TAE 2018 Javier Redondo Universidad de Zaragoza Max Planck Institute für Physik Overview
- Strong CP problem
- Axions
- Axion Dark matter
- Searching for axions in the sky in the lab Parity and Time reversal in particle physics (electroweak interactions)
P-violation (Wu 56) T-violation (CPLEAR 90’s)
R(K¯ 0 K0) R(K0 K¯ 0) ! ! R(K¯ 0 K0)+R(K0 K¯ 0) 60% ! !
40% ... but not in the strong interactions many theories based on SU(3)c (QCD) 1 ↵ = G Gµ⌫ + iq¯ µD q qmq¯ + s ✓G Gµ⌫ LQCD 4 µ⌫a a µ 8⇡ µ⌫a a q X e P,T conserving P,T violating
we tend to forget this
↵s µ⌫ ✓Gµ⌫aGa induces P and T (CP) violation ✓ 8⇡ / e ✓ ( ⇡, ⇡) infinitely versions of QCD... all are P,T violating 2 Neutron EDM
15 Most important P, T violating observable dn ✓ (10 )e cm ⇠ ⇥ O ✓ (1) ⇠ O
EDM violates P,T The theta angle of the strong interactions - The value of ✓ controls P,T violation in QCD
✓ ⇡ ⇡ 0 n n n n¯ n¯ n¯
10 Measured today ✓ < 10 | | (strong CP problem) Roberto Peccei and Helen Quinn 77 QCD vacuum energy minimised at theta = 0 - ... if ✓ ( t, x ) is dynamical field, relaxes to its minimum Energy generated by QCD!
✓ ⇡ ⇡ 0 n n¯
10 Measured today ✓ < 10 | | (strong CP problem) ain’t you forgetting something?
P. Higgs and a new particle is born ... - if ✓ ( t, x ) is dynamical field Energy generated by QCD!
✓ ⇡ ⇡ 0 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 ✓ ( t, x ) is dynamical field Energy generated by QCD!
✓ ⇡ ⇡ 0 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 Energy generated by QCD!
✓ = a/fa ⇡ ⇡ 0 ↵ 1 = s G Gµ⌫ ✓ + (@ ✓)(@µ✓)f 2 L✓ 8⇡ µ⌫a a 2 µ a e ↵s µ⌫ a 1 µ ✓ = Gµ⌫aGa + (@µa)(@ a) L 8⇡ fa 2 e How to get the axion-term? - Peccei-Quinn idea: New symmetry, spontaneously broken Goldstone theorem: Global continuous symmetry SB -> massless boson
Other terms that preserve the symmetry ✓
L
Quantum level .... If symmetry is color anomalous -> anomalous 2-gluon coupling
g ↵s µ ?+=N GG✓
JA µ L
- Peccei-Quinn symmetry, color anomalous, spontaneously broken at fa
1 µ 4 2 2 = + iQDQ¯ + (@ )(@ ⇤) (yQ¯ Q +h.c) + µ L LSM 2 µ L R | | | | a(x) i 2 (x)=⇢(x)e fa fa = µ /2 a
p f ~ 1 2 ↵s a - At energies below f a (SSB) (@a) + GG L22 8⇡ fa
0 e - At energies below ⇤ QCD , a ⌘ 0 ⇡ ⌘ ... mixing ~GeV
9 m⇡f⇡ 10 GeV axion mass ma 6meV ' fa ⇠ fa
¯ µ a ↵ µ⌫ a couplings a,I = cN,aN 5N + ca Fµ⌫ F + ... L fa 2⇡ fa XN nucleons ... photons ... e mesons ... ENERGY couplings
- Shift symmetry allows some generic types of interactions 1 ↵ = (@ ✓)(@µ✓)f 2 + c [f¯ µ f]@ ✓ E F F µ⌫ ✓ La 2 µ f 5 µ 8⇡ µ⌫ Xf 1 µ ga µe⌫ 1 a = (@µa)(@ a)+ gaf [f¯ 5f]a Fµ⌫ F a (canonically normalised) g
L 2 4
2 ↵ µ⌫ ↵s µ⌫ A 1 A 1 2 2 N heavy-Q N Gµ⌫ G ✓ Gµ⌫ G V (A) QCD = mAA 8⇡ ⌘ 8⇡ fA ⇠ 2 fA 2 n o n o ✓ ◆ e e electron coupling nucleon coupling g [¯e e]a g [N¯ N]a photon coupling ef 5 Nf 5 CP Neutron electric dipole
ga µ⌫ 1 µ⌫ A Fµ⌫ F a [Fµ⌫ n¯ 5n] 4 / mn fA FCNC e g f¯ f 0
- NGB models, hadronic, 2HDMs, families, axi-majorons…
a recent selection from arXiv:1801.08127 - Axions and axion-like particles are generic in BSM (not necessarily guaranteed!)
pseudo Goldstone Bosons stringy axions
- Global symmetry spontaneously broken - Im parts of moduli fields (control sizes)
(x)=⇢(x)ei✓(x)
- O(100) candidates in typical compactifications - masses from non-perturbative effects Axion couplings at low energy Mass 9 f⇡ 10 GeV ma m⇡ 6meV ' fa ' fa hadrons, Photons 1 1 a a fa fa
Leptons (in some models)
1 a fa
The lighter the more weakly interacting Axion Landscape
f v fa vEW a 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
Excluded Astro-hints?
Reactors Had. dec Dark Matters Axions and dark matter
- axion field relaxes to minimum & oscillates (DARK MATTER!), damping due to expansion of the Universe
Potential V (✓) generated by QCD!
time
✓(t)=✓0 cos(mat) ⇡ 0 ⇡ Oscillation frequency Coherent oscillations ! = ma = Energy density (harm. oscillator) 1 1 Dark Matter Axions ⇢ = m2f 2✓2 = (75MeV)4✓2 aDM 2 a a 0 2 0 Two scenarios
- Consider axion as a Goldstone boson: exists only below spontaneous symmetry breaking (PQ symmetry)
High T phase Low T phase PQ symmetry restored PQ symmetry spontaneous broken no axion axion = Goldstone boson (angle)
- PQ breaking after inflation - PQ breaking before inflation Axion dark matter
- The amount of axion DM produced depends on f a AND on the initial conditions
After PQ phase transition, theta IC conditions large fa, small acceleration, energy stored longer Inflation after PQ phase transition... no-correlation beyond causal horizon one domain stretched beyond our horizon! V (a)
⇡fa ✓I =? V (a)
⇡fa average over initial conditions! -> prediction! but which one??? no prediction!
���� ���� ���� ���� ���� ��� ��� ��� ��� ��� �� Obs. DM density �
Scenario B ��-� Scenario A
θ θ -� i θ = i �� = i = 0.01 0.1 1 -� �� Thermal axions
��-�
��-� ��-� ��-� ��-� ��-� ��-� ��-� ��-� ��-� � �� ��� SCENARIO I (N=1): axion evolution around t1 ⇡
✓
⇡ PQ Before inflation, one patch stretched to be our Universe ⇡
our Universe ✓
One misalignment angle singled out ⇡ Axion dark matter
- The amount of axion DM produced depends on fa
large fa, small acceleration, energy stored longer V (a) ���� ���� ���� ���� ���� ��� ��� ��� ��� ��� ⇡f �� a Obs. DM density � V (a) Scenario B ��-� Scenario A
θ θ -� i θ ⇡f �� = i = i a = 0.01 0.1 1 -� �� Thermal axions
��-�
��-� ��-� ��-� ��-� ��-� ��-� ��-� ��-� ��-� � �� ��� 2 What value of f a for ⌦ cdm h =0 . 12 ?
Dark Matter huge parameter space!
✓ 1 - AxionI ⌧ DM scenarios
✓ O(1) ⇡ I ⇠ ⇠ Excluded (too much DM) ok sub Excluded by Lab+Astro
- Less minimal axion models have further possibilities .... SCENARIO I, N=1
↵ = s G Gµ⌫ ✓ L✓ 8⇡ µ⌫a a ⇡fa ⇡fa ✓ ( ⇡, ⇡) 2 e SCENARIO I, N>1, Domain Walls stable-> cosmological disaster
↵s µ⌫ In some axion models, the Goldstone is ✓ g ( ⇡ , ⇡ ) but the anomaly leads to ✓ = Gµ⌫aG ✓gN 2 L 8⇡ a
-> the axion field is defined ✓ = ✓ g N up to Npi and has thefore N degenerate (CP conserving) minimae
N⇡fa N⇡f a SCENARIO I, N=1
a = N✓ fa ⇡f ⇡fa a
SCENARIO I, N>1, break slightly degeneracy (but tuning...)
⇡f ⇡fa a 2 What value of f a for ⌦ cdm h =0 . 12 ?
Dark Matter huge parameter space!
✓ 1 - AxionI ⌧ DM scenarios
✓ O(1) ⇡ I ⇠ ⇠ Excluded (too much DM) ok sub Excluded by Lab+Astro
Excluded (too much DM) ? tuned
- Less minimal axion models have further possibilities .... Most important constraints I
- PQ breaking after inflation -> DM inhomogeneous, Axion miniclusters DM density contrast DM density ~ 0.1 comoving pc
12 Mass ~ M 10 M ⇠ 7 Merging to heavier masses? 10 M ? Microlensing
DM minicluster fraction <0.1
Marsh 1701.04787 Scenario I Length scales
- Time scale 1 3H(T1)=ma(T1) t1 ⇠ 2H1 - Horizon size (shorter wavelengths decay)
1 L1 =2t1 ⇠ H1
11 - Full Axion DM in this model fa 10 GeV ⇠
1011GeV 0.16 T 1.5 GeV 1 ⇠ f ✓ a ◆ - Horizon scale at t1 L 104 AU (comoving) ⇠ - Mass scale in L-cube 12 M 10 M ⇠ today corresponds to distances ~ Oort cloud 3 D energy density
⇢ ⇢ = h i > 10 ⇢ h i
- axion miniclusters - axitons (axion stars in core) Minicluster size frozen ~1 GeV z~1.7x10^13 size expands with the Universe
local ⇢m = ⇢r collapse z zeq ⇠ MR z~1000
today z~O(1)
They expand with the Universe until ~ Matter-radiation equality (z~1000) L (1)A.U. ⇠ O A picture
axion “stars” instability line 5
... miniclusters 0
-5
-10 braaten unstable “dense stars”
-20 -15 -10 -5
Braaten 2016 Visinelli 2017 JR work in progress ... Most important constraints II
- PQ breaking after inflation - PQ breaking before inflation -> DM inhomogeneous, Axion miniclusters * Axion fluctuations during inflation -> CMB isocurvature DM density contrast DM density ~ 0.1 comoving pc
12 - Planck sees no Isocurvature fluctuations, strong limit! Mass ~ M 10 M d n d a2 H2 H2 a I I 10 ⇠ 7 Piso = h i h 2 i = 2 2 = 2 2 2 < 0.039Ps =0.88 10 Merging to heavier masses? 10 M ? na ⇠ aI ⇡ aI ⇡ fa ✓I ⇥ ���� Microlensing ��� ��� Depends on Hubble rate ��� ��� 1%DM ��� ���
during inflation ... HI ��� ���
��� ��� ��� 10%DM ��� ��� ���
��� ���
�� �� DM minicluster fraction <0.1 � 100%DM �
��-� ��-� ��-� ��-�
- If H I is measured by next generation CMB Polarisation Marsh 1701.04787 axion DM is excluded (avoided in some models)