Axions - Centro de Astrofísica da Universidade do Porto · Introduce a new dynamical variable a(x)...

Axions

Yvonne Y. Y. WongRWTH Aachen

COSMO2011, Porto, August 22--26, 2011

● The QCD lagrangian contains a CP-violating term:

● This induces a huge electric dipole moment for the neutron:

Strong CP problem...

LΘ=(θQCD+arg det M q)αs

8 πGμ ν a Ga

μ ν=Θαs

8πG G

∣d n∣≈∣∣10−16e cm vs ∣d n∣3×10−26 ecm

Quark mass matrix

Gluon field strength

Phase from QCD vacuum −≤≤

Theory Experiment

10−9 The strong CP problem= Why is Θ so small??

PDG 2010

● Introduce a new dynamical variable a(x) with coupling to GG:

Axion as a solution...

L La=12

∂ a2−s

8 a x f a

G G

ma≈mu md

mumd

f

f a

m= 6.0 eV

f a /106GeV

Peccei & Quinn 1977Wilczek 1978Weinberg 1978

Axion = fundamentally massless pseudoscalar satisfying a → a + const.

Axion decay constant; Peccei-Quinn scale

● aGG term induces axion mixing with π0, η and η'.

→ Effective mass for the axion:

→ Effective potential V(a) drives a(x) to zero. CP symmetry is dynamically restored!

V a=12ma

2 a2...

a

● Introduce a new complex scalar field with potential V(|φ|), which couples (directly or indirectly) to (SM or exotic) quark(s).

● Impose a chiral U(1)PQ

symmetry, spontaneously broken at E ~ fa.

Implementing the PQ mechanism: generic recipe...

θ=a / f a

E ~ faE ~ ΛQCD << fa

U(1)PQ explicitly broken by instanton effects at E ~ Λ

QCD~ 400 MeV.

Axion is the (pseudo) Nambu-Goldstone boson.

Tilting the Mexican hat;Axion acquires a mass.

V (θ)

αs

8 πa( x)f a

GG

θ=a / f a

Defining featureof the QCD axion!

● Benchmark models: “Invisible axions”

– KSVZ (hadronic)

– DFSZ

● The defining feature of the QCD axion is the aGG coupling:

– One fundamental parameter fa: any value will solve the strong CP

problem.

● Mixing with neutral pseudoscalar mesons means:

Axion parameter space and interactions...

Heaps of (fairly model-independent) phenomenology!

Axioncouplingt o SM ≈ Pion

couplingt o SM ×

f

f a

Details depend on exactly how U(1)PQ

is implemented.

Kim 1979; Shifman, Vainshtein & Zakharov 1980

Dine, Fischler & Srednicki 1981; Zhitnitsky 1980

αs

8 πa( x)f a

GG

Where we stand...

101033 101066 101099 10101212 [GeV] f[GeV] faa

eVeVkeVkeV meVmeV μμeVeVmmaa

Laboratory Telescope

Too much HDMBBN

Globular cluster stars

Too many events Burst duration SN1987AAst

roC

osm

oE

xp

Too much CDMClassic scenario

Anthropic scenario

Microwavecavity

CAST

Excluded

Current searches

Figure adapted from G. Raffelt

Where we stand...

101033 101066 101099 10101212 [GeV] f[GeV] faa


TelescopeLaboratory

Too much HDMBBN



roC

osm

oE

xp


Anthropic scenario

Microwavecavity

CAST

Excluded

Current searches


This talk

1. Axion cosmology...

● Misalignment mechanism (CDM)

● Radiating axion strings (CDM)

● Thermal production (HDM)

Three ways to get a cosmological axion population...

ma

f a

1012 GeV

109 GeV

1015 GeV

106 GeV

μeV

meV

peV

eV

Misalignment mechanism...

● PQ symmetry is spontaneously broken at T ~ fa.

● Tilted Mexican hat at T ~ Λ

QCD ~ 400 MeV leads to

coherent oscillations of axion field when m

a > H.

→ Zero momentum condensate.

→ Cold dark matter!

T ~ fa

T ~ ΛQCD

V (θ)

V (θ)

θ=a / f a

Preskill, Wise & Wilczek 1983Abbott & Sikivie 1983Dine & Fischler 1983

θ=a / f a

● Temperature-dependent instanton effects → m

a(T).

● Given ma(T), solve

to get energy density.

● (Approximate) analytic formula:

Axion energy density...

θ+3 H θ+ma2(T )sinθ=0

Ωah2≈0.195( f a

1012 GeV )1.184

θini2

Two scenarios

Wantz & Shellard 2010alsoBae, Huh & Kim 2008Turner 1986

Two scenarios for θini

...

● The “classic” window

● PQ symmetry breaking after recent phase of inflation and reheating:

● Many different -π ≤ θini

≤ π in the visible universe. Take average:

● The “anthropic” window

● PQ symmetry breaking before or during recent phase of inflation, and remains broken up to now:

● One unknown value of θini in our patch of the universe.

→ Ωah2 depends strongly on initial

conditions!

f a<Max [ H I

2 π,T max] f a>Max [ H I

2 π,T max]

Hubble parameterduring inflation

Max temperatureafter inflation

⟨θini2 ⟩= 1

2 π ∫−π

π

θ2d θ= π2

3

● If axions constitute all of cold dark matter, i.e., Ωah2 ~ 0.11, then

● Quantum fluctuations on massless axion field during inflation lead to isocurvature perturbations:

→ At T < ΛQCD

, uncorrelated Cold Dark matter Isocurvature mode, with power spectrum:

The anthropic window and CDI modes...

δ(na /s)≠0

θini≈0.75( 1012 GeVf a

)0.592

∼10−3

for fa ~ 1016 GeV

f a>Max [ H I

2 π,T max]

Natural?Fine-tuning?

⟨∣S 2(k )∣⟩≃ H I2

π2 f a2 θini

2 ∝( kk0

)niso−1

⟨∣R2(k )∣⟩≃ H I2

π M pl2 ϵ

∝( kk 0

)nad−1

cf curvature perturbation spectrum

● Isocurvature contribution to the CMB anisotropies:

Pure adiabatic

Pure axionisocurvature

Hamann, Hannestad, Raffelt & Y3W 2009

CMB anisotropies

Uncorrelated meansTotal = Incoherent sum of adiabatic+isocurvature

● Isocurvature fraction:

● Current limits and expected sensitivities:

Hamann, Hannestad, Raffelt & Y3W 2009alsoBeltran, Garcia-Bellido & Lesgourgues 2007Hertzberg, Tegmark & Wilczek 2008Visinelli & Gondolo 2009Wantz & Shellard 2010

α≡∣ ⟨∣R2(k )∣⟩⟨∣R2(k)∣⟩+ ⟨∣S 2(k )∣⟩∣k =k 0

α<0.090 (95 C.I.)α<0.042 (95 C.I.)α<0.017 (95 C.I.)

WMAP7Planck forecastCVL* forecast

Anthropic window

Pivot scalek

0 = 0.002 Mpc-1

* A hypothetical CMB probe limited only by cosmic variance in TT, TE and EE up to l=2000

Lines of constant Ωah2 = 0.11





ma

f a

1012 GeV

109 GeV

1015 GeV

106 GeV

μeV

meV

peV

eV

● PQ mechanism = spontaneous breaking of global U(1)

PQ.

→ Cosmic strings: expect one per Hubble volume at time of symmetry breaking.

Axion strings via the Kibble mechanism...

www.damtp.cam.ac.uk/research/gr/public/cs_home.html


PQ.



Anthropic windowSymmetry breaking

before/during inflation

Classic windowSymmetry breaking

after inflation

String population diluted → unimportant today

www.damtp.cam.ac.uk/research/gr/public/cs_home.html


PQ.



Anthropic windowSymmetry breaking

before/during inflation

Classic windowSymmetry breaking

after inflation

String population diluted → unimportant today

Low frequency (ω < ma) axion

radiation from strings = secondpopulation of CDM axions.

time

Field theoretic simulation of U(1)

PQ breaking

Hiramatsu et al. 2011

● No consensus yet: peaked or flat radiation power spectrum?

● Some representative values:

Axion energy density from string radiation...

Battye & Shellard 1997

Ωah2≈0.2( f a

1012GeV )1.17

Hagmann, Chang & Sikivie 2001

Hiramatsu et al. 2011Dominate over contribution from misalignment

Comparable to contribution from misalignment

Ωah2≈0.195( f a

1012 GeV )1.184

θini2

Ωah2≈1.66( f a

1012 GeV )1.19

Ωah2≈O (10)( f a

1012GeV )1.18

θini2 =π2/3≈3

● No consensus yet: peaked or flat radiation power spectrum?

● Some representative values:

Axion energy density from string radiation...

Battye & Shellard 1997

Ωah2≈0.2( f a

1012GeV )1.17

Hagmann, Chang & Sikivie 2001

Hiramatsu et al. 2011

Ωah2≈1.66( f a

1012 GeV )1.19

Ωah2≈O (10)( f a

1012GeV )1.18

f a<3.2×1010 GeV

f a<1011 GeV

f a<2×1011 GeV

Total axionenergy density

Observed CDMenergy density<

● Strictly speaking:

– KSVZ: N = 1

– DFSZ: N = 6; PQWW: N = 6

→ For N > 1, at T < ΩQCD

, N degenerate vacua separated by stable domain walls (nonrelativistic walls: ).

→ Not all axion models are compatible in the classic window.

Caution! Domain walls...

ρ∝a−1

f a=f PQ

NInteger number,“Colour anomaly”of model

⟨ϕ⟩= f PQexp (iθ)

Axion decay constant





ma

f a

1012 GeV

109 GeV

1015 GeV

106 GeV

μeV

meV

peV

eV

● Axion couples to SM fields:

● Production in the early universe via scattering with the cosmic plasma.

– Main process governing thermalisation/decoupling depends on fa.

Thermal axion production...

Linteraction=−αs

8π f a

Gμ νa Gaμ ν−

C γ α8π f a

F μ ν Fμ νa+

C i

2 f a

Ψi γμ γ5 Ψ j ∂μ a

+ Cπ

f a f π(π+π0 ∂μ π+...)∂μa+...

Standard model fermionsC = model-dependent factors

Small coupling (fa>108 GeV)...

Graf & Steffen 2011

Thermal production

Contribution frommisalignment

● Production from scattering of the quark-gluon plasma.

● Thermal population negligible. (even smaller than the CMB energy density).

● Axion decoupling at T < ΛQCD

.

– Dominant process (hadronic axions):

● Relic axion number density and temperature comparable to one species of neutrinos.

– Axion hot dark matter.

– Closure bound: ma < O(30) eV

– More powerful: free-streaming bound from CMB+LSS.

Rel

ativ

e nu

mbe

r de

nsity

Axion number density today(relative to 1 ν)Large coupling (f

a<108 GeV)...

Axion temperature today(relative to ν temperature)

Rel

ativ

e te

mpe

ratu

re

ma [eV]f a/GeV=6×107 6×105

π+π ↔π+a

Hannestad, Mirizzi & Raffelt 2005

Hannestad, Mirizzi, Raffelt & Y3W 2007, 2008, 2010Melchiorri, Mena & Slosar 2007

Large-scale matter power spectrum

ma=10 eV

ma=2.4 eV∑ mν=1.2 eVΛCDM

● Free-streaming of axion HDM suppresses small scale power similar to neutrinos.

– Different free-streaming scales...

Hannestad, Mirizzi, Raffelt & Y3W 2007, 2008, 2010Melchiorri, Mena & Slosar 2007

CMB TT

ma=10 eV

ma=2.4 eV

∑ mν=1.2 eV

ΛCDM

● Free-streaming of axion HDM suppresses small scale power similar to neutrinos.

– Different free-streaming scales...

● However, unlike neutrinos, axion HDM has no substantial effect on the CMB anisotropies.

Hannestad, Mirizzi, Raffelt & Y3W 2010

HPS =Halo power spectrum(SDSS DR7)

● Upper limit on ma from

CMB+LSS+HST:

(marginalised over Σmν)

ma<0.72 eV (95 C.I.)

f a>106 GeV

● Sub MeV mass axions decay after big bang nucleosynthesis.

→ Post-BBN entropy production leads to:

– Colder neutrinos → Neff

< 3.

– Mismatch between baryon-to-photon ratios at BBN and at recombination.

a → γ γ

Cadamuro, Hannestad, Raffelt & Redondo 2011

Deuterium abundance

Observed

Prediction assuming baryondensity measured by CMB.

Disfavoured

f a∼5×103 GeVEven larger coupling (fa<104 GeV)...

Where we stand...

101033 101066 101099 10101212 [GeV] f[GeV] faa



Too much HDMBBN



roC

osm

oE

xp


Anthropic scenario

Microwavecavity

CAST

Excluded

Current searches


2. Detecting axions in the lab...

● Exploit axion coupling with electromagnetic field:

● Make use of the inverse Primakoff effect to detect astrophysical and cosmological axions.

All based on the same idea...

Sikivie 1983

La γ=−14g a γ F μ ν

Fμ ν a=g a γ E⋅B a

Primakoff effect:Production of neutral pseudoscalar mesons in an external E or B field from photons.

Axion to photonconversion

Magnet in your lab

● Oscillation formulation of axion-photon conversion (relativistic axions):

● Axion-to-photon transition probability:

[ω−i∂z+(−mγ

2

2 ω+Δ⊥

CM ΔF 0

ΔF −mγ

2

2 ω+Δ∥

CM 12ga γ B

012

g a γ B −ma

2

2 ω)](A⊥

A∥

a )=0

Raffelt & Stodolsky 1988

Proba → γ=( g a γ B

q )2

sin2(q L2 ) q≡∣mγ

2−ma2

2 ω ∣

Propagationdirection

Transverse B field

Photon frequency

Photonpolarisation

Effective photon mass(refraction in medium)

Δ = Cotton-Mouton,Faraday effects

Axion,“3rd polarisation”

Axion helioscopes... Sikivie 1983

N

S

Magnet

X-raydetector

Sun

keV energy axions produced in the sun

Axion-photon conversion

Gas filling to generate m

γ to probe larger m

a.

Proba → γ=( g a γ B

q )2

sin2( q L2 )

q≡∣mγ2 −ma

2

2ω ∣Solar axion flux

CERN Axion Solar Telescope (CAST) L = 9.26 mB = 9 T (Decomissioned LHC test magnet)

Tokyo Axion Helioscope “Sumico”L = 2.3 m

B = 4 T

Aune et al. [CAST] arXiv:1106.3919

Inoue et al. 2008

Hot dark matter limit

CAST exclusion limit

Tokyo axion helioscopeexclusion limit

Axion modelspace

(had

roni

c ax

ion)

● Detect CDM axions clustering in the Galactic halo.

● Nonrelativistic axions conversion to photons:

→ Immerse microwave cavity (tuned to match axion mass) in a magnetic field.

– Power transferred:

Axion haloscopes... Sikivie 1983

Power=g a γ2 V B2ρaQ

ma

∼10−21 Watts

f a∼1012GeV →ma∼O (1)μ eV

ω∼O (1)GHz Microwave frequency

Volume Quality factor

Axion energy density

Asztalos et al. PRL 2010

Between 1996 and 2009, already excluded KSVZ (hadronic) axions in the mass range:

( f a∼1012 GeV)B = 8.5 T; h = 1 mQ ~ 105; d = 0.6 m

Axion Dark Matter EXperiment (ADMX)

1.9<ma /μ eV<3.53

ADMX “Phase 2”

Cosmic Axion Research with Rydberg Atoms in Cavities in Kyoto(CARRACK)

CARRACK I results

Yamamoto et al. hep-ph/0101200

CARRACK II goal

● Make your own axions with a laser!

Light-shining through a wall...

Jäckel & Ringwald 2010

Okun 1982Anslem 1985, 1988Van Bibber et al. 1987

Not sensitive enough to probe QCD axions yet...

Probγ → γ=Probγ → a(L1)Proba → γ(L2)

=( 2 ga γ Bω

ma2 )

4

sin2( ma2 L1

4 ω )sin2(ma2 L2

4ω )

Summary...

101033 101066 101099 10101212 [GeV] f[GeV] faa



Too much HDMBBN



roC

osm

oE

xp


Anthropic scenario

Microwavecavity

CAST

Excluded

Current searches


Open search windows...

Axions - Centro de Astrofísica da Universidade do Porto · Introduce a new dynamical variable a(x)...

Documents

Transcript of Axions - Centro de Astrofísica da Universidade do Porto · Introduce a new dynamical variable a(x)...