Search for lepton flavor violating Search for lepton flavor violating μμ Ｎ→Ｎ→ ττ Ｘ　Ｘ　 reaction with reaction with

high energy muons high energy muons

Shinya KANEMURA Shinya KANEMURA (Osaka Univ.)(Osaka Univ.)

withwith

Yoshitaka KUNO, Masahiro KUZE, Toshihiko OTAYoshitaka KUNO, Masahiro KUZE, Toshihiko OTA

TAU ‘04, Sep 16. 2004, Nara, JAPANTAU ‘04, Sep 16. 2004, Nara, JAPAN

IntroductionIntroduction LFV is a clear signal for physics beyond the SM.LFV is a clear signal for physics beyond the SM. Neutrino oscillation may indicate the possibility oNeutrino oscillation may indicate the possibility o

f LFV in the charged lepton sector.f LFV in the charged lepton sector. In new physics models, LFV naturally appears.In new physics models, LFV naturally appears.

SUSY (slepton mixing) SUSY (slepton mixing) Borzumati, MasieroBorzumati, Masiero

Hisano et al.Hisano et al. Zee type models for the ν mass Zee type models for the ν mass ZeeZee Models of dynamical flavor violationModels of dynamical flavor violation

　　　 　　　 (Topcolor, Top seesaw etc)(Topcolor, Top seesaw etc) 　 　　 　 Hill et al.Hill et al.

Experimenal bounds on Experimenal bounds on LFV processesLFV processes

　　　　 process branching ratio process branching ratio μ→eγ 1.2 ×10μ→eγ 1.2 ×10 ＾（－＾（－ 1111 ）　　　　　　）　　　　　　

　　 μ→μ→ ３３ ee 　　　　　　　　　　　　　　　　　　　　 1.11.1 　 　 ×10×10 ＾（－＾（－ 1212 ）） μTi→eTiμTi→eTi 　　　　　　　　 　　　　　　　　 6.1 ×106.1 ×10 ＾（－＾（－ 1313 ）） τ→μγ 3.1 ×10τ→μγ 3.1 ×10 ＾（－＾（－ 77 ）） τ→τ→ ３３ μ 1.4-3.1 ×10μ 1.4-3.1 ×10 ＾（－＾（－ 77 ）） τ→μητ→μη 　　　　　　 　　　　　　　　　 　　　 3.4 ×103.4 ×10 ＾（－＾（－ 77 ）　）　

Present experimental bounds on the tau associated Present experimental bounds on the tau associated processes are milder than those on the e-μLFV.processes are milder than those on the e-μLFV.

In this talk, weIn this talk, we consider tau-associated LFV consider tau-associated LFV The discovery of large mixing between νThe discovery of large mixing between νμμandνandντ τ may may

be relatedbe related to large LFV into large LFV in 　　 the μ-τsectorthe μ-τsector

In SUSY models, the Higgs mediated LFV can contrIn SUSY models, the Higgs mediated LFV can contribute to the tau-associated process with the enhancibute to the tau-associated process with the enhancement of the tau lepton mass. ement of the tau lepton mass.

Constraints on theτ-μeffective couplinConstraints on theτ-μeffective couplings from current datags from current data

Scalar coupling τ→μππ ΛScalar coupling τ→μππ Λ ～～ 2.6 TeV2.6 TeV Pseudo-scalar coupling τ→μη Pseudo-scalar coupling τ→μη ～～ 12 TeV12 TeV Vector τ→μφ Vector τ→μφ ～～ 1414 　　 TeVTeV Pseudo-vectorPseudo-vector 　　　　 　　　　 τ→μπ τ→μπ 　 ～　 ～ 1111 　　 TT

eVeV 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　

Black, Han, He, Sher, 2002Black, Han, He, Sher, 2002

LFV in SUSYLFV in SUSY

(pseudo) vector coupling(pseudo) vector coupling

tensor couplingtensor coupling

Higgs mediation = (pseudo) scalar couplingHiggs mediation = (pseudo) scalar coupling

∝∝ 　 　 lepton mass :lepton mass : → → 　　 τ-associated process τ-associated process

In SUSY model, effects of slepton mixing can induce LFVIn SUSY model, effects of slepton mixing can induce LFVvia loop diagramsvia loop diagrams

gauge mediationgauge mediation 　　 ==

LFV Yukawa coupling LFV Yukawa coupling

Slepton mixing induce LFV Slepton mixing induce LFV in SUSY models. in SUSY models.

Babu, Kolda;Babu, Kolda;Dedes,Ellis,Raidal;Dedes,Ellis,Raidal;Kitano, et al.Kitano, et al.

κκijij 　　 = Higgs LFV parameter= Higgs LFV parameter

Decoupling propertyDecoupling property

Gauge mediation (Dim=5) : Gauge mediation (Dim=5) :

decouple for large Mdecouple for large MSUSYSUSY

Higgs mediation (Dim=4)Higgs mediation (Dim=4)

Does not decouple in the large MDoes not decouple in the large MSUSYSUSY limit limit

Consider that MConsider that MSUSYSUSY is as large as O(1) TeV is as large as O(1) TeV with a fixed value of |μ|/M with a fixed value of |μ|/MSUSY SUSY

A sufficiently large Higgs mediated LFV coupling can be realized A sufficiently large Higgs mediated LFV coupling can be realized in a SUSY model, with the suppressed gauge mediated LFV. in a SUSY model, with the suppressed gauge mediated LFV. Babu,Kolda; Babu,Kolda; Brignole, RossiBrignole, Rossi

For mA=150GeV and tanβ=60,For mA=150GeV and tanβ=60,

Alternative process for the search Alternative process for the search of the Higgs LFV couplingof the Higgs LFV coupling

Future τ decay search may improve the upper liFuture τ decay search may improve the upper limit by one or two orders of magnitude. mit by one or two orders of magnitude.

Do we have another way to measure the Higgs LDo we have another way to measure the Higgs LFV coupling?FV coupling?

At future neutrino factories (muon colliders), 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 We here consider the DIS process the DIS process μμ Ｎ→Ｎ→ ττ ＸＸ from such intense muon beam. from such intense muon beam.

The DIS processThe DIS process 　　 μN→τX μN→τX

At either a neutrino factory or a muon collider At either a neutrino factory or a muon collider High energy muon beamHigh energy muon beam 　　 (E(Eμμ ＝２０－３００ ＝２０－３００ GeV)GeV) Intensity Intensity （（ 1010 ＾^ 2020 　　 muons/yearmuons/year ））

μL τR

N

qq

h, H, A

X

CERN SPS muon beamCERN SPS muon beam

S.N. Gninenko, et al.,S.N. Gninenko, et al., CERN-SPSC-2004-016CERN-SPSC-2004-016 SPSC-EOI-004 SPSC-EOI-004

SPS muon beam 10-100GeVSPS muon beam 10-100GeVTau detection by Tau detection by NOMADNOMAD

Quasi-Elastic scattering of Quasi-Elastic scattering of μμ Ｎ→Ｎ→ ττ ＮＮ　　　　　　　　　　　　　　　　　　　　　　 ↓　　　　　　　　　　　　　　　　　　　　　　　　　 ↓　　　

　　 τ→μνντ→μννDetails will be presented at the SPSC Villars MeetingDetails will be presented at the SPSC Villars Meeting22-28 Sept’0422-28 Sept’04

The cross section of μThe cross section of μ Ｎ→Ｎ→ ττ ＸＸEffective scalar coupling Effective scalar coupling 　 （　 （ using limit fromτ→μππusing limit fromτ→μππ ）） σσ 　＜～ 　＜～ 0.5 fb 0.5 fb 　 　 ShSh

erer

⇒ ⇒ 10^6×ρ[g/cm^3] tau’s 10^6×ρ[g/cm^3] tau’s from intensity 10^20 muonsfrom intensity 10^20 muons

Pseudo-scalar coupling Pseudo-scalar coupling 　 　 (using limit from τ→μη)(using limit from τ→μη)　　　　　　　　 σσ 　＜～　　＜～　 10^(-4) fb10^(-4) fb　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　In SUSY, In SUSY, scalar coupling scalar coupling = pseudo-scalar coupling= pseudo-scalar coupling The cross section isThe cross section is 10^(-4)10^(-4) －－ 10^(-5) smaller than 10^(-5) smaller than 　　　　 the scalar coupling casethe scalar coupling case

Enhancement of the SUSY cross sectionEnhancement of the SUSY cross section

Each sub-process Each sub-process μq→τq μq→τq is proportional to the quark masis proportional to the quark mas

ses because of the Yukawa couses because of the Yukawa coupling.pling.

For the energy > 50 GeV, the haFor the energy > 50 GeV, the hadronic cross section dronic cross section

is enhanced due to is enhanced due to the b-quark sub-processthe b-quark sub-process

EμEμ ＝＝ 50 GeV 10^(-5)fb50 GeV 10^(-5)fb 100 GeV100 GeV 　 　 10^(-4)fb 10^(-4)fb

300 GeV300 GeV 　 　 10^(-3)fb10^(-3)fb

Importance of higher energy beImportance of higher energy beam than 50 GeVam than 50 GeV

CTEQ6L

Angular distribution

μL

τR

θ

Target

Lab-frame

Lab-frame

Higgs mediationHiggs mediation → → 　　 chirality flippedchirality flipped　→　（　→　（ 11 －－ cosθcosθCMCM ））

2

Energy distribution for each angleEnergy distribution for each angleFrom theFrom theμμLL beam, beam, ττRR is emitted to the backward direction due t is emitted to the backward direction due t

o (1 o (1 ー ー cosθcosθCMCM)) 　　 nature in the CM frame. nature in the CM frame.

In Lab-frame, tau is emitted forward direction but with relatively In Lab-frame, tau is emitted forward direction but with relatively large angle with a Plarge angle with a PT.T.

EμEμ ＝＝ 50 GeV50 GeV EμEμ ＝＝ 100 GeV100 GeV EμEμ ＝＝ 500 GeV500 GeV

2

SignalSignal Number of tau for L =10^20 muons in a SUSY model 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): EμEμ ＝＝ 50 GeV 50 GeV 　　　 　　　 100×ρ[g/cm^3]100×ρ[g/cm^3] 　　 ofτleptonsofτleptons

　　　　　　　　　　　　　　　　 100 GeV 1000 100 GeV 1000 500 GeV 50000 500 GeV 50000 　　　　 We can consider its hadronic products as the signal We can consider its hadronic products as the signal τ→(πτ→(π 、、 ρ, aρ, a11, , …)…) ＋　＋　 missingsmissings Hard Hard hadrons emitted into the same direction as the parent hadrons emitted into the same direction as the parent

τ’s τ’s ττRR 　⇒　　⇒　 backward νbackward νLL 　　 + forward π,ρ+ forward π,ρ 、…、… ..

# of hard hadrons # of hard hadrons

　　≒ ≒ 0.3 ×0.3 × 　　 (# of tau) (# of tau)

τ R ν L π

Bullock, Hagiwara, MartinBullock, Hagiwara, Martin

BackgroundsBackgrounds Hadrons from the target (N) should be softer, anHadrons from the target (N) should be softer, an

d more unimportant for higher energies of the inid more unimportant for higher energies of the initial muon beam.tial muon beam.

Hard muons from μN→Hard muons from μN→μμX may be a fake signal X may be a fake signal via mis-ID of μas π. via mis-ID of μas π. Rate of mis-ID Rate of mis-ID 　　　 　　　 Emitted to forwad direction without large PEmitted to forwad direction without large PT T due to the due to the

Rutherford scattering Rutherford scattering 1/sin^4(θc1/sin^4(θcMM/2) ⇒/2) ⇒ 　 　 PPTT cuts cuts Other factors to reduce the fake Other factors to reduce the fake

Realistic Monte Carlo simulation is necessary to Realistic Monte Carlo simulation is necessary to see the feasibilitysee the feasibility

SummarySummary We discussed the possibility of measuring LFV via We discussed the possibility of measuring LFV via μN→τμN→τ

X X by the intense high energy beam.by the intense high energy beam. Non-observation of the signal can improve the present liNon-observation of the signal can improve the present li

mit on the scalar LFV coupling by mit on the scalar LFV coupling by ～～ 10^6. 10^6. In the SUSY model (scalar coupling=p-scalar coupling), In the SUSY model (scalar coupling=p-scalar coupling),

100-10000 tau leptons can be produced for Eμ=50-500 100-10000 tau leptons can be produced for Eμ=50-500 GeV.GeV.

For Eμ > 50 GeV, the cross section is enhanced due to tFor Eμ > 50 GeV, the cross section is enhanced due to the b-quark sub-process.he b-quark sub-process.

The signal is The signal is hard hadronshard hadrons from τ→πν from τ→πν 、、 ρν,ρν, aa11ν, .... , which go along the τdirection.ν, .... , which go along the τdirection. Main background: mis-ID of μ from μN→μX.Main background: mis-ID of μ from μN→μX. Different distribution: PDifferent distribution: PTT cut may be effective. cut may be effective. Realistic background simulation should be done.Realistic background simulation should be done.

Note addedNote added

In the similar way, we can consider search In the similar way, we can consider search for e-τconversion via the DIS process of for e-τconversion via the DIS process of e e N →τ X.N →τ X.

At a linear collider At a linear collider (E=500GeV L=10^34/cm^2/s)(E=500GeV L=10^34/cm^2/s)

10^22 electrons of E=250GeV available. 10^22 electrons of E=250GeV available. The constraint on the (eτqq) coupling can The constraint on the (eτqq) coupling can be improved via be improved via e N →τ X e N →τ X by 10^8 as coby 10^8 as compared to that bympared to that by 　　 τ→eππ. τ→eππ.