Neutrino Mass and Its Implication in BSM Theories Kai Wang Zhejiang Institute of Modern Physics Zhejiang University 浙江大学浙江近代物理中心王凯 BCVSPIN 2013

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1 Neutrino Mass and Its Implication in BSM Theories Kai Wang Zhejiang Institute of Modern Physics Zhejiang University BCVSPIN 013

2 Origin of electron mass (QCD is account for over 99% of visible matter mass.) Bohr Radius a 0 = m e cα m e 0, a 0 No atom No valence Bonding No stable matter... We don t exist!

3 Origin of electron mass

4 Origin of electron mass Lorentz Group SO(3, 1) locally isomorphic to SU() SU() [J i, J j ] = iɛ ijk J k [K i, K j ] = iɛ ijk J k [J i, K j ] = iɛ ijk K k. Two independent algebra A i = 1 (J i + ik i ); B i = 1 (J i ik i ) [A i, A j ] = iɛ ijk A k [B i, B j ] = iɛ ijk B k [A i, B j ] = 0. Weyl Spinor: (1/, 0) (A i = 1 σ ib i = 0) χ e i σ θ χ χ e 1 σ η χ

5 Origin of electron mass ψ D = ( χ ɛξ ) ψ L = ( χ 0 ) ψ R = ( 0 ɛξ ) ψ D = 1 + γ 5 ψ + 1 γ 5 ψ = ψ R + ψ L ψ Dψ ψ L Dψ L + ψ R Dψ R ψψ ψ L ψ R

6 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

Gauge structure of SM PHYSICAL REVIEW D VOLUME 39, NUMBER 15 JANUARY 1989 Uniqueness of quark and lepton representations in the standard model from the anomalies viewpoint C. Q.

7 Gauge structure of SM PHYSICAL REVIEW D VOLUME 39, NUMBER 15 JANUARY 1989 Uniqueness of quark and lepton representations in the standard model from the anomalies viewpoint C. Q. Geng TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, Canada V6T3 R. E. Marshak. Physics Department, Virginia Polytechnic Institute and State Uniuersity, Blacksburg, Virginia 4061 (Received 7 July 1988) The uniqueness of the Weyl representations of the standard gauge group is reexamined. We find that, prior to spontaneous breaking of the electroweak subgroup, the minimal Weyl representations and their charges are uniquely determined by insisting on all three known chiral gauge anomaly-free conditions in four dimensions: (1) cancellation of triangular anomalies; () absence of the global SU() anomaly; and (3) cancellation of the mixed-gauge-gravitational anomaly. The uniqueness question for the left-right-symmetric group and the simple (grand-unified-theory) group are discussed from the anomalies viewpoint. The standard theory of strong and electroweak interactions has been remarkably successful experimentally' and mysteriously compliant with the anomaly-free conditions arising from the theoretical requirements of renormalizability and self-consistency. Three anomalies have terms can be constructed without breaking the SU(3)c X SU()L XU(1)z symmetries, would help pin down the representations. In fact, this is not the case since the minimal set of triangular anomaly-free Weyl representations would then be (3, 1,Q), (3, 1, Q),

8 Gauge structure of SM SU(3) C SU() L Q L (3, ) u c R ( 3, 1) d c R( 3, 1) l L (1, ) e c R (1, 1) SU(3) C SU(3) C U(1) : (q + u + d) = 0 SU() L SU() L U(1) : (3q + l) = 0 U(1)] 3 : 6q 3 + 3u 3 + 3d 3 + l 3 + e 3 = 0 T r[u(1)] : 6q + 3u + 3d + l + e = 0

9 U(1) Y Hypercharge is uniquely defined except its normalization. Field Q u c e c d c l H 1 U(1) Y The only anomaly free U(1) symmetry in SM with universality. L i L j is also free of anomaly (i j, i, j = e, µ, τ)

10 Gauge anomalies of U(1) B and U(1) Lep A [SU()L ] U(1) X N f (3q + l) B and L have gauge anomalies and will be broken by the quantum gravity effects. llhh M Pl + QQQl M Pl m ν 10 5 ev, τ p yr

11 NuFIT 1.0 (01) 3 [10-3 ev ] Dm H H Dm sin q 13 Dm 1 [10-5 ev ] sin q 3 H H d CP H H JHEP1(01) sin q sin q 13 Figure 1. Global 3 oscillation analysis. Each panels shows two-dimensional projection of the allowed six-dimensional region after marginalization with respect to the undisplayed parameters.

12 Neutrino mass just as m e Right-handed neutrino n R Breaking of U(3) l U(3) nr : Yukawa y ν ll n R H with y ν 10 1 Electroweak Symmetry Breaking U(1) Y assignment can be shifted. (mille-charged neutrino) Bound: e ν < 10 1 e from n p + e + ν e (Planets are not electrically charged, Gravitational interaction dominated.) To ensure the charge quantization U(1) Y, if n R s charge is strictly zero.

13 If neutrino is strictly electric neutral ψ M = ( χ ɛχ ) ψ c M = ψ M (No unbroken U(1) gauge symmetry charge. Color octet is OK though.) spinor Majorana mass Dirac mass 1 Weyl m(χt ɛχ + h.c.) m(ξ T ɛχ + h.c.) Majorana 1 m ψ M ψ M 1 m( ψ M 1 ψ1 M + ψ M ψ M ) Dirac 1 m(ψt L Cψ L + h.c.) m((ψ c ) T L Cψ L + h.c.) Dirac 1 m((ψc ) R ψ L + h.c.) m ψψ Notice Dirac spinor can also form Majorana mass term. (Pseduo-Dirac) The charge quantization from anomaly cancellation condition is then preserved.

14 Type-I see-saw(...) y ν l L n R H u + M R n c R n R + h.c., ( 0 MD M = M D M R ) m = 1 ( ) M R 4Md + M R, 1 ( ) M R + 4M d + M R M R M D m ν M D M R

15 Global U(1) Lep is broken: y ν break U(3) l U(3) n U(1) Lep M R U(1) Lep Without tuning dimensionless y ν, tiny m ν from M GUT

16 Extension of SM gauge symmetry Field Q u c d c l e c n c R H U(1) B L SU(3) C SU() L U(1) Y U(1) B L SU(5) U(1) B L? SU(5) SO(10) E 6 : 7 =

17 Extension of SM gauge symmetry Q 1 Q Q 3 l 1 l l 3,, u R c R t R e R µ R τ R,, d R s R b R n e R n µ R n τ R SU(3) H Horizontal symmetry is anomaly free with introduction of right-handed neutrino. (Yanagida)

18 Type II seesaw (SU() L SU(R) U(1) B L Y = SU() L Triplet = 1 ( ) H + H ++ H 0 H + Breaking U(1) B L y ν l T LCiσ l + µh T iσ H + h.c µ is important to induce spontaneously symmetry breaking of v = µv 0 µv0 = m M ν = y ν M v violates SU() L+R Custodial symmetry, v < 1 GeV from ρ-parameter constraint.

19 Type-III see-saw

20 Wyler-Wolfenstein (Pati-Salam) 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

21 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 D m ν ɛ MD + M S

22 Loop-induced m ν -(I) 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 = M S 0 0 M D 0 0 M S M D M S M R ν = ν L + MD + M S N ± = 1 M± + M D + M S with mass eigenvalues as m ν = 0, M ± = 1 ( M R ± M D M D + M S s L (M D ν L + M S s L M ± n c R) ) 4MD + M R + 4M S

23 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

24 U(1) ν s is only an approximate chiral symmetry and SM interactions do not respect it. H u H u ν L ν c L n R n c R (M 1 loop ν ) ij = π M R k k=1 Y ik Y jk M ( A MA M R k ln φ=h,h Yik Y jk M ( ) φ M Mφ M R k ln φ MR k ) MA MR k

25 M R M φ M φ M R ln ( ) M φ M R M R M h,h restore the see-saw, M R < 10 1 GeV M R M h,h, inverse see-saw limit, M R KeV

26 ume 93B, number 4 h + : SM singlet Loop-induced m ν -(II): Zee Model PHYS X f ab = f ba I I m ~ e- v e Fig. f ab (l i acl j b )ɛ ijh uming that m h ~ me. The most favorable case of rse occurs in those graphs with an internal r so th

27 Fig. 1. Two trino masse The physical Higgs particles are Re go, h + and k + + with masses giv Loop-induced m ν -(III): Zee-Babu Model Volume 03, number 1, PHYSICS LETTERS B Consider the self-interaction of the scalar particles h +, k + + and t the Higgs potential V=~~$+~+~uh+h-+~L:k++k--+I,(~+d)+I(h+h-)+;l~(k++k--)+114( +n,(~+~)(k++k--)+l,(h+h-)(k++k--)+~(h+h+k--+h-h-k++).

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