Tau Physics at the Super B-Factory N. Sato (Nagoya Univ.) - - PowerPoint PPT Presentation

Tau Physics at the Super B-Factory

• N. Sato (Nagoya Univ.)

2005.04.21 Super B-Factory Workshop in Hawaii Introduction Lepton Flavor Violation CP Violation Summary

τ Physics at Super B-Factory, 2005.04.21 – p.1/17

Introduction

A fun of physics in τ lepton The heviest lepton known to date

⇒ Naively expected to be sensitive to the New Physics

The only lepton heavy enough to decay hadronically

⇒ Include a rich physical contents

Why τ in B-Factory? Production cross section @ √s = 10.58 GeV:

σ(e+e` → B ¯ B) = 1.05nb, σ(e+e` → τ +τ `) = 0.89nb ⇒ B-Factory = τ-Factory

Plan of this talk Two major topics to search for the phyiscs beyond the SM at the current and Super B-Factory: Search for the Lepton Flavor Violation in τ decays Search for the CP Violation in τ lepton

τ Physics at Super B-Factory, 2005.04.21 – p.2/17

Lepton Flavor Violation in τ Lepton

Lepton Flavor Violation (LFV) Forbidden in the SM (w/ massless ν) Charged lepton sector: Has not been observed Neutrino sector: Observation of the neutrino oscillation LFV in the SM with ν-oscillation

ν-oscillation induces the LFV in the charged lepton sector.

However, it is suppressed drastically:

Br(LFV τ decays) 10`40(m/1eV)4

LFV in Physics beyond the Standard Model: SUSY, GUT, · · ·

⇒ Predictions can be observed in the (Super) B-Factory.

Two promising modes expected in some SUSY models:

τ → µγ : cf) MSSM with Seesaw

(J. Hisano et al., PRD60(1999)055008), · · ·

τ → µη : cf) Higgs mediated in MSSM

(K. Babu and C. Kolda, PRL89(2002)241802), · · ·

τ Physics at Super B-Factory, 2005.04.21 – p.3/17

LFV: Current Experimental Status

3.0x10-6/2.7x10-6@CLEO 4.2x10-6@CLEO

τeγ τµγ

6.2x10-5/1.1x10-4@DELPHI 2.0x10-4@CRYSTAL BALL 1.1x10-6@CLEO 3.4x10-5/1.2x10-4@ARGUS

SUSY SM/GUT with νR SUSY SU(5) GUT w/o νR Upper Limit Year 1990 2000 2010 10−8 10−6 10−4 3.1x10-7 @Belle 3.9x10-7 @Belle 6.8x10-8 @BaBar(pre.)

τµη

9.6x10-6@CLEO

1.5x10-7 @Belle(pre.)

τ Physics at Super B-Factory, 2005.04.21 – p.4/17

LFV: τ → µγ of Belle/BaBar

• 0.4
• 0.2

0.2 1.6 1.8 2

Minv (GeV/c2) ∆E (GeV)

Belle Babar Luminosity 86.7 fb−1 232 fb−1 Signal Region

±3σ box ± 2σ ellipse

Efficiency 10.9% 7.42% Expected BG 20.2 ± 2.1 6.2 ± 0.5 Observed ev 19 4 UL of Br (×10−7) 3.1 0.68

τ Physics at Super B-Factory, 2005.04.21 – p.5/17

LFV: τ → µγ

• MSSM with Seesaw

(J. Hisano et al., PRD60(1999)055008):

Br(τ → µγ) ≃ 7 × 10−7 tan β 60 2 1TeV/c2 mSUSY 4

20 40 60 80 100 0.5 1 1.5 2 2.5

mSUSY (TeV/c2) tanβ Exculded Region by BaBar @232fb-1(Preliminary)

Expected@1ab-1 Expected@5ab-1

Upper Limit by BaBar’s Preliminary result:

Br(τ → µγ) < 6.8 × 10−8

@BaBar (hep-ex/0502032)

⇒ Constraint on tan β–mSUSY

(tan β ∝ m2

SUSY )

τ Physics at Super B-Factory, 2005.04.21 – p.6/17

LFV: τ → µη

• Higgs mediated in MSSM

(Babu & Kolda PRL89(2002)241802): Br(τ → µη) = 8.4 × 10−7 tan β 60 6 100GeV/c2 mA 4

20 40 60 80 100 100 150 200 250

mA (GeV/c2)

tanβ

Excluded by Belle@154 fb-1 (Preliminary)

CDF excluded LEP excluded

E x p e c t e d @ 1 a b-1 Expected @10ab-1 Upper Limit by Belle’s Preliminary result: Br(τ → µη) < 1.5 × 10−7 @Belle (hep-ex/0503041) ⇒ Constraint on tan β–mA (tan β ∝ m2/3

A )

We’ve obtained more strin- gent limit than CDF .

τ Physics at Super B-Factory, 2005.04.21 – p.7/17

CP Violation in τ Lepton

Thanks to Prof. I. Bigi, here is a summary of the CPV in τ Physics. CPV is necessary for baryogenesis. However, CKM dynamics is irrelvant for it. One attracitve alternative: Leptogenesis driving baryogenesis cf) Previous talk by H. Paes

⇒ Search for CPV in lepton sector

CPV in the lepton sector Has not been observed yet, in contrast with the quark sector. Search for CPV in the neutrino sector A very tough challenge. Search for EDM of charged leptons In some model, τ is most sensitive due to its heviest mass. Search for CPV in tau decays One of the most promising mode: τ → Kπν (J. K¨ uhn and E. Mirkes, PL B398(1997)407) Bigi pointed out: O(10`3) is expected in τ → KSπν

τ Physics at Super B-Factory, 2005.04.21 – p.8/17

τ’s EDM

Non-vainshing τ’s EDM, dτ

⇒ T Violation (⇔ CPV under CPT) dτ should be proportional to the spin S: dτ ∝ S

Under T transformation: dτ → dτ,

S → −S ⇒ If T is retained, dτ = 0.

Theoretical predictions SM (w/ massless ν): |dτ| 10−34e cm Mult-Higgs:

|dτ| 10−23e cm (∝ m3

ℓ/m2 φ)

Leptoquarks:

|dτ| 10−19e cm (∝ m2

t mτ)

• τ Physics at Super B-Factory, 2005.04.21 – p.9/17

τ’s EDM: Experimental Status

10−15 10−16 10−17 10−18 Upper Limit (e cm) 1990 2000 2010 Year Re(EDM) Im(EDM)

Grifols et al. Delaguila et al. OPAL L3 ARGUS

• 2.5 to 0.8 x10-17@Belle
• 2.2 to 4.5 x10-17 @Belle

Leptoquark Expected@1000 fb-1

τ Physics at Super B-Factory, 2005.04.21 – p.10/17

DCPV in τ → KSπν

According to the similar argument as the DCPV of D+ → KSπ+ν in the Bigi and Sanda’s famous text book, DCPV in τ − → KSπ−ν

ACP = Γ(τ + → KSπ+ν) − Γ(τ − → KSπ−ν) Γ(τ + → KSπ+ν) + Γ(τ − → KSπ−ν) ≃ 3 × 10−3

is expected due to the well-known CP impurity in KS:

KS = (1 − ǫ)K0 − (1 + ǫ)K0 √ 2 ⇒ This should be observed!

Only CLEO searched for CP V in this mode (PRL 88 (2002) 111803, PR D64 (2001) 092005):

−0.172 < Im(Λ) < 0.067

for the coupling constant Λ defined as

A(τ − → Kπ−ν) ∼ ¯ νγµ(1 − γ5)τfV Qµ + Λ¯ ν(1 + γ5)τfSM

10−1 10−2 10−3 UL(Sensitivity)

Luminosity(ab-1)

10−1 1

CLEO

10 10−2

We can reach the sensitivity of 10−3 order at a few ab−1

⇒ CPV in lepton sector can be found at the Super B-Factory!

τ Physics at Super B-Factory, 2005.04.21 – p.11/17

Summary

Current status of two major topics to search for the physics beyond the Standard Model in τ Lepton are reviewed: Lepton Flavor Viloation: τ → µγ,

τ → µη

CP Violation: τ’s EDM,

τ → KSπν

We discussed the expected sensitivities in these physics at the Super B-Factory. LFV We have already obtained the constraints on parameter spaces of the models of New Physics. More stringent limits can be obtained, or we can observe the New Physics at the Super B-Factory. CPV We’ve not observed any CPV in the lepton sector including τ. We can reach the sensitivity to the prediction of the New Physics at the Super B-Factory. Especially, DCPV in τ → KSπν should be

• bserved.

One of the important advantage of the B-Factory (e+e− collider) to the hadron collider: We can look for τ polarization depencent CP asymmetry w/o needing polarized beam!

τ Physics at Super B-Factory, 2005.04.21 – p.12/17

Backup

τ Physics at Super B-Factory, 2005.04.21 – p.13/17

τ’s EDM: How to measure?

Effective Lagrangian with non-zero EDM term: L = LSM + LEDM = ¯ ψ(i∂ / − eQA /)ψ− i 2 ¯ ψσµνγ5ψdτFµν ⇒ Deviation of the cross section, i.e. amplitude M, from the SM: M2

e+e−→τ +τ − = M2

SM + Re(dτ)M2 Re + Im(dτ)M2 Im + O(d2

τ)

where M2

Re ∼ (S+ × S−) · ˆ

k, (S+ × S−) · ˆ p, M2

Im ∼ (S+ − S−) · ˆ

k, (S+ − S−) · ˆ p S± : τ ± spin vector, ˆ p : e+ direction, ˆ k : τ + direction. Optimal Observable for the τ’s EDM: ORe = M2

Re/M2 SM,

OIm = M2

Im/M2 SM

⇒ Maximize S/N We can extract the τ’s EDM from O by using the following Eq.: ORe = aRe · Re(dτ) + bRe OIm = aIm · Im(dτ) + bIm

τ Physics at Super B-Factory, 2005.04.21 – p.14/17

Evaluation of ACP(τ + → KSπ+ν)

In the SM one has Γ(τ + → K0π+) = Γ(τ − → K0π−). And we know that KS is CP impurity as the experimental result: KS = 1 √ 2

• 1 − ǫ

√1 + ǫ2 K0 − 1 + ǫ √1 + ǫ2 K0

• ≡ qKK0 + pKK0.

We here consider the amplitude of this decay mode: A(τ + → KSπ+) = A(τ + → K0π+)KS|K

0 + A(τ + → K0π+)KS|K0

We can neglect A(τ + → K0π+)/A(τ + → K0π+) and obtain Γ(τ + → KSπ+) ≃ Γ(τ + → K0π+)|qK|2 and similarly, Γ(τ − → KSπ−) ≃ Γ(τ + → K0π+)|pK|2. Finally, ACP ≃ |qK|2 − |pK|2 |qK|2 + |pK|2 ≃ 2Re(ǫ) ≃ 10−3, we here used measured value of ǫ in KL → ππ.

τ Physics at Super B-Factory, 2005.04.21 – p.15/17

LFV: τ → µη vs τ → 3µ

• Babu and Kolda pointed out (PRL89(2002)241802)):

Br(τ → µη) : Br(τ → 3µ) : Br(τ → 3µ) = 8 : 1.5 : 1 for Higgs mediated process. Comparing τ → µη with τ → 3µη: Color factor: 3 Phase space: 2-body and 3-body decay Mass: ms > m—

τ Physics at Super B-Factory, 2005.04.21 – p.16/17

τ LFV: Other Modes

Red: Preliminary Blue: Published : CLEO Result △: BaBar Result

• : Belle Result

1 10 eγ µγ e-e-e- e-µ+µ- e+µ-µ- µ-e+e- µ+e-e- µ-µ

+µ-

eKs µKs eπ0 µπ0 eη µη eη, µη, pγ pπ0 Λπ Λπ

U.L of Br (x 10-7)

τ Physics at Super B-Factory, 2005.04.21 – p.17/17