Axions and saxions from the primordial supersymmetric plasma and extra radiation signatures [P.G.,Steffen, arXiv:1208.2951] Peter Graf Max-Planck-Institut für Physik DESY Theory Workshop 2012 “Lessons from the first phase of the LHC” Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Table of Content • Origin of the saxion • Couplings and decay rates • Additional radiation from saxion decay • Conclusion Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Origin of the saxion Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 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 10 θ¯ < 10− | | Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 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 DESY Theory Workshop 2012, 27. September 2012 Supersymmetric version • Two more particles: axino and saxion • Saxion mass: - SUSY requires superpotential to be holomorphic - Turns real U(1) into a complex symmetry Λ Φ e ΦΛC → ∈ - flat direction makes saxion massless [Kugo, Ojima, Yanagida, ‘84] - SUSY breaking gives saxion a mass Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Coupling and decay rates Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Saxion Couplings A =(σ + ia)/√2+√2θa˜ + FAθθ √2α = s d2θAW bW b + h.c. LPQ −8πf PQ ! α int = s σ Gbµν Gb 2DbDb 2ig˜¯b γµD g˜b LPQ 8πf µν − − M µ M PQ ! " bµν b ¯b µ 5 b # +a G Gµν +2g˜M γ γ Dµg˜M $ [γµ, γν ] & ia˜¯ % γ5g˜b Gb +2a˜¯ Dbg˜b − M 2 M µν M M ' Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Models of PQ sector • Focus on hadronic models • SM-singlet PQ fields ϕi with charges qi and VEVs vi • Near the VEVs the scalar part can be written as qi(σ + ia) φi = vi exp ! √2vPQ " Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Saxion coupling to axions N kin µ = ∂ φ ∂ φ∗ LPQ i µ i i=1 ! 2 N v q 2q σ = i i (∂ a)2 +(∂ σ)2 exp i √ µ µ √ i=1 " 2vPQ # " 2vPQ # ! $ % √2x 1 2 1 2 1+ σ (∂µa) + (∂µσ) + ... ∼ " vPQ # 2 2 & ' [Chun,Lukas,‘95] 3 2 2 2 qi vi vPQ = vi qi x = v2 ! i i PQ " ! Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Relation of two PQ scales • Kinetic term defines vPQ • Effective interaction defines fPQ • Relation via quark loop from superpotential: hΦ1QLQ¯R a int hv1αs bµν b = aG Gµν L 8π√2mQvPQ Q ! g g fPQ = √2vPQ [P.G.,Steffen, arXiv:1208.2951] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Saxion Decay The saxion is unstable with decay width • 3 mσ Γσ 2 ∝ fPQ • Decay into axions may be dominant 2 3 2 3 x mσ x mσ Γσ aa = 2 = 2 → 64πvPQ 32πfPQ • Decay into gluons 2 3 αsmσ Γσ gg = 3 2 → 16π fPQ Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Additional radiation from saxion decay Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Additional radiation • Radiation content of the Universe: 7 T 4 ρ (T )= 1+ N ν ρ (T ) rad 8 eff T γ ! " # $ • Extra radiation parametrized by dec Neff = 3 + ∆Neff T ! Tν dec Neff =3.046 + ∆Neff T ! Tν Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Axions from saxion decay • If all of extra rad are non-thermal axions ... 120 NTP ∆Neff(T )= 2 4 ρa (T ) 7π Tν • ... that come from saxion decays: 1/3 NTP mσ g S(T ) T eq/TP ρa (T )= ∗ 2Yσ s(T ) 2 g S(Tσ) Tσ ! ∗ " [Chang, Kim, ’96; Takahashi et al. ’07; Kawasaki et al., ’08; ] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Thermal Saxions Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Thermal Saxions • Saxions may reach thermal equilibrium (depends on TR and fPQ) eq eq n 3 Y = 1.2 10− σ s ! × Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Thermal Saxions • Saxions may reach thermal equilibrium (depends on TR and fPQ) eq eq n 3 Y = 1.2 10− σ s ! × • If they do not, still production via scattering q˜i σ q˜i σ ¯ q˜j ga q¯j g˜a 11 2 TP 3 6 1.01 10 GeV TR Y 1.33 10− g ln σ ! × s g f 108 GeV [P.G.,Steffen, arXiv:1208.2951] ! s "! PQ " ! " Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Additional radiation at BBN and CMB/LSS Theoretical BBN prediction done with PArthENoPE Data p.m./mean upper limit Yp + [D/H]p 0.76 < 1.97 (3σ) [Izotov, Thuan, ’10; Pettini et al., ’08] Yp + [D/H]p 0.77 < 3.53 (3σ) [Aver et al., ’10; Pettini et al., ’08] CMB + HPS + HST 1.73 < 3.59 (2σ) [Hamann et al., ’10] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Extra radiation: limits on saxions 1012 1012 10 TR = 10 GeV c 10 TR = 10 GeV = 1 MeV σ = 1 MeV T = 10 MeV σ T c 11 σ 11 10 T 10 c c N p.m. c (∆ eff)IT =076 c ∆N =0.26 c N p.m. eff (∆ eff)Av =077 c c ∆Neff =1.73 [GeV] [GeV] 10 3σ 10 PQ N . PQ 10 (∆ eff)IT =197 10 ∆Neff =3.59 f f (∆N )3σ =3.53 c eff Av c = 10 MeV 8 TR = 10 GeV T 8 σ R = 10 GeV T BBN CMB/LSS 109 109 0.1 1 10 102 103 104 0.1 1 10 102 103 104 mσ [GeV] [P.G.,Steffen, arXiv:1208.2951] mσ [GeV] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 TR upper limits 1012 12 GeV = 10 PQ f 12 GeV c ∆Neff =3.59 c = 10 fPQ 1010 c [GeV] 11 GeV GeV R = 10 11 T = 10 c fPQ fPQ 8 10 c ∆Neff =0.26 10 GeV = 10 fPQ 106 0.1 1 10 102 103 104 mσ [GeV] [P.G.,Steffen, arXiv:1208.2951; compare to: Kawasaki et al., ’08] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 TR limits (gravitino LSP) 1012 12 GeV = 10 PQ f 12 GeV c ∆Neff =3.59 c = 10 fPQ 1010 c [GeV] 11 GeV GeV R = 10 11 T = 10 c fPQ fPQ 8 10 c ∆Neff =0.26 10 GeV = 10 fPQ 106 0.1 1 10 102 103 104 [Pradler, Steffen, ’07] mσ [GeV] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 TR limits (gravitino LSP) 1012 12 GeV = 10 PQ f 12 GeV c ∆Neff =3.59 c = 10 fPQ 1010 c [GeV] 11 GeV GeV R = 10 11 T = 10 c fPQ fPQ 8 10 c ∆Neff =0.26 10 GeV = 10 fPQ 106 0.1 1 10 102 103 104 mσ [GeV] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 TR limits (gravitino LSP) 1012 12 GeV = 10 PQ f 12 GeV Gravitino LSP c ∆Neff =3.59 c = 10 • fPQ 1010 constraints are severe c [GeV] 11 GeV GeV R = 10 11 For mG ≃ 10 GeV, T = 10 c fPQ • fPQ 8 8 TR ≃ 10 GeV, 10 c ∆Neff =0.26 10 fPQ ≃ 3·10 GeV: 10 GeV = 10 fPQ ΔNeff ≃ 1 106 0.1 1 10 102 103 104 mσ [GeV] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 TR limits (gravitino NLSP) 1012 Light axino LSP 12 GeV • = 10 PQ f 12 GeV c ∆Neff =3.59 c = 10 10 fPQ For mG ≃ 100 GeV, 10 • 10 c TR ≃ 10 GeV, [GeV] 11 GeV GeV R = 10 11 12 T = 10 c fPQ fPQ fPQ ≃ 10 GeV: 8 c ∆ =026 10 Neff . ΔNeff ≃ 1 (saxions) 10 GeV = 10 ΔNeff ≃ 0.6 (gravitino) fPQ [Hasenkamp, ’12] 106 Axion CDM 0.1 1 10 102 103 104 • mσ [GeV] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Axion energy density 1 2 • Three different ΩCDMh populations: 10-2 c MIS 2 Ωa h -4 NTP 2 Thermally produced / Ωa h • 10 c ∆N =3.59 2 eff h thermal relics a ∆Neff =1.73 Ω =1 -6 θi 10 ∆Neff =0.26 c Non-thermal from Ωeq/TPh2 • .1 a =0 θi -8 T saxion decay T R 10 R = 10 = 10 10 8 GeV .01 GeV =0 Misalignment θi • 10-10 108 109 1010 1011 1012 fPQ [GeV] [P.G.,Steffen, arXiv:1208.2951] Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Conclusions • PQ mechanism introduces the axion • SUSY provides flat direction for the saxion • Production via scattering processes • Axions from saxion decay constitute extra radiation • Extra radiation might be hint towards saxions • Planck results will help to clarify Peter Graf - MPP DESY Theory Workshop 2012, 27. September 2012 Saxions non-relativistic at decay? • Saxions are non-relativistic, if 1/3 g S(Tσ) Tσ p(Tσ) = p(TD) ∗ mσ ! " ! " g S(TD) TD # ! ∗ " • This translates into 1/2 1/3 fPQ 7 mσ g S(Tσ) ∗ 8.4 10 GeV 1/4 x ! × 1 GeV g (Tσ) ! " ∗ Peter Graf - MPP DESY Theory Workshop 2012, 27.