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 , Nara, JAPAN

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.

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 ×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.

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.

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

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 =

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

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

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,

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 ( GeV) Energy 50 GeV ( GeV) 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.

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

CERN SPS muon beam S.N. Gninenko, et al., S.N. Gninenko, et al., CERN-SPSC CERN-SPSC SPSC-EOI-004 SPSC-EOI-004 SPS muon beam GeV 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 Sept’04

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

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

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

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

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 GeV GeV GeV  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

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

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), tau leptons can be produced for Eμ= 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.

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.