1. Lepton Flavor Violating Decays of Higgs Bosons under the Rare Tau Decay Results
This talk based on PLB599, 83 and hep-ph/
Koji TSUMURA
in collaboration with S. Kanemura and T. Ota
Osaka University
Contents
・ The 2 Higgs doublet model (2HDM)
Lepton flavor violation (LFV) in the Yukawa interaction Experimental bounds and Theoretical consistencies
・ Constraint from the rare tau decay results
・ Lepton flavor violating decay of the Higgs boson
・ Summary
The 8th ACFA Workshop on Physics and    Detector at the Linear Collider
July , 2005, EXCO. Daegu, Korea
Search for LFV Higgs boson decays can be a useful to further constrain the LFV Yukawa coupling

2. Motivation Sizable LFV = New physics signature
Why “LFV in Higgs sector” ?
Several new physics models (ex. SUSY, Extra dim., little Higgs, Zee model, etc. ) introduce extended Higgs sector.
LFV couplings are naturally generated in such Higgs sector.
Zee-model (2HDM + singlet scalar) Zee(80) :
Model for tiny neutrino masses are induced by radiative correction.
Zee singlet induces LFV Yukawa int.!!
Smirnov and Tanimoto(96); Kanemura et.al.(00)
MSSM + right-handed neutrinos :
Slepton mixing induces LFV Yukawa int.
Babu and Kolda(02); Borzumati and Masiero(86); Hisano et.al.(95)

3. Lepton flavor violation in the Yukawa interaction
2HDM Lagrangian for charged lepton Yukawa int.
・ Two independent Yukawa matrices can not diagonalize at the same time. → Extended Higgs sector naturally violate lepton flavor !!
・ For quark sector, We assumed Model II Yukawa interaction in order to suppress FCNC.
・ In the basis of each mass eigenstate, we can reduce
We concentrate on tau associated processes respect to its mass. We introduce the LFV parameter κ.
For Model II like (MSSM like) situation (ε<< 1 ), the LFV parameter κ can be expressed as

4. The 2 Higgs doublet model (2HDM)
Higgs potential in the 2HDM
In general, are complex.
We assume that are real. Under this assumption,
can be replaced by these physical parameters,
We restrict these parameters under conditions of experimental bounds and theoretical consistencies.

5. Experimental bounds and theoretical consistencies
ρ- parameter
Radiative corrections for gauge boson 2 point function are strongly constrained from LEP precision data.
ｂ→ｓγ Ciuchini et.al.(98); Belle collablation(04)
B-decay data do not allow light-charged Higgs boson.
Vacuum stability Deshpande et.al.(78); Kanemura, Kasai, Okada (98); Nie, Sher (99)
Perturbative unitarity Lee, Quigg, Thacker(77); Kanemura, Kubota, Takasugi (93); Akeroyd, Naimi(00)
Impose tree level unitarity for the elastic scattering of gauge-bosons & Higgs bosos.
are s-wave amplitudes.
Experimental bounds
Theoretical consistencies

6. Rare tau decay data @ B-factories
Upper limit on LFV rare tau decays
Mode
Belle(90%CL)
Babar(90%CL)
τ-→ e- π0
1.9×10-7
　 → e- η
2.4×10-7
　 → e- η’
10×10-7
→μ- π0
4.1×10-7
　 →μ- η
1.5×10-7
　 →μ- η’
4.7×10-7
　 → e- e+ e-
3.5×10-7
2.0×10-7
　 → e-μ+μ-
3.3×10-7
　 →μ- e+ e-
2.7×10-7
　 →μ-μ+μ-
Mode
Belle(90%CL)
Babar(90%CL)
τ-→ e-π+π-
8.4×10-7
1.2×10-7
　 → e-π+ K-
5.7×10-7
3.2×10-7
　 → e- K+π-
5.6×10-7
1.7×10-7
→ e- K+ K-
3.0×10-7
1.4×10-7
→μ-π+π-
2.8×10-7
2.9×10-7
　 →μ-π+ K-
6.3×10-7
2.6×10-7
　 →μ- K+π-
15.5×10-7
→μ- K+ K-
11.7×10-7
2.5×10-7
　 → e-γ
3.9×10-7
　 →μ-γ
3.1×10-7
6.8×10-8

7. Categories of rare tau decay
These processes give independent information for LFV Yukawa coupling respect to intermediate Higgs bosons.
τ→ 3lepton Babu Colda(02)
τ→ lepton meson-pair Dedes Ellis Raidal(02)
τ→ lepton photon Brignole Rossi (04)
τ→ lepton meson Sher(05)
In the following, we concentrate on |κ32|, because treatment of |κ31| is the same.

8. Example : Constraint from τ→μη
Br(τ→μη) is calculated as,
Br(τ→μη) is constrained from data.
We define possible maximal value |κ32Max|2 from experimental upper limit,
Excluded from τ→μη
Again, we must be consider all results for LFV rare tau decays.
Allowed

9. LFV decay of the lightest Higgs boson at the Linear collider
reconstruct from decay products
Kanemura, Matsuda, Ota, Shindou, Takasugi, Tsumura (PLB599, 83)
control
ex. MSSM + right-handed neutrinos
tag
We can identify the signal without
We assume that is tuned depending on the lightest Higgs boson mass (Here we take 120 GeV) and also assume L=1ab-1.
General 2HDM can be more large events !!

10. Background evaluation
Serious BGs are τ-pair production from Higgs boson
If , we can not distinguish between signals and BGs.
We require reasonable kinematic cut
Precise determination is important !!
If we can determine within 3 GeV, then
# of events
Significance
can be tested at 3 sigma level.
General 2HDM can be more tested !!

11. “Higgs boson decay” vs “rare tau decay”
Constraint from LFV Higgs boson decay
Excluded from τ- decays
Further constrain from Higgs LC
τ-decay data can not give any stringent bounds on κ in the low tanβ region.
LFV Higgs boson decay further constrain the upper side of blue line at the LC.

12. Possible maximal value for Br( h →τμ)
Possible maximal value for branching ratio of LFV Higgs boson decay
We use the LFV parameter κ32max which is obtained from LFV Higgs boson decay.
The dark (light) shaded area indicates the excluded region by theoretical consistencies with ξ = 1 (1/2).
Again, we note that Br( h →τμ) can be tested up to O(10-3).
The region of Br( h →τμ) greater than O(10-3) further constrain LFV Yukawa coupling.

13. Summary
Search for LFV Higgs boson decays can be a useful to further constrain the LFV Yukawa coupling, where rare tau decay data can not reach.
Future work
・ Extension for quark sector ・ Parameter correspondence between 2HDM and some new physics models
Excluded from τ- decays
Further constrain from Higgs LC
Thank you very much for your listening !!

14. Relations between model parameters

15. Theoretical consistencies
Perturbative unitarity
We impose tree level unitarity for the elastic scattering of gauge-bosons & Higgs bosos.
are s-wave amplitudes.
Case for ２HDM modes had been taken to be account
Lee, Quigg, Thacker(77)
Kanemura, Kubota, Takasugi (93); Akeroyd, Naimi(00)

16. Possible maximal value for |κ32|2
Contour for
・ The dark (light) shaded area indicates the excluded region by theoretical consistencies with ξ = 1 (1/2).
・ This means that the constraint for the LFV Yukawa coupling from rare tau decay are weak for low tanβ region.