How to explain the Universe with electroweak scale only

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1 How to explain the Universe with electroweak scale only Fedor Bezrukov Ludwig-Maximilians-Universität München ARNOLD SOMMERFELD CENTER for theoretical physics Germany Kosmologietag 2011 Bielefeld May 6, 2011

2 Outline 1 Our present knowledge of particle physics and the Universe Standard Model SM problems in laboratory and in cosmology 2 Higgs mass bounds 3 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys 4 The model with non-minimal gravity coupling Predictions May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 2 / 43

3 Standard Model SM problems in laboratory and in cosmology Standard Model describes nearly everything that we know Gauge theory SU(3) SU(2) U(I) Describes (together with Einstein gravity) all laboratory experiments electromagnetism, nuclear processes, etc. all processes in the evolution of the Universe after the Big Bang Nucleosynthesis (T < 1 MeV, t > 1sec) mass charge name Quarks Leptons ⅔ Three Generations of Matter (Fermions) spin ½ I II III 2.4 MeV 1.27 GeV ⅔ ⅔ u c up charm Right Right Right 4.8 MeV 104 MeV -⅓ -⅓ d s down strange ν e 0 ev 0 ν electron neutrino μ 0 ev 0 ν muon neutrino Right Right Right GeV t top 4.2 GeV -⅓ b bottom τ 0 ev 0 tau neutrino MeV MeV GeV e μ τ electron muon tau Right Right Right Bosons (Forces) spin g gluon γ photon 91.2 GeV Z 0 0 weak force 80.4 GeV W ± ± 1 weak force >114 GeV 0 0 H Higgs boson spin 0 May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 3 / 43

4 Standard Model SM problems in laboratory and in cosmology Standard Model has experimental problems Laboratory Neutrino oscillations Cosmology Baryon asymmetry of the Universe Dark Matter Inflation Horizon problem (and flatness, entropy,... ) Initial density perturbations Dark Energy May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 4 / 43

Neutrino oscillations SAGE neutrino observatory (solar oscillations evidence ν e ν µ ) SuperKamiokande (atmosferic oscillations ν µ ν

parameters m21 2 7.59±0.20 10 5 ev 2 sin 2 2θ 12 0.87 ± 0.03 m32 2 2.43±0.13 10 3 ev 2 sin 2 2θ 23 > 0.92 sin 2 2θ 13 < 0.

CHORUS NOMAD CHORUS LSND 90/99% SuperK 90/99% MINOS All limits are at 90%CL 10 12 unless otherwise noted 10 4 10 2 10 0 tan 2 θ

5 Neutrino oscillations SAGE neutrino observatory (solar oscillations evidence ν e ν µ ) SuperKamiokande (atmosferic oscillations ν µ ν τ ) Reactor neutrinos, accelerator neutrinos Standard Model SM problems in laboratory and in cosmology m 2 [ev 2 ] Oscillation parameters m ± ev 2 sin 2 2θ ± 0.03 m ± ev 2 sin 2 2θ 23 > 0.92 sin 2 2θ 13 < KARMEN2 Cl 95% NOMAD Ga 95% Bugey CHOOZ ν e ν X ν µ ν τ ν e ν τ ν e ν µ NOMAD all solar 95% SNO 95% CDHSW CHORUS NOMAD CHORUS LSND 90/99% SuperK 90/99% MINOS All limits are at 90%CL unless otherwise noted tan 2 θ May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 5 / 43 MiniBooNE K2K KamLAND 95% Super-K 95% 10 2

6 Baryon asymmetry of the Universe Standard Model SM problems in laboratory and in cosmology Current universe contains baryons and no antibarions Current baryon density η B n B n γ Yp D 0.24 H He D/H p 20. Big-Bang nucleosynthesis 3 Baryon density Ω b h BBN CMB 3 He/H p Does not fit into the SM (too weak CP violation, too smooth phase transition) Li/H p Baryon-to-photon ratio η Figure 20.1: The abundances of 4 He, D, 3 He, and 7 Li as predicted by the standard model of Big-Bang nucleosynthesis [11] the bands show the 95% CL range. Boxes indicate the observed light element abundances (smaller boxes: ±2σ statistical errors; larger boxes: ±2σ statistical and systematic errors). The narrow vertical band indicates the CMB measure of the cosmic baryon density, while the wider May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 6 / 43

Our present knowledge of particle physics and

21 May 6, 2011 CMB fluctuations Fedor Bezrukov

7 Our present knowledge of particle physics and the Universe Standard Model SM problems in laboratory and in cosmology Dark Matter Gravitational lensing Rotation curves ΩDM ' 0.21 May 6, 2011 CMB fluctuations Fedor Bezrukov Bullet cluster How to explain the Universe with electroweak scale 7 / 43

Our present knowledge of particle physics and the Universe Standard Model SM problems in laboratory and in cosmology Temperature fluctuations δ T /T 10 5 conformal time Microwave sky conformal time

8 Our present knowledge of particle physics and the Universe Standard Model SM problems in laboratory and in cosmology Temperature fluctuations δ T /T 10 5 conformal time Microwave sky conformal time Inflation evidence horizon problem particle horizon space coordinate casually connected regions inflationary expansion Universe is uniform! space coordinate May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 8 / 43

from inflation Temperature fluctuations CMB spectrum Polarization May 6,

9 Our present knowledge of particle physics and the Universe Standard Model SM problems in laboratory and in cosmology CMB gives measured predictions from inflation Temperature fluctuations CMB spectrum Polarization May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 9 / 43

10 Inflationary parameters from CMB Standard Model SM problems in laboratory and in cosmology Spectrum of primordial scalar density perturbations is just a bit not flat n s 1 d logp R d logk Tensor perturbations are compatible with zero r P grav P R (WMAP07 results) May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 10 / 43

11 Standard Model SM problems in laboratory and in cosmology Dark Energy Supernova type Ia redshifts accelerated expansion of the Universe today Ω Λ 0.74 Different from inflation Much lower scale No need to stop it Can be explained just by a cosmological constant (invented already by Einstein) May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 11 / 43

12 Universe history 2.7 K TODAY 14 Gyr 4.1 K accelerating expansion matter dominated expansion 7.1 Gyr 0.26 ev recombination 0.37 Myr matter dominated expansion 0.76 ev 57 kyr radiation dominated expansion baryogenesis 50 kev 5 min Big Bang Nucleosynthesis 1 MeV 1 s 2.5 MeV neutrino decoupling 0.1 s 200 MeV QCD phase transition 10 µs Electroweak phase transition 100 GeV 0.1 ns hot Universe preheating Standard Model SM problems in laboratory and in cosmology dark matter generation Standard Model works ok here inflation May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 12 / 43

13 Higgs mass bounds Let us expand the model in a minimal way I will follow a Minimal approach Explain the experimental facts with minimal number of new particles no new physical scales Different situation in usual approaches Solve hierarchy problems first } Supersymmetry, New physics at TeV energies Extra dimensions... masks us from early Universe May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 13 / 43

14 Higgs mass bounds Several examples of minimal extensions leading to inflation νmsm (for DM and Baryogenesys) + Inflation with light inflaton (Introduces new particle) Higgs boson inflation [Shaposhnikov, Tkachev 06] [Anisimov, Bartocci, FB 09] [FB, Gorbunov 10] [FB, Shaposhnikov 08] [FB, Gorbunov, Shaposhnikov 09] [FB, Magnin, Shapshnikov 09] (Modifies Higgs-gravity interaction, new scales M P /ξ, M P / ξ ) R 2 (scalaron) inflation (Modification only in the gravity sector) [Starobinsky 80] [Gorbunov, Panin 10] May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 14 / 43

15 Higgs mass bounds Common prediction: Higgs mass window interaction strength Λ The model should be valid up to inflationary scale: Radiative corrections to the Higgs potenital may spoil this Higgs mass bounds m H 174 = 190 GeV m H = 126 GeV m H GeV Μ,GeV inflationary M P 10scale 20 Energy scale 126GeV m H 190GeV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 15 / 43

16 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Chaotic inflation for a scalar field with quartic potential λ (20M P ) 4 4 U λ 4 φ 4 3M P Slow roll inflation 20M P φ δt /T 10 5 normalization quartic coupling: λ Not present in the SM? Just add it! May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 16 / 43

17 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Light inflaton model adds one scalar particle to the SM L = L SM + αh HX 2 + β 4 X 4 Standard Model Interaction Inflationary sector (where β β 0 = inflationary requirement) β m χ = m h the inflaton mass is defined by α 2α The Higgs-inflaton scalar potential is ( V (H,X) = λ H H α λ X 2) 2 β + 4 X µ2 X 2 + V 0 [Anisimov, Bartocci, FB 09, FB, Gorbunov 10] May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 17 / 43

18 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Radiative corrections require a small SM-inflaton coupling Radiative corrections induce quartic coupling which should not spoil the flatness of the potential X H X α α X X H X X X X This leads to an upper bound on the SM-inflaton interaction X α 2 log should be < X β 0 X X α 10 7 (roughly: α < β ) Lower bound for the inflaton mass m χ > 90 MeV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 18 / 43

19 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Radiative corrections require a small SM-inflaton coupling Radiative corrections induce quartic coupling which should not spoil the flatness of the potential δv = m4 (X) 64π 2 log m2 (X) should be µ 2 < V inflaton = β 4 X 4 m 2 h (X) = 4αX 2 (Higgs boson) This leads to an upper bound on the SM-inflaton interaction α 10 7 (roughly: α < β ) Lower bound for the inflaton mass m χ > 90 MeV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 18 / 43

20 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Preheating requires large SM-inflaton coupling After inflation: empty & cold Needed: hot, T r > 150 GeV (to get baryogenesis) Equating H production rate ( α 2 ) to Hubble expansion rate ( T 2 ) Γ XX HH H Lower bound on α α [Anisimov, Bartocci, FB 09] Parametric resonance? Not so easy to create the Higgs Number density Time Inflaton Higgs nχ nφ α =10 9 α =10 10 α =10 11 α =10 12 α = tpr The large Higgs self interaction destroys coherence and spoils parametric resonance. May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 19 / 43

21 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Inflaton is in the experimentally explorable range Inflaton mass window (from Cosmology) 90 MeV < m χ < 1.8 GeV Lower bound: radiative corrections Upper bound: sufficient reheating Also possible: 2m H < m χ 600 GeV Details May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 20 / 43

22 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Inflaton-SM Interactions As the Higgs boson, but light and suppressed by θ = 2βv/m χ Created: in meson decays Decays: the heaviest particle pairs (ee, ππ, µµ, KK ) Interacts with media: extremely weakly L χ f f =θ m f v χ f f = 2β m f χ f f m χ L χππ = 2κ ( χ 1 2β m χ L χγγ F γγα 4π χ mπ 2 m χ 2β χ F µν F µν L χgg F ggα s m χ 4 8π (3κ + 1) 2β ) 2 µπ 0 µ π 0 + µ π + µ π ( 1 2 π0 π 0 + π + π ) ( ) κ = 2/9 2β m χ χ G a µνg a µν May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 21 / 43

23 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Inflaton is relatively long lived 1 e + e - ππ cc KK τ + τ 0.1 µ + µ gg 0.01 ss γγ µ + µ e-05 1e-06 Branching τ χ, s Lifiteime 1e-07 1e-08 1e-09 1e-10 1e m χ, GeV Inflaton mass May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 22 / 43

24 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Produced in meson decays and in beam dumps Br(K + π + χ) Br ( K L π 0 χ ) Br ( η π 0 χ ) Br(B X s χ) 10 5 ( ) ( ) 2 ( ) β β 0 100MeV mχ m χ k m meson In a p-beam dump (via meson decays), ideal luminosity E, GeV N POT, NuTeV CNGS NuMi T2K N produced 1e+14 1e+12 1e+10 1e+08 1e Meson decay, NuTeV Meson decay, CNGS Meson decay, NuMi Meson decay, T2K gg fusion, T2K m χ, GeV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 23 / 43

25 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Hadron decays constrain inflaton mass Br(K->πχ) 1e-06 1e-07 1e-08 1e-09 Expected K + E949 K + E787 K + expected K L expected Bound from decay K + π + + nothing m χ > 120 MeV β 1e-10 1e-11 1e-08 1e-10 1e-12 β 0 1e-14 Excluded m χ, GeV Bound from X decay into e + e, µ + µ m χ > 270 MeV 1e m χ, GeV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 24 / 43

26 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys B-meson decays search for the inflaton! Br(K + π + χ) Br ( K L π 0 χ ) Br ( η π 0 χ ) Br(B X s χ) 10 5 In a p-beam dump (via meson decays), ideal luminosity E, GeV N POT, NuTeV CNGS NuMi T2K ( ) ( ) 2 ( ) β β 0 100MeV mχ m χ k m meson N produced LHCb: events with offset vertex 1e+14 1e+12 1e+10 1e+08 1e Meson decay, NuTeV Meson decay, CNGS Meson decay, NuMi Meson decay, T2K gg fusion, T2K m χ, GeV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 25 / 43

27 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Validity up to inflationary scale interaction strength Λ Radiative corrections screening of the Higgs self-interaction depending on scale Higgs mass bounds m H 174 = 190 GeV m H = 126 GeV m H GeV Μ,GeV inflationary M P 10scale 20 Energy scale 126GeV m H 190GeV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 26 / 43

28 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys Dark matter add νmsm and stir Light inflaton + mass charge name Quarks Leptons ⅔ 2.4 MeV u up Right Right Right ⅔ 1.27 GeV c charm 4.8 MeV 104 MeV -⅓ -⅓ d s down strange 0 ν ν e electron neutrino Three Generations of Matter (Fermions) spin ½ I II III Right Right Right ⅔ GeV t top 4.2 GeV -⅓ b bottom Right Right ~GeV ~GeV 0 μ 0ν τ 1 N2 N tau 3 N < ev ~10 kev ~0.01 ev ~0.04 ev sterile neutrino muon neutrino sterile neutrino neutrino sterile neutrino MeV MeV GeV e μ τ electron muon tau Right Bosons (Forces) spin g gluon γ photon 91.2 GeV Z 0 0 weak force 80.4 GeV W ± ± 1 weak force >114 GeV 0 0 H Higgs boson spin 0 +f I X N c N [Asaka, Blanchet, Shaposhnikov 05, Shaposhnikov, Tkachev 06] DM sterile neutrinos are produced in inflaton decays BAU via leptogenesis with two heavier sterile neutrinos DM neutrino mass bound from production mechanism M 1 80keV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 27 / 43

29 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys N 1 DM sterile neutrino properties DM sterile neutrino N 1, M keV X-ray line from the DM radiative decay N 1 νγ Neutrinoless double beta decay m ee < ev [FB 05] Details sin 2 (2θ 1 ) Phase-space density constraints X-ray constraints M 1 [kev] Production in inflaton decays during preheating ( m ) ( ) ( ) χ S 1/3 1/3 0.9 M MeV 4 f ( ) kev. m χ May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 28 / 43

30 Inflationary model Bounds from cosmology inflation and reheating Experimental detection of the inflaton Sterile neutrinos for the Dark Matter and letogenesys N 2,3 BAU generating sterile neutrino properties Lepton asymmetry generating N 2,3, M 2,3 GeV Neutrino production hadron decays: kinematics Missing energy in K decays Peaks in momentum of charged leptons for two body decays Neutrino decays into SM particles: nothing to leptons and hadrons Beam target experiments with high intensity proton beam, detector (preferably not dense) after the shielding. [D. Gorbunov, M.Shaposhnikov 07] θ νn CHARM PS191 Experiments BBN BEBC NuTeV BAU See saw M 2 [GeV] May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 29 / 43

31 The model with non-minimal gravity coupling Predictions Can we be even more minimal? Do we really need a new particle for inflation? We have a scalar in the SM Higgs boson However, it does not have a flat potential (λ 1) May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 30 / 43

32 The model with non-minimal gravity coupling Predictions Non-minimal coupling to gravity solves the problem Quite an old idea Add h 2 R term (required by renormalization) to of the usual M P R term in the gravitational action A.Zee 78, L.Smolin 79, B.Spokoiny 84 D.Salopek J.Bond J.Bardeen 89 Scalar part of the (Jordan frame) action S J = d 4 x { } g M2 P h2 R ξ 2 2 R +g µ h ν h µν λ 2 4 (h2 v 2 ) 2 h is the Higgs field; M P 1 = GeV 8πGN SM higgs vev v M P / ξ and can be neglected in the early Universe May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 31 / 43

33 The model with non-minimal gravity coupling Predictions Scale invariance at large Higgs field values is the cause of a good inflation For large Higgs field background h M P / ξ Effective Planck mass is M 2 Peff = M2 P + ξ h2 h 2 All other masses M 2 h,m2 W,m2 t h 2 No scale (h) dependence flat potential, scale invariant spectrum, etc. Exactly what is needed for inflation. A convenient way to see that Conformal transformation May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 32 / 43

34 The model with non-minimal gravity coupling Predictions Conformal transformation way to calculate It is possible to get rid of the non-minimal coupling by the conformal transformation (change of variables) ĝ µν = Ω 2 g µν, Ω ξ h2 M 2 P Redefinition of the Higgs field to get canonical kinetic term { dχ dh = Ω 2 + 6ξ 2 h 2 /MP 2 h χ for h < MP /ξ Ω 4 = ( ) Ω 2 exp 2χ 6MP for h > M P /ξ Resulting action (Einstein frame action) S E = d 4 x { } ĝ M2 P 2 ˆR + µ χ µ χ λ h(χ) Ω(χ) 4 May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 33 / 43

35 The model with non-minimal gravity coupling Predictions Potential different stages of the Universe λm 4 P 4ξ 2 U λ(χ 2 v 2 ) 2 4 λm 2 P χ2 6ξ 2 λmp 4 ( ) 2 4ξ 2 1 e 2χ/ 6M P M P/ξ M P χ WMAP 5.4M P χ Hot Big Bang Preheating Slow roll inflation δt /T 10 5 normalization ξ λ May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 34 / 43

36 CMB parameters are predicted 0.4 WMAP5 The model with non-minimal gravity coupling Predictions SM+ ξh 2 R spectral index n 1 8(4N+9) 0.97 (4N+3) 2 tensor/scalar ratio r (4N+3) 2 May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 35 / 43 5 ξ

37 The model with non-minimal gravity coupling Predictions Radiative corrections modify the inflationary potential If we assume the full UV theory respects the scale invariance at high fields (or shift invariance in the Einstein frame) the quadratic divergences are subtracted to zero (e.g. work in dimensional regularisation) then we can compute the radiative corrections to the inflationary potential and relate them to the parameters of the low energy physics (Higgs boson mass). [FB, Sibiryakov, Shaposhnikov 11] May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 36 / 43

38 The model with non-minimal gravity coupling Predictions Prescription to calculate potential with radiative corrections 1 Run all constants with SM two-loop RG equations from the EW scale up to M P / ξ 2 Run all constants λ i (µ) with chiral EW theory RG equations up to scale µ equal to a typical particle mass for the given field background χ µ 2 = κ 2 m 2 t (χ) = κ 2 y t(µ) 2 2 MP 2 ) (1 e 2χ 6MP. ξ (µ) 3 Calculate the effective potential U(χ) = U tree (λ i (µ), χ) +U 1 loop (λ i (µ), χ)+u 2 loop (λ i (µ), χ) 4 Calculate the inflationary properties for the resulting potential [FB, Magnin, Shapshnikov 09, FB, Shaposhnikov 09] May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 37 / 43

39 Validity of SM up to Planck scale Radiative corrections screening of the Higgs self-interaction depending on scale Higgs mass bounds 126.1GeV + m t α s The model with non-minimal gravity coupling Predictions interaction strength Λ m H 174 = 190 GeV < m H < 193.9GeV + m H = 126 GeV m H GeV Μ,GeV inflationary M P 10scale 20 Energy scale m t α s May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 38 / 43

40 The model with non-minimal gravity coupling Predictions Future experiments clue on Planck scale physics? 0.97 normalization prescription I 0.96 n s mt GeV, Α 0.95 s normalization prescription II 0.94 LHC & PLANCK precisions m H,GeV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 39 / 43

41 Dark matter just add νmsm The model with non-minimal gravity coupling Predictions SM+ HH ξ R + mass charge name Quarks Leptons ⅔ 2.4 MeV u up Right Right Right ⅔ 1.27 GeV c charm 4.8 MeV 104 MeV -⅓ -⅓ d s down strange 0 ν ν e electron neutrino Three Generations of Matter (Fermions) spin ½ I II III Right Right Right ⅔ GeV t top 4.2 GeV -⅓ b bottom Right Right ~GeV ~GeV 0 μ 0ν τ 1 N2 N tau 3 N < ev ~10 kev ~0.01 ev ~0.04 ev sterile neutrino [Asaka, Blanchet, Shaposhnikov 05] muon neutrino sterile neutrino neutrino sterile neutrino MeV MeV GeV e μ τ electron muon tau Right Bosons (Forces) spin g gluon γ photon 91.2 GeV Z 0 0 weak force 80.4 GeV W ± ± 1 weak force DM sterile neutrinos are produced by oscillations from active neutrinos Two heavier sterile neutrino provide for the baryon asymmetry (via low scale leptogenesis) >114 GeV 0 0 H Higgs boson spin 0 May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 40 / 43

42 N 1 DM sterile neutrino properties The model with non-minimal gravity coupling Predictions DM sterile neutrino N 1, M keV X-ray line from the DM radiative decay N 1 νγ Neutrinoless double beta decay m ee < ev [FB 05] Details sin 2 (2θ 1 ) Phase-space density constraints Ω N1 > Ω DM NRP Ω N1 < Ω DM L 6 =25 L 6 =70 L 6 max =700 BBN limit: L 6 BBN = 2500 X-ray constraints M 1 [kev] May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 41 / 43

43 The model with non-minimal gravity coupling Predictions N 2,3 BAU generating sterile neutrino properties Lepton asymmetry generating N 2,3, M 2,3 GeV Neutrino production hadron decays: kinematics Missing energy in K decays Peaks in momentum of charged leptons for two body decays Neutrino decays into SM particles: nothing to leptons and hadrons Beam target experiments with high intensity proton beam, detector (preferably not dense) after the shielding. [D. Gorbunov, M.Shaposhnikov 07] θ νn CHARM PS191 Experiments BBN BEBC NuTeV BAU DM preferred See saw M 2 [GeV] May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 42 / 43

44 The model with non-minimal gravity coupling Predictions Summary Start from: Explain every experimental fact Expand the Standard Model in a minimal way Arrive to: Predictions for low energy experiments! Easy to falsify any recent 2σ new physics discovery would do this, if it turnes true Higgs mass too light or too heavy Harder, but possible, to get direct evidence Light inflaton in rare B decays sterile neutrino in specific rare decay searches X-rays May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 43 / 43

45 Backup slides Based on WMAP-5 bounds 0.3 ξ= WMAP-5year 0.2 ξ= ξ= ξ= n s r ξ r Message With non-minimal coupling it is very natural for βφ 4 inflation to be compatible with observations! Return May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 44 / 43

46 May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale Return 45 / 43 Backup slides Based on Dark matter add νmsm and stir A νmsm inspired model with inflation χ (Shaposhnikov&Tkachev 06) L =(L SM + N I i µ γ µ N I F αi Lα N I Φ f I 2 N c I N IX + h.c.)+ 1 2 ( µx) 2 V (Φ,X) Ω N = 1.6f (m χ) S DM sterile neutrino mass bound ( M 1 13 ( ) β 3 ( ) M1 100 MeV 3, 10keV m χ 300 MeV ) ( ) ( S 1/ f ( m χ ) m χ ) 1/3 kev.

47 Backup slides Based on Parametric enchancement Let us suppose again that there is an inflaton X coupled to some particle φ. Then, during inflaton oscillations, for the φ modes with momentum k( we have ) k 2 φ k + 3H φ k + a 2 (t) + g2 X(t) 2 φ k = 0 Important X(t) oscillates Let us neglect the Universe expansion, and say that X(t) = Asin(ωt), then Mathieu equation d 2 φ k dη 2 + (A k 2q cos2η) = 0 where A k = k 2 /ω 2 + 2q, q = g 2 X 2 0 /4ω2, η = ωt. May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale Return 46 / 43

48 Backup slides Based on Temperature estimate for the reheating Equating mean free path nσ 2I 2H v n α2 πp 2 avg rate H = T 2 π 2 g m Pl 90 we get T R ζ (3)α2 π 4 90 g m Pl with the Hubble Requiring T R > 150GeV we can obtain the lower bound on α α , Return May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 47 / 43

49 Backup slides Based on Temperature estimate for the reheating II However, p avg T, the cross-section is enhanced, so ζ (3)α 2 T 4 T 2 π 3 pavg 3 90 M 8π 3 g Pl For this estimate the bound is weaker α Upper bound for the inflaton mass ( m ) H β m χ GeV GeV Return May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 48 / 43

50 Backup slides Based on Inflaton mass window Flatness from radiative corrections ( m χ > 120 Sufficient reheating ( m χ 1.5 m h 150 GeV m H 150 GeV To be precise, the window also exists ( m 2m H < m χ 460 h 150 GeV ) ( β ) 1 2 MeV ) ( β ) 1 2 GeV ) 4/3 ( ) β 1/ GeV Return May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 49 / 43

51 Backup slides Based on Production: beam dump 1e-06 1e-08 1e-10 1e-12 1e-14 1e-16 1e-18 1e-20 1e-22 1e-24 σ ( = M pp χ s (0.5Br(K + π + χ) Br(K L π 0 χ)) σ pp,total ) + χ c Br(B χx s ) Meson decay, NuTeV Meson decay, CNGS Meson decay, NuMi Meson decay, T2K gg fusion, T2K E, GeV NuTeV 800 CNGS 400 NuMi 120 T2K 50 May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 50 / 43 return

52 Backup slides Based on Inflaton decays and lifetime τ χ, s Branching e-05 1e-06 1e-07 1e-08 1e-09 1e-10 e + e - γγ ππ µ + µ KK τ + τ µ + µ e m χ, GeV May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 51 / 43 cc gg ss

53 May 6, Fedor Bezrukov How to explain the Universe with electroweak scale 52 / 43 Backup slides Based on Production: beam dump, ideal luminosity Number of inflatons produced (via meson decays) during one year of operation 1 N produced 1e+14 1e+12 1e+10 1e+08 1e Meson decay, NuTeV Meson decay, CNGS Meson decay, NuMi Meson decay, T2K gg fusion, T2K m χ, GeV E, GeV NuTeV 800 CNGS 400 NuMi 120 T2K 50 N POT, NuTeV 1 CNGS 4.5 NuMi 5 T2K 100

54 Backup slides Based on 0νβ β effective Majorana mass is small 1 QD m ee = m i Vei 2 i <m> [ev] IH NH m MIN [ev] contribution from N 1 is negligible M 1 θe ev For heavier active neutrinos the contribution is always negative m ee < i m i Vei 2 smaller prediction m ee < ev F.B., 2006 return May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 53 / 43

55 Backup slides Based on 0νβ β effective Majorana mass is small 1 QD m ee = m i Vei 2 i <m> [ev] IH NH m MIN [ev] contribution from N 1 is negligible M 1 θe ev For heavier active neutrinos the contribution is always negative m ee < i m i Vei 2 smaller prediction m ee < ev F.B., 2006 return May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 53 / 43

56 Backup slides Based on Field dependent cut-off makes the model consistent May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 54 / 43

57 Backup slides Based on Inflationary regime EW chiral theory L chiral = 1 2 ( µ χ) 2 U(χ) 1 2g 2 tr[w 2 µν] v 2 4 tr[v 2 µ ] + i Q L,R /DQ L,R ( y tv QL U Q R + + h.c.) 2 with U = exp[2iπ a T a ], V µ = ( µ U )U + iw µ iu B Y µ U and v 2 = h2 Ω 2 (h) = M2 ) P (1 e 2χ/ 1 6M P ξ May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 55 / 43

58 Backup slides Based on RG equations in the inflationary regime 16π 2 µ ( 1 µ g = 16π 2 µ µ g = 16π 2 µ ( 3 µ ξ = 16π 2 µ µ y t = ( λ ξ 2 16π 2 µ µ n ) f g 3, (1) 9 ( n ) f g 3. (2) 3 16π 2 µ µ g 3 = 7g3 2. (3) ) 2 g 2 + 3g 2 6yt 2 ξ. (v 2 1/ξ ) (4) ( 17 ) y t. (5) ) = 1 ξ 2 12 g g2 8g y t 2 ( 6yt ( 2g 2 + (g 2 + g 2 ) 2)). (6) May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 56 / 43

59 Backup slides Based on Effective potential can be obtained from the SM one by removing the terms corresponding to the Higgs scalar loops setting Goldstone boson masses to zero May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 57 / 43

60 Backup slides Based on FB, M. Shaposhnikov, Phys. Lett. B 659, 703 (2008) FB, D. Gorbunov, M. Shaposhnikov, JCAP 06, 029 (2009) FB, A. Magnin, M. Shaposhnikov, Phys. Lett. B 675, 88 (2009) FB, A. Magnin, M. Shaposhnikov, S. Sibiryakov, JHEP 1101, 016 (2011). FB, M. Shaposhnikov, JHEP 0907 (2009) 089 A. Anisimov, Y. Bartocci, F. L. Bezrukov, Phys. Lett. B 671, 211 (2009) FB, D. Gorbunov, JHEP 05 (2010) 010 T. Asaka, M. Shaposhnikov, Phys. Lett. B 620 (2005) 17 T. Asaka, S. Blanchet, M. Shaposhnikov, Phys. Lett. B 631 (2005) 151 M. Shaposhnikov, I. Tkachev, Phys. Lett. B 639 (2006) 414 D. S. Gorbunov, A. G. Panin, [arxiv: [hep-ph]] A. A. Starobinsky, Phys. Lett. B91 (1980) May 6, 2011 Fedor Bezrukov How to explain the Universe with electroweak scale 58 / 43

Higgs field as the main character in the early Universe. Dmitry Gorbunov

Higgs field as the main character in the early Universe Dmitry Gorbunov Institute for Nuclear Research, Moscow, Russia Dual year Russia-Spain, Particle Physics, Nuclear Physics and Astroparticle Physics