SUSY models of neutrino masses and mixings: the left-right connection

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1 SUSY models of neutrino masses and mixings: the left-right connection GK Workshop Bad Liebenzell Wolfgang Gregor Hollik October 10, 2012 INSTITUT FÜR THEORETISCHE TEILCHENPHYSIK KIT CAMPUS SÜD KIT University of the State of Baden-Wuerttemberg and National Laboratory of the Helmholtz Association

2 outline 1 Motivation 2 Neutrino Masses: Seesaw Mechanisms 3 Left-Right Symmetry & SUSYLR 4 Radiative Lepton Flavour Violation 5 Conclusion Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

3 Motivation Neutrinos seem to have mass Oscillations: m 21 2 = ev 2 m 2 31 = ev 2 large mixing angles Unknown: Absolute neutrino mass scale Katrin possible upper limit: 0.2 ev, discovery: 0.35 ev Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

4 Motivation Neutrinos seem to have mass Oscillations: m 21 2 = ev 2 m 2 31 = ev 2 large mixing angles Unknown: Absolute neutrino mass scale Katrin possible upper limit: 0.2 ev, discovery: 0.35 ev Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

5 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 neutrino & SUSYLR October 10, /15

6 CKM vs. PMNS matrix CKM matrix close to unity V CKM = small off-diagonal: generate mixings radiatively? different pattern for the leptonic mixing matrix: U PMNS = large mixings non-vanishing θ 13 : possible CP violation in ν oscillations [Weinberg 1972] [T2K, DoubleChooz, Reno, DayaBay] try to model quark and lepton mixing using the same mechanism? Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

7 Models of neutrino mass generation Seesaw mechanisms [Minkowski; Mohapatra, Senjanovic; Magg, Wetterich;... ] Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

8 The one and only Extend Standard Model Lagrangian by one single nonrenormalizable operator: [Weinberg 1979] O W = λ ij M ( ) ) L T i φ C (φ T L j C = iγ 2 γ 0 : charge conjugation matrix φ: standard Higgs doublet λ: dimensionless parameter M: some high scale rough estimate: m ν λ ij M v 2, v = φ 174 GeV if λ O(1) and O(0.1eV): M = GeV Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

9 The one and only Extend Standard Model Lagrangian by one single nonrenormalizable operator: [Weinberg 1979] O W = λ ij M ( ) ) L T i φ C (φ T L j φ φ ν L ν L Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

10 The one and only Extend Standard Model Lagrangian by one single nonrenormalizable operator: [Weinberg 1979] O W = λ ij M ( ) ) L T i φ C (φ T L j φ φ φ φ N, Σ ν L ν L ν L ν L Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

11 The one and only Extend Standard Model Lagrangian by one single nonrenormalizable operator: [Weinberg 1979] O W = λ ( ) ) ij L T i φ C (φ T L j M φ φ φ φ ν L ν L ν L ν L Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

12 Type I + II see-saw Type I: righthanded singlet L ν m = ν L m D ν R νc L m Rν R + h.c. v v ν R m R ν L ( 0 md M = m T D m R ) ν L m νl = m D m 1 R mt D Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

13 Type I + II see-saw Type I: righthanded singlet L ν m = ν L m D ν R νc L m Rν R + h.c. Type II: scalar triplet L ν m = h L ν c R L ν L + h R ν c L R ν R v v v v ν R m R L ν L ( ) 0 md M = m T D m R m νl = m D m 1 R mt D ν L ν L ν L L v L RΦ 2 M 2 v 2 M vev see-saw Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

14 Left-Right Symmetry Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

15 Left-Right Symmetry Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

16 Left-Right Symmetry Extend the Standard Model Gauge Group SU(3) c SU(2) L U(1) Y SU(3) c SU(2) L SU(2) R U(1) B L [Pati, Salam; Mohapatra, Pati; Mohapatra, Senjanovic; 1975] Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

17 Left-Right Symmetry Extend the Standard Model Gauge Group SU(3) c SU(2) L U(1) Y SU(3) c SU(2) L SU(2) R U(1) B L [Pati, Salam; Mohapatra, Pati; Mohapatra, Senjanovic; 1975] SU(2) L SU(2) R U(1) B L SU(2) L U(1) Y via triplet under SU(2) R with B L charge: ( δ + L,R L,R = / ) 2 δ ++ L,R δl,r 0 δ + L,R /, L = (1, 3, 1, 2), 2 R = (1, 1, 3, 2) Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

18 Left-Right Symmetry Extend the Standard Model Gauge Group SU(3) c SU(2) L U(1) Y SU(3) c SU(2) L SU(2) R U(1) B L [Pati, Salam; Mohapatra, Pati; Mohapatra, Senjanovic; 1975] SU(2) L SU(2) R U(1) B L SU(2) L U(1) Y via triplet under SU(2) R with B L charge: ( δ + L,R L,R = / ) 2 δ ++ L,R δl,r 0 δ + L,R /, L = (1, 3, 1, 2), 2 R = (1, 1, 3, 2) electric charge: Q = T 3L + T 3R + B L 2 Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

19 Left-Right Symmetry Extend the Standard Model Gauge Group SU(3) c SU(2) L U(1) Y SU(3) c SU(2) L SU(2) R U(1) B L [Pati, Salam; Mohapatra, Pati; Mohapatra, Senjanovic; 1975] SU(2) L SU(2) R U(1) B L SU(2) L U(1) Y via triplet under SU(2) R with B L charge: ( δ + L,R L,R = / ) 2 δ ++ L,R δl,r 0 δ + L,R /, L = (1, 3, 1, 2), 2 R = (1, 1, 3, 2) electric charge: Q = T 3L + T 3R + B L 2 scalar bidoublet (EWSB): Φ = (2, 2, 0) ( φ 0 Φ = 1 φ + ) ( 2 v1 0 φ 1 φ 0, Φ = 2 0 v 2 ), tan β = v 2 v 1 Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

20 left-right symmetric neutrino masses Leptonic Yukawa Lagrangian L Yuk l = y ij L i ΦR j + ỹ ij L i ΦR j + h ij ( L T i C L L j + R T i C R R j ) + h. c., where L = (ν L, e R ) SU(2) L and R = (ν R, e R ) SU(2) R. Charged lepton mass: m e = v 1 y + v 2 ỹ, Dirac neutrino mass: m D = v 1 ỹ + v 2 y, Majorana neutrino masses: m L = v L h, m R = v R h. 1 combined see-saw type I + II: ( ) ml m M = D m T D m R m νl = m L m D (m R ) 1 m T D 1 If parity symmetry is assumed, i.e. L inv. under L R Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

21 SUSY s tale Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

22 SUSY s tale Extending Poincaré symmetry: SM particles become part of larger multiplets (chiral and vector supermultiplets) holomorphy of the superpotential: no ỹ because of no Φ left-right symmetric SUSY: automatic R-parity conservation Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

23 SUSY s tale Extending Poincaré symmetry: SM particles become part of larger multiplets (chiral and vector supermultiplets) holomorphy of the superpotential: no ỹ because of no Φ left-right symmetric SUSY: automatic R-parity conservation Superpotential of the minimal SUSYLR model W l =y ij L i ΦR j + h ij (L i L L j + R i R R j ), [Cvetic, Pati 1984] where the chiral superfields are L L = (l L, l L ) (lefthanded) and L R = (l c R (l R) c, l R ) (righthanded). Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

24 SUSY s tail Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

25 SUSY s tail SUSY has to be broken Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

26 SUSY s tail SUSY has to be broken Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

27 SUSY s tail SUSY has to be broken Soft-breaking terms of MSSM w/o squarks V soft = l il ( ) M 2 l l jl + ẽ ( ir M 2ẽ) ij ij ẽjr + A e ijh 1 l il ẽjr + h. c. + m1 h m2 h (m12h 2 1 h 2 + h. c.) + 1 ( ) M 1 λ 0 P L λ 0 + h. c. + 1 ( ) M 2 λp L λ + h. c 2 2 Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

28 SUSY s tail SUSY has to be broken Soft-breaking terms of SUSYLR V soft = L i (M 2 L ) ij L j + R i (M 2 R ) ij R j [ + A l L ] ij i Φ R j + h. c. + [B ij ( L i L L j + R i R R j ) + h. c. ], SUSYLR constrains the soft breaking parameter space relations between up and down sector (A u = A d, A ν = A e and M 2 Q = M2 ũ = M2 d, M2 l = M2 ẽ = M2 ν LR scale RGE connection between SUSY and LR scale Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

29 super-seesaw mechanism Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

30 super-seesaw mechanism effective sneutrino mass matrix ) ( M M 2 ν 2 = LL M ( ) 2 LR M 2 LR M 2 RR ( O(M 2 SUSY ) O(M SUSY m R ) O(M SUSY m R ) O(mR 2 ) ) Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

31 super-seesaw mechanism effective sneutrino mass matrix ) ( M M 2 ν 2 = LL M ( ) 2 LR M 2 LR M 2 RR ( O(M 2 SUSY ) O(M SUSY m R ) O(M SUSY m R ) O(mR 2 ) ) matrix see-saw-like structure perturbative diagonalization: [Dedes, Haber, Rosiek 2007] ( U M 2 ν M ν U = l O(MSUSY 3 m 1 R ) ) O(MSUSY 3 m 1 R ) M2 RR + O(M2 SUSY ), Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

32 super-seesaw mechanism effective sneutrino mass matrix ) ( M M 2 ν 2 = LL M ( ) 2 LR M 2 LR M 2 RR ( O(M 2 SUSY ) O(M SUSY m R ) O(M SUSY m R ) O(mR 2 ) ) matrix see-saw-like structure perturbative diagonalization: [Dedes, Haber, Rosiek 2007] ( U M 2 ν M ν U = l O(MSUSY 3 m 1 R ) ) O(MSUSY 3 m 1 R ) M2 RR + O(M2 SUSY ), where M 2 ν l = M 2 LL ( ) M2 LR M 2 1 ( ) RR M 2 LR + O(M 4 SUSY m 2 R ). Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

33 super-seesaw mechanism effective sneutrino mass matrix ) ( M M 2 ν 2 = LL M ( ) 2 LR M 2 LR M 2 RR ( O(M 2 SUSY ) O(M SUSY m R ) O(M SUSY m R ) O(mR 2 ) ) matrix see-saw-like structure perturbative diagonalization: [Dedes, Haber, Rosiek 2007] ( U M 2 ν M ν U = l O(MSUSY 3 m 1 R ) ) O(MSUSY 3 m 1 R ) M2 RR + O(M2 SUSY ), where M 2 ν l = M 2 LL ( ) M2 LR M 2 1 ( ) RR M 2 LR + O(M 4 SUSY m 2 R ). ( M 2 ν m 2 l = L=0 (m 2 ) L=2 ) m 2 L=2 (m 2 + O ( M 2 ) L=0 ) SUSY m 2 R Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

34 super-seesaw mechanism effective sneutrino mass matrix ) ( M M 2 ν 2 = LL M ( ) 2 LR M 2 LR M 2 RR ( O(M 2 SUSY ) O(M SUSY m R ) O(M SUSY m R ) O(mR 2 ) ) matrix see-saw-like structure perturbative diagonalization: [Dedes, Haber, Rosiek 2007] ( U M 2 ν M ν U = l O(MSUSY 3 m 1 R ) ) O(MSUSY 3 m 1 R ) M2 RR + O(M2 SUSY ), where M 2 ν l = M 2 LL ( ) M2 LR M 2 1 ( ) RR M 2 LR + O(M 4 SUSY m 2 R ). m 2 L=2 = X νm D ν ( m 2 R + M 2 ν) 1 mr m DT ν +... X ν m D ν = µ cot βm D ν v u A ν Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

35 radiative lepton flavour violation Σ (e) ji e i ν f Σ (ν) fj e i ν f e i U (0) fi = δ fi ν f e j j i U (0) fj Uji e + + ν j j f U ν fj 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 (1 + U e + U ν ), flavour changing self energies and sensitivity to neutrino mass U ν fi m ν f Σ fi m 2 ν Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

36 enhanced corrections to PMNS mixing flavour changing self energies and sensitivity to neutrino mass U ν fi m ν f Σ fi m 2 ν m ν f m νi m 2 fi for m 0 ν 0.35 ev and f, i = 1, (1,2) (1,3)*10 (2,3) e-10 4e-10 6e-10 8e-10 1e e e e e-09 2e-09 Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

37 Results: m (0) ν = 0.3 ev Choice of parameters: M 2 l = M 2 ẽ = M2 ν m2 l start v R = GeV, tan β = 20, µ H = 500 GeV, M 1 = 1 2 M 2 = m l A 12 A 13 A A ij [GeV] m soft [GeV] Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

38 Results: m (0) ν = 0.3 ev Choice of parameters: M 2 l = M 2 ẽ = M2 ν m2 l start v R = GeV, tan β = 20, µ H = 500 GeV, M 1 = 1 2 M 2 = m l m 0 = 0.01 ev m 0 = 0.1 ev m 0 = 0.2 ev m 0 = 0.35 ev m 0 = 0.5 ev m 0 = 1 ev A 13 nu [GeV] m soft [GeV] Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

39 Conclusion radiative flavour violation (RFV) due to SUSY corrections flavour mixings in trilinear couplings A ν as remnant of heavy singlet neutrino superfields smoking gun of high scale physics in effective sneutrino mass matrix entanglement of heavy neutrino mass scale (= LR scale) and SUSY breaking terms ensure left-right symmetric boundary conditions at the high scale ( GeV) leptonic RFV prefers quasi-degenerate neutrino mass spectrum Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

40 Conclusion radiative flavour violation (RFV) due to SUSY corrections flavour mixings in trilinear couplings A ν as remnant of heavy singlet neutrino superfields smoking gun of high scale physics in effective sneutrino mass matrix entanglement of heavy neutrino mass scale (= LR scale) and SUSY breaking terms ensure left-right symmetric boundary conditions at the high scale ( GeV) leptonic RFV prefers quasi-degenerate neutrino mass spectrum BUT: LR symmetry in connection with RFV induces dangerously large LFV processes (l j l i γ) χ k γ χ 0 k l j l i l j l i ν s ẽ s Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15 γ

41 Backup Slides

42 See-saw and neutrino masses Puzzle of neutrino masses m ν 1 ev m τ 1 GeV. 1 heavy singlet neutrino ( righthanded ) 2 triplet scalar ( vev see-saw ) 3 left-right symmetry combines both features of left-right symmetry SU(2) L SU(2) R U(1) B L ESWB: Higgs Bidoublet (2, 2, 0) couples l L and l R via y l breaking SU(2) R U(1) B L : Higgs triplet R = (1, 3, 2) gives masses to ν R m R R v R GeV LR symmetric form: (3, 1, 2) giving rise to see-saw type II Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

43 How the mixing comes into the game SM: Lefthanded fields doublets, righthanded singlets under SU(2): Q L,i, u R,i, d R,i, L L,i, e R,i. i = 1,..., N generation index. Charged electroweak current: L cc = i g 2 2 W + µ (ū L,i γ µ d L,i + ē L,i γ µ ν L,i + h.c.), flavour blind, only lefthanded. Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

44 How the mixing comes into the game SM: Lefthanded fields doublets, righthanded singlets under SU(2): Q L,i, u R,i, d R,i, L L,i, e R,i. i = 1,..., N generation index. Charged electroweak current: L cc = i g 2 2 W + µ (ū L,i γ µ d L,i + ē L,i γ µ ν L,i + h.c.), flavour blind, only lefthanded. Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

45 How the mixing comes into the game SM: Lefthanded fields doublets, righthanded singlets under SU(2): Q L,i, u R,i, d R,i, L L,i, e R,i. i = 1,..., N generation index. Charged electroweak current: L cc = i g 2 2 W + µ (ū L,i γ µ d L,i + ē L,i γ µ ν L,i + h.c.), flavour blind, only lefthanded. Yukawa Lagrangian and fermion masses: L Yuk = y d ij Q L,i φd R,j + y u ij Q L,i φu R,j + y e ij L L,i φe R,j + h.c. Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

46 How the mixing comes into the game SM: Lefthanded fields doublets, righthanded singlets under SU(2): Q L,i, u R,i, d R,i, L L,i, e R,i. i = 1,..., N generation index. Charged electroweak current: L cc = i g 2 2 W + µ (ū L,i γ µ d L,i + ē L,i γ µ ν L,i + h.c.), flavour blind, only lefthanded. Yukawa Lagrangian and fermion masses: L Yuk = y d ij Q L,i φd R,j + y u ij Q L,i φu R,j + y e ij L L,i φe R,j + h.c. Masses: m f = v y f m f diag = V f L mf V R, V L,R V L,R = 1, such that f X,i f X,i = (V X ) ia f X,a, X = L, R. Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

47 How the mixing comes into the game SM: Lefthanded fields doublets, righthanded singlets under SU(2): Q L,i, u R,i, d R,i, L L,i, e R,i. i = 1,..., N generation index. Charged electroweak current: L cc = i g 2 2 W + µ only lefthanded. ( ) ū L,a VL,ai u V L,ia d γµ d L,a + ē L,a VL,ai e V L,ia ν γµ ν L,a + h.c., Yukawa Lagrangian and fermion masses: L Yuk = y d ij Q L,i φd R,j + y u ij Q L,i φu R,j + y e ij L L,i φe R,j + h.c. Masses: m f = v y f m f diag = V f L mf V R, V L,R V L,R = 1, such that f X,i f X,i = (V X ) ia f X,a, X = L, R. Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

48 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 neutrino & SUSYLR October 10, /15

49 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 neutrino & SUSYLR October 10, /15

50 Particle content of the minimal SUSYLR model Higgses and Leptons SU(2) L SU(2) R U(1) B L scalar bidoublet (EWSB): Φ = (2, 2, 0) Φ = ( φ 0 1 φ + 2 φ 1 φ 0 2 ) [Cvetic, Pati 1984] scalar triplets: L = (3, 1, +2), R = (1, 3, 2) L = ( δ 0 L / 2 δ + L δ ++ L δ 0 L / 2 ) ( δ 0, R = R / 2 δ R δ R δr 0 / 2 ) additional triplet fields: L = (3, 1, 2), R = (1, 3, +2) Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

51 Particle content of the minimal SUSYLR model Higgses and Leptons SU(2) L SU(2) R U(1) B L lepton doublets: L L = (2, 1, 1), L R = (1, 2, +1) both L L and L R left-chiral Superfields ( ) ( ) νl ν c L L, L e R ɛ R L er c [Cvetic, Pati 1984] = ( e c R ν c R Majorana mass terms out of triplet vev: ( ) 0 vr R = h 0 0 R L T R ɛ R L R = νr c m RνR c ) Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

52 Particle content of the minimal SUSYLR model leptonic and gauge sector multiplet of el. charge fields # SU(2) L SU(2) R U(1) B L Q el L L = (l L, l L ) 3 (2, 1, 1) (0, 1) L R = (l c R, l R ) 3 (1, 2, +1) (0, +1) Φ 1 (2, 2, 0) 1, 0, +1 1L 1 (3, 1, +2) 0, +1, +2 2L 1 (3, 1, 2) 0, 1, 2 1R 1 (1, 3, 2) 0, 1, 2 2R 1 (1, 3, +2) 0, +1, +2 G µ,a 1 (8, 1, 1, 0) 0 W µ,i L 1 (1, 3, 1, 0) ±1, 0 W µ,i R 1 (1, 1, 3, 0) ±1, 0 B µ 1 (1, 1, 1, 0) 0 Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

53 Majorana mass renormalization 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 v 2 R ( m 2 R + M 2 ν) 1 mr m DT ν with m R = v R h R Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15

54 LR symmetry at high scale v R GeV out of neutrino data: seesaw scale m R v R relating SUSY and LR scale: RGE running [Martin, Vaughn 1994] above the LR scale: using LR symmetric RGEs A[GeV] A u A d µ = M SUSY µ = v R t = log(µ/m SUSY ) Wolfgang Gregor Hollik neutrino & SUSYLR October 10, /15