Mixed axion/axino cold dark matter in SUSY: with implications for LHC Howard Baer University of Oklahoma OUTLINE ⋆ old ideas from 1970s ⋆ strong CP problem and PQWW solution ⋆ the PQMSSM ⋆ axion/axino CDM ⋆ mSUGRA (CMSSM) ⋆ Effective SUSY ⋆ Yukawa-unified SUSY 1 Howie Baer, GGI LHC mini workshop, June 10, 2010
Old ideas from the dawn of time: (1970s) ⋆ renormalizable gauge theories ⋆ QCD ⋆ the Standard Model ⋆ supersymmetry ⋆ GUTs ⋆ superstrings ⋆ see-saw neutrinos ⋆ PQ strong CP solution 2 Howie Baer, GGI LHC mini workshop, June 10, 2010
Origin of strong CP problem ⋆ QCD ∋ U (2) V × U (2) A global symmetry (2 light quarks) ⋆ U (2) V = SU (2) I × U (1) B realized; U (2) A broken spontaneously ⋆ expect 4 Goldstone bosons: πs and η , but instead m η ≫ m π : QCD does not respect somehow U (1) A (Weinberg) ⋆ t’Hooft resolution: QCD θ vacuum ⇒ theory not U (1) A symmetric, and m η ≫ m π explained ⋆ Generate additional term to QCD Lagrangian: L ∋ θ g 2 32 π F µν A ˜ F Aµν s • violates P and T ; conserves C ⋆ In addition, weak interactions ⇒ L ∋ Arg detM g 2 32 π F µν A ˜ F Aµν s • ¯ θ = θ + Arg detM ⋆ experiment: neutron EDM ⇒ ¯ < ∼ 10 − 10 θ ⋆ How can this be? The strong CP problem 3 Howie Baer, GGI LHC mini workshop, June 10, 2010
Solutions to the strong CP problem ⋆ Anthropic: ¯ θ luckily small ⋆ Spontaneously broken CP : induced ¯ θ is small (loop level) ⋆ a new chiral symmetry U P Q (1) exists (Peccei-Quinn); U P Q (1) spontaneously broken at scale f a ( ∼ 10 9 − 10 12 GeV) ⋆ Goldstone boson field a ( x ) , the axion must exist (Weinberg, Wilczek) g 2 ⋆ L ∋ − 1 32 π 2 F µν A ˜ 2 ∂ µ a∂ µ a + ξ a F Aµν + L int s f a ⋆ V eff ∼ − (1 − cos(¯ θ + ξ a f a )) ⋆ axion field settles to minimum of potential: � a � = − f a ξ ¯ θ ⋆ strong CP problem solved! a = � ∂ 2 V eff ⋆ m 2 ∂a 2 � 4 Howie Baer, GGI LHC mini workshop, June 10, 2010
Axion cosmology ⋆ Axion field eq’n of motion: θ = a ( x ) /f a – ¨ θ + 3 H ( T ) ˙ ∂V ( θ ) 1 θ + = 0 f 2 ∂θ a – V ( θ ) = m 2 a ( T ) f 2 a (1 − cos θ ) – Solution for T large, m a ( T ) ∼ 0 : θ = const. f a /N (GeV) 12 11 10 9 10 10 10 10 – m a ( T ) turn-on ∼ 1 GeV 0 10 2 (vacuum mis-alignment) WMAP 5: Ω CDM h 2 = 0.110 ± 0.006 ⋆ a(x) oscillates, -1 10 -2 10 creates axions with � p ∼ 0 : -3 10 production via vacuum mis-alignment Ω a h -4 10 � � 7 / 6 ⋆ Ω a h 2 ∼ 1 6 × 10 − 6 eV -5 θ 2 i h 2 10 -5 -4 -3 10 10 10 2 m a m a (eV) > ⋆ astro bound: stellar cooling ⇒ f a ∼ 10 9 GeV 5 Howie Baer, GGI LHC mini workshop, June 10, 2010
We also know MSSM (plus gauge singlets) is compelling effective theory between M weak and M GUT 6 Howie Baer, GGI LHC mini workshop, June 10, 2010
Most analyses work in mSUGRA (CMSSM) model • m 0 , m 1 / 2 , A 0 , tan β, sign ( µ ) 7 Howie Baer, GGI LHC mini workshop, June 10, 2010
Results of χ 2 fit using τ data for a µ : mSugra with tan β = 10, A 0 = 0, µ > 0 mSugra with tan β = 10, A 0 = 0, µ > 0 mSugra with tan β = 54, A 0 = 0, µ > 0 mSugra with tan β = 54, A 0 = 0, µ > 0 2000 2000 2000 2000 14 1 not LSP 1 not LSP 8 1750 1750 1750 1750 12 6 Ζ Ζ ~ ~ 1500 1500 1500 1500 10 1250 1250 1250 1250 4 8 ln( χ 2 /DOF) m 1/2 (GeV) ln( χ /DOF) m 1/2 (GeV) 1000 1000 1000 1000 6 2 750 750 750 750 4 0 500 500 500 500 2 250 250 -2 250 250 No REWSB No REWSB 0 0 0 0 0 0 0 1000 1000 2000 2000 3000 3000 4000 4000 5000 5000 6000 6000 0 0 1000 1000 2000 2000 3000 3000 4000 4000 5000 5000 6000 6000 m 0 (GeV) m 0 (GeV) m h =114.1GeV LEP2 excluded m h =114.1GeV LEP2 excluded SuperCDMS CDMSII CDMS SuperCDMS CDMSII CDMS • HB, C. Balazs: JCAP 0305, 006 (2003) • numerous recent χ 2 , MCMC fits to find preferred regions 8 Howie Baer, GGI LHC mini workshop, June 10, 2010
Z 1 h 2 as surface in m 0 vs. m 1 / 2 space Ω e • tan β = 10 , A 0 = 0 , µ > 0 (HB, A. Box) 9 Howie Baer, GGI LHC mini workshop, June 10, 2010
Fine-tuning in mSUGRA with neutralino CDM ⋆ contours of Ω e Z 1 h 2 Z 1 h 2 ∂ log Ω e ⋆ regions of fine-tune: ∆ ≡ : (HB, A. Box) ∂ log a i 10 Howie Baer, GGI LHC mini workshop, June 10, 2010
Fine-tuning zoomed in stau-co-annihilation ⋆ contours of Ω e Z 1 h 2 Z 1 h 2 ∂ log Ω e ⋆ regions of fine-tune: ∆ ≡ ∂ log a i 11 Howie Baer, GGI LHC mini workshop, June 10, 2010
General scan over 19 param. MSSM ⋆ dimensionful param’s defined at M GUT • m Q 1 , m U 1 , m D 1 , m L 1 , m E 1 : 0 → 3500 GeV • m Q 3 , m U 3 , m D 3 , m L 3 , m E 3 : 0 → 3500 GeV • M 1 , M 2 , M 3 : 0 → 3500 GeV • A t , A b , A τ : − 3500 → 3500 GeV • m H u , m H d : 0 → 3500 GeV • tan β : 2 → 60 ⋆ m f W 1 > 103 . 5 GeV ⋆ m f W 1 > 91 . 9 GeV (wino-like) ⋆ m h > 111 GeV 12 Howie Baer, GGI LHC mini workshop, June 10, 2010
8 10 Bino Wino 6 Higgsino 10 Mixed 4 10 2 Ω h 2 10 0 10 -2 10 -4 10 0 400 800 1200 1600 m Z 1 ~ 13 Howie Baer, GGI LHC mini workshop, June 10, 2010
General MSSM 19 param. scan Z 1 h 2 • histogram of models vs. Ω e Bino 800 Wino Total Number of Models Higgsino Mixed 600 400 200 0 7 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 8 10 2 Ω h 14 Howie Baer, GGI LHC mini workshop, June 10, 2010
Why WIMP miracle really is a miracle for SUSY Z 1 h 2 with m e • histogram of models vs. Ω e Z 1 < 500 GeV Bino 300 Wino Total Number of Models Higgsino Mixed 200 100 0 7 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 8 10 2 Ω h 15 Howie Baer, GGI LHC mini workshop, June 10, 2010
Gravitinos: spin- 3 2 partner of graviton • gravitino problem in generic SUGRA models: overproduction of ˜ G followed by late ˜ G decay can destroy successful BBN predictions: upper bound on T R (see Kawasaki, Kohri, Moroi, Yotsuyanagi; Cybert, Ellis, Fields, Olive) 16 Howie Baer, GGI LHC mini workshop, June 10, 2010
Gravitinos as dark matter: again the gravitino problem • neutralino production in generic SUGRA models: followed by late time Z 1 → ˜ � G + X decays can destroy successful BBN predictions: (see Kawasaki, Kohri, Moroi, Yotsuyanagi) 17 Howie Baer, GGI LHC mini workshop, June 10, 2010
Various leptogenesis scenarios • Upper bound on T R from BBN is below that for successful thermal ∼ 10 10 GeV > leptogenesis: need T R (Buchmuller, Plumacher) • Alternatively, one may have non-thermal leptogenesis where inflaton φ → N i N i decay (Lazarides, Shafi; Kumekawa, Moroi, Yanagida) • additional source of N i in early universe allows lower T R : � � � 2 m N 1 � � � n B T R m ν 3 ≃ 8 . 2 × 10 − 11 × δ eff (1) 10 6 GeV s m φ 0 . 05 eV √ Hℓ D -flat direction: T R ∼ 10 6 − 10 8 GeV • Also, AD leptogenesis in φ = allowed (Dine, Randall, Thomas; Murayama, Yanagida) • WMAP observation: n b /s ∼ 0 . 9 × 10 − 10 ⇒ T R ∼ 10 6 GeV > 18 Howie Baer, GGI LHC mini workshop, June 10, 2010
PQMSSM: Axions + SUSY ⇒ Axino ˜ a dark matter • axino is spin- 1 2 element of axion supermultiplet ( R -odd; can be LSP) – Raby, Nilles, Kim – Rajagopal, Wilczek, Turner • m ˜ a model dependent: keV → GeV • � f /N = 10 1 2 Z 1 → ˜ aγ a GeV 1 10 0 10 a production via � • non-thermal ˜ Z 1 decay: f /N = 10 1 1 a GeV -1 10 τ (s) -2 • axinos inherit neutralino number density 10 f /N = 10 1 0 a GeV -3 10 h 2 = m ˜ • Ω NT P Z 1 h 2 : Z 1 Ω e a -4 ˜ a m e 10 f /N = 10 9 a GeV -5 10 – Covi, Kim, Kim, Roszkowski 50 60 70 80 90 m χ 0 (GeV) ~ 1 19 Howie Baer, GGI LHC mini workshop, June 10, 2010
Thermally produced axinos ⋆ If T R < f a , then axinos never in thermal equilibrium in early universe ⋆ Can still produce ˜ a thermally via radiation off particles in thermal equilibrium ⋆ Brandenberg-Steffen calculation: � 1 . 108 � � 10 11 GeV � 2 � � � � m ˜ T R h 2 ≃ 5 . 5 g 6 a Ω T P s ln (2) 10 4 GeV ˜ a g s f a /N 0 . 1 GeV TP h 2 = 0.001 (solid), 0.01 (dashed), 0.1 (dashed-dotted) Ω a ~ m a ~ (GeV) = 0.0001 (purple), 0.01 (green), 1 (maroon) 9 10 8 10 = 0.1 7 2 10 h P T = 0.0001 (GeV), Ω ~ T R (GeV) a 6 10 = 0.01 2 5 h P 10 T m ~ = 0.01 (GeV), Ω a ~ a 4 10 m 3 ~ a 10 2 10 9 10 11 12 10 10 10 10 f a /N (GeV) 20 Howie Baer, GGI LHC mini workshop, June 10, 2010
mSUGRA model with mixed axion/axino CDM: m ˜ a fixed ⋆ ( m 0 , m 1 / 2 , A 0 , tan β, sgn ( µ )) = (1000 GeV , 300 GeV , 0 , 10 , +1) ⋆ Ω a h 2 + Ω T P h 2 + Ω NT P h 2 = 0 . 11 a ˜ a ˜ ⋆ model with mainly axion CDM seems favored! m a ~ = 100 keV (solid), 1 MeV (dashed) 0 7 10 10 2 WMAP Ω CDM h -1 10 Ω a TP h 2 ~ -2 6 10 10 2 Ω a h -3 10 -4 5 10 10 T R (GeV) NTP h 2 Ω a 2 ~ -5 Ω h 10 -6 4 10 10 -7 10 -8 3 10 10 -9 10 (a) (b) -10 2 10 10 9 10 11 12 9 10 11 12 10 10 10 10 10 10 10 10 f a /N (GeV) f a /N (GeV) 21 Howie Baer, GGI LHC mini workshop, June 10, 2010
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