Overview of Tau decays Emilie Passemar Indiana University/Jefferson Laboratory « New Vistas in Low-Energy Precision Physics » Mainz, April 6, 2016 Emilie Passemar
Outline : 1. Introduc+on and Mo+va+on 2. Hadronic τ-decays 3. LFV tau decays 4. Conclusion and outlook NB: several topics not covered: Lepton Universality, CP viola+on in tau decays, g-2 EDM, etc… see Alberto Lusiani’s talk
1. Introduction and Motivation Emilie Passemar
The τ lepton PDG’14 • τ lepton discovered in 1976 by M. Perl et al. (SLAC-LBL group) - Mass: - Life+me: m τ = τ = ⋅ − 1.77682(16) GeV 13 2.096(10) 10 s τ • Enormous progress in tau physics since then (CLEO, LEP, Babar, Belle, BES, VEPP-2M, neutrino experiments,...) – Early years: consolidate τ as a standard lepton no invisible decays and standard couplings – Better data: determination of fundamental SM parameters and QCD studies Number of τ pairs Experiment LEP ~3x10 5 CLEO ~1x10 7 BaBar ~5x10 8 Belle ~9x10 8 4
The τ lepton PDG’14 • τ lepton discovered in 1976 by M. Perl et al. (SLAC-LBL group) - Mass: - Life+me: m τ = τ = ⋅ − 1.77682(16) GeV 13 2.096(10) 10 s τ • Enormous progress in tau physics since then (CLEO, LEP, Babar, Belle, BES, VEPP-2M, neutrino experiments,...) – More recently: huge number of tau at the B factories: BaBar, Belle: • Tool to search for NP: rare decays, final states in hadron colliders • Precision physics: α S , |V us | etc Number of τ pairs Experiment LEP ~3x10 5 CLEO ~1x10 7 BaBar ~5x10 8 Belle ~9x10 8 5
2. Hadronic τ -decays Emilie Passemar
θ = = + + d V d V s ud us 2.1 Introduction • Tau, the only lepton heavy enough to decay into hadrons � � � � • use perturba(ve tools: OPE… m τ ~ 1.77GeV > Λ QCD � � � � ( ) ( ) , V us , m s Inclusive τ decays : ( ) • τ τ → ν ν fund. SM parameters α S m τ ud us , τ ( ) Γ τ − → ν τ + hadrons S = 0 • We consider ( ) Γ τ − → ν τ + hadrons S ≠ 0 • ALEPH and OPAL at LEP measured with precision not only the total BRs but also a the energy distribu+on of the hadronic system huge QCD ac(vity ! ( ) Γ τ − → ν τ + hadrons • Observable studied: R τ ≡ ( ) Γ τ − → ν τ e − ν e 7 Emilie Passemar
θ = = + + d V d V s ud us 2.2 Theory ( ) Γ τ − → ν τ + hadrons R τ ≡ ≈ N C • parton model predic+on ( ) Γ τ − → ν τ e − ν e QCD switch 2 N C + V us 2 N C NS + R τ S ≈ V ud R τ = R τ • 2 V us S 2 = R τ V us • NS R τ V ud ( α S =0) 8 Emilie Passemar
θ = = + + d V d V s ud us 2.2 Theory ( ) Γ τ − → ν τ + hadrons R τ ≡ ≈ N C • parton model predic+on ( ) Γ τ − → ν τ e − ν e QCD switch 2 N C + V us 2 N C NS + R τ S ≈ V ud R τ = R τ • − − − − 1 B B µ = = e = = ± Experimentally: • R 3.6291 0.0086 τ B e ( α S ≠ 0) 9 Emilie Passemar
θ = = + + d V d V s ud us 2.2 Theory ( ) Γ τ − → ν τ + hadrons R τ ≡ ≈ N C • parton model predic+on ( ) Γ τ − → ν τ e − ν e QCD switch 2 N C + V us 2 N C NS + R τ S ≈ V ud R τ = R τ • − − − − 1 B B µ = = e = = ± Experimentally: • R 3.6291 0.0086 τ B e ( ) ( α S ≠ 0) 2 2 • Due to QCD correc(ons : = = + + + Ο α R V N V N τ ud C us C S 10 Emilie Passemar
θ = = + + d V d V s ud us 2.3 Theory • From the measurement of the spectral func+ons, extrac+on of α S , |V us | QCD switch ( ) Γ τ − → ν τ + hadrons R τ ≡ ≈ N C • naïve QCD predic+on ( ) Γ τ − → ν τ e − ν e • Extrac+on of the strong coupling constant : 2 N C + O α S NS = V ud ( ) α R τ S calculated ( α S ≠ 0) measured 2 V us S 2 = R τ ( ) • Determina+on of V us : NS + O α S R τ V ud • Aim: compute the QCD correc+ons with the best accuracy 11 Emilie Passemar
2.4 Calculation of the QCD corrections Braaten, Narison, Pich’92 • Calcula+on of R τ : ud,V/A ( s ) = 1 Im Π (1) 2 π v 1 /a 1 ( s ) , ¯ 2 2 ⎡ ⎡ ( ) ( ( ) ( ⎤ ⎤ m ⎛ ⎛ ⎞ ⎞ ⎛ ⎞ τ ds s s ) ) ∫ = π π − + Π 1 + ε ε + Π 0 + ε 2 R m ( ) 12 S 1 ⎢ ⎢ 1 2 Im s i Im s i ⎥ ⎥ ⎜ ⎜ ⎟ ⎟ ⎜ ⎟ τ τ τ τ EW 2 2 2 m m m ⎢ ⎢ ⎥ ⎥ ⎝ ⎝ ⎠ ⎠ ⎝ ⎠ ⎣ ⎣ ⎦ ⎦ τ τ τ τ τ 0 12 Emilie Passemar
2.4 Calculation of the QCD corrections Braaten, Narison, Pich’92 • Calcula+on of R τ : 2 2 ⎡ ⎡ ( ) ( ( ) ( ⎤ ⎤ m ⎛ ⎛ ⎞ ⎞ ⎛ ⎞ τ ds s s ) ) ∫ = π π − + Π 1 + ε ε + Π 0 + ε 2 R m ( ) 12 S 1 ⎢ ⎢ 1 2 Im s i Im s i ⎥ ⎥ ⎜ ⎜ ⎟ ⎟ ⎜ ⎟ τ τ τ τ EW 2 2 2 m m m ⎢ ⎢ ⎥ ⎥ ⎝ ⎝ ⎠ ⎠ ⎝ ⎠ ⎣ ⎣ ⎦ ⎦ τ τ τ τ τ 0 Perturba(ve • We are in the non-perturba(ve region: we do not know how to compute! • Trick: use the analy+cal proper+es of Π! Non-Perturba(ve 13 Emilie Passemar
2.4 Calculation of the QCD corrections • Calcula+on of R τ : 2 2 ⎡ ⎡ ( ) ( ( ) ( ⎤ ⎤ m ⎛ ⎛ ⎞ ⎞ ⎛ ⎞ τ ds s s ) ) ∫ = π π − + Π 1 + ε ε + Π 0 + ε 2 R m ( ) 12 S 1 ⎢ ⎢ 1 2 Im s i Im s i ⎥ ⎥ Braaten, Narison, Pich’92 ⎜ ⎜ ⎟ ⎟ ⎜ ⎟ τ τ τ τ EW 2 2 2 m m m ⎢ ⎢ ⎥ ⎥ ⎝ ⎝ ⎠ ⎠ ⎝ ⎠ ⎣ ⎣ ⎦ ⎦ τ τ τ τ τ 0 • Analy+city: Π is analy+c in the en+re complex plane except for s real posi+ve Cauchy Theorem 2 ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ds 2 1 − s 1 + 2 s ( ) + Π ( ) ( ) s ( ) s ∫ 1 0 2 ) = 6 i π S EW ! ⎟ Π R τ ( m τ ⎢ ⎥ ⎜ ⎟ ⎜ 2 2 m τ ⎝ m τ ⎠ ⎝ m τ ⎠ 2 s = m τ ⎢ ⎥ ⎣ ⎦ • We are now at sufficient energy to use OPE: 1 ( ) ( ) ∑ ∑ ∑ C ∑ J Π J = µ µ µ µ ( ) s ( , ) s O ( ) − D D 2 ( s ) = = = = D 0,2,4... dim O D μ : separa+on scale between short and long distances Wilson coefficients Operators 14 Emilie Passemar
2.4 Calculation of the QCD corrections Braaten, Narison, Pich’92 • Calcula+on of R τ : ( ) ( ) 2 = = + + δ δ + δ δ R m N S 1 τ τ τ τ C EW P NP = • Electroweak correc+ons: S 1.0201(3) Marciano &Sirlin’88, Braaten & Li’90, Erler’04 EW 15 Emilie Passemar
2.4 Calculation of the QCD corrections Braaten, Narison, Pich’92 • Calcula+on of R τ : ( ) ( ) 2 = = + + δ δ + δ δ R m N S 1 τ τ τ τ C EW P NP = • Electroweak correc+ons: S 1.0201(3) Marciano &Sirlin’88, Braaten & Li’90, Erler’04 EW α s m ( ) δ = = + + + + + ≈ • Perturba+ve part (D=0): 2 3 4 a 5.20 a 26 a 127 a ... 20% = τ a τ τ τ τ τ τ τ P π Baikov, Chetyrkin, Kühn’08 16 Emilie Passemar
2.4 Calculation of the QCD corrections Braaten, Narison, Pich’92 • Calcula+on of R τ : ( ) ( ) 2 = = + + δ δ + δ δ R m N S 1 τ τ τ τ C EW P NP = • Electroweak correc+ons: S 1.0201(3) Marciano &Sirlin’88, Braaten & Li’90, Erler’04 EW α s m ( ) δ = = + + + + + ≈ • Perturba+ve part (D=0): 2 3 4 a 5.20 a 26 a 127 a ... 20% = τ a τ τ τ τ τ τ τ P π Baikov, Chetyrkin, Kühn’08 ( ) ( ) • D=2: quark mass correc+ons, neglected for but not for ∝ NS ∝ R m m , S R m τ u d τ s 17 Emilie Passemar
2.4 Calculation of the QCD corrections Braaten, Narison, Pich’92 • Calcula+on of R τ : ( ) ( ) 2 = = + + δ δ + δ δ R m N S 1 τ τ τ τ C EW P NP = • Electroweak correc+ons: S 1.0201(3) Marciano &Sirlin’88, Braaten & Li’90, Erler’04 EW α s m ( ) δ = = + + + + + ≈ • Perturba+ve part (D=0): 2 3 4 a 5.20 a 26 a 127 a ... 20% = τ a τ τ τ τ τ τ τ P π Baikov, Chetyrkin, Kühn’08 ( ) ( ) • D=2: quark mass correc+ons, neglected for but not for ∝ NS ∝ R m m , S R m τ u d τ s • D ≥ 4: Non perturba+ve part, not known, fiOed from the data Use of weighted distribu+ons 18 Emilie Passemar
2.4 Calculation of the QCD corrections Le Diberder & Pich’92 • D ≥ 4: Non perturba+ve part, not known, fiOed from the data Use of weighted distribu+ons Exploit shape of the spectral func+ons to obtain addi+onal experimental informa+on Zhang’Tau14 R τ ≡ R 00 τ ( ) ∝ S R m τ s Emilie Passemar 19
2.4 Calculation of the QCD corrections Braaten, Narison, Pich’92 • Calcula+on of R τ : ( ) ( ) 2 = = + + δ δ + δ δ R m N S 1 τ τ τ τ C EW P NP • Electroweak correc+ons: = S 1.0201(3) EW δ P ≈ 20% • Perturba+ve part (D=0): • D=2: quark mass correc+ons, neglected • D ≥ 4: Non perturba+ve part, not known, fiOed from the data Use of weighted distribu+ons δ NP = − 0.0064 ± 0.0013 Davier et al’14 ( ) Small unknown NP part very precise extrac+on of α S ! • δ δ δ δ : 3% NP P Emilie Passemar 20
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