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 Howie Baer, GGI LHC mini workshop, June 10, 2010 1 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 Howie Baer, GGI LHC mini workshop, June 10, 2010 2 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 mη mπ: QCD does not ≫ respect somehow U(1)A (Weinberg) ⋆ t’Hooft resolution: QCD θ vacuum theory not U(1)A symmetric, and ⇒ m m explained η ≫ π 2 gs µν ⋆ Generate additional term to QCD Lagrangian: θ F F˜Aµν L∋ 32π A violates P and T ; conserves C • 2 gs µν ⋆ In addition, weak interactions Arg detM F F˜Aµν ⇒L∋ 32π A θ¯ = θ + Arg detM • ⋆ experiment: neutron EDM θ¯ < 10−10 ⇒ ∼ ⋆ How can this be? The strong CP problem Howie Baer, GGI LHC mini workshop, June 10, 2010 3 Solutions to the strong CP problem ⋆ Anthropic: θ¯ luckily small ⋆ Spontaneously broken CP : induced θ¯ is small (loop level) ⋆ a new chiral symmetry UP Q(1) exists (Peccei-Quinn); UP Q(1) spontaneously broken at scale f ( 109 1012 GeV) a ∼ − ⋆ Goldstone boson field a(x), the axion must exist (Weinberg, Wilczek) 2 1 µ a gs µν ˜ ⋆ ∂ a∂µa + ξ 2 F FAµν + int L∋− 2 fa 32π A L ¯ a ⋆ Veff (1 cos(θ + ξ )) ∼− − fa ⋆ axion field settles to minimum of potential: a = fa θ¯ h i − ξ ⋆ strong CP problem solved! 2 2 ∂ Veff ⋆ m = 2 a h ∂a i Howie Baer, GGI LHC mini workshop, June 10, 2010 4 Axion cosmology ⋆ Axion field eq’n of motion: θ = a(x)/fa 1 ∂V (θ) – θ¨ + 3H(T )θ˙ + 2 = 0 fa ∂θ – V (θ)= m2(T )f 2(1 cos θ) a a − – Solution for T large, m (T ) 0: a ∼ fa /N (GeV) θ = const. 12 11 10 9 10 10 10 10 – 0 ma(T ) turn-on 1 GeV 10 2 ∼ WMAP 5: Ω h = 0.110 ± 0.006 -1 CDM ⋆ a(x) oscillates, 10 -2 10 creates axions with ~p 0: -3 ∼ 10 (vacuum mis-alignment) 2 h production via vacuum mis-alignment a -4 Ω 10 −6 7/6 -5 × 10 -5 -4 -3 2 1 6 10 eV 2 2 10 10 10 ⋆ Ωah θ h m (eV) 2 m i a ∼ h a i > 9 ⋆ astro bound: stellar cooling fa 10 GeV ⇒ ∼ Howie Baer, GGI LHC mini workshop, June 10, 2010 5 We also know MSSM (plus gauge singlets) is compelling effective theory between Mweak and MGUT Howie Baer, GGI LHC mini workshop, June 10, 2010 6 Most analyses work in mSUGRA (CMSSM) model m , m , A , tan β, sign(µ) • 0 1/2 0 Howie Baer, GGI LHC mini workshop, June 10, 2010 7 2 Results of χ fit using τ data for aµ: β µ > β µ > mSugra with tan = 10, A0 = 0, 0 mSugra with tan = 54, A0 = 0, 0 2000 2000 14 8 1750 1750 12 not LSP not LSP 1 1 ~ ~ Ζ Ζ 6 1500 1500 10 1250 1250 4 8 1000 1000 /DOF) /DOF) (GeV) (GeV) 2 χ 6 2 χ 1/2 1/2 m m ln( 750 750 ln( 4 0 500 500 2 250 No REWSB -2 250 No REWSB 0 0 0 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 m0 (GeV) m0 (GeV) mh=114.1GeV LEP2 excluded mh=114.1GeV LEP2 excluded SuperCDMS CDMSII CDMS SuperCDMS CDMSII CDMS HB, C. Balazs: JCAP 0305, 006 (2003) • numerous recent χ2, MCMC fits to find preferred regions • Howie Baer, GGI LHC mini workshop, June 10, 2010 8 2 e 0 1 2 ΩZ1 h as surface in m vs. m / space tan β = 10, A = 0, µ> 0 (HB, A. Box) • 0 Howie Baer, GGI LHC mini workshop, June 10, 2010 9 Fine-tuning in mSUGRA with neutralino CDM e 2 ⋆ contours of ΩZ1 h 2 ∂ log Ω e h ⋆ regions of fine-tune: ∆ Z1 : (HB, A. Box) ≡ ∂ log ai Howie Baer, GGI LHC mini workshop, June 10, 2010 10 Fine-tuning zoomed in stau-co-annihilation e 2 ⋆ contours of ΩZ1 h 2 ∂ log Ω e h ⋆ regions of fine-tune: ∆ Z1 ≡ ∂ log ai Howie Baer, GGI LHC mini workshop, June 10, 2010 11 General scan over 19 param. MSSM ⋆ dimensionful param’s defined at MGUT m , m , m , m , m : 0 3500 GeV • Q1 U1 D1 L1 E1 → m , m , m , m , m : 0 3500 GeV • Q3 U3 D3 L3 E3 → M , M , M : 0 3500 GeV • 1 2 3 → A , A , A : 3500 3500 GeV • t b τ − → m , m : 0 3500 GeV • Hu Hd → tan β : 2 60 • → mf > 103.5 GeV ⋆ W1 f ⋆ mW1 > 91.9 GeV (wino-like) ⋆ mh > 111 GeV Howie Baer, GGI LHC mini workshop, June 10, 2010 12 8 10 Bino Wino 6 10 Higgsino Mixed 4 10 2 h 2 Ω 10 0 10 -2 10 -4 10 0 400 800 1200 1600 m~ Z1 Howie Baer, GGI LHC mini workshop, June 10, 2010 13 General MSSM 19 param. scan histogram of models vs. Ω e h2 • Z1 Bino 800 Wino Higgsino Mixed 600 400 200 Total Number of Models 0 -3 -2 -1 0 1 2 3 4 5 6 7 8 10 10 10 10 10 10 10 10 10 10 10 10 2 Ωh Howie Baer, GGI LHC mini workshop, June 10, 2010 14 Why WIMP miracle really is a miracle for SUSY histogram of models vs. Ω e h2 with m e < 500 GeV • Z1 Z1 Bino 300 Wino Higgsino Mixed 200 100 Total Number of Models 0 -3 -2 -1 0 1 2 3 4 5 6 7 8 10 10 10 10 10 10 10 10 10 10 10 10 2 Ωh Howie Baer, GGI LHC mini workshop, June 10, 2010 15 3 Gravitinos: spin- 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 TR (see Kawasaki, Kohri, Moroi, Yotsuyanagi; Cybert, Ellis, Fields, Olive) Howie Baer, GGI LHC mini workshop, June 10, 2010 16 Gravitinos as dark matter: again the gravitino problem neutralino production in generic SUGRA models: followed by late time • Z G˜ + Xdecays can destroy successful BBN predictions: 1 → e (see Kawasaki, Kohri, Moroi, Yotsuyanagi) Howie Baer, GGI LHC mini workshop, June 10, 2010 17 Various leptogenesis scenarios Upper bound on T from BBN is below that for successful thermal • R leptogenesis: need T > 1010 GeV (Buchmuller, Plumacher) R ∼ Alternatively, one may have non-thermal leptogenesis where inflaton • φ N N decay (Lazarides, Shafi; Kumekawa, Moroi, Yanagida) → i i additional source of N in early universe allows lower T : • i R nB −11 TR 2mN1 mν3 8.2 10 6 δeff (1) s ≃ × × 10 GeV mφ 0.05 eV Also, AD leptogenesis in φ = √Hℓ D-flat direction: T 106 108 GeV • R ∼ − allowed (Dine, Randall, Thomas; Murayama, Yanagida) WMAP observation: n /s 0.9 10−10 T > 106 GeV • b ∼ × ⇒ R ∼ Howie Baer, GGI LHC mini workshop, June 10, 2010 18 PQMSSM: Axions + SUSY Axino a˜ dark matter ⇒ axino is spin- 1 element of axion supermultiplet (R-odd; can be LSP) • 2 – Raby, Nilles, Kim – Rajagopal, Wilczek, Turner m model dependent: keV GeV • a˜ → f 12 1 a /N = 10 GeV Z1 aγ˜ 10 • → 0 10 e f /N 11 non-thermal a˜ production via Z1 decay: -1 a = 10 GeV • 10 -2 (s) axinos inherit neutralino numbere density τ 10 f / 10 -3 a N = 10 GeV • 10 NTP 2 ma˜ 2 e -4 Ωa˜ h = e Ω 1 h : 10 mZ1 Z • f /N = 109 -5 a GeV – 10 Covi, Kim, Kim, Roszkowski 50 60 70 80 90 m~χ0 (GeV) 1 Howie Baer, GGI LHC mini workshop, June 10, 2010 19 Thermally produced axinos ⋆ If TR < fa, then axinos never in thermal equilibrium in early universe ⋆ Can still produce a˜ thermally via radiation off particles in thermal equilibrium ⋆ Brandenberg-Steffen calculation: 11 2 TP 2 6 1.108 10 GeV ma˜ TR Ωa˜ h 5.5gs ln 4 (2) ≃ gs fa/N 0.1 GeV 10 GeV ΩTP 2 ~a h = 0.001 (solid), 0.01 (dashed), 0.1 (dashed-dotted) m~a (GeV) = 0.0001 (purple), 0.01 (green), 1 (maroon) 9 10 8 10 7 10 2 = 0.1 TP h Ω~a 6 10 (GeV) R T 5 2 = 0.01 TP 10 ~ = 0.0001 (GeV), h m a Ω~a 4 10 3 = 0.01 (GeV), 10 m~a 2 10 9 10 11 12 10 10 10 10 fa /N (GeV) Howie Baer, GGI LHC mini workshop, June 10, 2010 20 mSUGRA model with mixed axion/axino CDM: ma˜ fixed ⋆ (m0, m1/2, A0, tan β,sgn(µ)) = (1000 GeV, 300 GeV, 0, 10, +1) 2 TP 2 NTP 2 ⋆ Ωah + Ωa˜ h + Ωa˜ h = 0.11 ⋆ model with mainly axion CDM seems favored! ma~ = 100 keV (solid), 1 MeV (dashed) 0 7 10 2 10 WMAP Ω h -1 CDM 10 ΩTP 2 ~a h -2 6 10 10 -3 Ω 2 10 ah -4 5 10 10 NTP 2 2 Ω~ h h -5 10 a Ω (GeV) R -6 T 4 10 10 -7 10 -8 3 10 10 -9 10 (a) (b) -10 2 10 9 10 11 12 10 9 10 11 12 10 10 10 10 10 10 10 10 fa /N (GeV) fa /N (GeV) Howie Baer, GGI LHC mini workshop, June 10, 2010 21 mSUGRA p-space with mainly axion cold DM ⋆ contours of log10 TR: mSUGRA w/ tan β = 10, A0 = 0 > 6 ⋆ TR 10 consistent with non-thermal leptogenesis ∼ ⋆ most dis-favored mSUGRA regions with neutralino DM are most favored by mSUGRA with mainly axion DM! (HB, Box, Summy) Howie Baer, GGI LHC mini workshop, June 10, 2010 22 Axion/axino relic density in mSUGRA Howie Baer, GGI LHC mini workshop, June 10, 2010 23 Fine-tuning for mainly axion CDM in mSUGRA a e 2 ⋆ ).