ...

La,I = X

N

cN,a ¯ Nγµγ5N a fa + caγ α 2π Fµν e F µν a fa + ...

nucleons ... photons ... mesons ...

axion mass couplings

ma ' mπfπ fa ⇠ 6meV109GeV fa

~GeV

L = LSM + i ¯ QDQ + 1 2(∂µσ)(∂µσ∗) − (y ¯ QLQRσ + h.c) − λ|σ|4 + µ2|σ|2

σ(x) = ρ(x)ei a(x)

fa

fa = p µ2/2λ

• PQ transition after inflation

time, 1/T Domains=horizon Cosmic strings

SSB

strings

θ = 0

QCD

• D. Walls

Damped

• scillations=CDM

1st typical scenario: random initial conditions in our Universe

PQ T-restored

2t

smoothing

• PQ transition after inflation

time, 1/T Domains=horizon Cosmic strings

SSB

strings

θ = 0

QCD

• D. Walls

Damped

• scillations=CDM

SCENARIO-I

realignment+CS+DWs O(1) inhomogeneous DM 1st typical scenario: random initial conditions in our Universe

PQ T-restored

2t

smoothing

time, 1/T

SSB

strings

θ = 0

QCD

• D. Walls

Damped

• scillations=CDM

INFLATION!!

• PQ phase transition before inflation

PQ T-restored

2nd typical scenario: 1 initial condition for our whole Universe

Already covered!!!

time, 1/T

SSB

strings

θ = 0

QCD

• D. Walls

Damped

• scillations=CDM

INFLATION!!

• PQ phase transition before inflation

PQ T-restored

2nd typical scenario: 1 initial condition for our whole Universe

Already covered!!!

SCENARIO-II

~homogeneous

−π θ π

SCENARIO I (N=1): axion evolution around t1

Strings

Axionic strings : cores

• Huge din. range!
• realistic strings have

d ~ 1/f_a distances ~ t d t ∼ H fa ∼ T 2 Mpfa

Axion DM, how much

ma eV meV µeV ρobs,DM

c

• s

m i c s t r i n g s + d

• m

a i n w a l l s thermal

10-5 10-4 10-3 10-2 10-1 1 10

ra@keVêcm3D

realignment

θI = 1

θ

I

= . 1

θI = 0.01

DM density today Axion decay

a

more interacting less interacting

Dark matter density, inhomogeneous at comoving mpc scales

minicluster seed! final overdensity

ρ− < ρ > < ρ >

do mc’s survive?

Minicluster size

z~1000 MR today T1 ??? z~1 z_1 ??? At Matter-radiation equality

ma ∼ 100µeV δ ∼ 1

Q: Horizon size at t1? H(t1)~m(T1) Q: What is the mass inside a Horizon^3 ? Q: what is the physical size at z~1000 Q: what will be the density in a MC today? Region with delta~1 and size ~ 1/H(t1) , axion field freezes out soon after t1, overdense region expands

Excluded (too much DM)

• k

sub

Phase transition (N=1)

strings+unstable DW’s

• Axion DM scenarios
• k

tuned (anthropic?) tuned

Inflation smooth

ΩaDMh2 ' θ2

I

✓80 µeV ma ◆1.19

Excluded

Axion dark matter

Initial conditions set by :

−πfa πfa −πfa πfa

SCENARIO I, N>1, Domain Walls stable-> cosmological disaster SCENARIO I, N=1

a fa = Nθ

−πfa πfa −πfa πfa

SCENARIO I, N>1, break slightly degeneracy (but tuning...) SCENARIO I, N=1

a fa = Nθ

Domain walls move by pressure difference, they are long-lived -> large misalignments for longer time -> more DM

Excluded (too much DM)

• k

sub

Phase transition (N=1)

strings+unstable DW’s

• Axion DM scenarios
• k

tuned (anthropic?) tuned Excluded (too much DM) ? tuned

Phase transition (N>1)

strings+long-lived DWs

Inflation smooth

ΩaDMh2 ' θ2

I

✓80 µeV ma ◆1.19

Excluded

What fa gives the correct relic abundance??

Initial conditions set by :

Fuzzy DM and small-scale structure problems

• If ALP DM has small mass,
• Typical value at odds with Ly-alpha

m ∼ 10−22eV

• Gradient pressure implies a Jeans mass in structure formation, which

suppresses small scale features (cusps, # low mass satelites...)

(Hu 2000, ..., Hui 2017) Schive 2014

Halos composed

• f central cores’

(Bose star) + CDM- like halo

Detecting Axions

ρaDM = 0.3GeV cm3 θ0 = 3.6 × 10−19

Axion experiments 2017

OSQAR, CERN

IAXO, (?)

ARIADNE, Reno ADMX, Wash. U

ABRACADABRA, Yale

ADMX,-HF Yale CASPER, Mainz ALPS-II, DESY CAST, CERN MADMAX, (?) QUAX QUAXgsgp

CAPP

ORGAN, UWA,Perth BMV, Toulouse PVLAS, Legnaro ADMX+, Fermilab BRASS, DESY

ma

Non-zero velocity in galaxy -> finite width

ω ' ma(1 + v2/2 + ...) δω = mav2 2

δω ω ∼ 10−6

δt ∼ 1 δω ∼ 0.13ms ✓10−5eV ma ◆ coherence time δL ∼ 1 δp ∼ 20m ✓10−5eV ma ◆ coherence length

Imperfect Vacuum realignment

θ(t) = θ0 cos(mat)

θ0 ∼ 3.6 × 10−19

ρCDM = 0.3GeV cm3 ≡ 1 2(˙ a)2 + 1 2m2

aa2 = 1

2m2

af 2 aθ2

Detecting Dark Matter

QCD axion

m2

Af 2 A = χQCD

~ 10^-6

Cavities Mirrors LC-circuit Spin precession Atomic transitions Optical

• In a static magnetic field, the oscillating axion field generates EM-fields

B-field

• Electric fields
• Oscillating at a frequency
• B-fields

(amp independent of mass!)

Axion DM in a B-field

LI = −Caγ α 2π a fa B · E

LI = −Caγ α 2π θ(t) Bext · E

source

ω ' ma / rθ |Ba| ⇠ hvi|Ea| Ea = Caγ αBext 2π θ0 cos(mat)

Radiation from a magnetised mirror

E(t) = cγ↵✓0B 2⇡✏ cos(mat) In a magnetised medium E|| = 0 Boundary conditions!

MIRROR

Radiation from a magnetised mirror

E|| = 0 Boundary conditions! Emitted EM-wave E(t) = cγ↵✓0B 2⇡✏ cos(mat) Eγ = cγ↵✓0B|| 2⇡✏ cos(ma(t − nx)) Bγ = nˆ s × Eγ tan(ma(t − nx))

MIRROR

Radiation from a magnetised mirror : Power

Emitted EM-wave P Area ∼ 2 × 10−27 W m2 ✓cγ 2 B|| 5T ◆2 1 ✏

MIRROR

spherical reflecting dish

Dish antenna experiment?

The Ea-field excites surface electrons coherently EM radiation from a reflecting surface

P ∼ |Ea|2Adish ∼ 10−26 ✓ B 5T Caγ 2 ◆2 Adish 1 m2 Watt

Horns 2012

Waves interfere constructively and resonate

Signal if tuned

ma = ωres P → P × Q

• Slow scan over frequencies
• Dominated by thermal+preamp noise

Cavity experiments

• Haloscope (Sikivie 83)

“Amplify resonantly the EM field in a cavity”

¨ E r2E = cγα 2π Bext ¨ θ r2ei = ω2

i ei.

Ci = 1 V B Z dV ei · Bext.

cα = cγα 2π

¨ Ei + ω2

i Ei + Γ ˙

Ei = −cαBCi¨ θ.

Ei = − cαBm2

aCi

(m2

a − ω2 i )2 + (maΓ)2

⇣ θ(t)(m2

a − ω2 i ) + ˙

θ(t)Γ ⌘ ,

Signal power in cavity experiments (haloscopes)

Combine MW equations into an oscillator Expand in eigenmodes of the cavity satisfy (with appropriate boundary conditions) Equation for the amplitude of one mode Forced oscillator solution

damping (energy loss by walls and pick up signal) damping (energy loss by walls and pick up signal) geometric factor ...

E(t, x) = X

i

Ei(t)ei.

Ui = V 1 2 ✓ω2 + ω2

i

2ω2 ◆ Ei(t0)2

dUi dt = −ΓiUi

Qi = ωi Γs,i + Γc,i

Psignal = Γs,iUi = V Γs,i 1 2 m2

a + ω2 i

2m2

a

✓ cαBm2

aθ0Ci

(m2

a − ω2 i )2 + (maΓ)2

◆2 ⇣ m2

a − ω2 i

2 + (maΓ)2⌘ ,

Psignal = Γs Γs + Γc Q ωi (gaγBCi)2 ρDMV.

Signal power in cavity experiments (haloscopes)

Energy stored in a mode Energy loss and quality factor

Γ = Γs + Γc

signal I pick from an antenna / intrinsic losses

Extracted power (Signal!) On resonance Outside the resonance

ωi = ma ωi ma Γ = ωi/Q

Psignal ∼ 0

(on resonance)

• Haloscope (Sikivie 83)
• Signal/noise in of time, t,

∆νa S N = Pout Pnoise p ∆νat

• Signal

(V ∝ m−3

a )

Pout ∝ V ma ∼ 1 m2

a

• Noise

Pnoise = Tsys∆νa ∝ m2

a

• Scanning rate

P ∼ Q|Ea|2(V ma)Gκ

• Naive ADMX scaling (e.g. an ADMX every octave)

1 ma d∆ma dt ∝ C4

Aγ

m7

a

Scanning over frequencies

Cavity resonators (Haloscopes)

Cavity experiments ADMX HAYSTAC ADMX-Fermilab CULTASK - CAPP -Korea

CAST-CAPP CARRACK (discontinued) RADES

Scenario II

10-7 10-6 10-5 10-4 10-3 10-1 1 10 102 103 10-1 1 10 102 10-1 1 10 102 103

cγ

ADMX

RBF

ADMX

ADMX2

HAYSTAC

CARRACK?

ν[GHz]

IAXO

I

Cavity experiments

ma[eV]

CAPP

Conclusions : a developing picture

• sc. EDM

CAPP ADMX HAYSTAC

Large freq ... Area vs volume

P ∼ Q|Ea|2(V ma)Gκ

P ∼ |Ea|2A

Q ∼ 104 ∼ Am2

a

comparable if

Mixed scheme?

If we could add the power emitted by many mirrors...

Radiation from a dielectric interface ...

Boundary conditions! E(t) = cγ↵✓0B 2⇡✏ cos(mat) E(t) = cγαθ0B 2π cos(mat) E||1 = E||2

Radiation from a dielectric interface ...

Emitted EM-wave E(t) = cγ↵✓0B 2⇡✏ cos(mat) E(t) = cγαθ0B 2π cos(mat) Boundary conditions! E||1 = E||2 Emitted EM-wave

Many dielectrics : MADMAX at MPP Munich

Emitted EM-waves from each interface + internal reflections ... ...

• Emission has large spatial coherence; adjusting plate separation -> coherence

P Area ∼ 2 × 10−27 W m2 ✓cγ 2 B|| 5T ◆2 1 ✏ × (!) boost factor

• Work in progress at Max Planck Institute fur Physik (Conceptual design)

Axion DM : A developing picture

• sc. EDM

Dielectic mirror 5th forces? QUAX?

LC

CAPP ADMX HAYSTAC

Axion Dark matter experiments (target areas)

• sc. EDM

MADMAX CAPP ADMX ADMX-HF QUAX?

LC

5th forces?

• nly one running