Puzzles of Neutrino Mixing and Anti-Matter: Hidden Symmetries and Symmetry Breaking. Shao-Feng Ge

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1 Puzzles of Neutrino Mixing and Anti-Matter: Hidden Symmetries and Symmetry Breaking Shao-Feng Ge Center for High Energy Physics, Tsinghua Univeristy Collaborators: Hong-Jian He & Fu-Rong Yin Based on arxiv: (to appear in JCAP)

2 December, 2009 arxiv: Common Origin of Soft µ τ and CP Breaking in Neutrino Seesaw and the Origin of Matter Shao-Feng Ge, Hong-Jian He, Fu-Rong Yin [hep-ph] Apr 200 Center for High Energy Physics and Institute of Modern Physics, Tsinghua University, Beijing 00084, China and Kavli Institute for Theoretical Physics China, Chinese Academy of Sciences, Beijing 0090, China Abstract Neutrino oscillation data strongly support µ τ symmetry as a good approximate flavor symmetry of the neutrino sector, which has to appear in any viable theory for neutrino mass-generation. The µ τ breakingis not only small, but alsothe sourceofdirac CP-violation. We conjecturethat both discrete µ τ and CP symmetries arefundamental symmetries ofthe seesawlagrangian(respected by interaction terms), and they are only softly broken, arising from a common origin via a unique dimension-3 Majorana mass-term of the heavy right-handed neutrinos. From this conceptually

3 Experimental Data Current Neutrino Oscillation Data ν-parameters Lower Limit Best Value Upper Limit (2σ) (2σ) m 2 2 (0 5 ev 2 ) m 2 3 (0 3 ev 2 ) sin 2 θ 2 (θ 2 ) (3.8 ) 0.32 (34.0 ) (36.4 ) sin 2 θ 23 (θ 23 ) (37.2 ) (43.0 ) (50.9 ) sin 2 θ 3 (θ 3 ) 0 (0 ) 0.06 (7.3 ) (0.9 )

4 Approximating Symmetry Evidence of µ τ Symmetry at Low Energy Two small deviations (2σ level): 7.8 < θ < < θ 3 < 0.9 with Best Fit Value: θ = 2.0 & θ 3 = 7.3. Zeroth Order Approximation: θ 23 = 45, θ 3 = 0. with Vanishing Dirac CP Phase & µ τ Symmetric Mass Matrix: A B B M ν (0) = C D C

5 Lagrangian, Symmetry & Breaking Leptogenesis & Minimal Seesaw Baryon Asymmetry Leptogenesis Seesaw Minimal Seesaw = SM + Two Heavy Majorana Neutrinos N T = ( N µ N τ ) Lagrangian associated with Neutrino Masses: L = L L Y l Φl R L L Y ν ΦN + 2 N T M R CN M R is Soft & High Dirac Mass Term: m D = Y ν Φ Φ is the ordinary SM Higgs Doublet, NO CP!

6 Lagrangian, Symmetry & Breaking Model Assignment at Zeroth Order M (0) ν Minimal Seesaw & µ τ & CP Symmetries: T µτ (3) = ( ) T µτ (2) = T µτm (3) D T (2) µτm R T (2) µτ m D & T (2) µτ M R : a a ( ) m D = b c m22 m, M R = 23 m c b 23 m 33 with all elements being REAL. Seesaw Mass Matrix for light neutrinos (M ± m 22 ± m 23 ): m D M R mt D = 2a 2 M + a(b+c) M + [ ] (b+c) 2 2 M + + (b c)2 M a(b+c) M + [ (b+c) 2 2 M + [ (b+c) 2 2 M + ] (b c)2 M ] + (b c)2 M

7 Lagrangian, Symmetry & Breaking Common µ τ & CP Soft Breaking Approximate µ τ Zeroth-Order vanishing θ 3 & Dirac CP Phase δ D ; So, µ τ breaking should be Small & Simultaneously generates δ D µ τ & Dirac CP broken by a Common Origin. Natural & Simple, so Tempting, to expect a Common Origin for all CP Phases; Conjecture: µ τ & CP Symmetries are Softly broken from a Common Origin which is Uniquely determined as: ( ) ( R M R = m 22 R ζe iω R m 23 m 22 Note: µ τ & CP Recover with ζ 0. Hard Symmetry Breaking? (Another paper in preparation) )

8 Lagrangian, Symmetry & Breaking Expected Consequences δ a ( θ ) & δ x ( θ 3 ) Common Origin & Linear δ a δ x ; Once θ 23 well measured Predict θ 3! Dirac CP Phase δ D & Majorana CP Phases Common Origin Correlated; Once Dirac CP Phase δ D is measured J & M ee ; Vice Versa, Constrains from Leptogenesis. Normal Hierarchy with m = 0. Fully reconstructed mass spectrum M ee ; Vice Versa.

9 Solving Low Energy Parameters M (0) ν = M () ν = Neutrino Mass Matrix from Seesaw Expanding the mass matrix M ν in terms of r & ζ up to Linear Order: with: (b c) 2 (2 X)M (0) M ν = m D M R mt D M(0) ν + M ν () + O(r 2,rζ,ζ 2 ) A with an Overall Phase (No Physical Consequence) 0 r (2 X) 2 a 2 0 (2 X)[( X)b + c]a (2 X)[b + ( X)c]a δm B (2 X) 2 M [( X)b + c] 2 ( X)(b + c) 2 + X 2 ee () δm eµ () δm () eτ C B δm () [b + ( X)c] 2 µµ δm µτ () C A δm ττ () where r R & X ζ r eiω and M (0) is the Zeroth-Order of the Lightest Eigenvalue of M R : M (0) = r M 22

10 Solving Low Energy Parameters Expanding Reconstructed Mass Matrix with: M (0) ν = 2 m 30e 2iα 20 M ν = VνD ν V ν M ν (0) + M ν () 0 0 0, M ν () δm ee () δm eµ () δm eτ () δm µµ () δm µτ () δm ττ () Note: Overall CP Phase (No Physical Consequences!!!) For Linear Order: δm () ee = m 30 s 2 s e 2i(α 0 φ 23 ) y δm µµ () = 2 m 30e 2iα 20 hcs 2 i e 2iφ 23y + z + 2δ a 2iδα 2 δm () ττ = 2 m 30e 2iα 20 hc 2 i s e 2iφ 23y + z 2δ a 2iδα 3 δm () eµ = δm () eτ = δm () µτ = m 30 e i(α 0 +α 20 ) h c ss se 2iφ 23y + e iδ i D δ x 2 m 30 e i(α 0 +α 20 ) h c ss se 2iφ 23y e iδ i D δ x 2 2 m 30e 2iα 20 h c 2 i s e 2iφ 23y z + i(δα 2 + δα 3 ) Details

11 Predictions Solutions & Predictions Zeroth-Order: 2(b c)2 m 0 = m 20 = 0, m 30 = (2 X)M 0, e2iα30 = r 2 X r 2 X Overall CP Phase (No Physical Consequence!) Linear Order: yss ζ δ x = 2 [ζ 2 4rζ cosδ D + 4r 2 ] /4 Correlations: δ a = yc s cosδ D ζ 2 [ζ 2 4rζ cosδ D + 4r 2 ] /4 δ x = tanθ s δ a δ x tan θ s δ a cosδ D Solar Mixing Angle θ s Dictated by Dirac Mass Matrix m D : 2a tanθ s = b + c Will be elaborated later.

12 Predictions Correlation between θ 3 & θ 23 7 δ x = tanθ s cos δ D δ a Θ Double Chooz RENO Daya Bay Daya Bay future Θ Constrained Correlation

13 Predictions Correlation between θ 3 & θ 23 7 δ x = tanθ s cos δ D δ a Θ Double Chooz RENO Daya Bay Daya Bay future Θ Constrained Correlation

14 Baryon Asymmetry Leptogenesis The Universe contains 4% Matter: η B n B n B = (6.2 ± 0.6) 0 0 n γ where n γ is Photon Number Density & n B is Baryon Number Density. Leptogenesis Mechanism generates η B from Lepton Asymmetry Y L via Sphaleron Interactions which violate B + L but preserve B L: η B = ξ f Nf B L = ξ f Nf L = 3ξ 4f κ fǫ f where ξ (8N F + 4N H )/(22N F + 3N H ) = 28/79 for SM, and f = N rec γ /N γ is the Dilution Factor. Efficiency Factor: ( κ f m ev with m ( m D m D) /M ( m D m D V R ). ) ev m

15 CP Asymmetry Parameter ǫ CP Asymmetry Parameter ǫ CP Asymmetry Parameter ǫ : ǫ Γ[N lh] Γ[N lh ] Γ[N lh] + Γ[N lh = ] 4πv 2 F M2 M j h «Im em D em D 2 em D em D Complex m D differs Γ[N lh] from Γ[N lh ]. In Minimally Extended SM (Heavy Majorana Neutrinos): F(x) x " ( + x 2 ) ln! # + x 2 x 2 + x 2 The expansion applies for x M 2 /M 5. i 2 ff = 3 «2x + O x 3 In Current Model: ǫ = m 3 (4y ) 2 ζ 3M 2 4rζ cosδ D + 4r 2 4πv 2 28 (ζ 2 4rζ cosδ D + 4r 2 (4r cosδ D ζ)sinδ D ζ 2 ) where m 3 is obtained by RG-running m 3 from M Z to Leptogenesis Scale. RGE

16 CP Asymmetry Parameter ǫ Lower Bound on θ 3 M = 4f 4πv 2 28(4r 2 4rζ cos δ D + ζ 2 ) η B» 3ξ κ f bm y q4r 2 4rζ cos δ D + ζ 2 (4r cos δ D ζ) sin δ D ζ 2 05 GeV 7 Θ Double Chooz RENO Daya Bay Daya Bay future Θ Free Correlation

17 Conjecture θ s Determined by m D As we have seen: 2a tanθ s = b + c which holds before and after soft breaking! Fully Determined by m D : a a m D = b c c b Not Affect by µ τ and CP symmetry breaking in M R! Protected or Accident?

18 Conjecture Extra Z 2 Symmetry θ s is Solely determined by m D ; Soft symmetry breaking comes from M R, m D is not affect; If extra symmetry exists, it shouldn t be affected by soft breaking; It only applies on m D, not M R. Can be realized by: ν L T s ν L, T s m D = m D N N Also respected by light neutrino s mass matrix M ν : T T s M ν T s = M ν which is Independent of M R.

19 Representation Representation of the Extra Symmetry Neutrino mass matrix Invariant under transformation: Diagonalization Scheme: T T s M νt s = M s V T M ν V = D ν The effect of transformation is just a Diagonal Rephasing: V T T T s M νt s V = d ν D ν d ν = d ν V T M ν Vd ν with d 2 ν = I 3 which constrains d ν = diag(±, ±, ±). General consequence: T s V = Vd ν T s = Vd ν V

20 Representation Representaion of the Extra Symmetry Two Nontrivial Independent possibilities of d ν : d () ν =, d (2) ν =. Mixing matrix with θ s parameterized in terms of k: V(k) = k 2+k 2 2+k 2 2+k k 0 2 k 2(2+k 2 ) 2 2 k 2(2+k 2 ) Two Independent symmetry transformations: T s = 2 k2 2k 2k 2k k 2 2, 2 + k 2 T µτ = 2k 2 k 2 T µτ is 3D Representation of µ τ symmetry. T (3) µτ

21 Summary Summary Oscillation Data strongly support µ τ symmetry as a Good Approximate Flavor Symmetry. The µ τ symmetry predicts (θ 23,θ 3 ) = (45,0 ) & Vanishing Dirac CP Phase. Conjecture: both µ τ and CP are Softly Broken by a Common Origin in M R. With this conceptually Simple and Attractive construction, θ 3 is Correlated with θ 23 (Lower Bound on δ x / Upper Bound on δ a ). Strong supports for up-coming experiments. Predictions on Baryon Asymmetry through leptogenesis. Constrain by leptogenesis scale: Lower Bound on θ 3. Extra Z 2 dictating solar mixing angle θ 2.

22 Thank You Thank You!

23 Spare Slides - Reconstruction of Low Energy Neutrino Mass Reconstruction of Light Neutrino Mass Matrix Note: Majorana Neutrino s mass matrix is Symmetric: m ee m eµ m eτ M ν V D ν V = m µµ m µτ with D ν m m 2 m ττ where: V U UU, U diag(e iα,e iα 2,e iα 3 ), U diag(e iφ,e iφ 2,e iφ 3 ); c s c x s s c x s x e iδ D U s s c a c s s a s x e iδ D c s c a + s s s a s x e iδ D s a c x s s s a + c s c a s x e iδ D c s s a s s c a s x e iδ d c a c x (θ x θ 3,θ s θ 2,θ a θ 23 ) Note: of the Six Rephasing Phases, only Five are Independent. Back m 3

24 Spare Slides - Reconstruction of Low Energy Neutrino Mass Reconstructed Mass Matrix Elements m ee = e i2α [ c 2 s cx 2 m + s2 s c2 x m 2 + ] s2 x m e 2iδD 3, m µµ = e i2α [ 2 (ss c a c s s a s x e iδ D ) 2 m + (c s c a + s s s a s x e iδ D ) 2 m 2 + sac 2 x 2 m ] 3, m ττ = e i2α [ 3 (ss s a + c s c a s x e iδ D ) 2 m + (c s s a s s c a s x e iδ D ) 2 m 2 + cac 2 x 2 m ] 3, m eµ = e i(α +α 2 )[ c s c x (s s c a c s s a s x e iδ D ) m s s c x (c s c a + s s s a s x e iδ D ) m 2 +s a s x c x e iδd m 3 ], m eτ = e i(α +α 3 )[ c s c x (s s s a +c s c a s x e iδ D ) m s s c x (c s s a s s c a s x e iδ D ) m 2 c a s x c x e iδd m 3 ], m µτ = e i(α 2 +α 3 )[ (s s c a c s s a s x e iδ D )(s s s a + c s c a s x e iδ D ) m + (c s c a + s s s a s x e iδ D )(c s s a s s c a s x e iδ D ) m 2 s a c a c 2 x m 3], with m i m i e 2iφ i. Back

25 Spare Slides - Reconstruction of Low Energy Neutrino Mass Tiny Variables of Reconstructed Mass Matrix From: M (0) ν = (b c)2 (2 X)M (0) we can get Two Vanishing Mass Eigenvalues: m = m 2 = 0 Normal Hierarchy Nonzero m 2 : Besides: y m 2 m 3 O(r,ζ) δ a,δ x,z δm 3 m 3,δα i (α i α j + φ 3 ) Back

26 Spare Slides - Prediction of Leptogenesis for Baryon Asymmetry Prediction of Leptogenesis - η B /M «2 η B = 3ξ 3 4y qζ M 4f κ bm 3 M 2 4rζ cos δ D + 4r 2 f 4πv 2 28 `ζ 2 4rζ cos δ D + 4r 2 (4r cos δ D ζ) sin δ D ζ a Η B M GeV D Constrains on δ D

27 Spare Slides - Prediction of Leptogenesis for Baryon Asymmetry Prediction of Leptogenesis - Lower Limit of M M = 4f 4πv 2 28(4r 2 4rζ cos δ D + ζ 2 ) η B» 3ξ κ f bm y q4r 2 4rζ cos δ D + ζ 2 (4r cos δ D ζ) sin δ D ζ 2 03 GeV a 0 7 M GeV J

28 Spare Slides - Constrains of Leptogenesis on Low Energy Observables Upper Limit on Leptogenesis Scale M M = (b c)2 0 5 GeV m M GeV b b c GeV

29 Low Energy Observables Jarlskog Invariant J J = 4 sin2 2θ s sinδ D δ x + O ( ) δx 2,δ xδ a,δa 2 Θ a J Constrained Jarlskog

30 Low Energy Observables 0ν2β Decay Observable M ee M ee m 3 s 4 sy 2 + 2s 2 s cos2(δ D φ 23 )yδ 2 x + (δ 4 x 2s 2 sy 2 δ 2 x) Θ b M ee mev Constrained M ee

31 Low Energy Observables Constrained Jarlskog Invariant J 8 6 Θ a J Free Jarlskog

32 Low Energy Observables Constrained 0ν2β Decay Observable M ee 8 6 Θ b M ee mev Free M ee

33 Spare Slides - CP Phase Constrained by Leptogenesis Constrained CP Phase δ D by Leptogenesis r = ζ 2 η B = 3ξ M 4f κ bm 3 3 4y p ζ 2 4rζ cos δ D + 4r 2 2 f 4πv 2 28 `ζ 2 4rζ cos δ D + 4r 2 (4r cos δ D ζ) sin δ D ζ 2 [ η B > 0 (4r cos δ D ζ)sinδ D > 0 cos δ D ± ] ss 4 y 2 ζ 2 6 δx 4 sin 2 δ D These two inequalities will lead to: ζ 4 δx 2 ss 2 y sin δ D cos 2 δ D 4 s 4 s δ 4 x y 2 ζ 2 Leptogenesis

34 Spare Slides - CP Phase Constrained by Leptogenesis Constrained CP Phase δ D v.s. J 0.02 a 0.0 J D Leptogenesis

35 Spare Slides - CP Phase Constrained by Leptogenesis Constrained CP Phase δ D v.s. M ee 3.5 b Mee mev D Leptogenesis

36 Spare Slides - RGE RG Running Effect Low Energy Observables RGE High Energy Observables Only mass eigenvalues are obviously affected: m j (µ) = χ(µ,µ 0 )m j (µ 0 ) which can be expressed as: [ t ] χ(µ,µ 0 ) exp 6π 2 α(t )dt 0 For leptogenesis: m j (M ) = χ(m,m Z )m j (M Z ) with α 2g 2 2+6y 2 t +λ CP Asymmetry ǫ

37 Spare Slides - RGE RG Running Effect ΧΑ Μ m i m i Μ GeV M H 5GeV CP Asymmetry ǫ