Topological Defects, Gravity Waves and Proton Decay

Transcription

1 Topological Defects, Gravity Waves and Proton Decay Qaisar Shafi Bartol Research Institute Department of Physics and Astronomy University of Delaware in collaboration with A. Ajaib, S. Boucenna, G. Dvali, I. Gogoladze, A. Hebbar, T. Kibble, B. Kyae, G. Lazarides, G. Leontaris, F. Nasir, C. Pallis, N. Okada, M. Rehman, N. Senoguz, C.S. Un 1 / 34

2 Non-SUSY SO(10) G = SO(10)/Spin(10) H = SU(3) c U(1) e.m. Π 2 (G/H) = Π 1 (H) Monopoles Π 1 (G/H) = Π 0 (H) = Z 2 Cosmic Strings (provided G H breaking uses only tensor representations) Z 2 Z 4 (center of SO(10)) Recent work suggests that this Z 2 symmetry can yield plausible cold dark matter candidates. Intermediate scale monopoles and cosmic strings may survive inflation. [Yann Mambrini, Natsumi Nagata, Keith A. Olive, Jeremi Quevillon, and Jiaming Zheng Phys.Rev. D91 (2015) no.9, ; Sofiane M. Boucenna, Martin B. Krauss, Enrico Nardi Phys.Lett. B755 (2016) ] 2 / 34

3 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. Sunday, May 21, :46 AM Examples: 1 SU(5) SM (3-2-1) Lightest monopole carries one unit of Dirac magnetic charge even though there exist fractionally charged quarks; SU(3) U(1) em monopole mass M G α G 3 / 34

4 3 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; 4 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. 5 E 6 breaking to the SM can yield lighter monopoles carrying three units of Dirac charge. 6 E 6 SU(3) c SU(3) L SU(3) R SU(3) c SU(2) L U(1) em The discovery of primordial magnetic monopoles would have far-reaching implications for high energy physics & cosmology. 4 / 34

5 Primordial Monopoles They are produced via the Kibble Mechanism as G H: Center of monopole has G symmetry φ = 0 Initial no. density Tc 3. With big bang cosmology such numbers are unacceptable. r in = Nm N γ Monopole Problem (Need Inflation) 5 / 34

6 Cosmic Strings from SO(10) Consider SO(10) M GUT M SU(4) SU(2) L SU(2) I GeV R SU(3) SU(2) U(1) Z 2 Cosmic Strings with Gµ should be around 6 / 34

7 Stochastic gravitational wave backgrounds compared with present and future experiments. The grey lines show the background from cosmic strings with the indicated energy scales G. The straight black line is the largest allowable background from SMBBH.[arxiv: ] 7 / 34

8 Inflationary Cosmology [Starobinsky, Mukhanov, Chibisov, Guth, Linde, Hawking, ] Successful Primordial Inflation should: Explain flatness, isotropy; Provide origin of δt T ; Offer testable predictions for n s, r (gravity waves), dn s /d lnk; Recover Hot Big Bang Cosmology; Explain the observed baryon asymmetry; Offer plausible CDM candidate; 8 / 34

9 Slow-roll inflation Inflation is driven by some potential V (φ): Slow-roll parameters: ɛ = m2 p 2 ( V V ) 2, ( ) η = m 2 V p V. The spectral index n s and the tensor to scalar ratio r are given by n s 1 d ln 2 R d ln k, r 2 h, 2 R where 2 h and 2 R are the spectra of primordial gravity waves and curvature perturbation respectively. Assuming slow-roll approximation (i.e. (ɛ, η ) 1), the spectral index n s and the tensor to scalar ratio r are given by n s 1 6ɛ + 2η, r 16ɛ. 9 / 34

10 Slow-roll inflation The tensor to scalar ratio r can be related to the energy scale of inflation via V (φ 0 ) 1/ r 1/4 GeV. The amplitude of the curvature perturbation is given by ( 2 R = 1 V/m 4 ) p 24π 2 ɛ = (WMAP7 normalization). φ=φ 0 The spectrum of the tensor perturbation is given by ( ) 2 h = 2 V 3 π 2 m 4 P φ=φ 0. The number of e-folds after the comoving scale l 0 = 2 π/k 0 has crossed the horizon is given by N 0 = 1 φ0 ( V ) m 2 p φ e V dφ. Inflation ends when max[ɛ(φ e ), η(φ e ) ] = / 34

11 Inflation with a Higgs Potential [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 Note: This is for minimal coupling to gravity Φ 11 / 34

12 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). 12 / 34

13 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). 13 / 34

14 Primordial Monopoles in SO(10) 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. 14 / 34

15 Relativistic Monopoles at IceCube Source: IceCube Collaboration, Eur. Phys. J. C (2016) 76: / 34

16 Where is SUSY? 0 ) [GeV] 1 m( χ s=13 TeV, 36.1 fb ATLAS Preliminary 0 g ~ qq χ 0 lep. [ ] 1 0 g ~ bb χ 3 b-jets [ ] 1 0 g ~ tt χ 3 b-jets + 2 lep. SS [ , ] 1 0 g ~ qqw χ 0 lep. + 1 lep. [ , ] 1 0 g ~ qqwz χ 7-11 jets + 1 lep. + 2 lep. SS 1 [ , , ] 0 ~ g ~ qq(ll/νν) χ via l/ ν 2 lep. OS SF + 3 lep. [ , ] 1 0 g ~ qq(ττ/τν/νν) χ via τ/ ν 1 τ [SUSY ] 1 0 g ~ qq(γ/z)g ~ via χ 1 γ [ ] 1 All limits at 95% CL July m( ~ g) [GeV] ) 0 m( ~ g)<m( χ 1 ) [GeV] 0 1 m( χ SUSY ~ m( l L / τ L / ν ) = m( χ ATLAS Preliminary [ m( ) = m( χ 0 0 χ 1 ) 1 ) + m( ± χ, 1 0 χ 2 ) ] -1 s=8,13 TeV, fb Observed limits at 95% CL + χ χ via 1 1 ~ l / ν L 2l arxiv: χ arxiv: arxiv: ν τl / τ 2τ arxiv: arxiv: WW 2l arxiv: ATLAS-CONF ± 0 χ via 1 2 ~ l / ν L 2l+3l arxiv: arxiv: WZ 2l+3l arxiv: arxiv: arxiv: arxiv: ± ± Wh lbb+l γγ+l l +3l arxiv: ± χ χ / χ χ via ± 0 / ν τl 2τ m( χ, χ ) [GeV] τ 1 2 arxiv: / 34

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18 SUSY Yukawa Unification Importance of finite SUSY threshold corrections b τ Yukawa coupling unification Without Supersymmetry yb yτ Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs Log(Energy/GeV) 18 / 34

19 b-τ YU and finite threshold corrections 1 Dominant contributions to the bottom quark mass from the gluino and chargino loop δy b g 3 2 µm g tan β + y 2 12π 2 m1 2 t µa t tan β π 2 m2 2 where m 1 (m b1 + m b2 )/2 and m 2 (m t 2 + µ)/2 where λ b = y b and λ t = y t 1 L. J. Hall, R. Rattazzi and U. Sarid, Phys. Rev.D 50, 7048 (1994) Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs 19 / 34

20 b τ YU in SU(5) 0 m TeV 0 m 5 20 TeV 0 M 1/2 5 TeV 3 A t /m A bτ /m tan β 60 0 m Hd 20 TeV 0 m Hu 20 TeV R Max(y b, y τ ) Min(y b, y τ ) 1.1 b τ YU Condition y b : y τ = (1 C) : (1 + 3C), C 0.2 b τ QYU Condition 20 / 34

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22 Non-minimal quartic inflation W = S[κ(X X M 2 )] + σh u H d S 22 / 34

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24 Non-minimal quartic inflation [Okada, QS, 2017] µ-inflation µ = σ S = σ κ m 3/2 σ = κ µ m 3/2, m 3/2 M Inflaton Decay (mass κm): Γ = σ2 2 8π m µ φ = 8π κ3 ( ) 2 M m 3/2 T r κ 3/2 µ ( )M 1/2 [GeV ] m 3/2 [with Nobuchika Okada] 24 / 34

25 Non-minimal quartic inflation µ-inflation / Phenomenological Constraints: Gravitino LSP, T r 10 6 GeV to avoid the gravitino problem κ ( m 3/2 µ )2/3 M 1/3 = M 1/3 ; m φ > m Hu,d 2κM 1000GeV

26 Κ M GeV Red T R = 10 6 GeV Blue m φ = m Hu,d = 1 TeV Black r = 0.1 Green shaded region satisfies all conditions, M(GeV ) M(GeV ) [ includes Axion case with f a M GeV, r axion 0.007] / 38 34

27 r M GeV 27 / 34

28 Gravitino LSP: Relic density from thermal productions Ωh GeV ( Tr m 3/2 ) ( ) 2 M T ev κ ( ) m 2 2/3 (3T ) 3/2 ev 4/3 µ M M 3 BBN constraint on NLSP lifetime: ( ) 100GeV 5 ( τ NLSP 10 4 m3/2 ) 2 sec < 1s 1GeV m NLSP 28 / 34

29 Gravitino LSP: Take µ 1T ev m NLSP τ NLSP < 1s m 3/2 3GeV For various m 3/2 = 3, 1, 0.32GeV ( from top to bottom) Κ M GeV To be able to find a solution, m 3/2 0.32GeV 29 / 34

30 Hyper-Kamiokande Physics Goals Astrophysical / / 34

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32 SUSY-SU(5) U(1) χ In presence of dimension five operators the unification condition is modified to (1+ɛ 1 ) 1 α 1 1 (M GUT ) = (1+ɛ 2 ) 1 α 1 2 (M GUT ) = (1+ɛ 3 ) 1 α 1 3 (M GUT ) where, ɛ 1 : ɛ 2 : ɛ 3 :: 1 : 6 : 4 ɛ 1 = 0.01, M G = GeV and Λ = / 34

33 Summary Unification of all forces remains a compelling idea. Grand unification explains charge quantization, predicts monopoles and proton decay. Stable cosmic strings predicted in realistic GUT. Also explains tiny neutrino masses via seesaw mechanism. Non-SUSY gauge coupling unification require new particles/new physics below M GUT. In non-susy inflation with Higgs potential, r 0.02 (minimal coupling to gravity). SUSY and Non-SUSY models offer plausible dark matter candidates such as TeV mass higgsino, axions... Higher dimensional operators can have significant impact on M GUT and proton decay predictions in GUTs; expecially if the ultraviolet cut-of scale is closer to M GUT Find dark matter, gravity waves and proton decay. 33 / 34

34 Thank You! 34 / 34