Lepton-flavor violation in tau-lepton decay and the related topics

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1 Lepton-flavor violation in tau-lepton decay and the related topics Junji Hisano Institute for Cosmic Ray Research Univ. of Tokyo International Workshop On Discoveries In Flavour Physics At E+ E- Colliders (DIF 06) 8 Feb - 3 Mar 006, Frascati, Rome, Italy

2 Contents of My talks 1, Introduction of charged lepton flavor violation Tau lepton-flavor violating signature in MSSM, Probe models beyond MSSM by tau lepton-flavor violation SUSY seesaw model SUSY GUTs 3, Summary of my talk

3 I, Introduction Lepton-flavor conservation is not exact in nature. LFV in neutrino sector: Global fit to three neutrinos = = m 3,4(1 0.15) 10 ev, sin θ µ (1 0.) m1 θ e θ e3 0.9 (Fogli et al) = 7.9(1 ± 0.09) 10 ev, sin = 0.314(1 ) sin = LFV in charged-lepton sector: Not yet observed. 000PDG current future τ µ ( e) γ < 1.1(.7) 10 < 6.8(11) τ µ ( e) η < 9.6(8.) (8 9) < 1.5(.3) (9 10) τ lll < ~10 < ~ 10 < ~10 µ eγ < µ e < 6 7 (9 10) 11 (13 14) (MEG) (?) 1 18 µ e:ti < ~10 (PRISM) MEG will start this year. 10

4 Lepton-flavor conservation is not exact in nature. However, size of LFV depends on models beyond SM. Supersymmetric Standard Model (MSSM) and extensions Bulk fermions in flat or warped extra-dimensions Multi-Higgs models Seesaw models at weak scale etc, etc,. MSSM is the most well-motivated model, and it is also a good prototype of models beyond SM. Flavor physics plays an important role in construction and establishment of MSSM. Introduction of SUSY breaking for squarks and sleptons leads to new flavor and CP violation. = + ( m 100GeV~1TeV) ( m ) ( m ) ( ) fm m f f j j f i i ij f L/ R L/ R L/ R SUSY SUSY 0 0 K K mixing and µ eγ give stringent constraints on structure of SUSY breaking. (SUSY flavor problem)

5 Ansatz for SUSY flavor problem and tau Lepton-flavor violation (I) Universal scalar mass scenario Slepton and squark masses are independent of the flavors at a high energy (messenger) scale ( m 1at Λ>> m / Weak ) q l. LFV slepton masses might be radiatively generated by the LFV interaction. (Ex, SUSY seesaw, SUSY GUTs). (-> second part in my talk) tan β tan β Br( τ µ ( e) + e + e ) 10 Br( τ µ ( e) + γ), 3 Br( τ µ ( e) + µ + µ ). 10 Br( τ µ ( e) + γ), 3 Br( τ µ ( e) + ρ).5 10 Br( τ µ ( e) + γ) Strong correlation in the processes. Competitor is mu->e gamma. C.f. PRISM sensitivity is comparable to q/l q/l 3 R( µ e;ti) 5 10 Br( µ eγ) Br( µ eγ) 10 (Brignole and Rossi) (15 16)

6 Ansatz for SUSY flavor problem and taulepton-flavor violation (II).Case I: m st nd (1, gene.) q / l Decoupling scenarios m Weak Tau LFV, τ µ / e + γ, is a window to probe flavor structure. Case II: msusy m Weak ( ) Br( ( e) ) 10 m τ /100GeV tan 6 τ µ γ β Anomalous LFV Higgs coupling might appear (Babu&Kolda) Case III: m q / l Change subject. m Weak (Split SUSY) (Paradisi)

7 R-party violation R parity: Proton stability and dark matter * * * * * WR = λijk LL i jerk + λ ijk LQ i jdrk + λ ijkuridrjdrk L L B.If L is violating, LFV processes are generated at tree level λλ : τ µ µ µ, µ ee, µ ee, ( µ e) λλ τ µ π µ µ η µ φ µ :, K,,, ( e) λλ τ µ π µ K µ η µ φ µ ρ µ e :,,,,,( ) Tau lepton might be more accessible to R parity violation.

8 , Probe models beyond MSSM by tau lepton-flavor violation Lepton-flavor symmetry is not exact in nature, and LFV Interaction is present beyond the MSSM. The radiative correction generates slepton mixing even in universal scalar mass scenario. (Hall, Kostelecky & Raby) SUSY Seesaw model (Introduction of right-handed neutrino) Motivated from neutrino mass, SO(10) GUTs, and leptogenesis ν Yukawa induces left-handed slepton mixing (Borzumati&Masiero) SUSY SU(5) model (Introduction of colored Higgs multiplet) Colored Higgs is SU(5) partner of doublet Higgs in MSSM. CKM mixing induces right-handed slepton mixing. (Barbieri&Hall) The radiative correction is not suppressed by power of LFV scale if it is smaller than the SUSY breaking messenger scale.

9 SUSY Seesaw model (Introduction of right-handed neutrino) L= f h + f + l erl 1 ν ν RLh M νν R R Non-vanishing LFV slepton masses by radiative correction ( ) 1 M m (3 ) log L ij m 0 + A0 fν fν ij 8π M G ( m ) 3 100GeV And then, Br τ γ β 6 L j 4 ( l j ) 3 10 ( ) ( ) tan m m L SUSY DOF in Seesaw model,m:6, φ:6, CP:4(mixing)+(Majorana)=18 T h mν ij fν fν ( ) M In light ν mass matrix ( m ν ) ij M:3, φ:3, CP:1(mixing)+ (Majorana) =9 ij M H ij fν log f M G H ij In (Hermitian) Real: 6,Phase:3 =9 ν ij (Ibarra&Davidson)

10 Br( τ µγ ) Br( τ eγ ) comes from H, and from. 3 H13 Question: How large they can be? e is generated if H and/or H. H 0. µ γ 1, 13 3 H (1) * 0 0 = 0 * * 0 * * (1) Model-building favors with, not. H H () H * 0 * = 0 * 0 * 0 * () H (1) : Br( τ µγ ) H () : Br( τ eγ ) (mu->e gamma is suppressed below the exp. bound.) (Ellis,JH, Raidal, Shimizu)

11 τ µγ v.s. µ eγ (Bottom-up approach) Working hypothesis: ( ) * m U U m 3M ( ) l e U mν3m3 l L 3 µ 3 τ3 ν 3 ( τ µγ ) * * m 1 U 3 µ 3 + UeUµ mν M ( µ eγ ) L f m MU ( U :MNSmatrix) ( ) ν ij νi i ij Br( µ eγ) U / U > Br( τ µ γ) 0.17 e3 τ 3 3 ~ 10 Ue3 /0.01

12 τ µγ v.s. µ eγ (Top-down approach) U(1) flavor symmetry (Sato&Tobe) E E E L L L N N N model I 1 0 A + 1 A A c b a model II Model I: m diag ε ε ε l A A A c b a 3 (,,1) ( 0.07) U µ 3 1/ Br( µ eγ ) ~ 0.03 ( / 0.07) ε (model I) Br( τ µ γ) Model II: Br( µ eγ ) ~6 (modelii) Br( τ µ γ) (8 9) We have to cover Br( τ µ γ) < ~ 10 from current bound. (13 14) MEG ( Br( µ eγ) 10 ) might be a crucial test for tau LFV searches.

13 SUSY SU(5) model (Introduction of colored Higgs multiplet) Right-handed slepton mixings are induced by CKM mixing in minimal model (without right-handed neutrinos), however, the branching ratios of charged LFVs are smaller. It is not end of the story since we have to care some illnesses (3- Higgs splitting, proton decay, fermion mass relation). Ex, orbifold SU(5) GUT in 5 dim. space. 8 Br( τ µγ ) 5 10 tan β Br( ) 3 10 tan 11 µ eγ β ( ~ 100GeV) m SUSY (Universality of slepton mass is hardly broken.) (Hall&Nomura)

14 SUSY SU(5) model with right-handed neutrinos Leptonic and hadonic flavor violations are correlated to each other in SUSY GUTs. ψ [10] = ( u, d, u, e ), φ[5 ] = (, ν, ), ν GUT relation: * L L R R dr L e L R * i 3 ( m ) 3 ( m ) e ϕ l d 3 (Moroi) L τ µγ R b-s quark transition (JH&Shimizu)

15 3, Summary of my talk Lepton-flavor conservation is not exact in nature, and then, charged lepton-flavor violation is a good window to probe models beyond SM. In this talk, I review tau lepton flavor violation in the SUSY models. Studies of LFV may give a clue for SUSY breaking mechanism and models beyond the MSSM. In conventional cases, tau->mu(e) gamma is the most sensitive to the SUSY models. However, other processes are also important in cases of a decoupling scenario and R parity breaking. Current experimental bounds on LFV tau decay modes exclude a part of the SUSY seesaw models. Search for them gives information for the model, which is independent of mu->e gamma and neutrino oscillation.

16 3, Summary of my talk From model-building points of view, in SUSY seesaw model ( 3) Br( τ µγ ) < ~ 10 Br( µ eγ). In this case, MEG might be a crucial test for tau LFV searches. SUSY SU(5) GUT also provides other LFV interaction. Minimal model predicts a small branching ratio of LFV tau 10 decay, Br( τ µ γ) < 10. But, non-minimal models may predict larger branching ratio. In SUSY GUTs, correlation between hadronic and leptonic flavor violation is a good test. If one of tau->mu gamma and b- s quark transition is observed, the other is promising in the model.