Yukawa unification in SUSY: assumptions some form of 4-d or x-d SO - PowerPoint PPT Presentation

Why SUSY GUTs imply that the bulk of dark matter is made of axions Howard Baer University of Oklahoma ⋆ SO (10) motivation ⋆ Yukawa unification ⋆ Sparticle mass calculation ⋆ Dark matter problem • mixed axion/axino DM ⋆ cosmology of SUSY SO (10) ⋆ SO (10) at LHC – can see with just 0.1 fb − 1 ! 1 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

SO (10) : synopsis ⋆ SO (10) is a rank-5 Lie group which contains the SM gauge symmetry. • matter unification in spinorial 16 • The 16 contains all the matter in a single generation of the SM, plus a RHN state ˆ N c : see-saw ν -masses • SO ( n ) (except n = 6 ) are naturally anomaly-free, thus explaining the seemingly fortuitous anomaly cancellation in the SM and in SU (5) . • Explains R -parity conservation • Explains why 2 Higgs doublets in MSSM • Expect t − b − τ Yukawa unification in simplest models 2 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

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: m ˜ G ∼ 1 TeV and soft SUSY breaking terms ∼ 1 TeV • SO (10) breaks to MSSM or MSSM plus gauge singlets at Q = M GUT either via Higgs mechanism (4-d) or x-d compactification • MSSM (or MSSM plus ˆ N c ) is correct effective theory between M SUSY and M GUT • EWSB broken radiatively due to large m t • we will assume that t − b − τ Yukawa couplings unify at Q = M GUT 3 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

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; 4 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

more recent work • H. Baer, M. Diaz, J. Ferrandis and X. Tata, PRD61 (2000)111701 • H. Baer, M. Brhlik, M. Diaz, J. Ferrandis, P. Mercadante, P. Quintana and X. Tata, PRD63 (2001)015007; • H. Baer and J. Ferrandis, PRL87 (2001)211803; • T. Blazek, R. Dermisek and S. Raby, PRL88 (2002)111804 and PRD65 (2002)115004; • D. Auto, H. Baer, C. Balazs, A. Belyaev, J. Ferrandis and X. Tata, JHEP0306 (2003)023 • D. Auto, H. Baer, A. Belyaev and T. Krupovnickas, JHEP0410 (2004)066; • R. Dermisek, S. Raby, L. Roszkowski and R. Ruiz de Austri, JHEP0304 (2003)037 and JHEP0509 (2005)029 • H. Baer, S. Kraml, S.Sekmen and H. Summy, arXiv:0801.1831 (2008). 5 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Sparticle mass spectra ⋆ Mass spectra codes ⋆ RGE running: M GUT → M weak • Isajet 7.78 (HB, Paige, Protopopescu, Tata) ∗ ≥ 7.72: Isatools • SuSpect (Djouadi, Kneur, Moultaka) • SoftSUSY (Allanach) • Spheno (Porod) ⋆ Comparison (Belanger, Kraml, Pukhov) ⋆ Website: http://kraml.home.cern.ch/kraml/comparison/ 6 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Yukawa unification requires precision calculation of SUSY spectrum: Hall, Rattazzi, Sarid; Pierce et al. (PBMZ) • need full 2-loop RGE running • full threshold corrections calculated at optimized scale – applies especially to b -quark self-energy g ˜ b i , � W i ˜ – ˜ t j , · · · loops included • off-sets Yukawa coupling RG trajectory • use Isajet/Isasugra spectrum generator 7 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Yukawa unification in MSSM: Isajet and SoftSUSY 1 0.9 f t 0.8 f i 0.7 f b 0.6 f τ 0.5 0.4 0 2 4 6 8 10 12 14 16 10 10 10 10 10 10 10 10 10 Q (GeV) 8 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

SO (10) -inspired parameter space: • m 16 , m 10 , M 2 D , m 1 / 2 , A 0 , tan β, sign ( µ ) • Here, M 2 D parametrizes splitting of Higgs soft terms at M GUT : m 2 m 2 10 ∓ 2 M 2 = H u,d D ⋆ The Higgs splitting only (HS) method gives better Yukawa unification than > full D -term splitting (DT) model for µ > 0 and m 16 ∼ 2 TeV 9 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Top-down scan of HS model with µ > 0 Auto, HB, Balazs, Belyaev, Ferrandis, Tata New analysis: HB, Kraml, Sekmen, Summy 10 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Correlation of SSB terms for YU models ⋆ Note correlation amongst parameters: • A 0 ∼ − 2 m 16 • m 10 ∼ 1 . 2 m 16 • tan β ∼ 50 ⋆ Earlier work: Bagger, Feng, Polonsky, Zhang derived A 2 0 = 2 m 2 10 = 4 m 2 16 with m 1 / 2 tiny and Yukawa unified couplings: in context of “radiatively induced inverted scalar mass hierarchy model” – Meant to reconcile naturalness with FCNC suppression by having m ( third gen. scalars ) ≪ m (1 st/ 2 nd ge. scalars ) – Original model needed to be reconciled with EWSB; get hierarchy, but much less than anticipated: HB, Balazs, Mercadante, Tata, Wang (2001) 11 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

t − b − τ Yukawa unification in HS model! √ • need m 10 ≃ 2 m 16 1.4 1.2 g 3 • A 0 ≃ − 2 m 16 f t 1.0 Couplings f b • inverted scalar mass hierarchy: Bagger et al. 0.8 g 2 0.6 • split Higgs: m 2 H u < m 2 f τ g 1 H d 0.4 0.2 • Auto, HB, Balazs, Belyaev, Ferrandis, Tata M Z M G 0.0 – m ˜ ℓ (1 , 2) ∼ 10 TeV 15 H d q, ˜ Soft Parameters (TeV) H u e L e R 10 u L,R ,d R – m ˜ t 1 , m A , µ ∼ 1 − 2 TeV τ L τ R 5 b R t L t R – m ˜ g ∼ 300 − 500 GeV 0 A b -5 A t • Blazek, Dermisek, Raby A τ -10 – small µ, m A ∼ 100 − 200 GeV -15 -20 2 4 6 8 10 12 14 16 18 1 10 10 10 10 10 10 10 10 10 Q (GeV) 12 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Neutralino dark matter ⋆ Why R -parity? natural in SO (10) SUSYGUTS if properly broken, or broken via compactification (Mohapatra, Martin, Kawamura, · · · ) ⋆ In thermal equilibrium in early universe ⋆ As universe expands and cools, freeze out ⋆ Number density obtained from Boltzmann eq’n • dn/dt = − 3 Hn − � σv rel � ( n 2 − n 2 0 ) • depends critically on thermally averaged annihilation cross section times velocity ⋆ many thousands of annihilation/co-annihilation diagrams ⋆ several computer codes available • DarkSUSY, Micromegas, IsaReD (part of Isajet) 13 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Problem: reconcile DM with Yukawa unification ⋆ best solution: axion/axino DM instead of neutralino a h 2 ∼ • each � m ˜ Z 1 h 2 : ⇒ warm DM Z 1 → ˜ aγ so Ω ˜ Z 1 Ω e a m e • also thermal component depending on T R : ⇒ CDM • also axion DM via vacuum mis-alignment 14 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Axions ⋆ PQ solution to strong CP problem in QCD ⋆ pseudo-Goldstone boson from f a /N (GeV) 12 11 10 9 10 10 10 10 PQ breaking at scale f a ∼ 10 9 − 10 12 GeV 0 10 2 (vacuum mis-alignment) 2 = 0.110 ± 0.006 WMAP 5: Ω CDM h ⋆ non-thermally produced -1 10 -2 via vacuum mis-alignment as cold DM 10 -3 QCD /f a ∼ 10 − 6 − 10 − 1 eV 10 • m a ∼ Λ 2 Ω a h -4 10 � � 7 / 6 • Ω a h 2 ∼ 1 6 × 10 − 6 eV -5 h 2 10 -5 -4 -3 10 10 10 m a 2 m a (eV) • astro bound: stellar cooling ⇒ m a < 10 − 1 eV • a couples to EM field: a − γ − γ coupling (Sikivie) • axion microwave cavity searches 15 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Axino ˜ a dark matter • axino is spin- 1 2 element of axion supermultiplet ( R -odd; can be LSP) • m ˜ a model dependent: keV → GeV • � f / Z 1 → ˜ aγ N 1 2 = 1 0 a 1 G e V 10 0 10 a production via � • non-thermal ˜ Z 1 decay: f / N 1 1 = 1 0 a -1 G e V 10 τ (s) -2 10 • axinos inherit neutralino number density f / N 1 0 = 1 0 a G e V -3 10 -4 h 2 = 10 m ˜ • Ω NT P Z 1 h 2 : Z 1 Ω e a f / N 9 = 1 0 a a G e ˜ V m e -5 10 50 60 70 80 90 m χ 0 (GeV) ~ 1 16 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

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 (1) 10 4 GeV a ˜ g s f a /N 0 . 1 GeV 10 10 9 10 f / a N 8 10 = 1 0 12 T R (GeV) G f e / a V N 7 10 = 1 0 11 G f e / NT leptogenesis a N V 6 10 = 1 0 10 G e V 5 10 hot warm cold 4 10 -7 -6 -5 -4 -3 -2 -1 0 10 10 10 10 10 10 10 10 m a ~ (GeV) 17 Howie Baer, UW Pheno 2009 meeting, May 12, 2009

Thermally produced axinos for f a /N = 10 12 GeV 10 10 12 GeV Ω f a /N = 10 TP ~ h a 2 = 0.1 9 10 Ω TP ~ h a 2 = 0.03 8 10 T R (GeV) 7 10 Ω TP ~ h a 2 = 0.01 NT leptogenesis 6 10 Ω TP 5 10 ~ h a 2 = 0.001 hot warm cold 4 10 -7 -6 -5 -4 -3 -2 -1 10 10 10 10 10 10 10 m a ~ (GeV) 18 Howie Baer, UW Pheno 2009 meeting, May 12, 2009