1. Search for tau-e (tau-mu) flavor mixing at a linear collider Shinya KANEMURA (Osaka Univ.) with Yoshitaka KUNO, Toshihiko OTA (Osaka Univ) Masahiro Kuze (Tokyo Inst. Tech.) ACFA’07, Nov 11. 2004, at National Taiwan University

2. Introduction LFV is a clear signal for physics beyond the SM. e ⇔ μ μ ⇔ τ τ ⇔ e e ⇔ μ μ ⇔ τ τ ⇔ e Neutrino oscillation may indicate LFV among charged leptons. In SUSY models, LFV can naturally appear. Borzumati, Masiero Borzumati, Masiero Hisano et al. Hisano et al.

3. In this talk, we discuss tau-associated LFV in SUSY models In this talk, we discuss tau-associated LFV in SUSY models τ ⇔ e & τ ⇔ μ τ ⇔ e & τ ⇔ μ The Higgs mediated LFV is proportional to the Yukawa coupling The Higgs mediated LFV is proportional to the Yukawa coupling ⇒ Tau-associated LFV processes. ⇒ Tau-associated LFV processes. It is less constraind by current data as compared to theμ ⇔ e mixing It is less constraind by current data as compared to theμ ⇔ e mixing 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 ）

4. LFV in SUSY LFV is induced at one loop due to slepton mixing Gauge mediation : Higgs mediation : Higgs mediation does not decouple in the large M SUSY limit

5. LFV Yukawa coupling Slepton mixing induces LFV in SUSY models. Babu, Kolda; Dedes,Ellis,Raidal; Kitano, Koike, Okada κ ij = Higgs LFV parameter

6. m SUSY ～ O(1) TeV Consider that M SUSY is as large as O(1) TeV with a fixed value of |μ|/M SUSY While gauge mediated LFVis suppressed While gauge mediated LFV is suppressed, the Higgs-LFV coupling κ ij can be sufficiently large. Babu,Kolda; Babu,Kolda; Brignole, Rossi Brignole, Rossi

7. Search for Higgs mediated τ- e & τ- μ mixing Tau’s rare decays τ→eππ （ μππ ） τ→eππ （ μππ ） τ→eη (μη) τ→eη (μη) τ→μe e (μμμ) 、 …. τ→μe e (μμμ) 、 …. In near future, τ decay searches will improve the upper limit by 1-2 orders of magnitude. In near future, τ decay searches will improve the upper limit by 1-2 orders of magnitude. Other possibilities ? Higgs decays into a tau-mu or tau-e pair Higgs decays into a tau-mu or tau-e pair The DIS process e Ｎ （ μ Ｎ） →τ Ｘ The DIS process e Ｎ （ μ Ｎ） →τ Ｘ by a fixed target experiment at a LC (μ Ｃ ) by a fixed target experiment at a LC (μ Ｃ )

8. Higgs boson decay After the Higgs boson is found, we can consider the possibility to measure the LFV Higgs couplings directly from the decay of the Higgs bosons. After the Higgs boson is found, we can consider the possibility to measure the LFV Higgs couplings directly from the decay of the Higgs bosons. LHC Assamagan et al; Brignole, Rossi LHC Assamagan et al; Brignole, Rossi LC Kanemura, Ota, et al., LC Kanemura, Ota, et al., PLB599(2004)83. PLB599(2004)83. Search for h →τμ (τe) at LC: Search for h →τμ (τe) at LC: Simple kinematic structure (Esp. Higgssrahlung process) Simple kinematic structure (Esp. Higgssrahlung process) Precise measurements: Precise measurements: property (m h,Γ,σ,Br,…) will be thoroughly measured property (m h,Γ,σ,Br,…) will be thoroughly measured Less backgrounds Less backgrounds

9. Higgs Production at a LC Higgs Production at a LC ～ 10^5 Higgs produced Decay branching ratio (h→τμ) The branching ratio of 10^(-4) – 10^(-3) is possible.

10. Signal The process can be identified by using Z recoil: Theτmomentum is reconstructed by using E cm, m h, p Z and p μ using E cm, m h, p Z and p μ It is not required to measure τ It is not required to measure τ The # of the signal event 11 event for leptonic decay of Z 118 event for hadronic decay

11. Backgrounds

12. Feasibility Resolution of Z momentum Signal / Fake 118 / 230 events 118 / 230 events (Z →jj 、 δ ＝３ GeV) (Z →jj 、 δ ＝３ GeV) 11 / 8 events 11 / 8 events (Z→ll, δ ＝ 1GeV) (Z→ll, δ ＝ 1GeV) For some specific parameter region, h → τμ （ τe ） can be studied at a LC. No big advantage, although it depends on machine.

13. Alternative process for search of the Higgs LFV coupling? At future ν factories (μ colliders), 10^20 muons of energy 50 GeV 10^20 muons of energy 50 GeV (100-500GeV) can be available. (100-500GeV) can be available. DIS μ Ｎ →τ Ｘ process DIS μ Ｎ →τ Ｘ process Sher, Turan, PRD69(2004)302 Sher, Turan, PRD69(2004)302 Kanemura, et al, hep-ph/0410044 Kanemura, et al, hep-ph/0410044 At a LC (Ecm=500GeV L=10^34/cm^2/s) 10^22 of 250GeV electrons available. 10^22 of 250GeV electrons available. We here consider the LFV DIS processes e Ｎ →τ Ｘ e Ｎ →τ Ｘ by using the electron (positron) beam of a LC by using the electron (positron) beam of a LC A fixed target experiment option of LC

14. Cross section in SUSY model CTEQ6L Each sub-process e q (μq) →τq e q (μq) →τq is proportional to the d-type quark masses. is proportional to the d-type quark masses. For the energy > 60 GeV, the total 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 250 GeV 10^(-3)fb 250 GeV 10^(-3)fb

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

16. Signal Number of taus (case of electron beam) E ＝ 250 GeV, L =10^34 /cm^2/s, ⇒ 10^22 electrons (positrons) E ＝ 250 GeV, L =10^34 /cm^2/s, ⇒ 10^22 electrons (positrons) in a SUSY model with |κ 3i |^2=0.3×10^(-6): σ=10^(-3) fb in a SUSY model with |κ 3i |^2=0.3×10^(-6): σ=10^(-3) fb 10^5 of τleptons are produced for the target of ρ=10 g/cm^2 10^5 of τleptons are produced for the target of ρ=10 g/cm^2 Naively, non-obervation of the e N → τ X process may improve the current upper limit on the e-τ-Φ coupling by around 4-5 orders of magnitude Naively, non-obervation of the e N → τ X process may improve the current upper limit on the e-τ-Φ coupling by around 4-5 orders of magnitude We may consider its hadronic products as the signal τ→(π 、 ρ, a 1, …) ＋ missings τ→(π 、 ρ, a 1, …) ＋ missings # of hadrons ≒ 0.3×(# of tau) # of hadrons ≒ 0.3×(# of tau) Hard hadrons emitted into the same direction as the parent τ’s Hard hadrons emitted into the same direction as the parent τ’s Bullock, Hagiwara, Martin

17. Backgrounds Hadrons from the target (N) should be softer, and more unimportant for higher energies of the initial e or μ beam. Hard leptons from l N→ l X would be be a fake signal via mis-ID of l as π. ( l = e or μ) Rate of mis-ID Rate of mis-ID Emitted to forwad direction without large P T due to the Rutherford scattering 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 Other factors to reduce the fake Realistic Monte Carlo simulation is necessary.

18. Summary Possibility of measuring LFV via e N→τX by using the high energy electron beam of a LC with a fixed- target. E cm =500GeV ⇒ σ ＝ 10^(-3) fb L=10^34/cm^2/s ⇒ 10^22 electrons available L=10^34/cm^2/s ⇒ 10^22 electrons available 10^5 of taus are produced for ρ=10 g/cm^2 10^5 of taus are produced for ρ=10 g/cm^2 Non-observation of the signal would improve the current limit on the τ-e-Φ coupling by 10^(4-5). The signal would be hard hadrons from τ→πν 、 ρν, a 1 ν,...., which go along the τdirection. Main background: mis-ID of e from eN→eX. Background simulation will be done.