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 The strong CP problem 2 The Peccei-Quinn mechanism and the axion 3 Experimental search for axions 4 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 Strong CP problem 1 The strong interaction is surprisingly symmetric under parity transformations Dark matter → Kálmán’s talk 2 27 % of the energy density of the universe consists of some form of 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: A a gluons: µ , a = 1 , . . . , 8 quarks: ψ , 3 ( color ) × 4 ( spin ) × 6 ( flavor ) components L QCD = − 1 + ψ ( iD µ γ µ − m ) ψ 4 G a µν G a µν , � �� � � �� � pure gauge part fermionic part where G a µν = ∂ µ A a ν − ∂ ν A a µ + gf abc A b µ A c field strength ν λ a gives quark–gluon D µ = ∂ µ + gA a covariant derivative − → µ 2 i interaction Sándor Katz Axion cosmology
Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions Quantum Chromodynamics (2) L QCD is invariant under local gauge transformations: G ( x ) A µ ( x ) G ( x ) † − i A ′ g ( ∂ µ G ( x )) G ( x ) † µ ( x ) = ψ ′ ( x ) = G ( x ) ψ ( x ) ′ ( x ) ψ ( x ) G † ( x ) ψ = 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: � [ d ψ ] [ d ψ ] [ d A µ ] O 1 ( x 1 ) · · · O n ( x n ) e iS [ ψ,ψ, A µ ] � 0 | T [ O 1 ( x 1 ) · · · O n ( x n )] | 0 � = � [ d ψ ] [ d ψ ] [ d A µ ] e iS [ ψ,ψ, A µ ] e iS oscillates − → hard to evaluate integrals. Wick rotation: t → − it analytic continuation to Euclidean spacetime. e iS − → e − S E , where = ⇒ � 1 � � � µν + ψ ( D µ γ µ + m ) ψ d 4 x L E = d 4 x 4 G a µν G a S E = 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? 32 π 2 ǫ µνρσ G a Θ µν G a ρσ = Θ · q term is allowed An additional � d 4 x q ( x ) is integer This term is topological, Q = Violates P → it would lead to a non-vanishing neutron EDM Experimental constrain: | Θ | < ∼ 10 − 10 Possible solutions m u = 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 = f a Θ , where f a is the symmetry breaking scale V eff (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 2 χ Θ 2 + . . . expansion: V eff (Θ) = 1 a a 2 + . . . where χ = T χ or for the axion: V eff ( a ) = 1 V � Q 2 � is the f 2 2 topological susceptibility The axion mass is m 2 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) Ψ L Ψ R + Φ ∗ ¯ L = ∂ µ Φ ∗ ∂ µ Φ + V (Φ ∗ Φ) + Φ¯ Ψ R Ψ L + ¯ Ψ D ( A )Ψ + L QCD where Ψ is a heavy ( m ∼ f A ) fermion with color charge Φ = ( f A + r ) e i Θ Φ has a vev of f A ; Simultaneous (chiral) U ( 1 ) rotations of Φ and Ψ L = ( f A + r ) 2 ∂ µ Θ ∂ µ Θ + ∂ µ r ∂ µ r + V (( f A + r ) 2 ) + ( f A + r )¯ ΨΨ + +¯ Ψ D ( A )Ψ + i Θ q + ∂ µ Θ¯ Ψ γ 5 γ µ Ψ + L QCD Integrating out Ψ and radial component leads to L = f 2 A ∂ µ Θ ∂ µ Θ + i Θ q + ∂ µ Θ · ( . . . ) + L QCD The axion is a = f A Θ If Θ QCD � = 0 then Θ → Θ + Θ QCD Sándor Katz Axion cosmology
Introduction The strong CP problem The Peccei-Quinn mechanism and the axion Experimental search for axions one can find the effective potential for Θ by integrating out all other fields for constant Θ this only contains moments of the topological � q ( x ) d 4 x charge Q = e − V Z (Θ) T V eff = Z (Θ= 0 ) = � e iQ Θ � � Q Z Q � O � Q for any gauge observable � O � = Z at high T only Q = 0 , ± 1 contributes for O = Q 2 we get χ = T V < Q 2 > = 2 T Z 1 V Z using O = e iQ Θ we get V eff = χ ( T )( 1 − cos (Θ)) = f 2 A m 2 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: α 1 m Ψ � F µν − aF µν ˜ a · ( ¯ i Ψ γ 5 Ψ) L = · · · − C A γ C A Ψ 8 π f A f A Ψ Here the C ’s are model dependent dimensionless couplings. E.g. for the KSVZ axion C A γ = − 1 . 92 and C Ap = − 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 5 th 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 β P , β R factors no observation yet, only limits on g a γ Sándor Katz Axion cosmology
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