Peter Graf Max-Planck-Institut Für Physik Young Scientists Workshop Wildbad Kreuth

Saxion Cosmology

Peter Graf Max-Planck-Institut für Physik Young Scientists Workshop Wildbad Kreuth

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Table of Content

• What is the Saxion? • Where does it come from? • What does it do to the Universe? • What do we learn?

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology

What is the Saxion?

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology The Strong CP Problem

• The θ-vacuum term is CP-violating g2 = θ¯ Gb Gbµν LCP 32π2 µν !

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology The Strong CP Problem

• The θ-vacuum term is CP-violating g2 = θ¯ Gb Gbµν LCP 32π2 µν • Prefactor is a sum of two independent! quantities θ¯ = θ arg det M QCD −

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology The Strong CP Problem

• The θ-vacuum term is CP-violating g2 = θ¯ Gb Gbµν LCP 32π2 µν • Prefactor is a sum of two independent! quantities θ¯ = θ arg det M QCD − • Measurements of the electric dipole moment of the neutron yield the constraint

11 θ¯ < 10− | | Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology The Peccei - Quinn solution [Peccei,Quinn, ‘77]

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology The Peccei - Quinn solution [Peccei,Quinn, ‘77] • A global chiral U(1) ensures CP conservation dynamically

• Spontaneous breaking at fPQ

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology The Peccei - Quinn solution [Peccei,Quinn, ‘77] • A global chiral U(1) ensures CP conservation dynamically

• Spontaneous breaking at fPQ Resulting Goldstone boson is the axion • 2 g b bµν PQ = 2 aGµν G L 32π fPQ !

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology The Peccei - Quinn solution [Peccei,Quinn, ‘77] • A global chiral U(1) ensures CP conservation dynamically

• Spontaneous breaking at fPQ Resulting Goldstone boson is the axion • 2 g b bµν PQ = 2 aGµν G L 32π fPQ • Axion acquires mass and restores CP!

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Supersymmetric Axions

• SUSY relates bosons and fermions

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Supersymmetric Axions

• SUSY relates bosons and fermions • Particles live in supermultiplets with equal numbers of bosonic and fermionic dof

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Supersymmetric Axions

• SUSY relates bosons and fermions • Particles live in supermultiplets with equal numbers of bosonic and fermionic dof • The PQ supermultiplet contains:

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Supersymmetric Axions

• SUSY relates bosons and fermions • Particles live in supermultiplets with equal numbers of bosonic and fermionic dof • The PQ supermultiplet contains: • Axion a (1 bosonic dof)

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Supersymmetric Axions

• SUSY relates bosons and fermions • Particles live in supermultiplets with equal numbers of bosonic and fermionic dof • The PQ supermultiplet contains: • Axion a (1 bosonic dof) • Axino ã (2 fermionic dof) • → Saxion s (1 bosonic dof) Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Properties of the Saxion

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Properties of the Saxion • Extremely weakly interacting

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Properties of the Saxion • Extremely weakly interacting • Rather heavy (compared to the axion) ...

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Properties of the Saxion • Extremely weakly interacting • Rather heavy (compared to the axion) ... - SUSY requires holomorphy of the superpotential - Turns real U(1) into complex symmetry Λ Φ e ΦΛC → ∈ - ﬂat direction for the saxion → massless [Kugo, Ojima, Yanagida, ‘84]

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Couplings

A =(s + ia)/√2+√2θa˜ + θ2F [Strumia, ‘10]

√2α = s d2θAW bW b + h.c. LPQ −8πf PQ !

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Couplings

A =(s + ia)/√2+√2θa˜ + θ2F [Strumia, ‘10]

√2α = s d2θAW bW b + h.c. LPQ −8πf PQ !

αs b bµν b b ¯b µ b PQ = s Gµν G 2D D 2ig˜ γ Dµg˜ L 8πfPQ − − ! " b bµν ¯b µ 5 b # + a Gµν G +2g˜ γ γ Dµg˜ $[γµ, γν ] & + ia˜¯ % g˜bGb +2aD˜¯ bg˜b 2 µν ' Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Couplings

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Couplings

• All couplings suppressed by 1/fPQ f 6 108 GeV [Raffelt,‘08] PQ ! ×

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Couplings

• All couplings suppressed by 1/fPQ f 6 108 GeV [Raffelt,‘08] PQ ! × • Coupling to gluons and gluinos: ga g˜a

s s ga g˜a gb g˜b b b g s g s

gc g˜c Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Couplings

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Couplings • Interaction from the kinetic term: √2x 1 1 ∂ Φ 2 = 1+ s (∂ a)2 + (∂ s)2 + ... | µ | f 2 µ 2 µ ! PQ " # $ [Chun,Lukas,‘95]

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Couplings • Interaction from the kinetic term: √2x 1 1 ∂ Φ 2 = 1+ s (∂ a)2 + (∂ s)2 + ... | µ | f 2 µ 2 µ ! PQ " # $ [Chun,Lukas,‘95] • Important for saxion decay:

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology

Where does it come from?

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Thermal Saxions

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Thermal Saxions • Saxions may reach thermal equilibrium (depends on TR and fPQ) eq eq n 3 Y = 1.2 10− s s ≈ ×

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Thermal Saxions • Saxions may reach thermal equilibrium (depends on TR and fPQ) eq eq n 3 Y = 1.2 10− s s ≈ × • If they do not, still production via scattering qi s q˜i s

q¯j ga q¯j g˜a 1.02 1010 GeV 2 T Y TP = 13.1g6 ln R s s g f 1010 GeV ! s "! PQ " ! " Peter Graf - MPP [P.G.,Steffen, in prep.] YSW, 27. July 2011 Saxion Cosmology Saxion Yield

-2 10

eq 3 Y 1.2 10− s ≈ ×

GeV GeV GeV 10 11 12 -4 10 = 10 = 10 = 10

PQ PQ PQ /s f f f s n = TP s

Y -6 10

-8 10 6 8 10 12 10 10 10 10 TR [GeV] [P.G.,Steffen, in prep.]

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxions from Coherent Oscillations

• Flat directions get lifted

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxions from Coherent Oscillations

• Flat directions get lifted • Initial value of saxion ﬁeld is random

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxions from Coherent Oscillations

• Flat directions get lifted • Initial value of saxion ﬁeld is random • Field starts to oscillate around true minimum

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxions from Coherent Oscillations

• Flat directions get lifted • Initial value of saxion ﬁeld is random • Field starts to oscillate around true minimum • Energy density from coherent oscillations

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxions from Coherent Oscillations 9 8 (fPQ, TR) = (10 , 10 ) GeV 9 9 (fPQ, TR) = (10 , 10 ) GeV 10 8 -6 (f , T ) = (10 , 10 ) GeV 10 PQ R 10 9 (fPQ, TR) = (10 , 10 ) GeV 11 8 (fPQ, TR) = (10 , 10 ) GeV -8 11 9 10 (fPQ, TR) = (10 , 10 ) GeV s Y -10 10

-12 10

-14 10 -2 2 4 10 1 10 10 ms [GeV]

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Decay

The saxion is unstable with decay width • 3 ms Γs 2 ∝ fPQ

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Decay

The saxion is unstable with decay width • 3 ms Γs 2 ∝ fPQ • Decay into axions may be dominant 2 3 x ms Γs aa = 2 → 64πfPQ

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Saxion Decay

The saxion is unstable with decay width • 3 ms Γs 2 ∝ fPQ • Decay into axions may be dominant 2 3 x ms Γs aa = 2 → 64πfPQ • Decay into gluons 2 3 αsms Γs gg = 3 2 → 32π fPQ

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology

What does it do to the Universe?

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Axions from Saxion Decay [Chun,Lukas,’84; Kawasaki,Nakayama,Senami,’08; P.G.,Steffen, in prep.]

• Decay rate into axions dominates

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Axions from Saxion Decay [Chun,Lukas,’84; Kawasaki,Nakayama,Senami,’08; P.G.,Steffen, in prep.]

• Decay rate into axions dominates • Focus on decay before BBN

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Axions from Saxion Decay [Chun,Lukas,’84; Kawasaki,Nakayama,Senami,’08; P.G.,Steffen, in prep.]

• Decay rate into axions dominates • Focus on decay before BBN • Axions contribute to relativistic energy density → ΔNν

7 T 4 ρ (T )= 1+ N ν ρ (T ), rad 8 ν T γ γ ! " γ # $ Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Extra Radiation

si = fPQ

13 TR = 10 GeV 10 c c 10 TR = 10 GeV

= 1 MeV = 10 MeV s s T T [GeV] 1011 PQ f

c CMB ∆Nν =0.26 c BBN c ∆Nν =2.29

BBN 9 N . 10 ∆ ν =330 1 102 104 ms [GeV] [P.G.,Steffen, in prep.]

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology

What do we learn?

Peter Graf - MPP YSW, 27. July 2011 Saxion Cosmology Conclusions

• PQ mechanism introduces the axion • SUSY provides ﬂat direction for the saxion • Cosmology of saxion depends on decay channels • Decay may affect BBN, blackbody of CMB, X(γ)- ray, reionization, entropy, ΔNν • Extra radiation might be hint towards saxions