axions

Georg Raffelt, MPI Physics, Munich Seminar, UNSW, Sydney, 5 March 2014

AxionsGeorg G. Raffelt, Max-Planck-Institut für Physik, München

AxionsMotivation, Cosmological Roleand Experimental Searches

Seminar, University of New South Wales, 5 March 2014


Axions as Cold Dark Matter of the Universe

Dark Energy ~70% (Cosmological Constant)

Neutrinos 0.1-2%

Dark Matter~25%

Ordinary Matter ~5%(of this only about 10% luminous)


Neutron

ProtonGravitation (Gravitons?)

Weak Interaction (W and Z Bosons)

Periodic System of Elementary Particles

Electromagnetic Interaction (Photon)

Strong Interaction (8 Gluons)

Down

Strange

Bottom

Electron

Muon

Tau

e-Neutrino

m-Neutrino

t-Neutrino nt

nm

nee

m

t

d

s

b

1st Family

2nd Family

3rd Family

Up

Charm

Top

u

c

t

Quarks Leptons

Charge -1/3

Down

Charge -1

Electron

Charge 0

e-Neutrino need

Charge +2/3

Up u

Higgs


v

Three-Flavor Neutrino Parameters

(𝜈𝑒𝜈𝜇

𝜈𝜏)=(1 0 0

0 𝑐23 𝑠23

0 −𝑠23 𝑐23)( 𝑐1 3 0 𝑒−𝑖 𝛿𝑠13

0 1 0−𝑒𝑖𝛿 𝑠13 0 𝑐13

)( 𝑐12 𝑠12 0−𝑠12 𝑐12 0

0 0 1)(1 0 0

0 𝑒𝑖𝛼2

2 0

0 0 𝑒𝑖 𝛼3

2 )(𝜈1

𝜈2

𝜈3)

Three mixing angles , , (Euler angles for 3D rotation), ,a CP-violating “Dirac phase” , and two “Majorana phases” and

⏟⏟⏟⏟39∘<𝜃23<53∘ 7∘<𝜃13<11∘ 33∘<𝜃12<37∘ Relevant for

0n2b decayAtmospheric/LBL-Beams Reactor Solar/KamLAND

me t

me t

m t

1Sun

Normal

2

3

Atmosphere

me t

me t

m t

1Sun

Inverted2

3

Atmosphere

72–80 meV2

2180–2640 meV2

Tasks and Open Questions• Precision for all angles• CP-violating phase d ?• Mass ordering ? (normal vs inverted)• Absolute masses ? (hierarchical vs degenerate)• Dirac or Majorana ?


Antineutrino Oscillations Different from Neutrinos?

Dirac phase causes different 3-flavor oscillationsfor neutrinos and antineutrinos

Distance [1000 km] for E = 1 GeV

same as

𝜈𝑒→𝜈𝜇

𝜈𝑒→𝜈𝜇

𝝂𝐞=𝑐12𝑐13𝝂𝟏+𝑠12𝑐13𝝂𝟐+𝑠13𝑒−𝑖 𝛿𝝂𝟑

𝝂𝐞=𝑐12𝑐13𝝂𝟏+𝑠12𝑐13𝝂𝟐+𝑠13𝑒+𝑖 𝛿𝝂𝟑


CP Violation in Particle Physics

Physics Nobel Prize 2008

Discrete symmetries in particle physicsC – Charge conjugation, transforms particles to antiparticles violated by weak interactionsP – Parity, changes left-handedness to right-handedness violated by weak interactionsT – Time reversal, changes direction of motion (forward to backward)CPT – exactly conserved in quantum field theoryCP – conserved by all gauge interactions violated by three-flavor quark mixing matrix

M. Kobayashi T. Maskawa

All measured CP-violating effects derive from a single phase in the quark mass matrix (Kobayashi-Maskawa phase), i.e. from complex Yukawa couplings Cosmic matter-antimatter asymmetry requires new ingredients


Cabbibo-Kobayashi-Maskawa (CKM) Matrix

Quark interaction with W boson(charged-current electroweak interaction)

Unitary Cabbibo-Kobayashi-Maskawa matrixrelates mass eigenstatesto weak interaction eigenstates

VCKM depends on three mixing angles and one phase d,explaining all observed CP-violation

Precision tests use “unitarity triangles” consisting of products of measuredcomponents of VCKM, for example:

𝑉 CKM=(𝑉 𝑢𝑑 𝑉 𝑢𝑠 𝑉 𝑢𝑏

𝑉 𝑐𝑑 𝑉 𝑐𝑠 𝑉 𝑐𝑏𝑉 𝑡𝑑 𝑉 𝑡𝑠 𝑉 𝑡𝑏

)


Measurements of CKM Unitarity Triangle

CKMfitter Grouphttp://ckmfitter.in2p3.fr

UTfit Collaborationhttp://www.utfit.org


The CP Problem of Strong Interactions

ℒQCD=∑𝑞𝜓𝑞( i𝐷−𝑚𝑞𝑒

i 𝜃𝑞 )𝜓𝑞−14𝐺𝜇𝜈𝑎𝐺𝑎

𝜇𝜈−Θ𝛼 s

8𝜋 𝐺𝜇𝜈 𝑎~𝐺𝑎

𝜇𝜈

𝜓𝑞→𝑒❑−𝑖𝛾 5𝜃𝑞 /2𝜓𝑞

ℒQCD=∑𝑞𝜓𝑞 (i𝐷−𝑚𝑞)𝜓𝑞−

14𝐺𝐺− (Θ− arg det 𝑀𝑞)⏟

−𝜋 ≤Θ≤+𝜋

𝛼s8𝜋 𝐺~𝐺

Real quarkmass

Phase fromYukawa coupling

Anglevariable

CP-oddquantity

Remove phase of mass term by chiral transformation of quark fields

can be traded between quark phases and term No physical impact if at least one Induces a large neutron electric dipole moment (a T-violating quantity)

Experimental limits: Why so small?


Neutron Electric Dipole Moment

Violates time reversal (T) andspace reflection (P) symmetries

Natural scale𝑒

2𝑚𝑁=1.06×10−14𝑒cm

Experimental limit|𝑑|=0.63×10− 25𝑒 cm

Limit on coefficient

Θ𝑚𝑞

𝑚𝑁≲10−11


Strong CP Problem

+𝜋−𝜋 Θ

ΛQCD4

QCD vacuum energy

• CP conserving vacuum has (Vafa and Witten 1984)• QCD could have any , is “constant of nature”• Energy can not be minimized: not dynamical

Equivalent Equivalent

−2𝜋 +2𝜋

Peccei-Quinn solution: Make dynamical, let system relax to lowest energy


35 Years of Axions


The Cleansing Axion

Frank Wilczek

“I named them after a laundry detergent, since they clean up

a problem with an axial current.” (Nobel lecture 2004)


Axion as a Nambu-Goldstone Boson

• New U(1) symmetry, spontaneously broken at a large scale • Axion is “phase” of new Higgs field: angular variable • By construction couples to term with strength , e.g. triangle loop with new heavy quark (KSVZ model)• Mixes with -- mesons• Axion mass (vanishes if or )

𝑚𝑎=√𝑚𝑢𝑚𝑑

𝑚𝑢+𝑚𝑑

𝑚𝜋

𝑓 𝜋 𝑓 𝑎

ℒCP=𝛼𝑠

8𝜋 Θ𝐺𝑎~𝐺𝑎→

α s8π (Θ− 𝑎(𝑥)

𝑓 𝑎 )⏟𝐺𝑎

~𝐺𝑎

Periodic variable (angle)

Φ=𝑓 𝑎+𝜌 (𝑥 )

√2𝑒

𝑖𝑎 (𝑥 )𝑓 𝑎


From Standard Model to Invisible Axions

Standard Model“Standard Axion”

Weinberg 1978, Wilczek 1978

Invisible AxionKim 1979, Shifman,Vainshtein, Zakharov 1980,Dine, Fischler, Srednicki 1981Zhitnitsky 1980

All Higgs degrees of freedom are used up

• Peccei-Quinn scale

fa = fEW

(electroweak scale)

• Two Higgs fields, separately giving mass to up-type quarks and down-type quarks

• Additional Higgs with

fa ≫ fEW

• Axions very light and and very weakly interacting

No room for Peccei-Quinn symmetry and axions

Standard axion quicklyruled out experimentally

• New scale required• Axions can be cold dark matter• Can be detected


Simplest Invisible Axion: KSVZ Model

Ingredients: Scalar field , breaks U(1)PQ spontaneously Very heavy colored quark with coupling to , provides term

Invariant under chiral phase transformations (Peccei Quinn symmetry) , , Mexican hat potential , expand fields as

Low-energy Lagrangian, where Lowest-order interaction term induces term

Couples axion to QCD sector


Axion Properties

Mass (generic)

Nucleon coupling (axial vector)

Electron coupling (optional)

Gluon coupling (generic)

Photon coupling

Pion coupling

N

Na

e

ea

aG

G

g

ga

a

pp

p

𝐿𝑎𝐺=𝛼𝑠

8 𝜋 𝑓 𝑎𝐺~𝐺𝑎

𝑚𝑎=√𝑚𝑢𝑚𝑑

𝑚𝑢+𝑚𝑑

𝑚𝜋

𝑓 𝜋 𝑓 𝑎≈ 6𝜇 eV𝑓 𝑎/1012GeV

𝐿𝑎𝜋=𝐶𝑎 𝜋

𝑓 𝜋 𝑓 𝑎¿

𝐿𝑎𝑁=𝐶𝑁

2 𝑓 𝑎Ψ 𝑁𝛾

𝜇𝛾 5Ψ 𝑁 𝜕𝜇𝑎

𝐿𝑎𝑒=𝐶𝑒

2 𝑓 𝑎Ψ 𝑒𝛾

𝜇𝛾5Ψ 𝑒𝜕𝜇𝑎


High- and Low-Energy Frontiers in Particle Physics

1027eV

Planckmass

GUTscale

Electroweakscale

QCDscale

Cosmologicalconstant

10241021101810151012109106103110− 310− 6

𝑚𝐷𝑚𝐷2 /𝑀 𝑀

Heavy right-handedneutrinos(see-saw mechanism)

WIMP dark matter(related to EW scale, perhaps SUSY)

Axion dark matter (related to Peccei-Quinn symmetry)

𝑓 𝑎𝑚𝜋 𝑓 𝜋 / 𝑓 𝑎 𝑚𝜋 , 𝑓 𝜋


Sanduleak -69 202Sanduleak -69 202

Large Magellanic Cloud Distance 50 kpc (160.000 light years)

Tarantula Nebula

Supernova 1987A23 February 1987


Supernova 1987A Energy-Loss Argument

SN 1987A neutrino signal

Late-time signal most sensitive observable

Emission of very weakly interactingparticles would “steal” energy from theneutrino burst and shorten it.(Early neutrino burst powered by accretion, not sensitive to volume energy loss.)

Neutrino diffusion

Neutrinosphere

Volume emission of new particles


SN 1987A Axion Limits

Excluded

Neutrino diffusion

Neutrino diffusion

Volume emission of new particles

Free streaming Trapping

Axiondiffusion


Axion Bounds and Searches

Directsearches

Too much CDM (misalignment)

TelescopeExperiments

Globular clusters(a-g-coupling)

SN 1987AToo many events

Too muchenergy loss

Too muchhot dark matter

CAST ADMX(Seattle & Yale)

103 106 109 1012 [GeV] fa

eVkeV meV meVmaneV

1015

Globular clusters (helium ignition)(a-e coupling)

Too much cold dark matter(re-alignment with Qi = 1)

Classicregion

Anthropicregion


Do White Dwarfs Need Axion Cooling?

Isern et al., arXiv:1204.3565

White dwarf luminosity function(number of WDs per brightness interval)No axions

With axion cooling( near SN1987A limit)


CP-Violating Forces

bulk bulk bulk spin spin spin𝑎 𝑎 𝑎Tests of Newton’s law& equivalence principle:Scalar axion coupling

Torsion balance usingpolarized electron spinsAxion couplings T-violating force

Spin-spin forceshard to measure Axion couplings

𝑔𝑠𝑁 𝑔𝑠

𝑁 𝑔𝑠𝑁 𝑔𝑝

𝑒 𝑔𝑝𝑒 𝑔𝑝

𝑒


Limits on CP Violation from Long-Range Forces

Assume axion scalar CP-violatingforce with nucleons

Eöt-Wash constraint provides bestlimit around [Hoedl et al. PRL 106 (2011) 041801]

Raffelt, arXiv:1205.1776


Long-Range Force ExperimentsLong-range force limits from tests ofNewton’s law and equivalence principle(Mostly from Eöt-Wash Group, Seattle)

Limits from long-range limits times astrophysical limits, compared withdirect constraints

bulk bulk bulk spin𝑎 𝑎

Torsion+astro

Torsion(bulk-spin)

Raffelt, arXiv:1205.1776 Raffelt, arXiv:1205.1776


Searching for Solar Axions

Searching forAxion-Like Particles


Axion and Relatives

Axions (1 parameter or )- Solve strong CP problem- Could be dark matter

String axions (almost massless pseudoscalars in string theory)Need not solve CP problem

Axion-like particles (ALPs)Generic two-photon vertex(2 parameters and )

Hidden photonsLow-mass gauge boson from U’(1)(Parameters: kinetic mixing, mass)

WISPs (Weakly Interacting Slim Particles)


Parameter Space for Axion-Like Particles (ALPs)

𝜋η

𝑎WW

Invisibleaxion (DM)

Axion Line 𝝉𝒂→

𝟐𝜸 =𝝉U


Experimental Tests of Invisible Axions

Primakoff effect:

Axion-photon transition in externalstatic E or B field(Originally discussed for by Henri Primakoff 1951)

Pierre Sikivie:

Macroscopic B-field can provide alarge coherent transition rate overa big volume (low-mass axions)• Axion helioscope: Look at the Sun through a dipole magnet• Axion haloscope: Look for dark-matter axions with A microwave resonant cavity


Search for Solar Axions

g a

Sun

Primakoff production

Axion Helioscope(Sikivie 1983)

gMagnet S

Na

Axion-Photon-Oscillation

Tokyo Axion Helioscope (“Sumico”) (Results since 1998, up again 2008) CERN Axion Solar Telescope (CAST) (Data since 2003)

Axion flux

Alternative technique: Bragg conversion in crystal Experimental limits on solar axion flux from dark-matter experiments (SOLAX, COSME, DAMA, CDMS ...)


CAST at CERN


Recent “shining-light-through-a-wall” or vacuum birefringence experiments:• ALPS • BMV • BFRT• GammeV • LIPPS • OSQAR • PVLAS

Photon Regeneration ExperimentsEhret et al. (ALPS Collaboration), arXiv:1004.1313

(DESY, using HERA dipole magnet) (Laboratoire National des Champs Magnétiques Intens, Toulouse) (Brookhaven, 1993) (Fermilab) (Jefferson Lab) (CERN, using LHC dipole magnets) (INFN Trieste)


Shining TeV Gamma Rays through the Universe

Figure from a talk by Manuel Meyer (Univ. Hamburg)


Parameter Space for Axion-Like Particles

𝜋η

𝑎WW

Invisibleaxion (DM)


𝟐𝜸 =𝝉U

𝜋η

𝑎WW

Invisibleaxion (DM)


𝟐𝜸 =𝝉U

HBStars 𝜋η

𝑎WW

Invisibleaxion (DM)


𝟐𝜸 =𝝉U

HBStars

CASTSolar Axions 𝜋η

𝑎WW

Invisibleaxion (DM)


𝟐𝜸 =𝝉U

HBStars

LaserExperiments

CASTSolar Axions

TeV g rays

How

to m

ake

prog

ress

?


Next Generation Axion Helioscope (IAXO) at CERN

• Irastorza et al.: Towards a new generation axion helioscope, arXiv:1103.5334• Armengaud et al.: Conceptual Design of the International Axion Observatory (IAXO), arXiv:1401.3233

Need new magnet w/– Much bigger aperture: per bore– Lighter (no iron yoke)– Bores at Troom



Neutrinos 0.1-2%

Dark Matter~20%


Axions as Cold Dark Matter of the Universe


Creation of Cosmological Axions (very early universe)

• UPQ(1) spontaneously broken• Higgs field settles in “Mexican hat”• Axion field sits fixed at

𝑎

𝑉 (𝑎)

𝑎

𝑉 (𝑎)

Θ=0

( eV)• Axion mass turns on quickly by thermal instanton gas• Field starts oscillating when • Classical field oscillations (axions at rest)

Axions are born as nonrelativistic, classical field oscillationsVery small mass, yet cold dark matter


Axion Cosmology in PLB 120 (1983)


Cosmic Axion DensityModern values for QCD parameters and temperature-dependent axion massimply (Bae, Huh & Kim, arXiv:0806.0497)

If axions provide the cold dark matter:

• implies GeV and meV (“classic window”)

• GeV (GUT scale) or larger (string inspired) requires (“anthropic window”)

Ω𝑎h2=0.195Θi

2( 𝑓 𝑎

1012 GeV )1.184

=0.105Θi2( 10𝜇eV

𝑚𝑎 )1.184

Θi=0.75( 1012 GeV𝑓 𝑎

)0.592

=1.0 ( 𝑚𝑎

10𝜇eV )0.592


Cold Axion Populations

Case 2Reheating restores PQ symmetry

• Cosmic strings of broken UPQ(1) form by Kibble mechanism• Radiate long-wavelength axions• independent of initial conditions• or else domain wall problem

Inhomogeneities of axion field large,self-couplings lead to formation of mini-clustersTypical properties• Mass • Radius cm• Mass fraction up to several 10%

Case 1Inflation after PQ symmetry breaking

Homogeneous mode oscillates after Dependence on initial misalignmentangle

• Isocurvature fluctuations from large quantum fluctuations of massless axion field created during inflation• Strong CMB bounds on isocurvature fluctuations• Scale of inflation required to be small

Dark matter density a cosmic randomnumber (“environmental parameter”)


Creation of Adiabatic vs. Isocurvature PerturbationsInflaton field Axion field

Slow roll

Reheating

De Sitter expansion imprintsscale invariant fluctuations

Inflaton decay matter & radiationBoth fluctuate the same:Adiabatic fluctuations

Inflaton decay radiationAxion field oscillates late matterMatter fluctuates relative to radiation:Entropy fluctuations

De Sitter expansion imprintsscale invariant fluctuations


Power Spectrum of CMB Temperature FluctuationsSky map of CMBR temperaturefluctuations

Multipole expansion

Angular power spectrum

Provides “acoustic peaks” and awealth of cosmological information

Planck

Acoustic Peaks


Adiabatic vs. Isocurvature Temperature Fluctuations

Adapted from Fox, Pierce & Thomas, hep-th/0409059


Isocurvature Forecast

Hubble scale during inflation

Axio

n de

cay

cons

tant

Hamann, Hannestad, Raffelt & Wong, arXiv:0904.0647


Axion Production by Domain Wall and String DecayRecent numerical studies of collapseof string-domain wall system

Implies a CDM axion mass of

Hiramatsu, Kawasaki, Saikawa &Sekiguchi, arXiv:1202.5851 (2012)

Remains to be confirmed,interpretation of numerical studiesnot entirely straightforward


Axion Bounds and Searches

Directsearches

Too much CDM (misalignment)

TelescopeExperiments

Globular clusters(a-g-coupling)

SN 1987AToo many events

Too muchenergy loss

Too muchhot dark matter

CAST ADMX(Seattle & Yale)

103 106 109 1012 [GeV] fa

eVkeV meV meVmaneV

1015

Globular clusters (He ignition), WD cooling(a-e coupling)

Too much cold dark matter (re-alignment with Qi = 1)

StringDW

AnthropicRange


Searching for Axion Dark Matter

Searching forAxion Dark Matter


Search for Galactic Axions (Cold Dark Matter)

Power

Frequency ma

Axion Signal

Thermal noise of cavity & detector

Power of galactic axion signal

Microwave Energies (1 GHz 4 meV)

Dark matter axions Velocities in galaxy Energies therefore

ma = 1-100 meV

va 10-3 c

Ea (1 10-6) maAxion Haloscope (Sikivie 1983)

Bext 8 Tesla

Microwave ResonatorQ 105

Primakoff Conversionga

Bext

Cavityovercomesmomentummismatch

4×10−21 W 𝑉0.22 m3 ( 𝐵

8.5 T )2 𝑄105×( 𝑚a

2 𝜋 GHz )( 𝜌𝑎

5×10−25 g / cm 3 )


Axion Dark Matter Experiment (ADMX), Seattle

Adapted from Gianpaolo Carosi


SQUID Microwave Amplifiers in ADMX

Adapted from Gianpaolo Carosi


Axion Dark Matter Searches

1. Rochester-Brookhaven- Fermilab, PRD 40 (1989) 3153

2. University of Florida PRD 42 (1990) 1297

3. US Axion Search ApJL 571 (2002) L27

4. CARRACK I (Kyoto) hep-ph/0101200

123

4

Limits assuming axions are the galactic dark matter with standard halo

KSVZ

DFSZ

ADMX-LF (Seattle) search range (2015+)


ADMX-HF at Yale (Steve Lamoreaux Group)

Design of cavity & magnet

Dilution refrigerator above & below deck

ADMX-HF will also be a test-bed for innovative concepts,e.g. thin-film superconducting cavities

Adapted from Karl van Bibber


Broadband Approaches„Focusing“ the DM signal w/ spherical reflector

Feasible above 10 GHzTOKAMAKs:- Optimize B2V factor in a radiometer mode- Good at low frequencies- Design study under way (Lobanov et al. 2013)

TOKAMAKFacility

B[T]

V[m3]

B2V[T2 m3]

ToreSupra 4 30 480JET 4 200 3200ITER 5 1200 30000MPP ASDEX 3.1 14 135TEXTOR 3.0 7 63

Microwave cavity experiment

B[T]

V[m3]

B2V[T2 m3]

ADMX 7.6 0.2 11.5

WISPDMX 1.1 0.46 0.6

Horns et al. 2013


Center for Axion and Precision Physics (CAPP)

New Institute for Basic Science (IBS), KoreaThe plan is to launch a competitive Axion Dark Matter Experiment in Korea, participate in state-of-the-art axion experiments around the world, play a leading role in the proposed proton electric-dipole-moment (EDM) experiment and take a significant role in storage-ring precision physics involving EDM and muon g–2 experiments.

15 Oct 2013

YannisSemertzidis


Oscillating Neutron EDM by Axion Dark Matter

Assume axions are galactic dark matter: 300 MeV/cm3

Independently of expect Expect time-varying neutron EDM, MHz frequency for GeV

8 orders of magnitude below limit on static EDM, but oscillates!

+𝜋−𝜋

ΛQCD4

Θ=a / f a Oscillating axion field (DM)→ Oscillating Q term→ Oscillating neutron EDM


Searching for Axions in the Anthropic Window

Graham & Rajendran, arXiv:1101.2691Budker, Graham, Ledbetter, Rajendran & Sushkov, arXiv:1306.6089

CASPEr experimentPrecise magnetometry to measuretiny deviations from Larmor frequency


Cosmic Axion Spin Precession Experiment (CASPEr)

Budker, Graham, Ledbetter, Rajendran & Sushkov, arXiv:1306.6089

Time-varying nucleon EDM caused by axion DM in Lead Titanate magnetometer

Phase I

Phase II

Magnetometer noise limit


Helmholtz Institute Mainz (HIM)

Building under construction

New institute onStructure, symmetry and stability of matter and antimatter

Dmitry BudkerMoving from Berkeley to HIM

Plans to pursue CASPEr


Dow Jones Index of Axion Physics

19771979

19811983

19851987

19891991

19931995

19971999

20012003

20052007

20092011

20130

50

100

150

200

250inSPIRE: Citation of Peccei-Quinn papers or title axion (and similar)


Pie Chart of Dark Universe


Neutrinos 0.1-2%

Dark Matter~25%


axions

Documents

mpi physics

uhiggsgeorg raffelt

gevgeorg raffelt

luminousgeorg raffelt

new ingredientsgeorg

weak interaction w

neutrino tneutrino

cp violation