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 ¯ σ ( e + e ` → τ + τ ` ) = 0 . 89 nb B ) = 1 . 05 nb , ⇒ 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 � / 1 eV ) 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., PR D60 (1999)055008), · · · τ → µη : cf) Higgs mediated in MSSM (K. Babu and C. Kolda, PRL 89 (2002)241802), · · · τ Physics at Super B-Factory, 2005.04.21 – p.3/17
LFV: Current Experimental Status 2.0x10 -4 @CRYSTAL BALL τ � µγ Upper Limit 3.4x10 -5 /1.2x10 -4 @ARGUS τ � e γ τ � µη 6.2x10 -5 /1.1x10 -4 @DELPHI 10 −4 3.0x10 -6 /2.7x10 -6 @CLEO 4.2x10 -6 @CLEO 1.1x10 -6 @CLEO 3.1x10 -7 @Belle 9.6x10 -6 @CLEO 10 −6 SUSY SM/GUT with ν R 3.9x10 -7 @Belle 1.5x10 -7 @Belle(pre.) 6.8x10 -8 @BaBar(pre.) 10 − 8 SUSY SU(5) GUT w/o ν R 1990 2000 2010 Year τ Physics at Super B-Factory, 2005.04.21 – p.4/17
LFV: τ → µγ of Belle/BaBar ∆ E (GeV) 0.2 0 -0.2 -0.4 1.6 1.8 2 M inv (GeV/c 2 ) Belle Babar 86.7 fb − 1 232 fb − 1 Luminosity Signal Region ± 3 σ box ± 2 σ 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., PR D60 (1999)055008): � � � � � � � 4 � 2 � 1 TeV/c 2 � tan β Br ( τ → µγ ) ≃ 7 × 10 − 7 60 m SUSY 100 Upper Limit by BaBar’s Preliminary result: 80 Br ( τ → µγ ) < 6 . 8 × 10 − 8 Exculded Region by BaBar 60 @BaBar (hep-ex/0502032) @232fb -1 (Preliminary) tan β ⇒ Constraint on Expected@1ab -1 40 tan β – m SUSY ( tan β ∝ m 2 SUSY ) 20 Expected@5ab -1 0 0 0.5 1 1.5 2 2.5 m SUSY (TeV/c 2 ) τ Physics at Super B-Factory, 2005.04.21 – p.6/17
LFV: τ → µη � � � � Higgs mediated in MSSM � � (Babu & Kolda PRL 89 (2002)241802): � � � 4 � 6 � 100 GeV/c 2 � tan β Br ( τ → µη ) = 8 . 4 × 10 − 7 60 m A 100 CDF excluded Upper Limit by Belle’s Excluded by Belle@154 fb -1 80 (Preliminary) Preliminary result: Br ( τ → µη ) < 1 . 5 × 10 − 7 60 tan β @Belle (hep-ex/0503041) b -1 a 1 ⇒ Constraint on tan β – m A @ d e 40 t c e p x E Expected @10ab -1 ( tan β ∝ m 2 / 3 A ) 20 We’ve obtained more strin- gent limit than CDF . LEP excluded 0 100 150 200 250 m A (GeV/c 2 ) 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 → K S πν τ Physics at Super B-Factory, 2005.04.21 – p.8/17
τ ’s EDM Non-vainshing τ ’s EDM, d τ T Violation ( ⇔ CPV under CPT) ⇒ d τ should be proportional to the spin S : d τ ∝ S Under T transformation: d τ → d τ , S → − S ⇒ If T is retained, d τ = 0 . Theoretical predictions SM (w/ massless ν ): | d τ | � 10 − 34 e cm | d τ | � 10 − 23 e cm ( ∝ m 3 ℓ /m 2 Mult-Higgs: φ ) | d τ | � 10 − 19 e cm ( ∝ m 2 Leptoquarks: t m τ ) � ���� ����� ����� ������ �� � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � τ Physics at Super B-Factory, 2005.04.21 – p.9/17
τ ’s EDM: Experimental Status Upper Limit (e cm) 10 −15 Re(EDM) OPAL Im(EDM) Grifols et al. ARGUS L3 Delaguila et al. 10 −16 10 −17 -2.2 to 4.5 x10 -17 @Belle -2.5 to 0.8 x10 -17 @Belle 10 −18 Expected@1000 fb -1 Leptoquark 2000 2010 1990 Year τ Physics at Super B-Factory, 2005.04.21 – p.10/17
DCPV in τ → K S πν According to the similar argument as the DCPV of D + → K S π + ν in the Bigi and Sanda’s famous text book, DCPV in τ − → K S π − ν A CP = Γ( τ + → K S π + ν ) − Γ( τ − → K S π − ν ) Γ( τ + → K S π + ν ) + Γ( τ − → K S π − ν ) ≃ 3 × 10 − 3 is expected due to the well-known CP impurity in K S : K S = (1 − ǫ ) K 0 − (1 + ǫ ) K 0 √ UL(Sensitivity) CLEO 2 10 −1 ⇒ This should be observed! 10 −2 Only CLEO searched for CP V in this mode 10 −3 (PRL 88 (2002) 111803, PR D64 (2001) 092005): − 0 . 172 < Im (Λ) < 0 . 067 10 −2 10 −1 1 10 Luminosity(ab -1 ) for the coupling constant Λ defined as A ( τ − → Kπ − ν ) ∼ ¯ νγ µ (1 − γ 5 ) τf V Q µ + Λ¯ ν (1 + γ 5 ) τf S M 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 → K S πν 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 → K S πν should be observed. 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: / ) ψ − i L = L SM + L EDM = ¯ ¯ ψσ µν γ 5 ψd τ F µν ψ ( i∂ / − eQA 2 ⇒ Deviation of the cross section, i.e. amplitude M , from the SM: M 2 e + e − → τ + τ − = M 2 SM + Re ( d τ ) M 2 Re + Im ( d τ ) M 2 Im + O ( d 2 τ ) where Re ∼ ( S + × S − ) · ˆ M 2 k , ( S + × S − ) · ˆ p , Im ∼ ( S + − S − ) · ˆ M 2 k , ( S + − S − ) · ˆ p S ± : τ ± spin vector, p : e + direction, k : τ + direction. ˆ ˆ Optimal Observable for the τ ’s EDM: O Re = M 2 Re / M 2 O Im = M 2 Im / M 2 SM , ⇒ Maximize S/N SM We can extract the τ ’s EDM from O by using the following Eq.: �O Re � = a Re · Re ( d τ ) + b Re �O Im � = a Im · Im ( d τ ) + b Im τ Physics at Super B-Factory, 2005.04.21 – p.14/17
Evaluation of A CP ( τ + → K S π + ν ) In the SM one has Γ( τ + → K 0 π + ) = Γ( τ − → K 0 π − ) . And we know that K S is CP impurity as the experimental result: 1 1 − ǫ 1 + ǫ � � √ 1 + ǫ 2 K 0 − ≡ q K K 0 + p K K 0 . K S = √ √ 1 + ǫ 2 K 0 2 We here consider the amplitude of this decay mode: A ( τ + → K S π + ) = A ( τ + → K 0 π + ) � K S | K 0 � + A ( τ + → K 0 π + ) � K S | K 0 � We can neglect A ( τ + → K 0 π + ) /A ( τ + → K 0 π + ) and obtain Γ( τ + → K S π + ) ≃ Γ( τ + → K 0 π + ) | q K | 2 and similarly, Γ( τ − → K S π − ) ≃ Γ( τ + → K 0 π + ) | p K | 2 . Finally, A CP ≃ | q K | 2 − | p K | 2 | q K | 2 + | p K | 2 ≃ 2 Re ( ǫ ) ≃ 10 − 3 , we here used measured value of ǫ in K L → ππ . τ Physics at Super B-Factory, 2005.04.21 – p.15/17
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