1. Systematic model building... based on QLC assumptions NuFact 07 Okayama University, Japan August 8, 2007 Walter Winter Universität Würzburg

2. August 8, 2007NuFact 07 - Walter Winter2 Contents Introduction Introduction Bottom-up model building Bottom-up model building Extended Quark-Lepton Complementarity Extended Quark-Lepton Complementarity Examples: Examples: –3x3 case –Introducing complex phases –The seesaw mechanism Towards model building Towards model building Summary Summary

3. August 8, 2007NuFact 07 - Walter Winter3 Neutrino mass models Mass models describe masses and mixings by symmetries, GUTs, anarchy arguments, etc. Mass models describe masses and mixings by symmetries, GUTs, anarchy arguments, etc. Predictions for  13,  23 -  /4, mass hierarchy, etc. Predictions for  13,  23 -  /4, mass hierarchy, etc. Example: Literature research for  13 Example: Literature research for  13 (Albright, Chen, 2006) Peak generic or biased? Experiments provide important hints for theory

4. August 8, 2007NuFact 07 - Walter Winter4 Systematic model building A conventional approach: A conventional approach: Bottom-up approach: Bottom-up approach: Theory (e.g. GUT, flavor symmetry) Yukawa coupling structure Fit (order one coeff.) to data!? Theory (e.g. flavor symmetry) Yukawa coupling structure Yukawa couplings with order one coeff. Connection to observables ModelTextureRealization Generic assumptions (e.g. QLC) m : 11 : nMost of this talk Diag., many d.o.f. No diag., reduce d.o.f. by knowledge on data

5. August 8, 2007NuFact 07 - Walter Winter5 Benefits of bottom-up approach Key features: 1. Construct all possibilities given a set of generic assumptions  New textures, models, etc. 2. Learn something about parameter space  Spin-off: Learn how experiments can most efficiently test this parameter space! Very generic assumptions Automated procedure: generate all possibilities Interpretation/ analysis Select solutions compatible with data Cannot foresee the outcome! Low bias!?

6. August 8, 2007NuFact 07 - Walter Winter6 Generic assumptions from quark-lepton unification? Phenomenological hint e.g. („Quark-Lepton- Complementarity“ - QLC) Phenomenological hint e.g. („Quark-Lepton- Complementarity“ - QLC) (Petcov, Smirnov, 1993; Smirnov, 2004; Raidal, 2004; Minakata, Smirnov, 2004; others) Is there one quantity  ~  C which describes all mixings and hierarchies? Is there one quantity  ~  C which describes all mixings and hierarchies? Remnant of a unified theory? Remnant of a unified theory? Lepton Sector Quark Sector Symmetry breaking(s) E Unified theory  

7. August 8, 2007NuFact 07 - Walter Winter7 Manifestation of  Mass hierarchies of quarks/charged leptons: m u :m c :m t =  6 :  4 :1, m d :m s :m b =  4 :  2 :1, m e :m  :m  =  4 :  2 :1 Mass hierarchies of quarks/charged leptons: m u :m c :m t =  6 :  4 :1, m d :m s :m b =  4 :  2 :1, m e :m  :m  =  4 :  2 :1 Neutrino masses: m 1 :m 2 :m 3 ~  2 :  :1, 1:1:  oder 1:1:1 Neutrino masses: m 1 :m 2 :m 3 ~  2 :  :1, 1:1:  oder 1:1:1 Mixings Mixings 1 3333 1 2222 3333 22221 V CKM ~ U PMNS ~ V CKM + U bimax ? Combination of  and max. mixings?

8. August 8, 2007NuFact 07 - Walter Winter8 Extended QLC in the 3x3-case 1. Generate all possible (real, std. param.) U l, U with mixing angles(262.144) 2. Calculate U PMNS and read off mixing angles; select only realizations compatible with data (2.468) 3. Calculate mass matrices using eigenvalues from last slide and determine leading order coeff.  a few Textures  No diagonalization necessary Charged lepton mass termsEffective neutrino mass terms cf., CC (interaction) Rotates left-handed fields Do not rotate away U l because you would change your symmetry base! Cutoff given by current precision ~  2

9. August 8, 2007NuFact 07 - Walter Winter9 New textures from extended QLC New sum rules and systematic classification of textures New sum rules and systematic classification of textures Example: „Diamond“ textures with new sum rules, such as (includes coefficients from underlying realizations) Example: „Diamond“ textures with new sum rules, such as (includes coefficients from underlying realizations) (Plentinger, Seidl, Winter, hep-ph/0612169)

10. August 8, 2007NuFact 07 - Walter Winter10 Distribution of observables Parameter space analysis based on realizations Parameter space analysis based on realizations Large   3 preferred Large   3 preferred Compared to the GUT literature: Some realizations with very small sin 2 2  13 ~3.3 10 -5 Compared to the GUT literature: Some realizations with very small sin 2 2  13 ~3.3 10 -5 (Plentinger, Seidl, Winter, hep-ph/0612169)

11. August 8, 2007NuFact 07 - Walter Winter11 How exps affect this parameter space Strong pressure from  13 and  12 measurements Strong pressure from  13 and  12 measurements  12 can emerge as a combination between maximal mixing and  C !  „Extended“ QLC  12 can emerge as a combination between maximal mixing and  C !  „Extended“ QLC (Plentinger, Seidl, Winter, hep-ph/0612169)

12. August 8, 2007NuFact 07 - Walter Winter12 Introducing complex phases Vary all complex phases with uniform distributions Vary all complex phases with uniform distributions Calculate all valid realizations and textures (n:1)  Landscape interpretation with some flavor structure? (see e.g. Hall, Salem, Watari, 2007) Calculate all valid realizations and textures (n:1)  Landscape interpretation with some flavor structure? (see e.g. Hall, Salem, Watari, 2007) Want ~  C -precision (~12 o ) for  CP ? Want ~  C -precision (~12 o ) for  CP ? (Winter, in preparation) PRELIMINARY (U l ≠ 1)

13. August 8, 2007NuFact 07 - Walter Winter13 Distributions in the  13 -  CP -plane delta ~ theta_C necessary! delta ~ theta_C necessary! PRELIMINARY (Winter, in preparation) Clusters contain 50% of all realizations of one texture

14. August 8, 2007NuFact 07 - Walter Winter14 The seesaw in extended QLC (Plentinger, Seidl, Winter, arXiv:0707.2379) Generate all mixing angles and hierarchies by Only real cases!

15. August 8, 2007NuFact 07 - Walter Winter15 See-saw statistics (NH) … based on realizations Often: Mild hierarchies in M R found Resonant leptogenesis? Flavor effects? Often: Mild hierarchies in M R found Resonant leptogenesis? Flavor effects? Charged lepton mixing is, in general, not small! Charged lepton mixing is, in general, not small! Special cases rare, except from M R ~ diagonal! Special cases rare, except from M R ~ diagonal! (Plentinger, Seidl, Winter, arXiv:0707.2379)

16. August 8, 2007NuFact 07 - Walter Winter16 Seesaw-Textures (NH,  13 small) Obtain 1981 texture sets {M l, M D, M R } Obtain 1981 texture sets {M l, M D, M R } (Plentinger, Seidl, Winter, arXiv:0707.2379; http://theorie.physik.uni-wuerzburg.de/~winter/Resources/SeeSawTex/ )  = 0,  2

17. August 8, 2007NuFact 07 - Walter Winter17 Outlook: Towards model building Example: Froggatt-Nielsen mechanism (  =v/M F v: universal VEVs breaking the flavor symmetry, M F : super-heavy fermion masses) Use M-fold Z N product flavor symmetry Example: Froggatt-Nielsen mechanism (  =v/M F v: universal VEVs breaking the flavor symmetry, M F : super-heavy fermion masses) Use M-fold Z N product flavor symmetry   -powers are determined by flavor symmetry quantum numbers of left- and right- handed fermions! How much complexity is actually needed to reproduce our textures?  Depends on structure in textures! How much complexity is actually needed to reproduce our textures?  Depends on structure in textures! (Plentinger, Seidl, Winter, in preparation) PRELIMINARY Our 1981 textures PRELIMINARY Systematic test of all possible charge assignments!

18. August 8, 2007NuFact 07 - Walter Winter18 One example Z 5 x Z 4 x Z 3 Z 5 x Z 4 x Z 3 Case 205, Texture 1679 Case 205, Texture 1679 (http://theorie.physik.uni-wuerzburg.de/~winter/Resources/SeeSawTex/) Quantum numbers (example): 1 c, 2 c, 3 c :(1,0,1), (0,3,2), (3,3,0) l 1, l 2, l 3 : (4,3,2), (0,1,0), (0,2,2) e 1 c, e 2 c, e 3 c : (3,0,2), (2,0,2), (1,2,0) Quantum numbers (example): 1 c, 2 c, 3 c :(1,0,1), (0,3,2), (3,3,0) l 1, l 2, l 3 : (4,3,2), (0,1,0), (0,2,2) e 1 c, e 2 c, e 3 c : (3,0,2), (2,0,2), (1,2,0) Realization: can e.g. be realized with (  12,  13,  23 ) ~ (33 o,0.2 o,52 o ) Realization: can e.g. be realized with (  12,  13,  23 ) ~ (33 o,0.2 o,52 o ) (Plentinger, Seidl, Winter, in preparation)

19. August 8, 2007NuFact 07 - Walter Winter19 Summary Experimental constraints on  13,  12 useful; precision of  CP ~ 12 o motivated? Experimental constraints on  13,  12 useful; precision of  CP ~ 12 o motivated? Outlook: Systematic model building, implications for leptogenesis (introduce phases!), LFV, etc. Outlook: Systematic model building, implications for leptogenesis (introduce phases!), LFV, etc. Theory (e.g. flavor symmetry) Yukawa coupling structure Yukawa couplings with order one coeff. ModelTextureRealization Generic assumptions (e.g. QLC) m : 11 : n Connection to observables Distribution of observables: Study parameter space Intermediate result: Know that order one coefficients OK Find matching classes of models; study the theory space Applications Bottom-up generation Top-down interpretation!

20. Backup

21. August 8, 2007NuFact 07 - Walter Winter21 Low-energy Lagrangian for lepton masses Charged lepton mass terms Effective neutrino mass terms cf., CC interaction Rotates left-handed fields Block-diag.

22. August 8, 2007NuFact 07 - Walter Winter22