Dark matter & Axions! Javier Redondo (Zaragoza U. & MPP - PowerPoint PPT Presentation

Dark matter & Axions! Javier Redondo (Zaragoza U. & MPP Munich)

Overview - Strong CP problem - Axions and ALPs - Axion Dark matter - Dark matter experiments

Parity and Time reversal

in particle physics (electroweak interactions) P-violation (Wu 56) T-violation (CPLEAR 90’s) R ( ¯ K 0 → K 0 ) − R ( K 0 → ¯ K 0 ) R ( ¯ K 0 → K 0 ) + R ( K 0 → ¯ K 0 ) 60% 40%

... but not in the strong interactions

many theories based on SU(3)c (QCD) X qmq + α s L QCD = − 1 8 π θ G µ ν a e 4 G µ ν a G µ ν q γ µ D µ q − ¯ G µ ν i ¯ a + a q P,T violating P,T conserving we tend to forget this α s 8 π θ G µ ν a e induces P and T (CP) violation ∝ θ G µ ν a θ ∈ ( − π , π ) infinitely versions of QCD... all are P,T violating

Neutron EDM Most important P, T violating observable d n ∼ θ × O (10 − 15 )e cm θ ∼ O (1) EDM violates P,T

The theta angle of the strong interactions - The value of controls P,T violation in QCD θ θ − π 0 π n n n ¯ ¯ ¯ n n n Measured today | θ | < 10 − 10 (strong CP problem)

Roberto Peccei and Helen Quinn 77

any special value? - QCD vacuum energy is minimum at θ = 0 Energy density (potential) as a function of (Euclidean path integral) t → − ix 0 θ R � R � Z µ ν e d 4 x E V [ θ ] = µ e − S E [ g a d 4 x E 8 π G a G µ ν α s D g a µ ] − i θ � � e − a � � � � R Z µ ] � � µ ν e µ e − S E [ g a d 4 x E 8 π G a G µ ν α s D g a � e − i θ ≤ � � a � R Z µ e − S E [ g a d 4 xV [0] µ ] = e − D g a ≤ *we have assumed S_E does not contain P, T violation->Real In the SM, CP-violation in the CKM will propagate (three loops) and shift slightly the minimum of the potential from 0 - Potential is periodic V ( θ ) = V ( θ + 2 π ) The theta-term is a total derivative and its integral a topological index Z Z Z d 4 x α s d 4 x ∂ µ K µ = d σ µ K µ = n ∈ Z µ ν e 8 π G a G µ ν = a e iS = e iS + i 2 π

QCD vacuum energy minimised at CP conservation!! - but ... theta is a constant of the SM Energy generated by QCD! θ − π 0 π n ¯ n Measured today | θ | < 10 − 10 (strong CP problem)

beyond the SM ... - ... if is dynamical field, relaxes to its minimum θ ( t, x ) Energy generated by QCD! θ − π 0 π n ¯ n Measured today | θ | < 10 − 10 (strong CP problem will be solved dynamically!)

a new particle is born ... - if is dynamical field θ ( t, x ) Energy generated by QCD! θ − π 0 π Field Excitations around the vacuum are particles clears the strong CP problem it’s a higgslet! like my favorite soap S. Weinberg F. Wiczek

and a new particle is born ... the axion - if is dynamical field θ ( t, x ) Energy generated by QCD! θ − π 0 π Field Excitations around the vacuum are particles clears the strong CP problem it’s a higgslet! like my favorite soap

and a new scale sets the game, fa - kinetic term for requires a new scale θ Energy generated by QCD! θ = a/f a − π 0 π a θ + 1 L θ = α s 8 π G µ ν a e G µ ν 2( ∂ µ θ )( ∂ µ θ ) f 2 a + 1 L θ = α s a 8 π G µ ν a e G µ ν 2( ∂ µ a )( ∂ µ a ) a f a And we have our simplest axion model (low energy theory ... of course!)

Example: Simple model KSVZ - Peccei-Quinn global U(1) symmetry, color anomalous + spontaneously broken at f a QDQ + 1 Q L Q R σ + h . c) − λ | σ | 4 + µ 2 | σ | 2 L = L SM + i ¯ 2( ∂ µ σ )( ∂ µ σ ∗ ) − ( y ¯ σ ( x ) = ρ ( x ) e i a ( x ) p f a = µ 2 / 2 λ fa ~ f a L ∈ 1 2( ∂ a ) 2 + α s G a f a - At energies below , (also PQ scale) 8 π G e f a ~GeV a − η 0 − π 0 − η − ... - At energies below , mixing Λ QCD ⇠ 6meV10 9 GeV m a ' m π f π axion mass f a f a X N γ µ γ 5 N a F µ ν a α couplings 2 π F µ ν e c N,a ¯ L a,I = + c a γ + ... ENERGY f a f a N mesons ... nucleons ... photons ...

Axion-like particles (ALPs) Axions and axion-like particles (ALPs) appear very naturally beyond the SM pseudo Goldstone Bosons stringy axions - Global symmetry spontaneously broken - Im parts of moduli fields (control sizes) φ ( x ) = ρ ( x ) e i θ ( x ) - massless Goldstone Boson @ Low Energy shift symmetry θ ( x ) → θ ( x ) + α L kin = 1 2( ∂ µ θ )( ∂ µ θ ) f 2 - O(100) candidates in compactification - HE decay constant, f = h ρ i - “decay constant” , string scale M s - masses from non-perturbative effects - small symmetry breaking small mass

Axion couplings at low energy - From -term, axion mixes with eta’ and the rest of mesons θ + 1 L θ = α s a 8 π G µ ν a e G µ ν 2( ∂ µ a )( ∂ µ a ) a f a η 0 a 1 f a θ α s In our simple axion theory, axion interactions are all generated from µ ν e 8 π G a G µ ν a so the axion field interations will always be suppressed by 1/fa

Axion couplings at low energy Mass ' 5 . 7 meV10 9 GeV V θθ ( θ ) 1 = p χ 1 p m a = f a f a f a hadrons, Photons 1 1 a a f a f a Leptons (in some models) 1 a f a

Axion couplings at low energy Mass ' 5 . 7 meV10 9 GeV V θθ ( θ ) 1 = p χ 1 p m a = f a f a f a hadrons, Photons 1 1 a a f a f a Leptons (in some models) 1 a f a The lighter the more weakly interacting

Axion Landscape f a � v EW f a ∼ v EW Invisible models PQWW models Reactors Had. dec

Bounds and hints from astrophysics - Axions emitted from stellar cores accelerate stellar evolution - Too much cooling is strongly excluded (obs. vs. simulations) - Some systems improve with additional axion cooling! Tip of the Red Giant branch (M5) White dwarf luminosity function HB stars in globular clusters Neutron Star CAS A

Axion Landscape Reactors Had. dec

Axion Landscape Astro-hints? Excluded Reactors Had. dec

Axions and dark matter - dynamical relaxes to its minimum ... θ ( t, x ) Energy generated by QCD! time θ ( t ) = θ 0 cos( m a t ) − π 0 π Oscillation frequency Coherent oscillations ω = m a Energy density (harm. oscillator) = Cold Dark Matter Axions ρ aDM = 1 0 = 1 2 m 2 a f 2 a θ 2 2(75MeV) 4 θ 2 0

Evolution of the axion dark matter field - We move back to the very early Universe ... - Assume some random set of initial conditions ... - Let us see how the field evolves ! - fa is soooooo small, and the relevant momenta sooooo small than we neglect all interactions of the axion - The evolution of a lonely scalar field

Field evolution ✓ f a ◆ Z Z d 4 x √− g L = d 4 x √− g 2 ( ∂ µ θ )( ∂ µ θ ) − V ( θ ) + L int S = ✓ 1 ◆ Z d 4 x √− g 2( ∂ µ a )( ∂ µ a ) − V ( a/f a ) + L int = Scale factor is now R ( t ) Equations of motion δ S = 0 R 2 r 2 a + ∂ V a � 1 ✓ ◆ δ L − δ L a + 3 H ˙ ¨ ∂ a = 0 δ a = 0 δ ( ∂ µ a ) ; µ ∂ V ∂ a = χ sin θ ∼ χ θ = m 2 a a For simplicity I linearised around a=0 f a f a Fourier transform (linear equation) and modes decouple a k + k 2 R 2 a k + m 2 a k + 3 H ˙ a a k ' 0 ¨

Energy density and pressure ν = ( ∂ µ a )( ∂ ν a ) − L δ µ T µ ν ρ = 1 a ) 2 + 1 2( r a ) 2 + V ( a ) 2(˙ p = 1 a ) 2 � 1 2( r a ) 2 � V ( a ) 2(˙

Relativistic modes Again a damped oscillator (time-dependent frequency...) a k + k 2 a k + ω 2 ( t ) a k = 0 a k + 3 H ˙ ¨ a k + 3 H ˙ R 2 a k = 0 ¨ 1.0 Radiation a frozen a ( t ) ρ ∼ ρ 0 /R ( t ) 4 0.5 ρ = cons a 0 0.0 time - 0.5 0.001 0.01 0.1 1 10 100 1000 ω = R t k ∼ 1 k (This corresponds to the wavelength entering the horizon) t = 1 /H → HR ∼ k

Zero and non-relativistic modes Again a damped oscillator ω = m a a k + m 2 (SIMPLIFIED) a k + 3 H ˙ ¨ a a k ' 0 1.0 DUST-like Lambda-like a ( t ) ρ ∼ ρ 0 /R ( t ) 3 0.5 ρ = cons a 0 0.0 time - 0.5 0.001 0.01 0.1 1 10 100 1000 1 1 t 1 = 2 H ∼ m a H ∼ m a

Equation of state and speed of sound a k + ( k 2 /R 2 + m 2 ¨ a k + 3 H ˙ a ) a k ' 0 Even for NR modes, k/R << ma, the fact that axions and ALPs have non-zero momentum can be important -> field gradients oppose to compression because of the uncertainty principle leading to a “uncertainty pressure”, (sometimes called “quantum pressure” ....)

Why the axion is so COLD ? ρ ∝ 1 /R 3 ρ ∝ 1 /R 4 k RH ( ∝ 1 /R ) ρ = const . R Modes above are quite suppressed k ∼ m a R

Energy density - Energy density redshifts as matter, from the onset of oscillations H ( t 1 ) ∼ m a ✓ R 1 ◆ 3 I χ m − 3 / 2 ρ a ( t ) ∼ θ 2 ∝ θ 2 I χ a R ( t ) ◆ 3 ◆ 3 ◆ 3 ◆ 3 ✓ R 1 ✓ T 0 ✓ ✓ T 0 T 0 - dilution until today ∝ m − 3 / 2 ∼ ∼ √ H 1 m Pl ∼ √ m a m Pl a R 0 T 1 Smaller mass axions, start oscillating later, and get less diluted ... 1 t osc ∼ ρ a ( t ) m a - with χ ∝ T − n − 6+ n ρ a ( t 0 ) ∝ θ 2 4+ n I m m a t ∼ 1 a time