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 ⋆ ). 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 24 supersymetric SO(10): synopsis
⋆ SO(10) is a rank-5 Lie group which contains the SM gauge symmetry. SO(n) (except n = 6) are naturally anomaly-free, thus explaining the • seemingly fortuitous anomaly cancellation in the SM and in SU(5). matter unification in spinorial 16: The 16 contains all the matter in a • single generation of the SM, plus a RHN state Nˆ c: see-saw ν-masses Higgs unification: explains why 2 Higgs doublets in MSSM • Explains R-parity conservation: only matter-matter-Higgs couplings • Expect t b τ Yukawa unification in simplest models • − − ⋆ These features have convinced many theorists that the main features of SUSY SO(10) are surely right!
Howie Baer, GGI LHC mini workshop, June 10, 2010 25 Yukawa unification in SUSY: assumptions
some form of 4-d or x-d SO(10) SUGRA-GUT valid at Q > M • GUT SUGRA breaking via superHiggs mechanism: will find m ˜ 10 TeV so soft • G ∼ SUSY breaking terms 10 TeV ∼ SO(10) breaks to MSSM or MSSM plus gauge singlets at Q M either • ≃ GUT via Higgs mechanism (4-d) or x-d compactification MSSM (or MSSM plus Nˆ c) is correct effective theory between M and • SUSY MGUT EWSB broken radiatively due to large m • t we will require that t b τ Yukawa couplings unify at Q = M • − − GUT
Howie Baer, GGI LHC mini workshop, June 10, 2010 26 lots of previous work!
B. Ananthanarayan, G. Lazarides and Q. Shafi, PRD44 (1991)1613 and • PLB300 (1993)245; V. Barger, M. Berger and P. Ohmann, PRD49 (1994)4908; • M. Carena, M. Olechowski, S. Pokorski and C. Wagner, NPB426 (1994)269; • B. Ananthanarayan, Q. Shafi and X. Wang, PRD50 (1994)5980; • L. Hall, R. Rattazzi and U. Sarid, PRD50 (1994)7048; • R. Rattazzi and U. Sarid, PRD53 (1996)1553; • T. Blazek, M. Carena, S. Raby and C. Wagner, PRD56 (1997)6919; T. Blazek • and S. Raby, PLB392 (1997)371 and PRD59 (1999)095002; T. Blazek, S. Raby and K. Tobe, PRD60 (1999)113001 and PRD62 (2000)055001;
Howie Baer, GGI LHC mini workshop, June 10, 2010 27 more recent work
HB, Diaz, Ferrandis, Tata, PRD61 (2000) 111701 • HB, Brhlik, Diaz, Ferrandis, Mercadante, Quintana, Tata, PRD63 • (2001)015007; HB, Ferrandis, PRL87 (2001) 211803; • Blazek, Dermisek and Raby, PRL88 (2002) 111804 and PRD65 (2002) • 115004; Tobe and Wells, NPB663 (2003) 123 Auto, HB, Balazs, Belyaev, Ferrandis, Tata, JHEP0306 (2003) 023 • Dermisek, Raby, Roszkowski, Ruiz de Austri, JHEP0304 (2003) 037 and • JHEP0509 (2005) 029 HB, Kraml, Sekmen, Summy, JHEP0803 (2008) 056 • HB, Kraml, Sekmen, JHEP0909 (2009) 005 •
Howie Baer, GGI LHC mini workshop, June 10, 2010 28 Yukawa unification requires precision calculation of SUSY spectrum:
need full 2-loop RGE running • full threshold corrections calculated at optimized scale • – applies especially to b-quark self-energy: include g˜˜b , W t˜ , loops i i j ··· – Hall, Rattazzi, Sarid; Pierce, Bagger, Matchev, Zhangf off-sets Yukawa coupling RG trajectory • minimize scalar potential away from unstable Q = M ; use • Z Q = MSUSY √m˜1 m˜2 instead ≡ t t we elect to use Isajet/Isasugra spectrum generator •
Howie Baer, GGI LHC mini workshop, June 10, 2010 29 Yukawa unification in MSSM+RHN model via Isajet
1
0.9
0.8 ft
f 0.7 fb 0.6 fτ f 0.5 ν
0.4
103 105 107 109 1011 1013 1015 1017 Q (GeV)
Howie Baer, GGI LHC mini workshop, June 10, 2010 30 SUSY SO(10) parameter space:
m , m , M 2 , m , A , tan β, sign(µ) • 16 10 D 1/2 0 Here, M 2 parametrizes D-term splitting of scalar soft terms at M : • D GUT
2 2 2 2 2 mQ = mE = mU = m16 + MD m2 = m2 = m2 3M 2 D L 16 − D 2 2 2 mν˜R = m16 + 5MD m2 = m2 2M 2 , Hu,d 10 ∓ D ⋆ Two cases: – “Just-so Higgs splitting” (HS model) – Full D-term splitting plus RHN plus 3rd gen. splitting (DR3 model)
Howie Baer, GGI LHC mini workshop, June 10, 2010 31 Top-down scan of HS model with µ > 0
Auto, HB, Balazs, Belyaev, Ferrandis, Tata; HB, Kraml, Sekmen, Summy • R = max(f , f , f )/min(f , f , f ) at Q = M • t b τ t b τ GUT
Howie Baer, GGI LHC mini workshop, June 10, 2010 32 Correlation of SSB terms for YU models
A 2m • 0 ∼− 16 m 1.2m • 10 ∼ 16 tan β 50 • ∼ m 10 TeV • 16 ∼ m small • 1/2 2 2 2 ⋆ Earlier work: Bagger, Feng, Polonsky, Zhang derived A0 = 2m10 = 4m16 with m1/2 tiny and Yukawa unified couplings: (RIMH model)
– Reconcile naturalness with decoupling via m ˜ m ˜ f3 ≪ f1,2 ⋆ Characteristic spectrum for Yukawa unified SUSY:
m ˜(1, 2) 10 TeV • q,˜ ℓ ∼ m˜ , m , µ 1 2 TeV • t1 A ∼ − m 300 500 GeV • g˜ ∼ −
Howie Baer, GGI LHC mini workshop, June 10, 2010 33 SO(10) sparticle spectra trouble for neutralino DM! ⇒ ⋆ use IsaReD (part of Isajet) to compute relic density large m suppresses neutralino annihilation ⋆ f˜1,2
⋆ Ω e h2 too large by 103 105! Z1 −
Howie Baer, GGI LHC mini workshop, June 10, 2010 34 Cold axion and cold/warm axino DM in the universe
Given Ω e h2 and m e and ΩNTP h2 can calculate m . • Z1 Z1 a˜ a˜ Given ΩTP h2, m and f /N, can calculate re-heat temperature of universe • a˜ a˜ a ⋆ Four cases:
11 2 1. Take fa/N = 10 GeV so Ωah = 0.017. Bulk of DM must be thermally TP NTP produced a˜. Take Ωa˜ = 0.083 and Ωa˜ = 0.01 11 2 2. Take fa/N = 4 10 GeV so Ωah = 0.084. (Bulk of DM is cold axions.) TP NTP× Take Ωa˜ = Ωa˜ = 0.013 12 2 3. Take fa/N = 10 GeV and lower mis-align error bar so Ωah = 0.084. (Bulk TP NTP of DM is cold axions.) Take Ωa˜ = Ωa˜ = 0.013 12 4. Take fa/N = 10 GeV but allow accidental near vacuum alignment so 2 TP Ωah 0. Bulk of DM must be thermally produced axinos. Take Ωa˜ = 0.1 ∼NTP and Ωa˜ = 0.01
Howie Baer, GGI LHC mini workshop, June 10, 2010 35 Consistent cosmology for SO(10) SUSY GUTs with mixed a/a˜ DM
Happily, T falls into the right range to give cold axion/axino DM with a • R small admixture of warm axino DM, preserve BBN predictions and have non-thermal leptogenesis! See HB and H. Summy, PLB666, 5 (2008) • HB, Kraml, Haider, Sekmen and Summy, JCAP0902 (2009) 002 •
Howie Baer, GGI LHC mini workshop, June 10, 2010 36 Howie Baer, GGI LHC mini workshop, June 10, 2010 37 Best Yukawa unification favors light gluino!
Possible to see at Tevatron pp¯ collider? m 440 GeV! HB, Kraml, Lessa, • g˜ ∼ Sekmen and Summy, arXiv:0910.2988 Possible to see in year 1 of LHC? m 640 GeV! HB, Kraml, Sekmen and • g˜ ∼ Summy, JHEP0810 (2008) 079; HB, Kraml, Lessa, Sekmen, arXiv:0911.4739
Howie Baer, GGI LHC mini workshop, June 10, 2010 38 LHC during year 1 with √s = 7 TeV
using multi-bjet final state, can see m 400 GeV with just 0.2 fb−1, even • g˜ ∼ without using E ! 6 T with 1 fb−1 and E , can see m 630 GeV • ∼ 6 T g˜ ∼ In HS and DR3 model, distinct m(µ+µ−) mass edge •
Howie Baer, GGI LHC mini workshop, June 10, 2010 39 6
BG m~z -m~z 2 1 HSb + BG 5 DR3b + BG HS (m~g = 522 GeV)
DR3 (m~g = 526 GeV) 4
3 /dm (fb/GeV) σ d 2
1
0 50 100 150 m(ll) (GeV)
Howie Baer, GGI LHC mini workshop, June 10, 2010 40 Axion microwave cavity searches
⋆ ongoing searches: ADMX experiment Livermore U Wash. • ⇒ Phase I: probe KSVZ • for m 10−6 10−5 eV a ∼ − Phase II: probe DFSZ • for m 10−6 10−5 eV a ∼ − beyond Phase II: • probe higher values ma
Howie Baer, GGI LHC mini workshop, June 10, 2010 41 Need for broader, deeper axion searches
⋆ axion param. space: Gondolo & Visinelli, 2009 study we have only begun • ···
10-12 18 Θ = 10 i 0.0001
Θi =0.001 1016 Axion isocurvature PLANCK -9 fluctuations 10 Θi =0.01 D 14 D 10 PLANCK eV @ GeV Θi =0.1 @ - 6 a
a 10 m f 12 ADMXI
10 Tensor modes Θ =1 ADMXII i Wa > W CARRACK CDM T GH 10 = Wa < WCDM -3 10 Θi =3.14 f a 10
108 White dwarfs cooling time 104 106 108 1010 1012 1014
HI @GeVD
Howie Baer, GGI LHC mini workshop, June 10, 2010 42 Conclusions
⋆ neutralino CDM: usually too much or too little
⋆ neutralino CDM with Ω e h2 0.1 fine-tuned Z1 ∼ ⋆ PQ strong CP solution + SUSY: why not both? ⋆ expect mixed axion/axino CDM if a˜ is LSP
2 ⋆ then low fine-tuning of Ωaa˜h
6 8 ⋆ TR 10 10 possible: ∼ − > solve gravitino problem if m ˜ 5 TeV • G ∼ allow for non-thermal leptogenesis • ⋆ Neutralino CDM dis-favored models now allowed Effective SUSY • Yukawa-unified SUSY •
Howie Baer, GGI LHC mini workshop, June 10, 2010 43