Entropy, Baryon Asymmetry and Dark Matter from Heavy Neutrino Decays.

Transcription

1 Entropy, Baryon Asymmetry and Dark Matter from Heavy Neutrino Decays. Kai Schmitz Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany Based on arxiv: [hep-ph] and arxiv: [hep-ph]. In collaboration with W. Buchmüller and G. Vertongen. 6. Kosmologietag, IBZ, Bielefeld University May 5, 2011

2 Outline 1 Idea Reheating through heavy neutrino decays Leptogenesis and gravitino dark matter 2 Scenario False vacuum decay Particle interactions 3 Analysis Parameter study Conclusion Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

3 Idea Reheating through heavy neutrino decays Origin of the hot phase of the early universe? Epoch dominated by energy in radiation: Evidence: CMB (T 0.25eV) and BBN (T 1MeV). Paradigm: Preceded by inflation (vacuum domination). Transition? Reheating mechanism and T RH unknown. Definition T RH : H (T =: T RH ) = Γ X T RH 0.2 Γ X M P. Γ X free parameter! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

4 Idea Reheating through heavy neutrino decays Origin of the hot phase of the early universe? Epoch dominated by energy in radiation: Evidence: CMB (T 0.25eV) and BBN (T 1MeV). Paradigm: Preceded by inflation (vacuum domination). Transition? Reheating mechanism and T RH unknown. Definition T RH : H (T =: T RH ) = Γ X T RH 0.2 Γ X M P. Γ X free parameter! Our idea: Entropy from heavy neutrino decays Assume dominant N 1 abundance after inflation. Type I seesaw: Add heavy Majorana neutrinos N i to the SM. At tree-level Γ N1 = m 1 8π (M 1/v EW ) 2, m 1 := ( m Dm D )11 /M 1. T RH = T RH ( m 1,M 1 ) GeV for typical m 1 & M 1. Baryon asymmetry & dark matter are natural by-products. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

5 Idea Reheating through heavy neutrino decays Origin of the hot phase of the early universe? Epoch dominated by energy in radiation: Evidence: CMB (T 0.25eV) and BBN (T 1MeV). Paradigm: Preceded by inflation (vacuum domination). Transition? Reheating mechanism and T RH unknown. Definition T RH : H (T =: T RH ) = Γ X T RH 0.2 Γ X M P. Γ X free parameter! Our idea: Entropy from heavy neutrino decays Assume dominant N 1 abundance after inflation. Type I seesaw: Add heavy Majorana neutrinos N i to the SM. At tree-level Γ N1 = m 1 8π (M 1/v EW ) 2, m 1 := ( m Dm D )11 /M 1. T RH = T RH ( m 1,M 1 ) GeV for typical m 1 & M 1. Baryon asymmetry & dark matter are natural by-products. Consistent cosmology and non-trivial parameter relations! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

6 Idea Leptogenesis and gravitino dark matter Baryon asymmetry and dark matter [Fukugita & Yanagida 86] [Buchmüller et al. 05] [Bolz et al. 01] [Steffen & Pradler 07] Baryogenesis through leptogenesis: η B := n B /n γ η sym B SM sphalerons convert L into B asymmetry (c sph ). Seesaw & neutrino data: M 1 T L GeV. (Non-)thermal N 1 production: η B = η B ( m 1,M 1 ). ε 1 = Γ Γ Γ+ Γ CP-violating out-of-equilibrium N 1 neutrino decays Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

7 Idea Leptogenesis and gravitino dark matter Baryon asymmetry and dark matter [Fukugita & Yanagida 86] [Buchmüller et al. 05] [Bolz et al. 01] [Steffen & Pradler 07] Baryogenesis through leptogenesis: η B := n B /n γ η sym B SM sphalerons convert L into B asymmetry (c sph ). Seesaw & neutrino data: M 1 T L GeV. (Non-)thermal N 1 production: η B = η B ( m 1,M 1 ). ε 1 = Γ Γ Γ+ Γ CP-violating out-of-equilibrium N 1 neutrino decays Th. prod. of gravitinos in SUSY QCD: Do not spoil BBN or overclose the universe. DM for free if gravitino is heavy stable LSP. Ω Gh 2 (T RH,m G,m g ) 0.11 Ω DM h 2. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

8 Idea Leptogenesis and gravitino dark matter Baryon asymmetry and dark matter [Fukugita & Yanagida 86] [Buchmüller et al. 05] [Bolz et al. 01] [Steffen & Pradler 07] Baryogenesis through leptogenesis: η B := n B /n γ η sym B SM sphalerons convert L into B asymmetry (c sph ). Seesaw & neutrino data: M 1 T L GeV. (Non-)thermal N 1 production: η B = η B ( m 1,M 1 ). ε 1 = Γ Γ Γ+ Γ CP-violating out-of-equilibrium N 1 neutrino decays Connect the two sectors! Ω Gh 2 ( m 1,M 1,m G,m g ) = Ω DM h 2 Keep m g fixed & solve for M 1. M 1,T RH,η B = f ( m 1,m G). Th. prod. of gravitinos in SUSY QCD: Do not spoil BBN or overclose the universe. DM for free if gravitino is heavy stable LSP. Ω Gh 2 (T RH,m G,m g ) 0.11 Ω DM h 2. Impose η B ( m 1,m G) η obs B. Mutual bounds m 1 m G. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

9 Scenario False vacuum decay Generating a dominant nonthermal N 1 abundance SSB of U(1) B L at v B L by gauge singlet S: ( Seesaw: 1 2 M i n C n Ri Ri + h.c. ) violates lepton number L. ( Interpretation: 1 2 h(n) i n C n Ri RiS + h.c. ), S v B L + 1 S. 2 Hybrid inflation = Chaotic inflation+ssb S be the field coupling to the inflaton φ in hybrid inflation. False vacuum decay breaks B L and ends inflation. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

10 Scenario False vacuum decay Generating a dominant nonthermal N 1 abundance SSB of U(1) B L at v B L by gauge singlet S: ( Seesaw: 1 2 M i n C n Ri Ri + h.c. ) violates lepton number L. ( Interpretation: 1 2 h(n) i n C n Ri RiS + h.c. ), S v B L + 1 S. 2 Hybrid inflation = Chaotic inflation+ssb S be the field coupling to the inflaton φ in hybrid inflation. False vacuum decay breaks B L and ends inflation. Tachyonic preheating: [Felder et al. 01] [García-Bellido & Ruiz Morales 02] Instability for φ < φ crit causes explosive spinodal growth of long-wavelength S modes: Waterfall transition! False vacuum energy density transferred to non-relativistic S bosons and due to expected h (n) i to N 2,3 neutrinos. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

11 Scenario False vacuum decay Generating a dominant nonthermal N 1 abundance SSB of U(1) B L at v B L by gauge singlet S: ( Seesaw: 1 2 M i n C n Ri Ri + h.c. ) violates lepton number L. ( Interpretation: 1 2 h(n) i n C n Ri RiS + h.c. ), S v B L + 1 S. 2 Hybrid inflation = Chaotic inflation+ssb S be the field coupling to the inflaton φ in hybrid inflation. False vacuum decay breaks B L and ends inflation. Tachyonic preheating: [Felder et al. 01] [García-Bellido & Ruiz Morales 02] Instability for φ < φ crit causes explosive spinodal growth of long-wavelength S modes: Waterfall transition! False vacuum energy density transferred to non-relativistic S bosons and due to expected h (n) i to N 2,3 neutrinos. Assume 2M 1 m S 2M 2,3 s.t. S decays after SSB yield dominant N 1 abundance. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

12 Scenario Particle interactions Initial State after N 2,3 Decay Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

13 Scenario Particle interactions Decay of Non-Thermally Produced N 1 Neutrinos Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

14 Scenario Particle interactions Decay of Thermally Produced N 1 Neutrinos Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

15 Scenario Particle interactions Boltzmann equations (S) ˆLf S (t,p) = m S E S Γ 0 S f S (t,p) ( N S 1 ) ( N T 1 ) ˆLf S N 1 (t,p) = M 1 E N1 Γ 0 N 1 f S N 1 (t,p) + 2 π2 Γ 0 S N S δ(e N1 m S /2) a 3 EN 2 1 ( ) ah d da NT N 1 = Γ T N 1 NN T 1 N eq N 1 ( ) (B L) ah d da N B L = ε 1 Γ S N 1 NN S 1 + ε 1 Γ T N 1 NN T 1 N eq N 1 ( G) 1 (2M 1 /m S ) 2 Neq N 1 2N eq l ( ) [ ah d da N G = κ G a 3 (T ) m2 g 54ζ (3)gs (T ) π 2 T 6 ln M p 3m 2 G ( ) (R) ah d da N R = r S R Γ S N 1 NN S 1 + r T R Γ T N 1 NN T 1 N eq N 1 Γ T N 1 N B L ( T 2 m 2 g(t ) ) ] with ˆL = t Hp, Γ S/T p N 1 = M1 E N1 Γ S/T 0 N 1, κ G O(1) and r S/T R = 3ρS/T N n R 1. 4n S/T N ρ R 1 Coupled system of non-linear first-order partial differential eqns. Solve for phase space distr. funcs. & number densities in an expanding FLRW background. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

16 Analysis Parameter study Reheating temperature and baryon asymmetry M 1 (v B L, m 1,m G,m g ) s. t. Ω Gh 2 = 0.11 η B (v B L, m 1,M 1 ) = η S B + η T B > η obs B Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

17 Analysis Parameter study Reheating temperature and baryon asymmetry M 1 (v B L, m 1,m G,m g ) s. t. Ω Gh 2 = 0.11 η B (v B L, m 1,M 1 ) = η S B + η T B > η obs B Appreciate: Thermal bounds significantly alleviated! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

18 Analysis Parameter study Reheating temperature and baryon asymmetry M 1 (v B L, m 1,m G,m g ) s. t. Ω Gh 2 = 0.11 η B (v B L, m 1,M 1 ) = η S B + η T B > η obs B Appreciate: Thermal bounds significantly alleviated! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

19 Analysis Parameter study Reheating temperature and baryon asymmetry M 1 (v B L, m 1,m G,m g ) s. t. Ω Gh 2 = 0.11 η B (v B L, m 1,M 1 (v B L, m 1,m G,m g )) > η obs B Appreciate: Thermal bounds significantly alleviated! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

20 Analysis Parameter study Connection between SUGRA and neutrino parameters Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

21 Analysis Parameter study Connection between SUGRA and neutrino parameters Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

22 Analysis Parameter study Connection between SUGRA and neutrino parameters Scenario works in large region of parameter space! T RH bound lowered: 10 9 GeV 10 7 GeV. m 1 and m G mutually constrain each other. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

23 Analysis Conclusion All you need is neutrino decays! Idea: Neutrino decays produce all entropy of the hot early universe. Reheating temperature T RH determined by neutrino lifetime Γ N1 ( m 1,M 1 ). BAU through leptogenesis and gravitino DM follow naturally + interrelated. Scenario: Dominant nonth. N 1 abundance after false vacuum decay. Hybrid inflation ends in SSB of local U(1) B L and tachyonic preheating. Vacuum energy density Higgs bosons of B L breaking N 1 neutrinos. Analysis: Quantitative results after solving the Boltzmann equations. T RH, η B and Ω Gh 2 from Lagrangian parameters v B L, m 1, M 1, m G and m g. m 1 constrains m G and vice versa. Falsification: Measure m i 0.1eV. Connection b/t collider searches, laboratory exps. and cosmological obs. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

24 Analysis Conclusion All you need is neutrino decays! Idea: Neutrino decays produce all entropy of the hot early universe. Reheating temperature T RH determined by neutrino lifetime Γ N1 ( m 1,M 1 ). BAU through leptogenesis and gravitino DM follow naturally + interrelated. Scenario: Dominant nonth. N 1 abundance after false vacuum decay. Hybrid inflation ends in SSB of local U(1) B L and tachyonic preheating. Vacuum energy density Higgs bosons of B L breaking N 1 neutrinos. Analysis: Quantitative results after solving the Boltzmann equations. T RH, η B and Ω Gh 2 from Lagrangian parameters v B L, m 1, M 1, m G and m g. m 1 constrains m G and vice versa. Falsification: Measure m i 0.1eV. Connection b/t collider searches, laboratory exps. and cosmological obs. Thank you for your attention! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 10

25 Appendix Froggatt-Nielson flavor model Yukawa couplings Superpotential for matter fields in SU(5) notation: W M = h (u) ij 10 i 10 j H u + h (d) ij 5 i 10 j H d + h (ν) ij 5 i 1 j H u + h (n) i 1 i 1 i S. Fermion irreps: 10 i = (q i,ui c,ei c) ; 5 i = (di c,l i ) ; 1 i = (n i ) ; N i := n i + ni c. Froggatt-Nielson U(1) FN flavor symmetry: [Buchmüller & Yanagida 99] Yukawa terms are generated from non-renorm. U(1) FN -inv. higher-dim. operators: h ij η Q i +Q j ; η := v FN /Λ 1/ 300 ; Λ > Λ GUT. FN parameter η and charges Q i determined from quark and lepton mass hierarchies. ψ i Q i a a a + 1 b c d Specific example: a = 0.5, d = 1.5. Require M 1 M 2,3 = m S b = c = d 1 = 0.5. v B L GeV ; M Gev ; M 2,3 = m S v B L. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 4

26 i Appendix f Exemplary parameter point Comoving number densities Inverse temperature M 1 T N(a) = a 3 n(a) abs N a N 1 T S N 1 eq N 1 S a RH a ts a t1 a trh a RH R B L Scale factor a G v B L = GeV M 1 = GeV m 1 = ev m G = 100GeV m g = 800GeV ε max 1 = ε2,3 max = η max B = > η obs B Ω Gh 2 = 0.11 = Ω obs DM h N 1 eq N 1 T B L Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 4

27 Appendix Generalization to different gluino masses Rescaling the gravitino mass for m g 800GeV ( Solve Ω Gh 2 T RH,m 0 G,800GeV ) = Ω Gh 2 (T RH,m G,m g ). ( ) Quadratic eq. for m G m g,m 0 G w/ two solutions m ±. G For m 0 G m g : m G = m 0 G (m g /800GeV) 2. T RH and η B unaffected as long as v B L, m 1 and M 1 are kept constant. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 4

28 Appendix Theoretical uncertainty in the gravitino production rate Connection between SUGRA and neutrino parameters Scenario works in large region of parameter space! T RH bound lowered: 10 9 GeV 10 7 GeV. m 1 and m G mutually constrain each other. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 4

29 Appendix Theoretical uncertainty in the gravitino production rate Connection between SUGRA and neutrino parameters Scenario works in large region of parameter space! T RH bound lowered: 10 9 GeV 10 7 GeV. m 1 and m G mutually constrain each other. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 4

30 Appendix Theoretical uncertainty in the gravitino production rate Connection between SUGRA and neutrino parameters Scenario works in large region of parameter space! T RH bound lowered: 10 9 GeV 10 7 GeV. m 1 and m G mutually constrain each other. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, / 4