Axion cosmology I. Sndor Katz Institute for Theoretical Physics, - - PowerPoint PPT Presentation

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Axion cosmology I.

Sándor Katz

Institute for Theoretical Physics, Eötvös University

ELFT Summer School, Mátraháza, 2018

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Outline

1

Introduction

2

The strong CP problem

3

The Peccei-Quinn mechanism and the axion

4

Experimental search for axions

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Introduction

Let’s try and solve two important problems with a single idea

1

Strong CP problem The strong interaction is surprisingly symmetric under parity transformations

2

Dark matter → Kálmán’s talk 27 % of the energy density of the universe consists of some form

• f matter which is not visible

A hypothetical new particle, the axion which was proposed in the 70’s to solve problem #1 may also solve #2 Assuming it gives all (or most) dark matter we can put constraints on its mass We need to understand its precise coupling to quarks and gluons

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Quantum Chromodynamics (QCD)

QCD: Currently the best known theory to describe the strong interaction. SU(3) gauge theory with fermions in fundamental representation. Fundamental degrees of freedom: gluons: Aa

µ,

a = 1, . . . , 8 quarks: ψ, 3(color) × 4(spin) × 6(flavor) components LQCD = −1 4Ga

µνGaµν

• pure gauge part

+ ψ(iDµγµ − m)ψ

• fermionic part

, where Ga

µν = ∂µAa ν − ∂νAa µ + gf abcAb µAc ν

field strength Dµ = ∂µ + gAa

µ

λa 2i covariant derivative − → gives quark–gluon interaction

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Quantum Chromodynamics (2)

LQCD is invariant under local gauge transformations: A′

µ(x)

= G(x)Aµ(x)G(x)† − i g (∂µG(x)) G(x)† ψ′(x) = G(x)ψ(x) ψ

′(x)

= ψ(x)G†(x) Only gauge invariant quantities are physical. Properties of QCD: Asymptotic freedom: Coupling constant g → 0 when energy scale µ → ∞. = ⇒ Perturbation theory can be used at high energies. Confinement: Coupling constant is large at low energies. = ⇒ Nonperturbative methods are required.

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Quantum Chromodynamics (3)

Quantization using Feynman path integral:

0| T[O1(x1) · · · On(xn)] |0 =

• [dψ] [dψ] [dAµ] O1(x1) · · · On(xn) eiS[ψ,ψ,Aµ]
• [dψ] [dψ] [dAµ] eiS[ψ,ψ,Aµ]

eiS oscillates − → hard to evaluate integrals. Wick rotation: t → −it analytic continuation to Euclidean spacetime. = ⇒ eiS − → e−SE, where SE =

• d4x LE =
• d4x

1 4Ga

µνGa µν + ψ(Dµγµ + m)ψ

• positive definite Euclidean action.

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Strong CP problem

possible particle interactions are determined by symmetries The QCD Lagrangian respects Poincaré and gauge symmetries What about discrete symmetries?

C, P & T are violated by weak interactions, why should QCD respect them? An additional

Θ 32π2 ǫµνρσGa µνGa ρσ = Θ · q term is allowed

This term is topological, Q =

• d4x q(x) is integer

Violates P → it would lead to a non-vanishing neutron EDM Experimental constrain: |Θ|< ∼10−10

Possible solutions

mu = 0 → Θ becomes irrelevant (ruled out by lattice results) Spontaneous CP violation Axion

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Peccei-Quinn mechanism

Observation: − T

V log Z(Θ) has a minimum at Θ = 0

→ promote Θ to a dynamical field Elegant solution: Peccei-Quinn mechanism. Complex scalar field with a U(1) symmetric Mexican hat potential. Spontaneous symmetry breaking → axion is the (pseudo) Goldstone-boson The axion will play the role of Θ a = faΘ, where fa is the symmetry breaking scale Veff(Θ) = − T

V log Z(Θ)/Z(0) will become the effective potential

for the axion.

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Peccei-Quinn mechanism

expansion: Veff(Θ) = 1

2χΘ2 + . . .

• r for the axion: Veff(a) = 1

2 χ f 2

a a2 + . . . where χ = T

V Q2 is the

topological susceptibility The axion mass is m2

a(T) = χ(T)/f 2 a

In order to calculate axion production we need to solve the classical equations of motions for the axion (or Θ) using the above potential in an expanding universe The axion also couples to photons in a model dependent way → axions can convert to photons in a strong magnetic field → possibility of experimental detection

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Peccei-Quinn mechanism in detail

example: The KSVZ axion (Kim 1979, Shifman, Vainshtein, Zakharov 1980) L = ∂µΦ∗∂µΦ + V(Φ∗Φ) + Φ¯ ΨLΨR + Φ∗ ¯ ΨRΨL + ¯ ΨD(A)Ψ + LQCD where Ψ is a heavy (m ∼ fA) fermion with color charge Φ has a vev of fA; Φ = (fA + r)eiΘ Simultaneous (chiral) U(1) rotations of Φ and Ψ L = (fA + r)2∂µΘ∂µΘ + ∂µr∂µr + V((fA + r)2) + (fA + r)¯ ΨΨ + +¯ ΨD(A)Ψ + iΘq + ∂µΘ¯ Ψγ5γµΨ + LQCD Integrating out Ψ and radial component leads to L = f 2

A∂µΘ∂µΘ + iΘq + ∂µΘ · (. . . ) + LQCD

The axion is a = fAΘ If ΘQCD = 0 then Θ → Θ + ΘQCD

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

• ne can find the effective potential for Θ by integrating out all
• ther fields

for constant Θ this only contains moments of the topological charge Q =

• q(x)d4x

e− V

T Veff =

Z(Θ) Z(Θ=0) = eiQΘ

for any gauge observable O =

• Q ZQOQ

Z

at high T only Q = 0, ±1 contributes for O = Q2 we get χ = T

V < Q2 >= 2 T V Z1 Z

using O = eiQΘ we get Veff = χ(T)(1 − cos(Θ)) = f 2

Am2 A(T)(1 − cos(Θ))

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Experimental search for axions

Based on the review Irastorza & Redondo, Prog.Part.Nucl.Phys. 102 (2018) 89-159

The axion-gluon coupling and the derivative couplings to fermions generate effective interactions between axion-photon and axion-fermions: L = · · · − CAγ α 8π 1 fA aFµν ˜ F µν −

• Ψ

CAΨ mΨ fA a · ( ¯ iΨγ5Ψ) Here the C’s are model dependent dimensionless couplings. E.g. for the KSVZ axion CAγ = −1.92 and CAp = −0.47 These couplings provide the possibility for experimental detection

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Classification by the source of axions

Laboratory experiments (axions are produced in the lab) → light shining through wall (photon → axion → photon) → short distance 5th force (axion mediated p-p interaction) no additional model dependence Helioscopes (axions are produced in the Sun) → axions from the sun convert to photons in magnetic field axion flux depends on Sun modell Haloscopes (axions are dark matter particles) → dark matter axions convert to photons in magnetic field axion flux depends on local dark matter density

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Light shining through wall

Mueller et.al., PRD80 (2009) 072004

axions can penetrate wall and then convert back to photons. both primary and regenerated photons are amplified in cavities by βP, βR factors no observation yet, only limits on gaγ

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Overview of LSW experiments

Experiment status B (T) L (m) Input power (W) βP βR gaγ[GeV−1] ALPS-I completed 5 4.3 4 300 1 5×10−8 CROWS completed 3 0.15 50 104 104 9.9×10−8 OSQAR

• ngoing

9 14.3 18.5

• 3.5×10−8

ALPS-II in preparation 5 100 30 5000 40000 2×10−11 ALPS-III concept 13 426 200 12500 105 10−12 STAX1 concept 15 0.5 105 104

• 5×10−11

STAX2 concept 15 0.5 106 104 104 3×10−12 Irastorza & Redondo, Prog.Part.Nucl.Phys. 102 (2018) 89-159

ma(eV) 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 |gaγ|(GeV−1) 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 CAST ALPS-II ALPS-III STAX1 STAX2

T hints HB hint

OSQAR ALPS-I CROWS PVLAS

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Helioscopes

MAGNET COIL MAGNET COIL

B field A L

Solar axion flux

γ

X-ray detectors Shielding X-ray optics Movable platform

1 2 3 4 5 6 7 8 9 10 0.5 1 1.5 2 2.5 3

E keV dΦ dE 1020keV1year1 m2 Irastorza et.al., JCAP 1106 (2011) 013. IAXO collaboration,Tech.Rep.CERN-SPSC-2013-022.SPSC-I-242

dominantly Primakoff conversion of plasma photons into axions axion spectrum can be estimated (also including other processes with electrons)

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Overview of helioscope experiments

Experiment status B (T) L (m) A (cm2) focusing gaγ · 1010 GeV Brookhaven past 2.2 1.8 130 no 36 SUMICO past 4 2.5 18 no 6 CAST

• ngoing

9 9.3 30 partially 0.66 TASTE concept 3.5 12 2.8×103 yes 0.2 BabyIAXO in design ∼2.5 10 2.8×103 yes 0.15 IAXO in design ∼2.5 22 2.3×104 yes 0.04 Irastorza & Redondo, Prog.Part.Nucl.Phys. 102 (2018) 89-159

ma(eV) 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 |gaγ|(GeV−1) 10−13 10−12 10−11 10−10 10−9

QCD axion models

CAST BabyIAXO

IAXO

IAXO+ ALPSII

HESS T Hint SN1987A Fermi SN prospects Fermi NG1275 KSVZ HB

AMELIE HB hint

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Haloscopes

Dark matter axions detected by their coupling to various particles local dark matter density is not well known: ρ = 0.2 − 0.56 GeV cm−3 J. Read,J.Phys. G41 (2014) 063101 Various techniques

cavities: aγ coupling, photon conversion + resonant amplification dish antennas/dielectric haloscope: aγ coupling, photon conversion in large volume + amplification using dielectric layers netron EDM oscillation: aN coupling atomic transitions: ae coupling. Zeeman effect can be used to split ground state level to become resonant with the axion mass.

Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Comparison of cavity experiment results

HAYSTAC coll., Phys.Rev. D97 (2018) no.9, 092001 Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Overview of haloscope results

ma(eV) 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 |Caγ|˜ ̺1/2

a

10−1 1 10 102 103

CAST

BabyIAXO IAXO

Axion models

KSVZ BNL+UF

KLASH

ADMX

HAYSTAC ACTION / IAXO-DM ORGAN

ADMX CAPP

MADMAX ABRACADABRA / DM-Radio

Irastorza & Redondo, Prog.Part.Nucl.Phys. 102 (2018) 89-159 Sándor Katz Axion cosmology

Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions

Current experimental constraints on the axion

ma(eV) 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 |gaγ|(GeV−1) 10−17 10−16 10−15 10−14 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6

A x i

• n

m

• d

e l s ALPS-II

Helioscopes

IAXO

Laboratory Haloscopes

KSVZ Telescopes HB

Irastorza & Redondo, Prog.Part.Nucl.Phys. 102 (2018) 89-159 Sándor Katz Axion cosmology