Effects of Reheating on Leptogenesis

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1 Effects of Reheating on Leptogenesis Florian Hahn-Woernle Max-Planck-Institut für Physik München 2. Kosmologietag Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

2 Outline 1 Leptogenesis 2 N Production via Inflaton Decay 3 Efficiency factor 4 Lower bound on M 1 and T RH 5 Conclusions Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

3 Matter-Antimatter Asymmetry from Nucleosynthesis and CMB: η CMB B = n B n B n γ = (6.3 ± 0.3) necessary ingredients (Sakharov, 1967): 1 Baryon number violation 2 C and CP violation 3 Departure from thermal equilibrium Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

4 Matter-Antimatter Asymmetry from Nucleosynthesis and CMB: η CMB B = n B n B n γ = (6.3 ± 0.3) necessary ingredients (Sakharov, 1967): 1 Baryon number violation 2 C and CP violation 3 Departure from thermal equilibrium Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

5 Seesaw Mechanism introduce right-handed neutrinos with mass M into the SM L N = ( LHλ ν N ) 1 ( N 2 c MN ) + h.c. Yukawa couplings lead to Dirac mass: m D = λ ν v seesaw mechanism: assuming M m D : N with m N M 1 ν with m ν m D M mt D = O ( ) v2 M Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

6 Seesaw Mechanism introduce right-handed neutrinos with mass M into the SM L N = ( LHλ ν N ) 1 ( N 2 c MN ) + h.c. Yukawa couplings lead to Dirac mass: m D = λ ν v seesaw mechanism: assuming M m D : N with m N M 1 ν with m ν m D M mt D = O ( ) v2 M Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

7 CP violation N are Majorana particles L violation N s decay into lepton-higgs pairs: Γ N m 1 = v 2 (λ M νλ ν ) 11 1 Assumptions: hierarchical neutrino masses M 1 M 2,3 and m 1 m 2,3 one-flavor approximation CP violation by interference of tree level and one loop amplitude: ε max 1 = 3 M 1 m atm 16π v 2 ( ) 10 6 M1 ( matm ) GeV 0.05eV Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

8 CP violation N are Majorana particles L violation N s decay into lepton-higgs pairs: Γ N m 1 = v 2 (λ M νλ ν ) 11 1 Assumptions: hierarchical neutrino masses M 1 M 2,3 and m 1 m 2,3 one-flavor approximation CP violation by interference of tree level and one loop amplitude: ε max 1 = 3 M 1 m atm 16π v 2 ( ) 10 6 M1 ( matm ) GeV 0.05eV Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

9 From L to B Asymmetry L asymmetry is partially transformed into a B asymmetry by sphalerons: (Klinkhammer & Manton 84; Kuzmin et al. 85) sphalerons in thermal equilibrium at temperatures: T EW 100 GeV T GeV η B = α sph η B L = α sph α sph 1 η L, s L s L t L with α sph 1 3 c L b L d L Sphaleron b L d L ν τ u L ν e ν µ Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

10 Problems of Thermal Leptogenesis lower bound on M 1 to produce enough asymmetry: ε max 1 M 1 yields a lower bound on T RH M GeV conflict with BBN in SUGRA: T RH GeV too large abundance of gravitinos spoils successful BBN Production mechanism of N s not known 1 N produced through scatterings in the thermal bath 2 assuming thermal initial N abundance 3 non-thermal production Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

11 Problems of Thermal Leptogenesis lower bound on M 1 to produce enough asymmetry: ε max 1 M 1 yields a lower bound on T RH M GeV conflict with BBN in SUGRA: T RH GeV too large abundance of gravitinos spoils successful BBN Production mechanism of N s not known 1 N produced through scatterings in the thermal bath 2 assuming thermal initial N abundance 3 non-thermal production Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

12 N Production in Inflaton Decays inflationary epoch at the beginning of the universe decay chain: 1 Φ N 1 + N 1, with Γ Φ γ 2 4π M Φ 2 N 1 l L + H, with Γ N m 1 resulting reheating temperatures 1 T RH Γ Φ M Pl γ M Φ M Pl, parametrization of inflaton-neutrino coupling 2 TRH N m Γ N M Pl M ev, physical reheating temperature Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

13 N Production in Inflaton Decays inflationary epoch at the beginning of the universe decay chain: 1 Φ N 1 + N 1, with Γ Φ γ 2 4π M Φ 2 N 1 l L + H, with Γ N m 1 resulting reheating temperatures 1 T RH Γ Φ M Pl γ M Φ M Pl, parametrization of inflaton-neutrino coupling 2 TRH N m Γ N M Pl M ev, physical reheating temperature Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

14 Boltzmann Equations quantitative analysis with a network of Boltzmann equations: ρ Φ = 3Hρ Φ Γ Φ ρ Φ ρ N = 3Hρ N + Γ Φ ρ Φ Γ N (ρ N ρ eq N ) ρ R = 4Hρ R + Γ N (ρ N ρ eq N ) ṅ B L = 3Hn B L ε 1 Γ N (n N n eq N ) Γ ID n B L produced baryon asymmetry: η B 10 2 ε 1 κ( m 1 ) efficiency factor κ parametrizes N interactions (from integration of Boltzmann eqs.) Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

15 Efficiency Factor κ f as Function of m Ø ÖÑ Ð Æ Þ ÖÓ Æ ½¼ Î ½¼ Î ½¼ Πѽ ε chosen values: M Φ = GeV, M 1 = 10 9 GeV maximal efficiency: κ max f 80 for m ev and dominant initial N abundance for m ev: large κ f for dom. initial abundance for m ev: strong washout reduces asymmetry independent on initial conditions for M 1 T RH in the range: m sol < m 1 < m atm Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

16 Efficiency Factor κ f as Function of m Ø ÖÑ Ð Æ Þ ÖÓ Æ ½¼ Î ½¼ Î ½¼ Πѽ ε chosen values: M Φ = GeV, M 1 = 10 9 GeV maximal efficiency: κ max f 80 for m ev and dominant initial N abundance for m ev: large κ f for dom. initial abundance for m ev: strong washout reduces asymmetry independent on initial conditions for M 1 T RH in the range: m sol < m 1 < m atm Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

17 Extreme Case: Γ Φ Γ N ½¼ Î Ø ÖÑ Ð Æ Þ ÖÓ Æ ½¼ Î for T RH M 1 : N 1 decays totally out-of-equilibrium κ f 40 larger than in thermal LG, almost independent of m ѽ ε small effect of: entropy production for m 1 0 washout for m 10 3 ev Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

18 Extreme Case: Γ Φ Γ N ½¼ Î Ø ÖÑ Ð Æ Þ ÖÓ Æ ½¼ Î for T RH M 1 : N 1 decays totally out-of-equilibrium κ f 40 larger than in thermal LG, almost independent of m ѽ ε small effect of: entropy production for m 1 0 washout for m 10 3 ev Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

19 Dependence on M Φ and M 1 condition for inflaton decay: M Φ 2M 1 variation of M Φ, M 1 has no effect on the final efficiency factor N decay always when they are non-relativistic evolution of the universe in the interval between inflaton decay and neutrino decay not interesting for our purpose Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

20 Ž ½¼ ΠŽ ½¼ Î Æ ÙÒ Ò Dependence on M Φ and M 1 N decay always when they are non-relativistic 10 0 Ì ÊÀ ½¼ Î Á Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

21 Dependence on M Φ and M 1 condition for inflaton decay: M Φ 2M 1 variation of M Φ, M 1 has no effect on the final efficiency factor N decay always when they are non-relativistic evolution of the universe in the interval between inflaton decay and neutrino decay not interesting for our purpose Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

22 Lower Bound on T N RH condition: η max B = 10 2 ε max 1 κ f ( m 1 ) ηb CMB Ž ε Þ ÖÓ Æ Ø ÖÑ Ð Æ ½¼ Î ½¼ Î ½¼ Î Lower bound on reheating temperature: T N RH M 1 reduction even in the strong washout for low T RH ѽ ε new absolute minimum: (T N RH )min GeV (in agreement with: Giudice et al., hep-ph/ ) compatible with BBN in SUGRA theories! Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

23 Lower Bound on T N RH condition: η max B = 10 2 ε max 1 κ f ( m 1 ) ηb CMB Ž ε Þ ÖÓ Æ Ø ÖÑ Ð Æ ½¼ Î ½¼ Î ½¼ Î Lower bound on reheating temperature: T N RH M 1 reduction even in the strong washout for low T RH ѽ ε new absolute minimum: (T N RH )min GeV (in agreement with: Giudice et al., hep-ph/ ) compatible with BBN in SUGRA theories! Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

24 Lower Bound on T N RH for Γ Φ Γ N Þ ÖÓ Æ Å½ ε Ø ÖÑ Ð Æ ½¼ Î ½¼ Πѽ ε large reduction of (T N RH )min even in the strong washout regime (T N RH )min almost independent of m 1 : (T N RH )min 10 7 GeV Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

25 Conclusions Summary Leptogenesis independent of the initial conditions in the regime of strong washout for T RH M 1 Reduction of (T N RH )min of up to 2 orders of magnitude, depending on the inflaton-neutrino coupling Outlook Considering branching ratios less than 100% Considering explicit inflation models Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15

26 Conclusions Summary Leptogenesis independent of the initial conditions in the regime of strong washout for T RH M 1 Reduction of (T N RH )min of up to 2 orders of magnitude, depending on the inflaton-neutrino coupling Outlook Considering branching ratios less than 100% Considering explicit inflation models Florian Hahn-Woernle (MPI-München) Effects of Reheating on Leptogenesis Kosmologietag / 15