Chuan-Hung Chen
Department of Physics,
National Cheng-Kung U.,
Tainan, Taiwan
seminar@nthu.11.23.06.tw
Introduction & Motivation
Higgs-mediated LFV
Implications of LFV in tau decays
Speculation of Higgs-mediated effects
Introduction & Motivation
What we can learn from B factories:
z CP violations: time-dependence CP asymmetry & direct CP violation
ICHEP2006: φ1 with b → s Penguins
z Test QCD theories: PQCD, QCDF, final state interactions etc.
z Determine the parameters of CKM matrix elements, or fB
Vcb ⇒ B → X c l ν l
Vub ⇒ B → X u l ν l
Vtd / Vts ⇒ Bd − Bd / Bs − Bs
Vub f B ⇒ B → τν τ
z Probe flavor structures:
1. B → K *γ , B → K (*) l + l − 2. B → l + l − , l + l −γ
Future tau (τ) physics
B-factory:
1 ×109 τ
Super-B: 100 ×109 τ
τ
CLEO-c:
10 ×106 τ
BES-III: 100 ×106
• results up to 2005
mode
x10-7
mode
x10-7
τJμγ
BaBar
0.68
τJlll
τJeγ
Belle
3.1
τ−Jμ+e−e− BaBar
1.1
τJμη
Belle
1.5
τ−Jμ−e−e+ Belle
1.9
τJeη
Belle
2.4
τJμη'
Belle
10
τJeη'
Belle
4.7
τJμπ0
Belle
4.1
τJeπ0
Belle
1.9
τJμKs
CLEO
9.5
τJeKs
CLEO
9.1
τJlhh
1.1-3.5
BaBar
0.7-4.8
τ−Jμ+π−π− BaBar
0.7
τJlV0
CLEO
20-75
CLEO
20
τ−JΛπ−
Belle
1.4
τ−JΛπ−
Belle
0.72
τJeρ0
mode
x10-7
mode
x10-7
τJμγ
Belle
0.45
τJlll
τJeγ
BaBar
1.1
τ−Jμ+e−e− BaBar
1.1
τJμη
Belle
0.65
τ−Jμ−e−e+ Belle
1.9
τJeη
Belle
0.92
τJlhh
τJμη'
Belle
τJeη'
1.1-3.5
BaBar
0.7-4.8
1.3
τ−Jμ+π−π− BaBar
0.7
Belle
1.6
τJlV0
Belle
2.0-7.7
τJμπ0
Belle
1.2
τJμρ0
Belle
2.0
τJeπ0
Belle
0.80
τ−JΛπ−
BaBar
0.59
τJμKs
Belle
0.52
τ−JΛπ−
BaBar
0.58
τJeKs
Belle
0.60
τ−JΛΚ−
BaBar
0.72
τ−JΛΚ−
BaBar
1.5
Lepton flavor violation (LFV)
¾ quark flavor changing via charged current; charged weak current is written as
⎛d ⎞
1− γ 5
⎜ ⎟
PL =
J μ = ( u , c , t ) γ μ PL ⎜ s ⎟ = U iγ μ PL D j
2
⎜b⎟
⎝ ⎠
In terms of physical eigenstates
J μ = u pγ μ PL V
V F dp
E5555
= VCKM
UL
DL†
u p = V U L U w , d p = V DL Dw
By Wolfenstein parametrization
VCKM
⎛
λ2
1−
λ
⎜
2
⎜
⎜
λ2
1−
=⎜
−λ
2
⎜ 3
2
⎜ Aλ (1 − ρ − iη ) − Aλ
⎜
⎝
A ≈ 0.82, λ ≈ 0.224
⎞
Aλ 3 ( ρ − iη ) ⎟
⎟
⎟
2
Aλ
⎟
⎟
1
⎟
⎟
⎠
¾ In the standard model (SM), the flavor changing neutral currents (FCNCs)
arise from loop
¾ Rare decays induced from loop will be sensitive to new physics.
¾ In the SM, since neutrinos are massless, there are no flavor violations in
lepton sector
νL
J μ = νγ μ PL U
E5F U l p = νγ μ PL l
l
=1
l †L
p
¾ According to observed neutrino oscillations, we know that
neutrinos have masses so that
Maki-Nakagawa-Suzuki-Pontecorvo (MNSP)
Higgs-mediated LFV
z Nonzero neutrino masses are definite.
z It is found that seesaw mechanism, by introducing singlet right-handed
Majorana neutrinos, is one of natural ways to solve the tiny neutrino
masses which are less than eV.
z In non-SUSY models, the effects of LFV are suppressed by
1/MR which is around GUTs scale 1015 GeV.
z However, in models with SUSY, due to the right-handed Majorana
introduced, the flavor conservation in the slepton sector at unified
Borzumati,
scale will be violated at the MR scale via renormalization. Masiero, PRL57,961;
Hall, Rattazzi, Sarid,
PRD50,7048;Babu, Kolda,
PRL89,241802
Babu & Kolda’s mechanism for lepton flavor violation
nonholomophic terms
z At large tanβ ~ mt/mb, or cosβ << 1, the Higgs-mediated LFV will be
enhanced
Implications of LFV in τ decays
τ→ μ (γ, 3μ, φ, KK) induced by slepton mixings with large tanβ
Due to slepton mixings
Dipole operators
Rμ ~ Re ~ O(10−3 )
Γ (τ → l φ )
Γ (τ → l γ )
~
Γ (τ → l KK )
Γ (τ → l γ )
~ O (10−3 )
LFV with Higgs-mediated
nonholomophic terms
Y: diagonalized Yukawa matrix of leptons
¾ Due to nonholomophic effects, M l0 is not diagonal matrix
¾ Since L2 are loop effects, they are much less than 1,
the LFV can be regarded as a leading expansion of L2Iij
¾ Employ the physical mass eigenstates of the Higgses
⎛ H d+ ⎞
Hd = ⎜ 0 ⎟ ,
⎝ Hd ⎠
⎛ H u0* ⎞
Hu = ⎜
−⎟
H
−
u
⎝
⎠
¾ The interactions for the LFV via the Higgs-mediated mechanism
are expressed by
τ→ μ γ
+ −
(')
¾ Since the LFVs in τ → l γ and τ → l X ( X = l l ,η , f 0 (980), KK )
decay are driving by the same mechanism, to simplify the discussions,
we take M1~M2~m0~μ~ ml%
¾ MU ~ 1019 GeV , MR ~ 1014 GeV
¾ tanβ=60
¾ BRexp < (0.45, 0.68) × 10−7
l
τ→ l (η ,η ′ )
τ
A
s
η, η’
s
• φ=39.30
• fs=0.17 GeV
• mss=0.69 GeV
• BRexp < 0.65× 10−7
l
τ→ l ( f 0 (980), σ (600) )
s
h, H
τ
f 0 (980), σ (600)
s
• cs: cos(α-β)sin α ; sc=sin(α-β)cosα
• decoupling limit: α→ β−π/2
• θ = 300,
• ms = 0.15 GeV,
s
%s
• f%
σ ~ f f = 0.33GeV
0
τ→l μ + μ −
l
τ
h, H
τ
μ+
• decoupling limit: α→ β−π/2
l
μ−
μ−
A
μ+
l
τ→ l K + K −
τ
K
h, H
K
Cheng,Chua, Soni, PRD72,094003
• v=2.87 GeV, κ=-10.4 GeV4
s
s
• f%f0 (1530) ~ f%f0 (980) = 0.33 GeV
• g f0 (980)→KK = 1.50, g f0 (1530)→KK = 3.18 GeV
Speculation of Higgs-mediated effects
z In terms of squark mixings,
Babu,Kolda,
PRL84,228(00)
z It is interesting to examine the effects on B decays
¾ Charged Higgs on B→τν
¾ Higgs-mediated on Bq − Bq
¾ Higgs-mediated on Bq → l + l − , B → K (*) l + l −
¾ Higgs-mediated on B → K (η ′,η )