GUTs, Inflation, and Phenomenology
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1 GUTs, Inflation, and Phenomenology Qaisar Shafi Bartol Research Institute Department of Physics and Astronomy University of Delaware in collaboration with G. Dvali, R. K. Schaefer, G. Lazarides, N. Okada, B. Kyae, K.Pallis, M. Rehman, N. Senoguz, J. Wickman, A. Vilenkin, M. Bastero-Gil, S. Antusch, S. King, S.Boucenna, S. Morisi, J.Valle DSU 2015, Kyoto, Japan. December / 34
2 Introduction GUTs, Inflation & Primordial Monopoles Supersymmetry & Inflation Low Energy Predictions Summary 2 / 34
3 Physics Beyond the Standard Model Neutrino Physics: SM + Gravity suggests m ν 10 5 ev, which disagrees with neutrino data; Dark Matter: SM offers no plausible DM candidate; Origin of matter in the universe: Electric Charge Quantization: Unexplained in the SM; CMB Isotropy / Anisotropy, Origin of Structure require ideas beyond Hot Big Bang Cosmology (which comes from SM + General Relativity.) Strong CP Problem. 3 / 34
4 Grand Unified Theories (GUTs) Unification of SM / MSSM gauge couplings; Unification of matter/quark-lepton multiplets; Electric charge quantization; Magnetic monopoles. Seesaw physics / neutrino oscillations; Quark-Lepton mass relations; New source for baryo-leptogenesis; Inflation / Observable gravity waves (Planck) Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs 4 / 34
5 Magnetic Monopoles in Unified Theories Any unified theory with electric charge quantization predicts the existence of topologically stable ( thooft-polyakov ) magnetic monopoles. Their mass is about an order of magnitude larger than the associated symmetry breaking scale. Examples: 1 SU(5) SM (3-2-1) Lightest monopole carries one unit of Dirac magnetic charge even though there exist fractionally charged quarks; 2 SU(4) c SU(2) L SU(2) R (Pati-Salam) Electric charge is quantized with the smallest permissible charge being ±(e/6); Lightest monopole carries two units of Dirac magnetic charge; 5 / 34
6 Magnetic Monopoles in Unified Theories Examples: 3 SO(10) Two sets of monopoles: First breaking produces monopoles with a single unit of Dirac charge. Second breaking yields monopoles with two Dirac units. 4 E 6 breaking to the SM can yield lighter monopoles carrying three units of Dirac charge. The discovery of primordial magnetic monopoles would have far-reaching implications for high energy physics & cosmology. 6 / 34
7 Tree Level Gauge Singlet Higgs Inflation [Kallosh and Linde, 07; Rehman, Shafi and Wickman, 08] Consider the following Higgs Potential: V (φ) = V 0 [1 ( φ M ) 2 ] 2 (tree level) Here φ is a gauge singlet field. V Φ Below vev BV inflation Above vev AV inflation WMAP/Planck data favors BV inflation (r 0.1). M Φ 7 / 34
8 Higgs Potential: n s vs. r for Higgs potential, superimposed on Planck and Planck+BKP 68% and 95% CL regions taken from arxiv: The dashed portions are for φ > v. N is taken as 50 (left curves) and 60 (right curves). 8 / 34
9 Coleman Weinberg Potential: n s vs. r for Coleman Weinberg potential, superimposed on Planck and Planck+BKP 68% and 95% CL regions taken from arxiv: The dashed portions are for φ > v. N is taken as 50 (left curves) and 60 (right curves). 9 / 34
10 Coleman-Weinberg Potential Higgs Potential M X 2 V 1/4 0 (GeV) τ(p π 0 e + ) (years) M X V 1/4 0 (GeV) τ(p π 0 e + ) (years) Table: Superheavy gauge bosons masses and corresponding proton lifetimes with α G = 1 35 in the CW and Higgs models. Note that since the lifetime depends only on M X, the results shown here apply equally well to the BV and AV branches in each model. 10 / 34
11 H GeV Coleman Weinberg Potential: n s vs. H for Coleman Weinberg potential, superimposed on Planck TT+lowP+BKP 95% CL region taken from arxiv: The dashed portions are for φ > v. N is taken as 50 (left curves) and 60 (right curves). s 11 / 34
12 Higgs Potential: H GeV n s 12 / 34
13 Primordial Monopoles Let s consider how much dilution of the monopoles is necessary. M I GeV corresponds to monopole masses of order M M GeV. For these intermediate mass monopoles the MACRO experiment has put an upper bound on the flux of cm 2 s 1 sr 1. For monopole mass GeV, this bound corresponds to a monopole number per comoving volume of Y M n M /s There is also a stronger but indirect bound on the flux of (M M /10 17 GeV)10 16 cm 2 s 1 sr 1 obtained by considering the evolution of the seed Galactic magnetic field. At production, the monopole number density n M is of order Hx, 3 which gets diluted to Hxe 3 3Nx, where N x is the number of e-folds after φ = φ x. Using Y M H3 xe 3Nx, s where s = (2π 2 g S /45)T 3 r, we find that sufficient dilution requires N x ln(h x /T r ) Thus, for T r 10 9 GeV, N x 30 yields a monopole flux close to the observable level. 13 / 34
14 SUSY Higgs (Hybrid) Inflation [Dvali, Shafi, Schaefer; Copeland, Liddle, Lyth, Stewart, Wands 94] [Lazarides, Schaefer, Shafi 97][Senoguz, Shafi 04; Linde, Riotto 97] Attractive scenario in which inflation can be associated with symmetry breaking G H Simplest inflation model is based on W = κ S (Φ Φ M 2 ) S = gauge singlet superfield, (Φ, Φ) belong to suitable representation of G Need Φ, Φ pair in order to preserve SUSY while breaking G H at scale M TeV, SUSY breaking scale. R-symmetry Φ Φ Φ Φ, S e iα S, W e iα W W is a unique renormalizable superpotential 14 / 34
15 Tree Level Potential V F = κ 2 (M 2 Φ 2 ) 2 + 2κ 2 S 2 Φ 2 SUSY vacua Φ = Φ = M, S = 0 S M V Κ 2 M M 1 15 / 34
16 Tree level + radiative corrections + minimal Kähler potential yield: n s = 1 1 N δt/t proportional to M 2 /M 2 p, where M denotes the gauge symmetry breaking scale. Thus we expect M M GUT for this simple model. Since observations suggest that n s lie close to 0.97, there are at least two ways to realize this slightly lower value: (1) include soft SUSY breaking terms, especially a linear term in S; (2) employ non-minimal Kähler potential. 16 / 34
17 MSSM µ-problem and Inflation U(1) R symmetry prevents a direct µ term but allows the superpotential coupling λh u H d S Since S acquires a non-zero VEV m 3/2 from supersymmetry breaking, the MSSM µ term of the desired magnitude is realized. 17 / 34
18 µ-term Inflation U(1) R-symmetry yields the following unique renormalizable superpotential: W = S(κΦΦ κm 2 + λh u H d ). Include SUSY breaking/sugra, the inflationary potential is [ ]) φ V (φ) = m (1 4 + A ln 2 2m G m 2 φ, φ 0 φ = 2Re[S], m κm, A = 1 ( 4π 2 λ 2 + N ) Φ 2 κ2. Successful inflation/gauge symmetry breaking requires λ > κ. 18 / 34
19 µ-term Inflation MSSM µ-term µ = λ κ m G γm G. n s 1 2 N 0 f(b), B = 2 2 m G φ 0 A m 2 For N 0 =60: 1) B = 0 f(b) = 1/2 n s ) B = 0.7 f(b) = 1.03 n s / 34
20 Figure: Spectral index n s vs. B. The region between the two dotted (dashed) lines corresponds to 1σ (2σ) limit obtained by Planck / 34
21 Inflaton Decay: Γ(φ H u Hd ) = λ2 8π m φ. T r GeV. Cosmology with gravitinos: 1) LSP gravitino not realized. 2) If m G is sufficiently large, LSP is still in thermal equilibrium when inflaton/gravitino decay m G ( GeV ) ( m ) LSP 2/3. 2TeV 21 / 34
22 Minimal scenario yields Split Susy m 0 m G µ( tan β 2, m h 125GeV) M 1/2 TeV Wino dark matter m0 GeV tanβ Figure: Soft scalar mass m 0 as a function of tan β. 22 / 34
23 Non-minimal Kähler potential K = S 2 + Φ 2 + Φ 2 + κ S S 4 + κ Sφ S 2 Φ 2 m 2 p 4m 2 p + κ Sφ S 2 Φ 2 m 2 p S 6 + κ SS 6m 4 + p S Allowed region Figure: The region in the κ and κ S plane satisfying R = / 34
24 Non-minimal Kähler potential In some cases, n s κ s. n s s = 0 s = s = s = 0.01 s = Figure: n s as a function of κ for different values of κ S (N = 1). The red and pink bands correspond to the WMAP 1σ and 2σ range [?]. 24 / 34
25 µ term, axion and hybrid inflation Consider the superpotential: W = κs( H c H c M 2 ) βs ( H c H c ) 2 M S M 2 S + λ 1 N 2 h 2 M S + λ 2 N 2 N 2 M S + λ ij Fi c Hc Hc F j h + γ i Fi c Fi c + agh c H c + bg H c Hc R : H c (0), H c (0), S(1), G(1), F (1/2), F c (1/2), N(1/2), N(0), h(0); P Q : H c (0), H c (0), S(0), G(0), F ( 1), F c (0), N( 1), N(1), h(1). V P Q = 2 N 2 m 2 3/2 ( 4λ 2 N 4 2 m 2 3/2 M S 2 N = ( N = (m 3/2 M S ) 1/2 ) N 2 A λ m 3/2 M S A + A λ 2 ) 1/2. 25 / 34
26 µ term, axion and hybrid inflation The inflaton potential contains, in addition to the desired minimum at f a, a local minimum at the origin, with a barrier separating the two. One should make sure that the desired minimum is reached after inflation, without generating excessive amount of entropy. In this case the subsequent reheating and leptogenesis proceeds in a more conventional way and the µ term m 3/2 TeV. 26 / 34
27 SUSY SO(10) Fermion families reside in 16 i (i=1,2,3); predicts right handed neutrino non-zero neutrino masses through seesaw mechanism. Automatic Z 2 matter parity if SO(10) MSSM using only tensor repsns. Also means stable cosmic strings (in addition to monopoles) Yukawa couplings include 16 i 16 j 10, 16 i 16 j 126, etc yields t b τ unification Y t = Y b = Y τ = Y ν (not so in non-susy SO(10)) In the old days (B. Ananthanarayan, G. Lazarides and Q. Shafi, 1991) it was used to predict the top quark mass Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs 27 / 34
28 Nowadays, one employs t b τ unification to make predictions, such as sparticle masses, which can be tested at the LHC (Baer et al.,raby et al.,...); t b τ Yukawa unification can also be realized in SU(4) c SU(2) L SU(2) R, a maximal subgroup of SO(10); Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs 28 / 34
29 t-b-τ Yukawa Unification at LHC m 16, m 2 H u, m 2 H d, m 1/2, A 0, tan β, sign(µ) 0 m TeV 0 m Hu 35 TeV 0 m Hd 35 TeV 0 m 1/2 5 TeV 30 tan β 60 3 A 0 /m 0 3 In order to quantify Yukawa coupling unification, we define the quantity R tbτ = max(y t, y b, y τ ) min(y t, y b, y τ ). 29 / 34
30 Point 1 Point 2 Point 3 Point 4 m m 1/ A 0 /m tan β m Hd m Hu m h m H m A m H ± m g m χ 0 1,2 122, , , ,1114 m χ 0 3, , , , ,6315 m ± 286, , , ,6275 χ 1,2 mũl,r 21389, , , ,26079 m t1,2 7389, , , ,7901 m dl,r 21389, , , ,26304 m b1,2 7836, , , ,9652 m ν m ν mẽl,r 21193, , , ,26319 m τ1,2 7490, , , ,19455 Ω CDM h R tbτ BF ( b b i ) BF ( t t i ) BF ( t b j + c.c.) / 34
31 SO(10) t b τ YU with NUGM Consider M 3 : M 2 : M 1 = 2 : 3 : 1. Point 1 Point 2 Point 3 µ m h m H m A m H ± m χ 0 1,2 895, , , 2540 m χ 0 3,4 3742, , , 3849 m ± 3789, , , 3809 χ 1,2 m g mũl,r 7667, , , 5635 m t1,2 5331, , , 5370 m dl,r 7668, , , 5628 m b1,2 5553, , , 5341 m ν1, m ν mẽl,r 4153, , , 2068 m τ1,2 1094, , , 3225 (g 2) µ σ SI (pb) σ SD (pb) Ω CDM h R tbτ / 34
32 b-τ YU in SU(4) SU(2) L SU(2) R (422) m 16, m Hi, M i, A 0, tan β, sign(µ) m 16 Universal soft SUSY breaking (SSB) sfermion mass m Hd,H u Universal SSB MSSM Higgs masses. M i SSB gaugino masses. M 1 = 3 5 M M 3 A 0 Universal SSB trilinear interaction tan β = vu v d µ SUSY bilinear Higgs parameter µ > 0 32 / 34
33 Random scans for the following parameter range (NUHM2): 0 m TeV, 0 M 2 5 TeV, 0 M 3 5 TeV, 3 A 0 /m 16 3, 0 m Hd 20 TeV, 0 m Hu 20 TeV 2 tan β 60, µ > 0, m t = GeV. 33 / 34
34 Point 1 Point 2 Point 3 Point 4 Point 5 m M M M m Hd, m Hu 11720, , , , , 5478 tan β A 0 /m m t µ (g 2) µ m h m H m A m H ± m χ 0 1,2 641, , , , , 2441 m χ 0 3,4 4973, , , , , m ± 1697, , , , , χ 1,2 m g mũl,r 12743, , , , , m t1,2 689, , , , , 5263 m dl,r 12743, , , , , m b1,2 6234, , , , , 7047 m ν m ν mẽl,r 12846, , , , , m τ1,2 9129, , , , , σ SI (pb) σ SD (pb) Ω CDM h R / 34
35 Point 1 Point 2 Point 3 m M M M m Hd m Hu A 0 /m tan β m h m H m A m H ± m χ 0 1,2 932, , , 2988 m χ 0 3, , , , m ± 2748, , , χ 1,2 m g mũl,r 19187, , , m t1,2 4640, , , 7283 m dl,r 19187, , , m b1,2 6664, , , 8091 m ν m ν mẽl,r 19111, , , m τ1,2 6372, , , σ SI (pb) σ SD (pb) Ω CDM h R tbτ / 34
36 Summary If r , then inflation models based on the Higgs / Coleman-Weinberg potentials can provide simple / realistic frameworks for inflation, with minimal coupling to gravity. There is a lower bound on H (Hubble constant) in these models. This is important for topological defects in GUT models involving intermediate scales. If r 0.01, then supersymmetric hybrid inflation models are especially interesting. These work with inflaton field values below M Planck, and supergravity corrections are under control. The simplest versions employ TeV scale SUSY, and hopefully LHC 14 will find it. µ-term assisted hybrid inflation consistent with Wino dark matter and a 125 GeV SM-like Higgs. Gluino mass in the TeV range. Susy hybrid inflation compatible with axion physics. b-τ YU in 4-2-2: NLSP Gluino, NLSP Stop t-b-τ YU in (NUHM2): Gluino lightest colored particle (can be 2-3 TeV) 36 / 34
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