1. Search for tau-e (tau-mu) flavor mixing at a future collider Shinya KANEMURA (Osaka Univ.) with Yoshitaka KUNO, Toshihiko OTA (Osaka Univ.) Masahiro Kuze (Tokyo Inst. Tech.) CP の破れと物質創生＠基礎物理学研究所 CP の破れと物質創生＠基礎物理学研究所 Jan 12-14. 2005 Jan 12-14. 2005

2. Contents Introduction Tau associated LFV processes Tau associated LFV processes Lepton flavor violating Yukawa coupling Lepton flavor violating Yukawa coupling The bound from current data The bound from current data Search for tau associated LFV at future colliders h → τμ （ τe ） at a LC h → τμ （ τe ） at a LC e N (μN)→τX at a LC (a neutrino factory) e N (μN)→τX at a LC (a neutrino factory)Summary SK, Matsuda, Ota, Shindou, Takasugi, Tsumura SK, Kuno, Kuze, Ota

3. 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.

4. LFV in SUSY It is known that sizable LFV can be induced at loop due to slepton mixing Up to now, however, no LFV evidence has been observed at experiments. μ→e γ, μ→eee, …. Large M SUSY ? so that the SUSY effects decouple? Even in such a case, we may be able to search LFV through the Higgs boson mediation, which does not necessarily decouple for a large M SUSY limit

5. 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. Different behavior from LFV in theμ ⇔ e mixing. Different behavior from LFV in theμ ⇔ e mixing. It is less constrained by current data as compared to theμ ⇔ e mixing It is less constrained 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 ）

6. 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

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

8. Experimental Bound on κ 32 For κ ３１, similar bound is obtained because of the similar experimental results for τ→μηand τ→eη. The strongest bound on κ 32 comes from the result of τ→μη.

9. A source of slepton mixing in the MSSM+RN Slepton mixing induces both the Higgs mediated LFV and the gauge mediation. Off-diagonal elements can be induced in the slepton mass matrix at low energies, even when it is diagonal at the GUT scale. RGE RGE

10. The correlation between Higgs mediated LFV and gauge mediation For relatively low m SUSY, the Higgs mediated LFV is constrained by the data of gauge mediated LFV. For m SUSY > O(1)TeV, the gauge mediation becomes suppressed, while the Higgs mediated LFV can be large.

11. m SUSY ～ O(1) TeV Let us consider that M SUSY is as large as O(1) TeV with a fixed value of |μ|/M SUSY Gauge mediated LFVis suppressed Gauge mediated LFV is suppressed, the Higgs-LFV coupling κ ij the Higgs-LFV coupling κ ij can be sufficiently large. Babu,Kolda; Babu,Kolda; Brignole, Rossi Brignole, Rossi The non-decoupling property of the Higgs LFV coupling (κ ij )

12. Search for Higgs mediated τ- e & τ- μ mixing Tau’s rare decays at B factories. 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 about 1 order of magnitude. In near future, τ decay searches will improve the upper limit by about 1 order of magnitude. We here discuss the 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 )

13. Higgs boson decay After the Higgs boson is discovered, we can consider the possibility to measure the LFV Yukawa couplings directly from the decay of the Higgs bosons. After the Higgs boson is discovered, we can consider the possibility to measure the LFV Yukawa couplings directly from the decay of the Higgs bosons. LHC Assamagan et al; Brignole, Rossi LHC Assamagan et al; Brignole, Rossi LC SK, Matsuda, Ota, Shindou, LC SK, Matsuda, Ota, Shindou, Takasugi, Tsumura Takasugi, Tsumura 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 measurement of the lightest Higgs boson: Precise measurement of the lightest Higgs boson: property (m h,Γ,σ,Br,…) will be thoroughly measured property (m h,Γ,σ,Br,…) will be thoroughly measured Less backgrounds Less backgrounds

14. GLC （ former JLC ） (201x?-) A Linear Collider （ LC ） collision 1 st stage 2 nd stage Roadmap report JLC

15. Higgs Production at a LC Higgs Production at a LC via gauge interaction In 2HDM (MSSM), At low energies, the Higgsstrahlung process is dominant.

16. A LC = A Higgs Factory A electron-positron collider Energy E cm = 200 – 1000 GeV Energy E cm = 200 – 1000 GeV Luminosity L = 500 – 1000 fb^(-1) Luminosity L = 500 – 1000 fb^(-1) 10^5-10^6 Higgs bosons can be produced. A Higgs factory! A Higgs factory! Less backgrounds Simple kinematic structure

17. Decay branching ratio When mA is large, the experimental bound is relaxed, and branching ratio of 10^(-4)-10^(-3) is allowed.

18. Branching ratios

19. 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

20. Backgrounds The background is huge, but most of them can be cut by appropriate kinematic cuts. Except for when

21. The fake signal In order to resuce the fake signal events, it is important to determine Eh with high precision from pZ, Ecm, pμ. Strongly depend on the resolusion of pZ and pμ, beam energy spread rate, …

22. 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.

23. Alternative process for search of the Higgs LFV coupling. At future ν factories (μ colliders), (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 At a LC (Ecm=500GeV L=10^34/cm^2/s) 10^22 of 250GeV electrons available. 10^22 of 250GeV electrons available. DIS process e Ｎ →τ Ｘ process DIS process e Ｎ →τ Ｘ process A fixed target experiment option of LC

25. Cross section in SUSY model CTEQ6L Each sub-process e q (μq) →τq e q (μq) →τq is proportional to the down- type quark masses. is proportional to the down- 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 E ＝ 50 GeV 10^(-5)fb E ＝ 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

26. 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

27. 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

28. 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 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.

29. Summary 1 We discussed LFV in the Higgs coupling Direct search via the decay process h →τμat a LC Direct search via the decay process h →τμat a LC DIS process e N (μN)→τX by using the high energy electron beam of a LC (a μC) with a fixed-target. DIS process e N (μN)→τX by using the high energy electron beam of a LC (a μC) with a fixed-target. h →τμat a LC: The backgrounds can be reduced by kinematic cuts The backgrounds can be reduced by kinematic cuts The signal may be detectable, if the LFV Higgs coupling κ 32 is large within the limit from the τ→μη result. The signal may be detectable, if the LFV Higgs coupling κ 32 is large within the limit from the τ→μη result. Such a significant κ 32 can be realized only when M SUSY is as large as TeV with μ/M SUSY being O(1-10). Such a significant κ 32 can be realized only when M SUSY is as large as TeV with μ/M SUSY being O(1-10). In the general 2HDM, larger significance is obtained under the current bound on κ 32. In the general 2HDM, larger significance is obtained under the current bound on κ 32.

30. Summary 2 DIS processes e N (μN)→τX : DIS processes e N (μN)→τX : For E > 60 GeV, the cross section is enhanced due to the sub-process with sea b-quarks For E > 60 GeV, the cross section is enhanced due to the sub-process with sea b-quarks At a LC with E cm =500GeV ⇒ σ ＝ 10^(-3) fb At a LC with 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). Non-observation of the signal would improve the current limit on the τ-e-Φ coupling by 10^(4-5). Realistic background simulation is necessary. Realistic background simulation is necessary.