Flavorful Leptogenesis and Collider Signals Bhupal Dev Washington University in St. Louis Matter over Antimatter: The Sakharov Conditions After 50 Years Lorentz Center, Leiden May 10, 2017 Two parts: 1. Flavor-covariant formalism. BD, A. Pilaftsis, P . Millington, D. Teresi [1404.1003; 1410.6434; 1504.07640] 2. A predictive model based on flavor and CP symmetries. BD, C. Hagedorn, E. Molinaro (in prep).
Leptogenesis [Fukugita, Yanagida ’86] A cosmological consequence of the seesaw mechanism. Naturally satisfies the Sakharov conditions. L violation due to the Majorana nature of heavy RH neutrinos. / L → / B through sphaleron interactions. New source of CP violation in the leptonic sector (through complex Dirac Yukawa couplings and/or PMNS CP phases). Departure from thermal equilibrium when Γ N � H . Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 2 / 38
For Pedestrians [Buchm¨ uller, Di Bari, Pl¨ umacher ’05] Generation of L asymmetry by heavy Majorana neutrino decay: 1 Partial washout of the asymmetry due to inverse decay (and scatterings): 2 Conversion of the left-over L asymmetry to B asymmetry at T > T sph . 3 Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 3 / 38
Boltzmann Equations [Buchm¨ uller, Di Bari, Pl¨ umacher ’02] dN N − ( D + S )( N N − N eq = N ) , dz dN ∆ L ε D ( N N − N eq = N ) − N ∆ L W , dz (where z = m N 1 / T and D , S , W = Γ D , S , W / Hz for decay, scattering and washout rates.) FInal baryon asymmetry: η ∆ B = d · ε · κ f d ≃ 28 1 27 ≃ 0 . 02 ( / L → / B conversion at T c + entropy dilution from T c to 51 recombination epoch). κ f ≡ κ ( z f ) is the final efficiency factor, where � z − � z D dN N z ′ dz ′′ W ( z ′′ ) dz ′ κ ( z ) = dz ′ e D + S z i Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 4 / 38
CP Asymmetry Φ † Φ † Φ † Φ L N β N α N α N α N α × × N β L × L C L C Φ L C l l l (a) (b) (c) tree self-energy vertex h l α | 2 − | � | � Γ( N α → L l Φ) − Γ( N α → L c l Φ c ) h c l α | 2 � k Φ c ) � ≡ ε l α = � ( � h † � h ) αα + ( � h c † � Γ( N α → L k Φ) + Γ( N α → L c h c ) αα k with the one-loop resummed Yukawa couplings [Pilaftsis, Underwood ’03] � � h l α = � | ǫ αβγ | � h l α − i h l β β,γ m α ( m α A αβ + m β A βα ) − iR αγ [ m α A γβ ( m α A αγ + m γ A γα ) + m β A βγ ( m α A γα + m γ A αγ )] × , α | A βγ | 2 + m β m γ Re ( A 2 m 2 α − m 2 β + 2 im 2 α A ββ + 2 i Im ( R αγ )[ m 2 βγ )] � m 2 1 A αβ ( � � h l α � α h ∗ R αβ = ; h ) = l β . m 2 α − m 2 β + 2 im 2 α A ββ 16 π l Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 5 / 38
Vanilla Leptogenesis Hierarchical heavy neutrino spectrum ( m N 1 ≪ m N 2 < m N 3 ). Both vertex correction and self-energy diagrams are relevant. For type-I seesaw, the maximal CP asymmetry is given by � m N 1 3 ε max = ∆ m 2 1 atm v 2 16 π Lower bound on m N 1 : [Davidson, Ibarra ’02; Buchm¨ uller, Di Bari, Pl¨ umacher ’02] � � � � η B 0 . 05 eV m N 1 > 6 . 4 × 10 8 GeV κ − 1 � f 6 × 10 − 10 ∆ m 2 atm Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 6 / 38
Vanilla Leptogenesis Hierarchical heavy neutrino spectrum ( m N 1 ≪ m N 2 < m N 3 ). Both vertex correction and self-energy diagrams are relevant. For type-I seesaw, the maximal CP asymmetry is given by � m N 1 3 ε max = ∆ m 2 1 atm v 2 16 π Lower bound on m N 1 : [Davidson, Ibarra ’02; Buchm¨ uller, Di Bari, Pl¨ umacher ’02] � � � � η B 0 . 05 eV m N 1 > 6 . 4 × 10 8 GeV κ − 1 � f 6 × 10 − 10 ∆ m 2 atm Experimentally inaccessible mass range! Also leads to a lower limit on the reheat temperature T rh � 10 9 GeV. In many supergravity scenarios, need T rh � 10 6 − 10 9 GeV to avoid the gravitino problem. [Khlopov, Linde ’84; Ellis, Kim, Nanopoulos ’84; Cyburt, Ellis, Fields, Olive ’02; Kawasaki, Kohri, Moroi, Yotsuyanagi ’08] Also in conflict with the Higgs naturalness bound m N � 10 7 GeV. [Vissani ’97; Clarke, Foot, Volkas ’15; Bambhaniya, BD, Goswami, Khan, Rodejohann ’16] Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 6 / 38
Resonant Leptogenesis L l ( k, r ) N α ( p, s ) � ε ε ′ Φ( q ) Dominant self-energy effects on the CP -asymmetry ( ε -type) [Flanz, Paschos, Sarkar ’95; Covi, Roulet, Vissani ’96] . Resonantly enhanced, even up to order 1, when ∆ m N ∼ Γ N / 2 ≪ m N 1 , 2 . [Pilaftsis ’97; Pilaftsis, Underwood ’03] The quasi-degeneracy can be naturally motivated as due to approximate breaking of some symmetry in the leptonic sector. Heavy neutrino mass scale can be as low as the EW scale. [Pilaftsis ’04; Pilaftsis, Underwood ’05] A testable scenario of leptogenesis, with implications at both Energy and Intensity Frontiers. [BD, Millington, Pilaftsis, Teresi ’14, ’15; BD, Hagedorn, Molinaro ’17 (in prep)] Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 7 / 38
Flavor-diagonal Resonant Leptogenesis � � � n γ H N d η N 1 − η N α α γ N α = L l Φ η N z d z eq l � � � � n γ H N d δη L η N α γ N α l = − 1 ε l α L k Φ η N z d z eq α k � �� � � − 2 3 δη L γ L l Φ k Φ c + γ L l Φ L k Φ + δη L γ L k Φ l Φ c − γ L k Φ l k L c L c L l Φ k L l ( k , r ) L k ( k , r ) b b N α ( p , s ) N β ( p , s ) [ b [ b c ] β h ˜ c ] l h ˜ α k Φ ( q ) Φ ( q ) L n ( k 2 , r 2 ) L k ( k 1 , r 1 ) [ L ˜ c ( k 2 , r 2 )] m L k ( k 1 , r 1 ) b h n [ b h ˜ c ] β [ b [ b c ] β h ˜ c ] β h ˜ β k m k b N β ( p ) b N β ( p ) Φ ( q 2 ) Φ ( q 1 ) Φ ˜ c ( q 2 ) Φ ( q 1 ) Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 8 / 38
Analytic Solution [Deppisch, Pilaftsis ’11] 10 4 N 1 10 5 10 6 N 10 7 L L , 10 8 10 9 z 1 z 2 z c z 3 10 10 10 2 10 1 10 0 10 1 10 2 z � � α ε l α 3 η L ( z ) ≃ ( z 2 < z < z 3 ) 2 z K eff l l Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 9 / 38
Flavordynamics of RL Important flavor effects in the time-evolution of lepton asymmetry in RL. [Abada, Davidson, Ibarra, Josse-Michaux, Losada, Riotto ’06; Nardi, Nir, Roulet, Racker ’06; Blanchet, Di Bari ’06; De Simone, Riotto ’06; Blanchet, Di Bari, Jones, Marzola ’12] M i � 10 12 GeV � 10 9 GeV M i � 10 12 GeV � 10 9 GeV Two sources of flavor effects: Heavy neutrino Yukawa couplings h α [Pilaftsis ’04; Endoh, Morozumi, Xiong ’04] l Charged lepton Yukawa couplings y k [Barbieri, Creminelli, Strumia, Tetradis ’00] l Three distinct physical phenomena: mixing, oscillation and decoherence. Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 10 / 38
Flavordynamics of RL Important flavor effects in the time-evolution of lepton asymmetry in RL. [Abada, Davidson, Ibarra, Josse-Michaux, Losada, Riotto ’06; Nardi, Nir, Roulet, Racker ’06; Blanchet, Di Bari ’06; De Simone, Riotto ’06; Blanchet, Di Bari, Jones, Marzola ’12] M i � 10 12 GeV � 10 9 GeV M i � 10 12 GeV � 10 9 GeV Two sources of flavor effects: Heavy neutrino Yukawa couplings h α [Pilaftsis ’04; Endoh, Morozumi, Xiong ’04] l Charged lepton Yukawa couplings y k [Barbieri, Creminelli, Strumia, Tetradis ’00] l Three distinct physical phenomena: mixing, oscillation and decoherence. Boltzmann approach: captured by ‘density matrix’ formalism. [Sigl, Raffelt ’93] Fully flavor-covariant formalism. [BD, Millington, Pilaftsis, Teresi ’14; ’15] Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 10 / 38
Flavor Transformations l � Φ N R ,α + 1 R ,α [ M N ] αβ N R ,β + H . c . . C −L N = h α L 2 N l Under U ( N L ) ⊗ U ( N N ) , L l ≡ ( L l ) † → L ′ l = V l m L m , L l → L ′ l = V m L m , l ≡ ( N R ,α ) † → N ′ α N R ,α → N ′ β N α = U α β N β R ,α = U N R ,β , . α R R R [ M N ] αβ → [ M ′ N ] αβ = U α δ [ M N ] γδ . h α → h ′ α = V m U α β γ U β β h , l l l m Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 11 / 38
Flavor Transformations l � Φ N R ,α + 1 R ,α [ M N ] αβ N R ,β + H . c . . C −L N = h α L 2 N l Under U ( N L ) ⊗ U ( N N ) , L l ≡ ( L l ) † → L ′ l = V l m L m , L l → L ′ l = V m L m , l ≡ ( N R ,α ) † → N ′ α N R ,α → N ′ β N α = U α β N β R ,α = U N R ,β , . α R R R [ M N ] αβ → [ M ′ N ] αβ = U α δ [ M N ] γδ . h α → h ′ α = V m U α β γ U β β h , l l l m Number densities: 1 [ n L s 1 s 2 ( p , t )] m � b m ( p , s 2 , ˜ t ) b l ( p , s 1 , ˜ ≡ t ) � t , l V 3 1 n L s 1 s 2 ( p , t )] m � d † l ( p , s 1 , ˜ t ) d † , m ( p , s 2 , ˜ [¯ ≡ t ) � t , l V 3 1 [ n N β � a β ( k , r 2 , ˜ t ) a α ( k , r 1 , ˜ ≡ t ) � t , r 1 r 2 ( k , t )] α V 3 ≡ 1 t ) G βδ a δ ( k , r 2 , ˜ n N β � G αγ a γ ( k , r 1 , ˜ [¯ r 1 r 2 ( k , t )] t ) � t , α V 3 Total number density: � � � � n N ( t ) ≡ n N n L ( t ) ≡ Tr n L rr ( k , t ) , ss ( p , t ) . iso k p r = − , + s = − , + Bhupal Dev (Washington U.) Flavorful Leptogenesis Snellius Workshop 11 / 38
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