axions - physics.smu.edu · the axion dark matter scenario peccei-quinn symmetry breaks at t ~...

CTEQ 2006 Summer School – Rhodes, Greece G. K. Fanourakis - Demokritos

AxionsIn QCD and Cosmology

George K. FanourakisInstitute of Nuclear Physics – NCSR ‘Demokritos’


Outline

• The U(1)A Problem of QCD

• The QCD Vacuum and the Strong CP Problem

• A solution: U(1)PQ and Axions

• Invisible Axion Models

• Cosmological implications

• Experimental techniques

• The CERN Axion Solar Telescope (CAST)

• Concluding Remarks


( ) aaN

n

nn

aa

n GGmtAgiL µνµν

µµ

µµ ψγγψ

4

1

1

−−−∂=∑=

cb

abc

aaaAAgfAAG νµµννµµν −∂−∂=

The QCD Lagrangian density for N flavors:

are the field strength tensors of the gluon fields:

Where:

The U(1)A Problem

aAµ ,α=1,2,…,8

at are the generators of the group of rotations of the quark fields in the color space

In the 1970’s the strong interactions had a puzzling problem, becoming more clear with the development of QCD.

Defining the covariant derivative: µµµµµ ieAtieADaa −∂=−∂=

The Lagrangian becomes:

n

txi

n

aae ψψ α )(→


( ) aaN

n

nnn GGmDiL µνµν

µµ ψγψ

4

1

1

−−=∑=

The QCD Lagrangian is invariant under SU(3)c , but it has also, in the limit of mn 0, a global symmetry:

U(N)VxU(N)A

n

ti

n

a

a

e ψψα

2→n

ti

n

a

a

e ψψγα

25

→

Vector Axial Vector

U(1) axial symmetry, because the associated Noether current:

)()()( 5

, xtxxj aa

A ψγγψ µµ ≡ is an axial vector


In reality only u and d quarks are approximately zero

We expect the strong interactions to be approximately

U(2)VxU(2)A invariant

Indeed: U(2)V = SU(2)VxU(1)V = Isospin x Baryon #

Baryon# is an exact symmetry and Isospin is a good

approximate symmetry of nature

(p, n) and (π+, π-, πo) multiplets in spectrum

However the corresponding axial symmetries are not seen in the spectrum !

Reason: the SU(2)A symmetry is not preserved by the vacuum and by spontaneous breaking we get NG bosons (the pions)

BUT we have no pseudoscalar NG candidate for the spontaneous breaking of the global U(1)A symmetry

THE U(1) PROBLEM


The QCD Vacuum and the Strong CP problem

The resolution of the U(1) problem came with the deeper study of the QCD vacuum

Two CP violating terms enter the QCD Lagrangian

µνµνθ π

θα aas GGL~

8= µν

µνπα aas

m GGMArg

L~

8

)(det=

)(det MArg+= θθ

( ) µνµνµν

µνµ

µ

πθα

ψγψ aasaaN

n

nnn GGGGmDiL~

84

1

1

+−−=∑=

µνµνθ π

θαGGL s

rr ~

8⋅=


We do not observe any CP violating effects in the strong interactions the theta parameter must be very small

Indeed if we calculate the neutron electric dipole moment we get: dn ≈ 10

-16θ e·cm

Given the experimental limit: dn<0.63x10-25 e·cm

θ ≈ 10-9

Why is theta so small ?

The Strong CP PROBLEM

Why CP is conserved in Strong Interactions ?

OR


The neutron has magnetic moment The neutron may have

an electric dipole moment

Let us have a look in the neutron


A solution: U(1)PQ and Axions

Peccei and Quinn (1977) proposed the existence of a global chiral U(1)PQ quasi-symmetry, which:

•Is a symmetry of the theory at the Lagrangian level.

•Is broken explicitly by the non-perturbative effects which introduce the parameter theta.

•It is spontaneously broken.

µνµνπ

αξ GGxa

fL

a

sa

rr ~)(

8⋅=

α(x) is the axion field

fα is the axion decay constant

• A pseudo-NG boson particle appears: the axion

• The parameter theta is driven dynamically to zero.

µνµν

µµ

µµν

µν πα

ξψα

ααπθα aasaas

SM

eff

SM GGf

a

fLGGLL

~

8;

2

1~

8int +

∂+∂∂−+=


The last term in the Lagrangian provides an effective potential for the axion field

µνµνπ

αξ GGxa

fa

s

rr ~)(

8⋅

The minimum of the potential is the VEV of the axion field

0|~

8=⋅−=

∂∂

αµν

µνπα

ξα

GGf

Veff

a

s

rr

which results in:ξθ

α αf−=

Then by defining the physical axion as ααα −=phys

We get a Lagrangian with no CP violating theta parameter


αα

f

GeVeVm

710

6.0≈

The axion interacts with photons, electrons, hadrons with a strength ~ fα

-1

expanding the Veffaround its minimum α

µνµνα απ

αξ

αGG

f

Veffm

a

s

rr ~

82

2

2 ⋅∂∂

−=∂

∂=

The axion gets its mass via the instanton effects


Invisible Axion models

Initially fα was tied to the Electroweak scale and the CP breaking with the Electroweak breaking

The so-called PQWW (Peccei-Quinn-Weinberg-Wilzcek) axion was subsequently ruled out by the experiments

The realization that the axion scale can be very big (and its coupling very weak) initiated the

‘invisible axion’ models

The KSVZ (Kim-Shifman-Vainstein-Zacharov) and the DFSZ (Dine-Fischler-Srednicki-Zhitniski) models have

viable possibilities


DFSZ

• fα>> few

• Two Higgs fields and

• one scalar field.

• Fermions: carry PQ charge.

KSVZ

• fα>> few

• One Higgs field,

• one scalar field

• one exotic quark with PQ charge.

BEf

xaL

finerr

⋅−=α

αγγ π

α 710)(

36.0 BEf

xaL

finerr

⋅=α

αγγ π

α 710)(

97.0

The axion always couples with the photons


Flatness CP invariance


Leveling mechanism PQ mechanism


(Remnant) Oscillations (Halo) axions


The universe is composed of dark matter and dark energy

But we don’t know what the dark energy or what the dark matter is

Science (20 June 2003)

• A particle relic from the Big Bang is strongly implied for DM

—WIMPs ?—Axions ?

Cosmological Implications


The axion dark matter scenario

Peccei-Quinn symmetry breaks at T ~ fa ≤ 109GeV

•The axion is created, but it is massless

•A network of axion strings is created, slowly decaying into cosmic background axions

The axions acquire mass at T ~ ΛQCD

• Instanton effects ‘switch on’ and the axion gets asmall mass

• Domain walls form between the strings and the complex hybrid network annihilates into axions


Present day cold axion abundance

6/7

5

≈Ω

αα

µm

eV

axions in stellar evolution

The evolution of any star is controlled by its thermal emission. Axions can easily transport energy since they are very weakly interacting.

the ratio of the axion energy density to the critical density for closing the universe:

New energy loss channel accelerates star evolution


Axion mass window

10-(5 to 6) eV < mα < 10-(2 to 3) eV

Overclosure SN1987a

Nucleon-Nucleon Bremsstrahlung

NN NNα


Experimental Techniques

RF cavity experiments

Laser Experiments

Helioscopes

Examples: ADMX, CARRACK

Example: PVLAS

Examples: Tokyo, CAST


(Direct) Axion production and detection

)()()()()()( 21 aa kapekpeorkaZkZ +→++→+ γγ

Via the Primakoff and inverse Primakoff effect


The principle of the RF cavity experiments

Energy exchange between Galactic Halo Axions and E&M field

Galactic halo axions have speeds β=10-3

When the frequency ω=2πf of a cavity mode equals ma, galactic halo axions convert resonantly into quanta of excitation (photons) of that cavity mode (ma=4.14 meV corresponds to f =1 GHz). Very sensitive amplifiers are used to monitor the microwave cavity power (HFET, HEMT, SQUID, Rydberg atoms)


The principle of the laser experiment PVLAS

If linearly polarised light enters a birefringent medium

with its polarisation vector at 45 degrees to the axis

(field) direction, the two components of this vector,

parallel and normal to the axis, will propagate with

different velocities and become out of phase. When

exiting the medium the light polarisation state will have

changed from linear to elliptical. This causes retardation of

the real photon ellipticity.

This causes loss of photons

in the beam dichroism.

virtual production

real production


Axions are produced in the core of the sun via the Primakoff effect. Then, they travel to earth where by interacting with a transverse magnetic field they are converted into X-ray photons and detected by appropriate X-ray detectors.

The principle of Axion Helioscopes


The CERN Axion Solar Telescope (CAST)

• LHC prototype dipole magnet.

• Superconducting: Τ=1.8Κ, Ι=13,000Α.

• Β=9Τ, L=9.26m.

• ±8o vertical movement, 80ο horizontal

movement.

• 3h sun tracking daily.


Magnetic field: B = 9T

Length: L = 10m

X-ray detector requirements:

Low background rate.

Positional sensitivity.

Fiducial area ~14cm2.

Good energy resolution.

Excellent stability.

Sunrise detectors: Micromegas,CCD with focusing telescope

Sunset detector: TPC


Axion flux on Earth

solar axions - detection plan

keVcmaxionsekeV

E

GeV

g

dE

d keV

E

sec///10

1002.62205.1

481.22

110

10

−

−−

×=

Φ αγγα


Conversion probability in transverse magnetic field

224

110

12

0.926.91051.0

=Φ

−−−−

T

B

m

L

GeV

gdaycm

αγγ

X-ray flux expected in CAST (for low mass axions)

To detect higher mass axions the effective photon mass needs adjustment to retain the coherencebetween the axion and photon amplitudes along

the detection volume.

( )( )

2 2

2

2

sin / 2

2 / 2

a

a

Bg qLP L

qL

γγγ→

=


Ε=4.2 keV


The Micromegas principle as implemented at CAST


The very first Micromegas with X-Y readout

384 X-Y strips (192 X, 192 Y)

Strip width: 350µm

Readout plane and grid: made at CERN


CAST Micromesh gaseous detector

Low background materials

The operating gas is at

atmospheric pressure.

104 amplification is easily

achievable.

High field ratio: 100%

electron transparency.

No space charge effects due

to fast collection of positive

ions.

Sensitive region

Gassiplex cards

Development/construction/operation

Saclay-Demokritos-CERN

Drift space


4.5 keV photons from PANTHER + focusing telescope

1.5 mm

X

3 mm

Y


The Micromegas of CAST in action

Stable operation at < 1 Hz


Micromegas analysis

ANALYSIS STRATEGY Main background:• natural radioactivity • cosmic raysRejection based on:• micromesh pulse shape• topology of strip cluster

Tracking (1.5 h/day)Background (the rest of the time)Fe55 Calibration (once per day)

Mesh(MATACQ digitizing board)

Strips (Gassiplex)


The power of the background rejection

Trigger rate < 1 Hz

Raw data

filtered dataCu peak


Phase II CAST started October 2005

4He 74 pressure stepsma ≤ 0.26 eV/c

2

3He590 pressure stepsma ≤ 0.8 eV/c

2

Zioutas et al., PRL 94 (2005) 121301


MC created fake axion signal


The particle astrophysics approach complements accelerator-based research on the most fundamental problems in physics and cosmology.

Axions could be the main component of the dark matter.

Concluding Remarks

If the axions are discovered, a half-century long puzzle in the Standard Model will be finally put to rest.


1. ‘QCD, Strong CP and Axions’, R.D. Peccei in arXiv:hep-ph/9606475 v1 28 June 1996.

2. ‘Quantum Field Theory’, Mark Srednicki, U.C. Santa Barbara.

3. ‘Dark Matter Axions ’96’, Pierre Sikivie in arXiv:hep-ph/9611339 v1 15 November 1996.

4. ‘An Introduction to axions’, E. Daw, lecture slides, lecture 18,PHY-323.

5. ‘Searching for Dark Matter Axions’, L.J. Rosenberg & K.A. VanBibber, Beamline Magazine Fall 1997.

6. The ADMX (cavity axion search) experiment web page: http://www.phys.ufl.edu/~axion/Welcome.html

7. PVLAS experiment web page: http://www.ts.infn.it/experiments/pvlas/

8. CAST experiment web page: http://cast.web.cern.ch/CAST/

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