Neutrino Mixing from SUSY breaking

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1 Summer School and Workshop on the Standard Model and Beyond Corfu, Greece 2013 Neutrino Mixing from SUSY breaking in collaboration with Ulrich Nierste Wolfgang Gregor Hollik September 5, 2013 INSTITUT FOR THEORETICAL PARTICLE PHYSICS KARLSRUHE INSTITUTE OF TECHNOLOGY (KIT) KIT University of the State of Baden-Wuerttemberg and National Laboratory of the Helmholtz Association

2 CKM vs. PMNS matrix CKM matrix close to unity V CKM = small off-diagonal: get them from loops? different pattern for the leptonic mixing matrix: U PMNS = large mixings non-vanishing θ 13 : possible CP violation in ν oscillations [T2K, DoubleChooz, Reno, DayaBay] try to model quark and lepton mixing using the same mechanism? Wolfgang Gregor Hollik Corfu 2013 September 5, /10

3 Radiative Flavour Violation in the MSSM Theories with Additional Sources of Flavour Violation non-minimal flavour violating MSSM arbitrary flavour structurn the soft breaking terms? M 2 Q, M2 ũ, M 2 d, M2 l, M2 ẽ, A u, A d, A e additional flavour mixing in fermion sfermion gaugino interaction especially non-ckm-like: e.g. quark squark gluino and lepton slepton neutralino g f i f f [Crivellin, Nierste 2009] f if i ff Wolfgang Gregor Hollik Corfu 2013 September 5, /10

4 Radiative Flavour Violation in the MSSM Theories with Additional Sources of Flavour Violation non-minimal flavour violating MSSM arbitrary flavour structurn the soft breaking terms? M 2 Q, M2 ũ, M 2 d, M2 l, M2 ẽ, A u, A d, A e additional flavour mixing in fermion sfermion gaugino interaction especially non-ckm-like: e.g. quark squark gluino and lepton slepton neutralino χ 0 k ν i Do the same for sleptons and sneutrinos! ν i if Wolfgang Gregor Hollik Corfu 2013 September 5, /10

5 The MSSM with righthanded neutrinos Superpotential of the νmssm W l = µh d H u Y IJ l H d L I L E J R + Y IJ ν H u L I L NJ R mij R NI R NJ R, with L L = (l L, l L ) SU(2) L and E R = (e c L, ẽ R ), N R = (ν c L, ν R ). Soft-breaking terms V soft =(M 2 l) IJ LI L LJ L + (M 2 ẽ) IJ ẽ RẽJ I R + (M2 ν) IJ ν I R νj R [ ] (B ν ) IJ ν R I νj R + AIJ e H 1 L I LẽJ R AIJ ν H 2 L I L νj R + h.c.. Wolfgang Gregor Hollik Corfu 2013 September 5, /10

6 Neutrino masses and seesaw Standard Model + righthanded Neutrinos = Seesaw Type I L ν,mass = ν L m D ν }{{ R + 1 } 2 νc L m Rν R + h. c. }{{} Dirac mass Majorana mass Wolfgang Gregor Hollik Corfu 2013 September 5, /10

7 SUSY seesaw loops v u v u v u ν H v u ν H ν R ν l,i Y ν ij v u M jk M jk Ykl ν ν l,l ν l,i A ν ij Ykl ν ν l,l v u ν L,i Y ν ij M jk Y ν kl ν L,l ν L,i ν L,l ν i ν L,l χ 0 χ 0 effects of righthanded Neutrinos ν L,k trilinear couplings A ν see-saw-like terms in sneutrino mass matrix ( δ ν LL ) χ 0 kl ν l ν l δ ν LL X νm D ν ν L,l v ua ν m R ( m 2 R + M 2 ν) 1 mr m DT ν Wolfgang Gregor Hollik Corfu 2013 September 5, /10

8 radiative lepton flavour violation Σ (e) ji Σ (ν) fj U (0) fi e j j i U (0) fj Uji e + + ν j j f U j U (0) ji W µ W µ W µ PMNS matrix renormalization g i γ µ P L U 2 PMNS i g 2 γ µ P L (U (0) + U e U (0 ) + U ν U (0 ) ), flavour changing self energies and sensitivity to neutrino mass U i m Σ fi m 2 fi Wolfgang Gregor Hollik Corfu 2013 September 5, /10

9 enhanced corrections to PMNS mixing enhancement by degeneracy of neutrino mass spectrum U i m Σ fi m 2 ν neutrinomass m ν i [ev] m m νi m 2 fi 0.1 m ν 0 [ev ] m ν 1 m ν 1 m ν for m (0) ν 0.35 ev and f, i = 1, 2 1 m ν i mν j / m2 ij m ν 0 [ev ] f 12 f 13 f f ij = m νi m νj / m 2 ij Wolfgang Gregor Hollik Corfu 2013 September 5, /10

10 Some results non-decoupling effect if all SUSY parameters scaled the same way e.g. tan β = 24, m (0) ν = 0.3eV, M 2 l,ẽ, ν = m2 soft 1, M 1,2 = m soft : A ν if [GeV] A ν 12 A ν 13 A ν 23 A ν if /m soft a 12 a 13 a m soft [GeV] m soft [GeV] Wolfgang Gregor Hollik Corfu 2013 September 5, /10

11 Some results correlation: light neutrino mass scale flavour changing SUSY breaking parameters left: basically no influence from gaugino masses (m soft = 2000GeV) A ν if /m soft A ν 12 A ν 13 A ν m (0) ν [0.01eV] 150 A ν if /m soft a 12 a 13 a M 1 = ηm 2 [GeV] Wolfgang Gregor Hollik Corfu 2013 September 5, /10

12 Some results safe: contributions to radiative lepton flavour decays on top of others negligible charged lepton effects neglected so far BR(lj liγ) BR(τ µγ) BR(τ eγ) BR(µ eγ) m soft [GeV] BR(lj liγ) 500 BR(τ µγ) BR(τ eγ) BR(µ eγ) 1000 A ν ij [GeV] Wolfgang Gregor Hollik Corfu 2013 September 5, /10

13 Conclusion described corrections very general to theories with new flavour structures can completely spoil tree-level mixing patterns simple extension of MSSM to incorporate ν masses can lead to lepton mixing from SUSY breaking in sneutrino sector non-decoupling effect most likely for quasi-degenerate neutrino masses new flavour structurn sneutrino sector: no large BR(l j l i γ) Wolfgang Gregor Hollik Corfu 2013 September 5, /10

14 Backup Slides

15 Splitting of the neutrino mass spectrum 10 degeneracy of neutrino mass spectrum m 1 m 2 m 3 neutrino mass [ev] neutrino mass scale m 0 [ev] Wolfgang Gregor Hollik Corfu 2013 September 5, /10

16 see-saw extended MSSM Superpotential of the νmssm W l = µh d H u Y IJ l H d L I L E J R + Y IJ ν H u L I L NJ R mij R NI R NJ R, where the chiral superfields are L L = (l L, l L ) SU(2) L and E R = (e c R (e R) c, ẽ R ), N R = (ν c L, ν R ) SU(2) R, but leftchiral. Soft-breaking terms I V soft =(M 2 l) IJ L + (M2 ν) IJ ν I R νj R L L J L + (M2 ẽ) IJ ẽ RẽJ I R [ ] (B ν ) IJ ν R I νj R + AIJ e H 1 L I LẽJ R AIJ ν H 2 L I L νj R + h.c., Wolfgang Gregor Hollik Corfu 2013 September 5, /10

17 effects on sneutrino mass matrix charged slepton mass matrix as in the MSSM sneutrino mass matrix in the MSSM: simple ( M M 2 ν 2 l = + M2 Z T 3L ν cos 2β Majorana mass term νr T m Rν R inflates sneutrino mass matrix: additional terms ν R ν R, ν R ν R M 2 ν = ) M 2 L L M 2 L L M 2 L R M 2 L R M 2 LL M 2 LL M 2 LR M 2 LR M 2 RL M 2 RL M 2 RR M 2 RR M 2 R L M 2 R L M 2 R R M 2 R R Matrix Wolfgang Gregor Hollik Corfu 2013 September 5, /10

18 effects on sneutrino mass matrix charged slepton mass matrix as in the MSSM sneutrino mass matrix in the MSSM: simple ( M M 2 ν 2 l = + MZ 2 T 3L ν cos 2β Majorana mass term νr T m Rν R inflates sneutrino mass matrix: additional terms ν R ν R, ν R ν R ) ( M M 2 ν 2 = LL M ( ) 2 LR M 2 LR M 2 RR ) Matrix Wolfgang Gregor Hollik Corfu 2013 September 5, /10

19 full sneutrino squared mass matrix in the νmssm ( M 2 LL M 2 LR ) M 2 ν = 1 2 ( M 2 LR ) M 2 RR M 2 LL = ( M 2 l M2 Z cos 2β1 + m νm ν 0 0 ( ) M 2 RL = ( 1 2 m νm R µ cot βm ν v 2 A ν µ cot βm ν v 2 A ν 1 2 m νm R ( (M M 2 2 ν RR = ) T + m T ν m ν m R m R 2B ), ), 2B M 2 ν + m νm ν m Rm R ). Wolfgang Gregor Hollik Corfu 2013 September 5, /10

20 effective sneutrino mass matrix M 2 νl = ( m 2 L=0 (m 2 L=2 ) m 2 L=2 (m 2 L=0 ) ) + O ( MSUSY 2 ) m 2 R, m 2 L=0 = MSSM + md ν m D ν m 2 L=2 = X νm D ν ( m D ν m R m 2 R + M 2 ν ) 1 mr m D ν, ( m 2 R + M 2 ν) 1 mr m DT ν + ( ) T 2m D ν m R [m ] 2 R + (M2 ν) T 1 ( B m 2 R + M 2 ν) 1 mr m D ν. X ν m D ν = µ cot βm D ν v 2 A ν Wolfgang Gregor Hollik Corfu 2013 September 5, /10

21 radiative flavour violation in the lepton sector U (0) fi Σ (e) ji e j j i U (0) fj Uji e + + Σ (ν) fj ν j j f U j U (0) ji W µ W µ W µ Wolfgang Gregor Hollik Corfu 2013 September 5, /10

22 radiative flavour violation in the lepton sector U (0) fi Σ (e) ji e j j i U (0) fj Uji e + + Σ (ν) fj ν j j f U j U (0) ji W µ W µ W µ flavour changing self energies Σ l fi (p) = ΣlRL fi (p 2 )P L + Σ llr fi (p 2 )P R + /p [ Σ lll fi PMNS matrix renormalization g i γ µ P L U g i γ µ P L (1 + D L,fi + D R,fi ), 2 2 (p2 )P L + Σ lrr fi (p 2 )P R ] Wolfgang Gregor Hollik Corfu 2013 September 5, /10

23 radiative flavour violation in the lepton sector U (0) fi Σ (e) ji e j j i U (0) fj Uji e + + Σ (ν) fj ν j j f U j U (0) ji W µ W µ W µ PMNS matrix renormalization ( D L,fi = m νf Σ (ν)lr fj j f + m νf Σ (ν)rr fj )+ m νj ( Σ (ν)rl fj ) + m νf Σ (ν)ll fi mν 2 j mν 2 U (0) ji f 3 j=1 [ U ν L ] fj U(0) ji Wolfgang Gregor Hollik Corfu 2013 September 5, /10