1. Search for lepton flavor violating μ Ｎ →τ Ｘ reaction with high energy muons Shinya KANEMURA (Osaka Univ.) with Yoshitaka KUNO, Masahiro KUZE, Toshihiko OTA TAU ‘04, Sep 16. 2004, Nara, JAPAN

2. Introduction  LFV is a clear signal for physics beyond the SM.  Neutrino oscillation may indicate the possibility of LFV in the charged lepton sector.  In new physics models, LFV naturally appears.  SUSY (slepton mixing) Borzumati, Masiero Hisano et al. Hisano et al.  Zee type models for the ν mass Zee  Models of dynamical flavor violation (Topcolor, Top seesaw etc) Hill et al. (Topcolor, Top seesaw etc) Hill et al.

3. Experimenal bounds on LFV processes process branching ratio process branching ratio  μ→eγ 1.2 ×10 ＾（－ 11 ）  μ→eγ 1.2 ×10 ＾（－ 11 ）  μ→ ３ e 1.1 ×10 ＾（－ 12 ）  μTi→eTi 6.1 ×10 ＾（－ 13 ）  τ→μγ 3.1 ×10 ＾（－ 7 ）  τ→ ３ μ 1.4-3.1 ×10 ＾（－ 7 ）  τ→μη 3.4 ×10 ＾（－ 7 ）  τ→μη 3.4 ×10 ＾（－ 7 ） Present experimental bounds on the tau associated processes are milder than those on the e-μLFV.

4. In this talk, we consider tau-associated LFV In this talk, we consider tau-associated LFV  The discovery of large mixing between ν μ andν τ may be related to large LFV in the μ-τsector  In SUSY models, the Higgs mediated LFV can contribute to the tau-associated process with the enhancement of the tau lepton mass.

5. Constraints on theτ-μeffective couplings from current data  Scalar coupling τ→μππ Λ ～ 2.6 TeV  Pseudo-scalar coupling τ→μη ～ 12 TeV  Vector τ→μφ ～ 14 TeV  Pseudo-vector τ→μπ ～ 11 TeV  Pseudo-vector τ→μπ ～ 11 TeV Black, Han, He, Sher, 2002

6. LFV in SUSY (pseudo) vector coupling (pseudo) vector coupling tensor coupling tensor coupling Higgs mediation = (pseudo) scalar coupling ∝ lepton mass : → τ-associated process ∝ lepton mass : → τ-associated process In SUSY model, effects of slepton mixing can induce LFV via loop diagrams gauge mediation =

7. LFV Yukawa coupling Slepton mixing induce LFV in SUSY models. Babu, Kolda; Dedes,Ellis,Raidal; Kitano, et al. κ ij = Higgs LFV parameter

8. Decoupling property  Gauge mediation (Dim=5) : decouple for large M SUSY decouple for large M SUSY  Higgs mediation (Dim=4) Does not decouple in the large M SUSY limit

9. Consider that M SUSY is as large as O(1) TeV with a fixed value of |μ|/M SUSY A sufficiently large Higgs mediated LFV coupling can be realized in a SUSY model, with the suppressed gauge mediated LFV. Babu,Kolda; Babu,Kolda; Brignole, Rossi Brignole, Rossi For mA=150GeV and tanβ=60,

10. Alternative process for the search of the Higgs LFV coupling  Future τ decay search may improve the upper limit by one or two orders of magnitude.  Do we have another way to measure the Higgs LFV coupling?  At future neutrino factories (muon colliders), Energy 50 GeV (100-500GeV) Energy 50 GeV (100-500GeV) 10^20 muons can be available. 10^20 muons can be available.  We here consider the DIS process μ Ｎ →τ Ｘ the DIS process μ Ｎ →τ Ｘ from such intense muon beam. from such intense muon beam.

11. The DIS process μN→τX At either a neutrino factory or a muon collider  High energy muon beam (E μ ＝２０－３００ GeV)  Intensity （ 10 ＾ 20 muons/year ） μLμL τRτR N q q h, H, A X

13. CERN SPS muon beam S.N. Gninenko, et al., S.N. Gninenko, et al., CERN-SPSC-2004-016 CERN-SPSC-2004-016 SPSC-EOI-004 SPSC-EOI-004 SPS muon beam 10-100GeV Tau detection by NOMAD Quasi-Elastic scattering of μ Ｎ →τ Ｎ ↓ ↓ τ→μνν τ→μνν Details will be presented at the SPSC Villars Meeting 22-28 Sept’04

14. The cross section of μ Ｎ →τ Ｘ Effective scalar coupling （ using limit fromτ→μππ ） （ using limit fromτ→μππ ） σ ＜～ 0.5 fb Sher σ ＜～ 0.5 fb Sher ⇒ 10^6×ρ[g/cm^3] tau’s ⇒ 10^6×ρ[g/cm^3] tau’s from intensity 10^20 muons from intensity 10^20 muons Pseudo-scalar coupling (using limit from τ→μη) (using limit from τ→μη) σ ＜～ 10^(-4) fb σ ＜～ 10^(-4) fb In SUSY, scalar coupling scalar coupling = pseudo-scalar coupling = pseudo-scalar coupling The cross section is The cross section is 10^(-4) － 10^(-5) smaller than 10^(-4) － 10^(-5) smaller than the scalar coupling case the scalar coupling case

15. Enhancement of the SUSY cross section  Each sub-process μq→τq μq→τq is proportional to the quark masses because of the Yukawa coupling. is proportional to the quark masses because of the Yukawa coupling.  For the energy > 50 GeV, the hadronic cross section is enhanced due to is enhanced due to the b-quark sub-process the b-quark sub-process Eμ ＝ 50 GeV 10^(-5)fb Eμ ＝ 50 GeV 10^(-5)fb 100 GeV 10^(-4)fb 100 GeV 10^(-4)fb 300 GeV 10^(-3)fb 300 GeV 10^(-3)fb  Importance of higher energy beam than 50 GeV CTEQ6L

16. Angular distribution μLμL τRτR θ Target Lab-frame Higgs mediation → chirality flipped → chirality flipped → （ 1 － cosθ CM ） → （ 1 － cosθ CM ） 2

17. Energy distribution for each angle  From the μ L beam, τ R is emitted to the backward direction due to (1 ー cosθ CM ) nature in the CM frame.  In Lab-frame, tau is emitted forward direction but with relatively large angle with a P T. Eμ ＝ 50 GeV Eμ ＝ 100 GeV Eμ ＝ 500 GeV 2

18. Signal  Number of tau for L =10^20 muons in a SUSY model with |κ32|^2=0.3×10^(-6): with |κ32|^2=0.3×10^(-6): Eμ ＝ 50 GeV 100×ρ[g/cm^3] ofτleptons Eμ ＝ 50 GeV 100×ρ[g/cm^3] ofτleptons 100 GeV 1000 100 GeV 1000 500 GeV 50000 500 GeV 50000  We can consider its hadronic products as the signal τ→(π 、 ρ, a 1, …) ＋ missings τ→(π 、 ρ, a 1, …) ＋ missings  Hard hadrons emitted into the same direction as the parent τ’s τ R ⇒ backward ν L + forward π,ρ 、 …. τ R ⇒ backward ν L + forward π,ρ 、 ….  # of hard hadrons ≒ 0.3 × (# of tau) ≒ 0.3 × (# of tau) Bullock, Hagiwara, Martin

19. Backgrounds  Hadrons from the target (N) should be softer, and more unimportant for higher energies of the initial muon beam.  Hard muons from μN→μX may be a fake signal via mis-ID of μas π.  Rate of mis-ID  Rate of mis-ID  Emitted to forwad direction without large P T due to the Rutherford scattering 1/sin^4(θc M /2) ⇒ P T cuts 1/sin^4(θc M /2) ⇒ P T cuts  Other factors to reduce the fake  Realistic Monte Carlo simulation is necessary to see the feasibility

20. Summary  We discussed the possibility of measuring LFV via μN→τX by the intense high energy beam.  Non-observation of the signal can improve the present limit on the scalar LFV coupling by ～ 10^6.  In the SUSY model (scalar coupling=p-scalar coupling), 100-10000 tau leptons can be produced for Eμ=50-500 GeV.  For Eμ > 50 GeV, the cross section is enhanced due to the b-quark sub-process.  The signal is hard hadrons from τ→πν 、 ρν, a 1 ν,...., which go along the τdirection. a 1 ν,...., which go along the τdirection.  Main background: mis-ID of μ from μN→μX.  Different distribution: P T cut may be effective.  Realistic background simulation should be done.

21. Note added  In the similar way, we can consider search for e-τconversion via the DIS process of e N →τ X.  At a linear collider (E=500GeV L=10^34/cm^2/s) 10^22 electrons of E=250GeV available. The constraint on the (eτqq) coupling can be improved via e N →τ X by 10^8 as compared to that by τ→eππ.