Inverse See-saw in Supersymmetry

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1 Inverse See-saw in Supersymmetry Kai Wang IPMU, the University of Tokyo Cornell Particle Theory Seminar September 15, 2010 hep-ph/10xx.xxxx with Seong-Chan Park

2 See-saw is perhaps the most elegant mechanism for neutrino mass generation, n R is well motivated from SO(10) and SU(3) H. but.. y ν l L n R H u + M R n c R n R+M S s L n R Then, in the basis of (ν L, s L, n c R ) M = 0 0 M D 0 0 M S M D M S M R Lightest mass eigenstate remain massless... Is there any exact chiral symmetry to protect m ν? Why is there an additional singlet? E 6? What is the Lepton number violation scale ΛL? Can it be within weak scale?

3 In this talk... Two examples that tree-level masses are suppressed but only arise radiatively. generate neutrino mass in a modified Wyler-Wolfenstein model from radiative corrections. (with Seong-chan Park, hep-ph/1010.xxxx) generate charged lepton masses m e and down-type quark masses m d radiatively from H u in MSSM (large tan β limit, see for example, Dobrescu-Fox, upper-lifted MSSM, hep-ph/ ) So no unbroken chiral symmetry...

4 Lessons from Upper-lifted MSSM Dobrescu-Fox, H u H d, m e, m d from H u Accidental symmetries in SM lagrangian i Q i L DQi L + iū i R Dui R + i d i R Ddi R +... Q i L U ij Q Qj L, ui R U ij u u j R, di R U ij d dj R With three generations, U(3) Q U(3) u U(3) d U(3) l U(3) e y ij u Q i LɛH u j R yij d Q i LHd j R +... break the above [U(3)] 5 into U(1) B U(1) Lep Q i L e iθ/3 Q i L, u i R e iθ/3 u i R, d i R e iθ/3 d i R l i L e iφ l i L, e i R e iφ e i R

5 Fermion mass is not only a electroweak symmetry breaking (EWSB) effect. If y 0, U(3) symmetry will be restored and the corresponding fermion will be massless up to all loops. m t ( or m u ) 0 m d, m e must break the U(3)s. (for instance, topcolor model) To eliminate the tree-level contribution, tune the vev...possible in 2HDM (large tan β) H u H d Non-zero Yukawa couplings ensure that the chiral symmetries have been broken. The masses can be generated radiatively.

6 MSSM is a natural 2HDM Superpotential is holomorphic and ɛh is forbidden in superpotential. H u, H d contributes to anomaly [SU(2) L ] 2 U(1) Y,... and Witten Anomaly W = y u Qu c H u + y d Qd c H d + y e le c H d + µh u H d

7 2HDM has Peccei-Quinn symmetry (DFSZ axion, 1981). A [SU(3)C ] 2 U(1) = 3α + 3 (2(q α) + (u α) + (d α)) 2 = 3α 3 2 (h u + h d ) q + u + h u = 2α, q + d + h d = 2α h u + h d 2α A 3 0 M PQ M Intermediate, Kim-Nilles

8 10 10H u H d Field 10 5 H u H d θ R-charge PQ H u : R : = 0 2, PQ

9 W = µh u H d PQ L soft m 2 f f 2 R invariant If PQ, R and [U3] 5, + M 1 λλ + A u QũHu BµH u H d R, PQ R 10 5H u m e, m d 0 Another PQ source, (proportional to µ) F Hd = W H d = y d Qd c + y e le c + µh u V F Hd 2 = y d µ H u Q d + y e µ H u lẽ

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12 Physics Implications If all Yukawa couplings in MSSM are perturbative at M GUT, 2 tan β 50. But what if m b arise from H u radiatively...

13 ν L does not carry any unbroken gauge symmetry (SU(3) C U(1) EM )... Type-I see-saw 1 2 M ij ν ν it L Cv j L y ν l L n R H u + M R n c R n R + h.c., For one generation y ν break U(1) l U(1) n U(1) Lep M R U(1) Lep m ν = M T DM 1 R M D Without tuning dimensionless y ν, tiny m ν from M GUT U(1) B L becomes anomaly free, easily embedded into SO(10)

14 Pati-Salam(Wyler-Wolfenstein) y ν l L n R H u + M S s L n R + h.c. In basis (ν L, s L, n c R ) M = 0 0 M D 0 0 M S M D M S 0 m ν = 0

15 Inverse see-saw (Mohapatra, Valle) y ν l L n R H u + M S s L n R + ɛs c L s L In basis (ν L, s L, n c R ) M = 0 0 M D 0 ɛ M S M D M S 0 M 2 D m ν ɛ MD 2 + M S 2

16 Tuning: Dimensionless y ν or dimension-one M y e 10 6, y ν 10 12? Dimension One: see-saw vs inverse In see-saw, M R breaks U(1) B L gauge symmetry at ultra-high scale, for instance, M GUT. Now n, s are both SM gauge singlet..., the scale vanishes to restore the U(1) Lep, can be identified as soft breaking of U(1) Lep.

17 In basis (ν L, s L, n c R ) y ν l L n R H u + M S s L n R + M R n c R n R M = 0 0 M D 0 0 M S M D M S M R M S ν = ν L + MD 2 + M S 2 N ± = 1 M± 2 + M D 2 + M S 2 M D M 2 D + M 2 S s L (M D ν L + M S s L M ± n c R) with mass eigenvalues as m ν = 0, M ± = 1 ( ) M R ± 4MD M R 2 + 4M S 2

18 U(1) ν U(1) n U(1) s In basis (ν L, s L, n c R ) 0 0 M D M = 0 0 M S M D M S M R With M D, M S Under U(1) Lep U(1) ν U(1) n U(1) s U(1) ν s U(1) Lep ν L e iα ν L s L e iα s L n c R e iα n c R With M R unbroken U(1) Lep U(1) ν s

19 Why no M R sc L s L? SUSY Supersymmetry does not forbid lepton number violation but only stabilize the model. So it is just Technically Natural. W = y ν ln c H u + M S sn c + M R n c n c Field l e c n c s H u H d θ R-charge U(1) L W eff m R-charge of m U(1) L charge n c n c n c R n R θ = 0-2 lsh u νl c s 1 L θ = 0 2 llh u H u νl c ν 1 L θ = 0 2 ss s c L s L θ = 0 2

20 New gauge interaction? Under E 6 27 = s L is completely gauge singlet and any term involving s L will be only gravitationally induced in Kähler potential Lepton number violation B-terms in soft-breaking lagrangian

21 R-invariant piece U(1) B L becomes anomalous so the leading is Yukawa interaction induced llh u H u Non-SUSY contribution H u H u ν L ν c L n R n c R (M 1 loop ν ) ij = π 2 M R k k=1 Y ik Y jk M ( A 2 MA 2 M R k 2 ln φ=h,h Yik Y jk M ( ) φ 2 M 2 Mφ 2 M R k 2 ln φ MR k 2 ) MA 2 MR k 2

22 M R M 2 φ M 2 φ M R 2 ln ( ) M 2 φ M 2 R M R M h,h restore the see-saw, M R < GeV M R M h,h, inverse see-saw limit, M R KeV We take the inverse see-saw limit (non-canonical Kälher potential) to ensure light neutrino mass.

23 After M susy, V = W n R 2 = (lh u + M s s L + M R n R ) 2 = M Rñ R lh u + M RM s ñ R s L H u ñ ν ν L ν c L χ 0 j χ 0 i H u m 2 ñ M 2 susy + M 2 R M R M susy M R M susy

24 R Contribution The effective operators do not break R-symmetry L soft B R M R ñ R ñ R + B S ɛ s s L s L + A s M R ll s L H u + B ν M ν ν L ν L m ν only arise with gaugino mass insertion. Soft SUSY breaking terms that also violate U(1) Lep but 1/M Pl suppression.

25 Conclusions I present two examples that the fermion masses arise from radiative correction where the tree level masses are suppressed but all the chiral symmetries are broken. Supersymmetry plays an important role in stabilizing the suppressed tree level masses.