Neutrino Mixing and Mass Sum Rules

Transcription

1 Neutrino Mixing and Mass Sum Rules Mar4n Spinrath Na4onal Center for Theore4cal Sciences, Hsinchu, Taiwan Rencontres du Vietnam: Neutrinos - 19/07/2017 Based on collabora-ons with: Julia Gehrlein, Alexander Merle, Jens P. Oppermann, Daniela Schäfer, Serguey T. Petcov, Arsenii V. Titov

2 Outline Introduc4on Neutrino Mixing Sum Rules Neutrino Mass Sum Rules Summary and Conclusions 2

3 Outline Introduc-on Neutrino Mixing Sum Rules Neutrino Mass Sum Rules Summary and Conclusions 3

4 The Flavour Puzzle Why do we have three genera4ons? Why are the SM fermion masses so vastly different? What is the origin of CP viola4on? Why are the quark mixing angles rather small and the leptonic mixing angles rather large? 4

5 Non-Abelian (discrete) family symmetries [for a recent review see King, Luhn 2013] e.g.: Z n 3 symmetry of m e G e G F A 4, S 4, T', SO(3), SU(3),... U PMNS (tri-)bimaximal, golden ra4o, trimaximal,... Gn e.g.: Z 2 x Z 2 symmetry of mn 5

6 Sum Rules in the Lepton Sector Mixing sum rules, e.g., sin p 2 Mass sum rules, e.g., 3 sin 13 cos [Antusch, Aranda, BalleR, Boudjemaa, Damanik, de Medeiros-Varzielas, Ding, Gehrlein, Girardi, Hagedorn, He, Hochmuth, King, Luhn, Malinsky, Marzocca, Masina, Merle, Pascoli, Petcov, Rodejohann, Romanino, Schmidt, Stuart, Tanimoto, Titov, Valle, Volkas,.?] m 1 e i 1 + m 2 e i 2 m 3 =0 [Antusch, Aranda, BalleR, Boudjemaa, Damanik, de Medeiros-Varzielas, Ding, Gehrlein, Girardi, Hagedorn, He, Hochmuth, King, Luhn, Malinsky, Marzocca, Masina, Merle, Pascoli, Petcov, Rodejohann, Romanino, Schmidt, Stuart, Tanimoto, Titov, Valle, Volkas,.?] 6

7 Outline Introduc4on Neutrino Mixing Sum Rules Neutrino Mass Sum Rules Summary and Conclusions 7

8 Mixing Sum Rules Known for a long 4me and many people worked on them Rela4ons between angles and Dirac CP phase s a ( ij, )=0 8

9 Mixing Sum Rules Origin The PMNS matrix is a combina4on U PMNS = U e U Without 1-3 neutrino mixing and only small 1-2 charged lepton mixing sin 13 e 12 sin 23 Correc4ons to symmetry values by charged lepton mixing 9

10 Mixing Sum Rules Examples In general to lowest order [not the first ones, but e.g.: Marzocca, Romanino, Petcov, MS 2011] sin 2 12 sin O( e 12) For Bimaximal mixing: sin sin 13 cos For Tri-Bimaximal mixing: sin p 2 3 sin 13 cos 10

11 Note on RGE effects [e.g., Antusch, Kersten, Lindner, Ratz 03] Typical size of the correc4ons ij 10 6 (1 + tan 2 ) m2 m 2 i 10 6 (1 + tan 2 ) m2 m 2 m i (O(1) (1 + tan 2 ))m i Small in Standard Model Possibly large in the MSSM 11

12 RGE corrected Likelihoods NO Systema4c study of RGE effects Example for tribimaximal mixing sin 12 = 1 3, sin 23 = 1 2, sin 13 =0, e 13 = e 23 =0= e 12 L L L m 1 = 0.01 ev Global analysis SM MSSM tan = 30 MSSM tan = 50 m 1 = 0.05 ev m 1 = 0.1 ev e 23 = 0, TBM m 3 = 0.01 ev m 3 = 0.05 ev m 3 = 0.1 ev IO [Gehrlein, Petcov, MS, Titov 16; see also Zhang, Zhou '16] /07/17 - Rencontres du Vietnam: 0.0 Neutrinos [ ] [ ] 12

13 Outline Introduc4on Neutrino Mixing Sum Rules Neutrino Mass Sum Rules Summary and Conclusions 13

14 General remarks Not specific to a special family symmetry Not related to any residual symmetry [Gehrlein, MS '17] Not specific to any mass mechanism Only in common: 3 complex neutrino masses depend on 2 complex parameters 2 Rela4ons 14

15 One example [Gehrlein, Oppermann, Schäfer, MS 14] SU(5) x A 5 GUT Flavour Model Type I seesaw with 0 q Y A and M RR gives mass sum rule (v p 2 + v 3 ) 3v2 p p q 3v2 6v3 p 3v2 q + 2 = 1 m 1 m 2 m (v 2 + v 3 ) p 1 3v2 2 3 (v 2 + v 3 ) C p A 6v3 15

16 The Parametrisa4on [King, Stuart, Merle 13; Gehrlein, Merle, MS 15] s c 1 m 1 e i 1 d e i 13 + c 2 m 2 e i 2 d e i 23 + m d 3! =0 c 1, c 2, d, Dc 13 and Dc 23 fixed by the model For instance, in the previous example, c 1 = c 2 =1 d = 1 13 = 23 = ) = 1 m 1 m 2 m 3 16

17 Known Rules [King, Stuart, Merle 13; Gehrlein, Merle, MS 15] Sum rule c 1 c 2 d /2 1/ p 3+1 p 3 1 p /2, 3 / /2, 0, /2 0,, /2 11 1/3 1 1/ /2 1/2 1/2 17

18 Geometrical Interpreta4on [King, Stuart, Merle 13; Gehrlein, Merle, MS 15] α=- ϕ +Δχ ( - ϕ ) Δχ π+α-β ( - ϕ ) Δχ π-α β-π β=- ϕ +Δχ 18

19 Ques4ons Can we recons4tute forbidden orderings with small correc4ons? How big is the impact of small correc4ons on predic4ons for neutrinoless double beta decay? 19

20 Forbidden Orderings [Gehrlein, Merle, MS 15] Sum Rule 2 m 1 e i 1 +2m 2 e i 2 m 3 =0 From geometry and inverted ordering cos tree = m2 1 4m 2 2 m 2 3 4m 2 m 3 < 1 3 m2 2 4 m < 1 No inverted ordering on tree level 20

21 Forbidden Orderings [Gehrlein, Merle, MS 15] RGE correc4ons in MSSM (cos ) RGE Cy {z } >0 2.8m m m 2 3 m 2 m {z 3 } >0 log M S M Z {z } >0 Forbidden orderings possibly allowed only in very extreme regions of parameter space 21

22 Map of Orderings Rule NO X X IO X X X X 22

23 Numerical Results (RG correc4ons only) [Gehrlein, Merle, MS 15] 1 Rule 06 1 Rule 06 1 Rule 06 Disfavoured by 0nbb Disfavoured by 0nbb Disfavoured by 0nbb 0.1 SM 0.1 tanb= Dm 2 31 < 0 Dm 2 31 > 0 nu-fit.org v2.0 Best & 3s Disfavoured by Dm 2 31 < 0 Dm 2 31 > 0 nu-fit.org v2.0 Best & 3s Disfavoured by Dm 2 31 < 0 Dm 2 31 > 0 nu-fit.org v2.0 Best & 3s Disfavoured by Cosmology = 1 m 1 m 2 m 3 IO Sum Rule & IO Sum Rule & NO BF w/o Sum Rule 3s w/o Sum Rule 23

24 Outline Introduc4on Neutrino Mixing Sum Rules Neutrino Mass Sum Rules Summary and Conclusions 24

25 Summary and Conclusions Neutrino Flavour Models s4ll interes4ng Constraints on CP viola4on, neutrino mass scale and ordering Mass sum rule predic4ons are rather robust Mixing and mass sum rules combined are very powerful! 25

26 Thanks a lot for your amen4on! 26

27 Backup 27

28 RGE corrected Likelihoods NO Systema4c study of RGE effects Example for tribimaximal mixing sin 12 = 1 3, sin 23 = 1 2, sin 13 =0, e 13 =0= e 23 and 0 = e 12 L L L m 1 = 0.01 ev Global analysis SM MSSM tan = 30 MSSM tan = 50 m 1 = 0.05 ev m 1 = 0.1 ev e 23 0, TBM m 3 = 0.01 ev m 3 = 0.05 ev m 3 = 0.1 ev IO [Gehrlein, Petcov, MS, Titov 16; see also Zhang, Zhou '16] /07/17 - Rencontres du Vietnam: 0.0 Neutrinos [ ] [ ] 28

29 The Model [Gehrlein, Oppermann, Schäfer, MS 2014] SU(5) x A 5 GUT Flavour Model Golden Ra4o Neutrino Mixing tan 12 = 2 1+ p 5, 23 = /4, 13 =0 Cabibbo-like 1-2 charged lepton mixing e 12 C ) 13 C p

30 Model Constraints [Gehrlein, Oppermann, Schäfer, MS 2014] Mixing sum rule PMNS C cos Mass sum rule e i 1 m 1 + ei 2 m 2 = 1 m 3 From fermion mass ra4os tan & 30 30

31 Implica4ons [Gehrlein, Oppermann, Schäfer, MS 2014] From the mixing sum rule 24. PMNS 12 (M S ). 39 From the mass sum rule ev. m 1 for NO ev. m ev for IO From RGEs 12 (M S ) (M S )