Full Boltzmann equations for Leptogenesis (FHW, M. Plmacher, Y.Y.Y - PowerPoint PPT Presentation

Full Boltzmann equations for Leptogenesis (FHW, M. Plümacher, Y.Y.Y Wong: arXiv:0907.0205) Florian Hahn-Woernle Max-Planck-Institut für Physik München Ringberg Young Scientist Workshop 2009 Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 1 / 18

time evolution and energy budget of the universe 10 − 34 s I n fl a t i o n 10 14 GeV T RH ? e s i s B a r y o g e n 1 s e c o u p l i n g N e u t r i n o d 1 s 1 MeV B B N 100 s 0.1 M eV M a t t e r - R a d i a t i o n 10 5 yr 1 eV d e c o u p l i n g M B 10 13 Gyr 10 − 4 eV C Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 2 / 18

Outline Matter-Antimatter Asymmetry 1 Leptogenesis 2 Detailed look at Boltzmann equations 3 Conclusions 4 Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 3 / 18

Matter-Antimatter Asymmetry from Nucleosynthesis and CMB: = n B − n B η CMB = ( 6 . 2 ± 0 . 15 ) × 10 − 10 B n γ Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

Matter-Antimatter Asymmetry from Nucleosynthesis and CMB: = n B − n B η CMB = ( 6 . 2 ± 0 . 15 ) × 10 − 10 B n γ 3 necessary ingredients (Sakharov, 1967): Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

Matter-Antimatter Asymmetry from Nucleosynthesis and CMB: = n B − n B η CMB = ( 6 . 2 ± 0 . 15 ) × 10 − 10 B n γ 3 necessary ingredients (Sakharov, 1967): Baryon number violation 1 Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

Matter-Antimatter Asymmetry from Nucleosynthesis and CMB: = n B − n B η CMB = ( 6 . 2 ± 0 . 15 ) × 10 − 10 B n γ 3 necessary ingredients (Sakharov, 1967): Baryon number violation 1 C and CP violation 2 Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

Matter-Antimatter Asymmetry from Nucleosynthesis and CMB: = n B − n B η CMB = ( 6 . 2 ± 0 . 15 ) × 10 − 10 B n γ 3 necessary ingredients (Sakharov, 1967): Baryon number violation 1 C and CP violation 2 Departure from thermal equilibrium 3 Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

Matter-Antimatter Asymmetry from Nucleosynthesis and CMB: = n B − n B η CMB = ( 6 . 2 ± 0 . 15 ) × 10 − 10 B n γ 3 necessary ingredients (Sakharov, 1967): Baryon number violation 1 C and CP violation 2 Departure from thermal equilibrium 3 n γ ≃ 10 − 20 n γ = n B SM: relic density of baryons: n B proton annihilation into pions Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

Electroweak Baryogenesis The SM contains all ingredients → Electroweak Baryogenesis Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 5 / 18

Electroweak Baryogenesis The SM contains all ingredients → Electroweak Baryogenesis But: CP-violation too small and phase transition needs to be strongly first order: ∆ v f ( T ) > 1 ⇒ m H < 45 GeV T C Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 5 / 18

Electroweak Baryogenesis The SM contains all ingredients → Electroweak Baryogenesis But: CP-violation too small and phase transition needs to be strongly first order: ∆ v f ( T ) > 1 ⇒ m H < 45 GeV T C Ruled out by LEP: m H > 114 GeV Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 5 / 18

Electroweak Baryogenesis The SM contains all ingredients → Electroweak Baryogenesis But: CP-violation too small and phase transition needs to be strongly first order: ∆ v f ( T ) > 1 ⇒ m H < 45 GeV T C Ruled out by LEP: m H > 114 GeV Still possible in SUSY models but constrained → non-minimal models Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 5 / 18

Neutrino Masses Neutrino masses: m 1 < m 2 < m 3 (neutrino mixing data) ∆ m 2 atm = m 2 3 − m 2 ∆ m 2 atm ≃ 0 . 05 eV � 2 , with m atm = � ∆ m 2 sol = m 2 2 − m 2 ∆ m 2 sol ≃ 0 . 009 eV 1 , with m sol = Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 6 / 18

Seesaw Mechanism introduce right-handed neutrinos with mass M into the SM − 1 � � � N c MN � L N = LH λ ν N + h . c . 2 Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 7 / 18

Seesaw Mechanism introduce right-handed neutrinos with mass M into the SM − 1 � � � N c MN � L N = LH λ ν N + h . c . 2 Yukawa couplings lead to Dirac mass: m D = λ ν v � � 0 � � �� L ν = − 1 m T ν L ν c D � � L , N + h . c . 2 m D M N Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 7 / 18

Seesaw Mechanism seesaw mechanism: 1 eV assuming M ≫ m D : N with m N ≃ M 100 GeV ν with m ν ≃ − m D 1 � v 2 � 10 14 GeV M m T D = O M M Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 7 / 18

CP violation N are Majorana particles → L violation m 1 = v 2 ( λ † N ’s decay into lepton-Higgs pairs: Γ N ∝ ˜ ν λ ν ) 11 M 1 Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 8 / 18

l � l l � � CP violation N N j;k i CP violation by interference of tree level and one loop amplitude N i � � l � � � N i N j;k l � � Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 8 / 18

CP violation N are Majorana particles → L violation m 1 = v 2 ( λ † N ’s decay into lepton-Higgs pairs: Γ N ∝ ˜ ν λ ν ) 11 M 1 Assumptions: ◮ hierarchical neutrino masses M 1 ≪ M 2 , 3 , m 1 < m 2 < m 3 ◮ one-flavor approximation CP violation by interference of tree level and one loop amplitude: [Asaka et al. ’01; Davidson, Ibarra ’02; Buchmüller, Di Bari, Plümacher ’02] ε max m 1 , m 1 , m 3 ) = ε max β ≤ 1 . ( M 1 , ˜ ( M 1 ) β (˜ m 1 , m 1 , m 3 ) , 1 1 � � m atm 3 � M 1 m atm M 1 ε max ≈ 10 − 6 � ( M 1 ) = , 1 16 π v 2 10 10 GeV 0 . 05eV Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 8 / 18

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 ≤ 10 12 GeV s L s L α sph t L η B = α sph η B − L = α sph − 1 η L , c L b L α sph ≈ 1 with 3 Sphaleron d L b L ν τ d L ν µ u L ν e Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 9 / 18

Boltzmann Equations distribution functions in the expanding universe ∂ f N ( z , y ) z z = M / T = H ( M ) C [ f N ( z , y )] ∂ z y = p / T ∂ f l − l ( z , y ) z = H ( M ) C [ f l − l ( z , y )] ∂ z C [ f ( N , l − l ( z , y )] : change of f i due to interactions Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 10 / 18

Boltzmann Equations distribution functions in the expanding universe ∂ f N ( z , y ) z z = M / T = H ( M ) C [ f N ( z , y )] ∂ z y = p / T ∂ f l − l ( z , y ) z = H ( M ) C [ f l − l ( z , y )] ∂ z C [ f ( N , l − l ( z , y )] : change of f i due to interactions assumptions needed for BE of number densities I kinetic equilibrium Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 10 / 18

Boltzmann Equations distribution functions in the expanding universe ∂ f N ( z , y ) z z = M / T = H ( M ) C [ f N ( z , y )] ∂ z y = p / T ∂ f l − l ( z , y ) z = H ( M ) C [ f l − l ( z , y )] ∂ z C [ f ( N , l − l ( z , y )] : change of f i due to interactions assumptions needed for BE of number densities I kinetic equilibrium II neglecting Pauli-Blocking and Bose-emission factors Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 10 / 18

Boltzmann Equations distribution functions in the expanding universe ∂ f N ( z , y ) z z = M / T = H ( M ) C [ f N ( z , y )] ∂ z y = p / T ∂ f l − l ( z , y ) z = H ( M ) C [ f l − l ( z , y )] ∂ z C [ f ( N , l − l ( z , y )] : change of f i due to interactions assumptions needed for BE of number densities I kinetic equilibrium II neglecting Pauli-Blocking and Bose-emission factors d 3 p N III analytical solution for number density: dn N df N � dz = ( 2 π ) 3 dz Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 10 / 18