Review of Tau physics
Emilie Passemar Indiana University/Jefferson Laboratory
Searching for Physics Beyond the Standard Model Using Charged Leptons COFI Workshop, Puerto Rico, May 21, 2018
Emilie Passemar Outline :
1. Tau lepton as a laboratory to explore the Standard Model and possible extensions
2. Lepton Flavour Violation
3. CP violation in tau decays
4. Other interesting topics in tau physics: 1. Lepton Universality
2. Extraction of Vus from hadronic Tau decays and test of the CKM unitarity
5. Conclusion and outlook
Emilie Passemar 1. Introduction and Motivation
Emilie Passemar 1.1 Quest for New Physics
• New era in particle physics : (unexpected) success of the Standard Model: a successful theory of G. G.Isidori Isidori – Kaon– Kaon Physics: Physics: the the next next step step Kaon Kaon 2016, 2016, Birmingham, Birmingham, Sept Sept 2016 2016 microscopic phenomena with no intrinsic energy limitation
• Where do we look? Everywhere! G. Isidori searchLepton –Lepton Kaon for New Physics:Flavor Flavor Physics the Universality next Universality with step broad Kaon 2016, Birmingham, Sept 2016 search strategy given lack of clear indications onG. Isidori the – SM-EFT Kaon Physics: boundaries the next step Kaon 2016, Birmingham, Sept 2016 (both in energies and effective couplings) A Arenewed renewed2.2 Lepton interest interest in universalityin possible possible violations violations & NP of of LFU LFU has has been been triggered triggered by by two two Leptonveryvery different LeptonFlavordifferent Flavor sets Universality sets Universalityof of observations observations in in B Bphysics physics: : • HintA renewed from Binterest physics in possible anomalies? violations of LFU has been triggered by two A I)renewed I)LFU LFU• testA testinterestrenewed in inb →b ininterest→ c possible chargedc charged in possible violationscurrents currents violations: τ : of vs.τ vs.LFU light of light LFU has leptons leptonshas been been ( triggeredμ (, μ triggerede,) e) by by two two b → veryc charged different currents:sets of observations in B physics: very differentvery differentsets of observationssets of observations in B physics in B physics:: τ vs.I) light LFU leptonstest in b →(µ, c e)charged [R(D), currents R(D*)]: τ vs. light leptons (μ, e) I) LFU test1. in LFU b → test c charged in b → c currentscharged currents:: τ vs. light τ vs. leptons light leptons (μ, e (µ,) e) :
b c b c b L c L b L Lc New Belle result LbL L cL LbL L cL W NP NPNP τL WW νL τL νL EmilieEmilie Passemar Passemar b c b c 4 LτL τL LνL νL LτL τL νLL νL
SMW prediction quite solid:NP f.f. uncertainty cancel (to a good extent...) in the ratio Consistent results by 3 different exps. → 4σ excess over SM (combining D and D*) τ SM predic*on solid: ν τ f.f. uncertainty ν L D & D*L channelsL are well consistent L with a universal enhancement (~15%) of the SMSMcancels (to a good extent...) prediction prediction quite quite solid: solid: f.f. f.f. uncertainty uncertainty cancel cancel (to ( toa gooda good extent... extent...) in) in the the ratio ratio SM bL → cL τL νL amplitude (RH or scalar amplitudes disfavored) ConsistentConsistentin the ra*o results results by by 3 different3 different exps. exps. → → 4σ 4σ excess excess over over SM SM (combining (combining D Dand and D* D*) )
D D&Consistent results by 3 different &D* D* channels channels are are well well consistent consistentexps with 4σ excess over SM (combining D and D with a universala universal enhancement enhancement (~15%) (~15%) of *of )the the SM prediction quite solid: f.f. uncertainty cancel (to a good extent...) in the ratio SMSM b b → → c c τ τν ν amplitude amplitude ( RH (RH or or scalar scalar amplitudes amplitudes disfavored disfavored) ) Consistent L L New resultsL resultsLL LL byL from3 different LHCb on exps. Friday, → see 4σ talkexcess by Kristof over De SMBruyn (combining D and D*) Emilie Passemar 22 D & D* channels are well consistent with a universal enhancement (~15%) of the
SM bL → cL τL νL amplitude (RH or scalar amplitudes disfavored)
1.1 Quest for New Physics
• New era in particle physics : G.G. Isidori Isidori – – SimultaneousSimultaneous (unexpected explanations) success ofof B-physicsB-physics of the anomalies anomaliesStandard Model : a successful theory PSI, of PSI, Dec. Dec. 2017 2017 microscopic phenomena with no intrinsic energy limitation
• EFT-typeEFT-typeWhere do considerationsconsiderationswe look? Everywhere! search for New Physics with broad search strategy given lack of clear indications on the SM-EFT boundaries RecentRecent datadata showshow some convincingconvincing evidences evidences of of L Leptonepton F lavorFlavor U niversalityUniversality violations(both in energies and effective couplings) violations
bb →→ c charged currentscurrents:: τ τ vs. vs. light light leptons leptons• Hint ( μ(,μ e,from )e )[ R [ BDR, D physicsR, D*RD*] ] anomalies?
bb →→ s neutral currents:currents: μμ vs. vs. e e [R [RKK, ,R RK*K*b →(+ (+ cP 5Pcharged 5et et al. al.) ]) currents:]
τ vs. light leptons (µ, e) [R(D), R(D*)]
b Lb L c LcL bL b L c L cL WW NPNP τ , ℓ ν τ ν Lτ L , LℓL L νL L τL L νL
R(D)Key and unique R(D*) role consistent of Tau physics with a R(D) and R(D*) consistent with a EmilieEmilie Passemar Passemar universaluniversal enhancement enhancement (~30%) (~30%) of5 of the SM b → c τ ν amplitude the SM LbL →L cLL τ LL νL amplitude
The new physics flavor scale 1.2 τ lepton as a unique probeThe of newnew physicsphysics flavor scale
• In theK questphysics: of NewϵK Physics, can be sensitive to veryK highphysics: scale: ϵK E sdsd 5 2 ⇒ Λ ! 10 TeV – Kaon physics: sΛdsd 5 2 ⇒ Λ ! 10 TeV [εK] Λ ΛNP Charged leptons: µ → eγ, µ → e,etc. Charged leptons: µ → eγ, µ → e,etc. – Tau Leptons: τµµeff 342 2 ⇒ Λ ! 10 TeV [τ → µγ] µΛeff 3 2 ⇒ Λ ! 10 TeV Λ There is no exact symmetry that can forbid such • At low energy: lots of experiments e.g., operatorsThere is no exact symmetry that can forbid such BaBar, Belle, BESIII, LHCb important operators improvementsAll other bounds on measurements on NP, like protonand bounds decay, maybe due obtainedtoAll exact other and symmetry boundsmore expected on NP, like(Belle proton II, LHCb decay,, ATLAS, maybe due
CMSto) exact symmetry ΛLE • In many cases no SM background: Y. Grossman Charged lepton theory Lecce, May 6, 2013 p. 10 e.g., LFV, EDMs Y. Grossman Charged lepton theory Lecce, May 6, 2013 p. 10 • For some modes accurate calculations of hadronic uncertainties essential, e.g. CPV in
hadronic Tau decays, Vus, αS extraction, etc
Tau leptons very important to look for New Physics! 6
1.2 τ lepton as a unique probe of new physics
• Unique probe of Lepton Universaity and Charged Lepton Flavour Violation No SM background Indirect probe of flavor-violating NP occurring at energies not directly accessible at accelerators
• Tool to search for New Physics at colliders: Ex: h à τ τ, LFV in h à τ µ
Emilie Passemar 7
1.2 τ lepton as a unique probe of new physics
• Unique probe of Lepton Universaity and Charged Lepton Flavour Violation No SM background Indirect probe of flavor-violating NP occurring at energies not directly accessible at accelerators
• Tool to search for New Physics at colliders: Ex: h à τ τ, LFV in h à τ µ
• Studying its hadronic decays: inclusive & exclusive – Unique probe of some of the fundamental SM parameters
αS, |Vus|, ms
Emilie Passemar 8
1.2 τ lepton as a unique probe of new physics
• Unique probe of Lepton Universaity and Charged Lepton Flavour Violation No SM background Indirect probe of flavor-violating NP occurring at energies not directly accessible at accelerators
• Tool to search for New Physics at colliders: Ex: h à τ τ, LFV in h à τ µ
• Studying its hadronic decays: inclusive & exclusive – Unique probe of some of the fundamental SM parameters
αS, |Vus|, ms
– Ideal set-up for the “R&D” of theory tools about non perturbative & perturbative dynamics: OPE, Chiral Perturbation Theory, Resonances,
large Nc, dispersion relations lattice QCD, etc…
improve our understanding of the SM and QCD at low energy
Emilie Passemar 9
1.2 τ lepton as a unique probe of new physics
• Unique probe of Lepton Universaity and Charged Lepton Flavour Violation No SM background Indirect probe of flavor-violating NP occurring at energies not directly accessible at accelerators
• Tool to search for New Physics at colliders: Ex: h à τ τ, LFV in h à τ µ
• Studying its hadronic decays: inclusive & exclusive – Unique probe of some of the fundamental SM parameters
αS, |Vus|, ms
– Ideal set-up for the “R&D” of theory tools about non perturbative & perturbative dynamics: OPE, Chiral Perturbation Theory, Resonances,
large Nc, dispersion relations lattice QCD, etc… – Inputs for the muon g-2
Emilie Passemar 10
1.2 τ lepton as a unique probe of new physics
• A lot of progress in tau physics since its discovery on all the items described before important experimental efforts from LEP, CLEO, B factories: Babar, Belle, BES, VEPP-2M, LHCb, neutrino experiments,… Experiment Number of τ pairs More to come from LHCb, BES, LEP ~3x105 VEPP-2M, Belle II, CMS, ATLAS CLEO ~1x107 BaBar ~5x108
Belle ~9x108 • But τ physics has still potential Belle II ~1012 “unexplored frontiers” deserve future exp. & th. efforts
• In the following, some selected examples and J. Berryman will give more
Emilie Passemar 11
1.3The The veryProgram basic of charged leptons
Adapted from Talk by Y. Grossman@CLFV2013 Muon LFV Intensity Frontier Charged Lepton µ+ → e+γ νe ↔ νµ − WG’13 µ+ → e+e+e νe ↔ ντ − − µ N → e N νµ ↔ ντ µ−N → e+N′ µ+e− → µ−e+ NeutrinoOscillations
τ → ℓγ → + − µ → µγ LFV τ ℓℓi ℓj − (g 2)µ, (EDM)µ τ → ℓ + hadrons Tau LFV Muon LFC τ → τγ (g − 2)τ , (EDM)τ CPV in τ → Kπν τ τ → Kππν Tau LFC τ τ → Nπν τ
Emilie Passemar Thanks to Babu 12
Y. Grossman Charged lepton theory Lecce, May 6, 2013 p. 15 2. Charged Lepton-Flavour Violation 2.1 Introduction and Motivation
• Lepton Flavour Number is an « accidental » symmetry of the SM (mν=0)
• In the SM with massive neutrinos effec ve CLFV ver ces are ny due to GIM suppression unobservably small rates!
E.g.: µ → eγ e, µ,τ µ 2 3α Δm 2 Br e U * U 1i 5x10−53 ( µ → γ ) = µi ei 2 < 32π ∑ M i=2,3 W Petcov’77, Marciano & Sanda’77, Lee & Shrock’77…
40 Br 10− ⎡ (τ → µγ ) < ⎤ ⎣ ⎦
• Extremely clean probe of beyond SM physics • In New Physics models: seazible effects Comparison in muonic and tauonic channels of branching ra os, conversion rates and spectra is model-diagnos c
Emilie Passemar 14
Lepton Flavor Violation in example BSM models 2.1 Introduction and Motivation Neutrino-less t decays: optimal hunting ground for non-Standard Model LFV effects
Topologies are similar to those of t hadronic decays • In NewCurrent Physics limits (down scenarios to ~ 10-8), CLFV or limits can anticipated reach atobservable next generation levels e+e- colliders, in several directly channelsconfront many New Physics models Talk by D. Hitlin @ CLFV2013
• But the sensitivity of particular modes to CLFV couplings is model 3
dependent David Hitlin 1st Conference on CFLV - Lecce May 8, 2013 • Comparison in muonic and tauonic channels of branching ratios, conversion rates and spectra is model-diagnostic Emilie Passemar 15
2.2 Tau LFV
• Several processes: τ → ℓγ , τ → ℓ α ℓβ ℓ β , τ → ℓY
P, S, V , PP,... 90% CL upper limits on τ LFV decays HFLAV Spring 2017
10−6
●
10−8
− 0 0 0 0 ) ) 0 0 0 0 0 0 ) ) − − − − − − − − − − − − − 0 − − − − − 0 − − − − γ − γ η η − φ − φ S S − − − ω − ω ) ) ) ) S S − Λ − Λ µ − π − π − ρ − ρ + e + µ + µ + e + e + µ + π − π + π − π + K + π − K + K − K + K + π − K + K − K − + µ e µ − K − K 0 K 0 K e µ e µ e µ π π e 958 958 e 980 980 − e µ − e − e − µ µ − π + π − π + π S S µ µ µ e µ µ − − − π − K + π − K + K − π − K + π − K + K ′( ′( 892 892 892 892 ( ( − K − K p p ( ( ( ( 0 0 e e e e ∗ ∗ ∗ ∗ − f − f e µ µ µ µ µ e e e e e µ µ µ − η − η e µ µ µ K K K K e µ − − − − e µ e µ e µ ● ATLAS BaBar Belle CLEO LHCb
• 48 LFV modes studied at Belle and BaBar Emilie Passemar 16
•
2.2 Tau LFV
• Several processes: τ → ℓγ , τ → ℓ α ℓβ ℓ β , τ → ℓY
P, S, V , PP,... 90% CL upper limits on τ LFV decays HFLAV Spring 2017
10−6
●
10−8
− 0 0 0 0 ) ) 0 0 0 0 0 0 ) ) − − − − − − − − − − − − − 0 − − − − − 0 − − − − γ − γ η η − φ − φ S S − − − ω − ω ) ) ) ) S S − Λ − Λ µ − π − π − ρ − ρ + e + µ + µ + e + e + µ + π − π + π − π + K + π − K + K − K + K + π − K + K − K − + µ e µ − K − K 0 K 0 K e µ e µ e µ π π e 958 958 e 980 980 − e µ − e − e − µ µ − π + π − π + π S S µ µ µ e µ µ − − − π − K + π − K + K − π − K + π − K + K ′( ′( 892 892 892 892 ( ( − K − K p p ( ( ( ( 0 0 e e e e ∗ ∗ ∗ ∗ − f − f e µ µ µ µ µ e e e e e µ µ µ − η − η e µ µ µ K K K K e µ − − − − e µ e µ e µ ● ATLAS BaBar Belle CLEO LHCb
• Expected sensi vity 10-9 or be er at LHCb, ATLAS, CMS Belle II? Emilie Passemar 17
•
A much sharper picture to emerge
CERN-LHCC-2017-003 Evolution of LFV limits D0 mixing CPV Approximate number of τ decays studied 105 106 107 108 109 1010 10-2 today S. Banerjee’17 MarkII τ → µ γ NP models τ → µ η ARGUS 10-4 DELPHI τ → µ µ µ
w/300 fbCLEO-1 10-6 LHCb Belle BaBar LHCb
-8 10 mSUGRA + seesaw SUSY + SO(10) SM + seesaw SUSY +Belle Higgs II physics prospect – tau LFVBelle II 10-10
90% CL Upper Limit on Upper Branching Ratio 90% CL 1980 1990 2000 2010 2020 LFV is suppressed in SM → a few models predict enhancements within Belle YEARII's reach. B2TIP’18
Sensitivity to lepton Belle II can reduce most of theese limits by 1 ~2 orders of magnitude Flavor Violation in tau I. Heredia decays MWPF2015 Overview B() B() Swagato main background from ee mSUGRA+seesaw30 10-7 10-9 PRD 66(2002) 115013 of τ physics ISR Banerjee reduce sensitivity by a factor ~7 SUSY+SO(10) 10-8 10-10 PRD 68(2003) 033012 SM+seesaw 10-9 10-10 PRD 66(2002) 034008 very clean mode Non-Universal Z' 10-9 10-8 PLB 547(2002) 252 reduce sensitivity by a factor of 50 -10 -7 Emilie Passemar SUSY+Higgs 10 10 PLB 566(2003) 217 18 possible reach by Belle II (50 ab-1) <10-9 < 10-10 → good to test NP 27 2.3 Effective Field Theory approach
See e.g. C (5) C (6) Black, Han, He, Sher’02 (5) i (6) Brignole & Rossi’04 L = L + O + Oi + ... SM ∑ 2 Λ i Λ Dassinger et al.’07 Matsuzaki & Sanda’08
Giffels et al.’08 Crivellin, Najjari, Rosiek’13 • Build all D>5 LFV operators: Petrov & Zhuridov’14 Cirigliano, Celis, E.P.’14 Rich structure at dim=6 Ø Dipole:
τ! D C µν ! Dipole D m P F e.g. µ • Le ff ⊃ − 2 τ µσ L,Rτ µν τ µ Λ Dominant in SUSY-GUT and SUSY see-saw scenarios
Emilie Passemar 19
•
2.3 Effective Field Theory approach
See e.g. C (5) C (6) Black, Han, He, Sher’02 (5) i (6) Brignole & Rossi’04 L = L + O + Oi + ... SM ∑ 2 Λ i Λ Dassinger et al.’07 Rich structure at dim=6 Matsuzaki & Sanda’08 Rich structure at dim=6 Giffels et al.’08 Crivellin, Najjari, Rosiek’13 • Build all D>5 LFV operators: Petrov & Zhuridov’14 Cirigliano, Celis, E.P.’14 Dipole Dipole C • • D D µν Ø Dipole: Leff ⊃ − 2 mτ µσ PL,Rτ Fµν Λ DominantDominant in SUSY-GUT in SUSY-GUT and and Ø Lepton-quark (SUSY see-sawSUSYScalar see-saw scenarios, Pseudo- scenariosscalar, Vector, Axial-vector):
q 0 0 0 q ϕ ≡ h , H , A S,V CS,V τ Scalar m m G P q q Γ ≡ 1 Scalar• Leff ⊃ − 2 τ q F µ Γ L,Rτ Γ e.g. • Λ q (Pseudo-scalar) Dominant in RPV SUSY and RPC q (Pseudo-scalar) µ DominantSUSY in forRPV large SUSY tan( βand) and RPC low mA , SUSY for large tan(leptoquarksβ) and low mA, leptoquarks τμ eµ
µ Vector• Γ ≡ γ • (Axial-vector) Emilie Passemar Enhanced in Type III seesaw (Z-penguin), q q 20 Type II seesaw, LRSM, leptoquarks 2.3 Effective Field Theory approach
See e.g. C (5) C (6) Black, Han, He, Sher’02 (5) i (6) Brignole & Rossi’04 L = L + O + Oi + ... SM ∑ 2 Λ i Λ Dassinger et al.’07 Matsuzaki & Sanda’08
Giffels et al.’08 Crivellin, Najjari, Rosiek’13 • Build all D>5 LFV operators: Petrov & Zhuridov’14 Cirigliano, Celis, E.P.’14 C D D µν Ø Dipole: Leff ⊃ − 2 mτ µσ PL,Rτ Fµν Λ C Rich structure at dim=6 LS S,V m m G P q q Ø Lepton-quark (Scalar, Pseudo-scalar, Vector, Axial-vector): eff ⊃ − 2 τ q F µ Γ L,Rτ Γ Λ
Ø Integrating out heavy quarks generates gluonic operator • Dipole 1 C µP τQQ G G a µν Dominant in SUSY-GUT and 2 L,R à Leff ⊃ − 2 mτ GF µPL,Rτ GµνGa SUSY see-saw scenarios Λ Λ
0 0 0 q • τ ϕ ≡ h , H , A Scalar • q (Pseudo-scalar) Dominant in RPV SUSY and RPC µ Emilie Passemar 21 SUSY for large tan(β) and low mA, leptoquarks Rich structure at dim=6
• Dipole 2.3 Effective Field Theory approach Dominant in SUSY-GUT and See e.g. SUSY see-saw scenarios C (5) C (6) Black, Han, He, Sher’02 (5) i (6) Brignole & Rossi’04 L = L + O + Oi + ... SM ∑ 2 Λ i Λ q Dassinger et al.’07 Matsuzaki & Sanda’08
Scalar Giffels et al.’08 • q Crivellin, Najjari, Rosiek’13 (Pseudo-scalar) Dominant• Buildin RPV all D>5 LFV SUSY and RPC operators: Petrov & Zhuridov’14 SUSY for large tan(β) and low mA , Cirigliano, Celis, E.P.’14 C leptoquarks D D µν Ø Dipole: Leff ⊃ − m µσ PL,Rτ F Λ 2 τ µν μ e S CS,V Ø Lepton-quark (Scalar, Pseudo-scalar, Vector, Axial-vector): Leff ⊃ − 2 mτ mqGF µ ΓPL,Rτ qΓq Λ
Vector • 4 C ℓ 4ℓ S,V (Axial-vector) Ø 4 leptons (Scalar, Pseudo-scalar, Vector, Axial-vector): Leff ⊃ − 2 µ ΓPL,Rτ µ ΓPL,R µ Enhanced in Type III seesaw (Z-penguin), q q Λ Type II seesaw, LRSM, leptoquarks
µ µ Γ ≡ 1 ,γ τ • 4 Leptons, ... e.g. µ • Type II and III seesaw, RPV SUSY, LRSM µ Emilie Passemar 22 2.3 Effective Field Theory approach
See e.g. C (5) C (6) Black, Han, He, Sher’02 (5) i (6) Brignole & Rossi’04 L = L + O + Oi + ... SM ∑ 2 Λ i Λ Dassinger et al.’07 Matsuzaki & Sanda’08
Giffels et al.’08 Crivellin, Najjari, Rosiek’13 • Build all D>5 LFV operators: Petrov & Zhuridov’14 Cirigliano, Celis, E.P.’14 C D D µν Ø Dipole: Leff ⊃ − 2 mτ µσ PL,Rτ Fµν Λ S CS,V Ø Lepton-quark (Scalar, Pseudo-scalar, Vector, Axial-vector): Leff ⊃ − 2 mτ mqGF µ ΓPL,Rτ qΓq Λ
G CG a µν
Ø Lepton-gluon (Scalar, Pseudo-scalar): Leff ⊃ − 2 mτ GF µPL,Rτ GµνGa Λ
C 4ℓ 4ℓ S,V Ø 4 leptons (Scalar, Pseudo-scalar, Vector, Axial-vector): Leff ⊃ − 2 µ ΓPL,Rτ µ ΓPL,R µ Λ
µ • Each UV model generates a specific pa ern of them Γ ≡ 1 ,γ
Emilie Passemar 23
•
2.4 Model discriminating power of Tau processes
Celis, Cirigliano, E.P.’14 • Summary table: Discriminating power: τLFV matrix
• In addi on to leptonic and radia ve decays, hadronic decays are very important sensi ve to large number of operators!
• But need reliable determina ons of the hadronic part: form factors and decay constants (e.g. fη, fη’)
Emilie Passemar 24 2.4 Model discriminating power of Tau processes
• Summary table: Discriminating power: τLFV Celismatrix, Cirigliano, E.P.’14
• Form factors for τ → µ(e)ππ determined using dispersive techniques Form Donoghue factors, Gasser, Leutwyler’90 • Hadronic part: with Moussallam’99 iL i 2 H V A e QCD 0 Lor Twoentz channelstruct. F unitaritys condition (ππ, KK) Daub(OK et al’13 up to √s ~ 1.4 GeV) µ = ππ µ − µ = (• ) i ( ) s = p + + p − ( ) µ ( π π ) Celis, Cirigliano, E.P.’14
• 2-channel unitarity condi on is solved with I=0 S-wave ππ and KK sca ering data as input n = ππ, KK Emilie Passemar n = ππ , KK 25 • General solution:
Polynomials Canonical solution falling as 1/s for large s determined by (obey un-subtracted dispersion relation) matching to ChPT
• Solved iteratively, using input on s- wave I=0 meson meson scattering 2.4 Model discriminating power of Tau processes
Celis, Cirigliano, E.P.’14 • Summary table: Discriminating power: τLFV matrix
• The no on of “best probe” (process with largest decay rate) is model dependent
• If observed, compare rate of processes key handle on rela ve strength between operators and hence on the underlying mechanism
Emilie Passemar 26 2.5 Handles
• Two handles: Γ (τ → F ) Ø Branching ratios: R ≡ with F dominant LFV mode for F ,M Γ τ → F M ( M ) model M
Ø Spectra for > 2 bodies in the final state: dBR (τ → µµµ ) d s
• Benchmarks:
Ø Dipole model: CD ≠ 0, Celse= 0
Ø Scalar model: CS ≠ 0, Celse= 0
Ø Vector (gamma,Z) model: CV ≠ 0, Celse= 0
Ø Gluonic model: CGG ≠ 0, Celse= 0
Emilie Passemar 27
2.6 Model discriminating of BRs
Celis-VC-PassemarCelis, Cirigliano, E.P.’14 1403.5781 • Two handles: Two basic handles: 1) PatternΓ (τ → ofF )BRs • Ø Branching ratios: R ≡ with F dominant LFV mode for model M F ,M Γ τ → F M ( M )
Benchmark IllustrativeEmilie Passemar benchmark model Dominant LFV decay mode for model “M” to the ranges given in Table 3 for the SM4 and the LHT model.
4.7 Patterns of Correlations and Comparison with the MSSM and the LHT
In [4,55] a number of correlations have been identified that allow to distinguish the LHT model from the MSSM. These results are recalled in Table 3. In the last column of this table we also show the results obtained in the SM4. We observe:
For most of the ratios considered here the values found in the SM4 are significantly • larger than in the LHT and by one to two orders of magnitude larger than in the MSSM.
In the case of µ e conversion the predictions of the SM4 and the LHT model • ! are very uncertain but finding said ratio to be of order one would favour the SM4 and the LHT model over the MSSM. 2.6 Model discriminating of BRs Similarly, in the case of several ratios considered in this table, finding them to be • of order one will choose the SM4 as a clear winner in this competition. • Studies in specific models Buras et al.’10
ratio LHT MSSM (dipole) MSSM (Higgs) SM4
+ Br(µ e e e ) 3 3 ! Br(µ e ) 0.02. . . 1 6 10 6 10 0.06 ...2.2 ! ⇠ · ⇠ · + Br(⌧ e e e ) 2 2 ! Br(⌧ e ) 0.04. . . 0.4 1 10 1 10 0.07 ...2.2 ! ⇠ · ⇠ · + Br(⌧ µ µ µ ) 3 ! Br(⌧ µ ) 0.04. . . 0.4 2 10 0.06 ...0.1 0.06 ...2.2 ! ⇠ · + Br(⌧ e µ µ ) 3 ! Br(⌧ e ) 0.04. . . 0.3 2 10 0.02 ...0.04 0.03 ...1.3 ! ⇠ · + Br(⌧ µ e e ) 2 2 ! Br(⌧ µ ) 0.04. . . 0.3 1 10 1 10 0.04 ...1.4 ! ⇠ · ⇠ · Br(⌧ e e+e ) ! Br(⌧ e µ+µ ) 0.8. . . 2 5 0.3. . . 0.5 1.5 ...2.3 ! ⇠ Br(⌧ µ µ+µ ) ! Br(⌧ µ e+e ) 0.7. . . 1.6 0.2 5. . . 10 1.4 ...1.7 ! ⇠ R(µTi eTi) 3 2 3 12 ! Br(µ e ) 10 ...10 5 10 0.08 ...0.15 10 ...26 ! ⇠ ·
Table 3: Disentangle the Comparison of variousunderlying dynamics ratios of branchingof NP ratios in the LHT model [55], the
Emilie PassemarMSSM without [63,64] and with significant Higgs contributions [65,66] and the SM4 29 calculated here.
20
used to discriminate among di↵erent e↵ective operators. In the case where dipole operators dominate, the distribution of events in the Dalitz plot concentrates on borders of the phase space as shown in Fig. 3 (left-plot).3 Other e↵ective operators also produce distinctive patterns on a Dalitz plot, see Figs. 3 and 4. One would expect a flat distribution for the same-sign muon invariant mass spectrum (dBR/dm2 ) in the case of dipole operators as shown in Fig. 5. µ µ The vector operators CVRL,VLR would produce a spectrum peaked towards low invariant masses 2 m , the scalar operators CSLL,SRR on the other hand would give rise to a peaked spectrum µ µ around m2 1GeV2, see Fig. 5. The discrimination of di↵erent kinds of NP through a µ µ Dalitz plot analysis⇠ in LFV leptonic ⌧ decays has been discussed in detail in Refs. [42,43].
Dassinger, Feldman, Mannel, Turczyk’ 07 Celis, Cirigliano, E.P.’14
Figure 3: Dalitz plot for ⌧ µ µ+µ decays when all operators are assumed to vanish with the ! exception of CDL,DR =1(left) and CSLL,SRR =1(right), taking ⇤ =1TeV in both cases. Colors 2 2 2 denote the density for d BR/(dm + dm ), small values being represented by darker colors and µ µ µ µ 2 2 2 large values in lighter ones. Here m + represents m or m , defined in Sec. 3.1. µ µ 12 23
Angular analysis 5 Future prospects with polarized taus 8 Present experimental limits on LFV ⌧ decays are at the 10 level thanks to the large amount of data collected at Belle and BaBar. As a comparison, before Belle and BaBar the best Dassinger, Feldman, 1 upper bound on BR(⌧ µ )wassetattheCLEOdetectorwithL 13.8fb of integrated ! 6 ⇠ Mannel, Turczyk’ 07 luminosity, finding BR(⌧ µ ) < 1.1 10 (90% CL) [68]. Belle and BaBar have finally ! ⇥ 1 1 stopped collecting data, reaching a final integrated luminosity of L & 1ab and L 550 fb respectively. The upcoming Belle II experiment at the SuperKEKB collider is expected⇠ to 1 deliver L 50 ab of data [34]. In cases where the number of background events is not ⇠ negligible, the 90% CL upper limit on the BR (BR90)isexpectedtoimprovewiththeintegrated luminosity L as BR90 1/pL. One can then expect an improvement of the present upper / 1 bounds by a factor of ten approximately with L 50 ab of collected data at Belle II. ⇠ 3We have kept the muon mass at its physical value for obtaining Figs. 3, 4 and 5. Figure 4: Dalitz plot for ⌧ µ µ+µ decays when all operators are assumed to vanish with the ! exception of CVRL,VLR =1(left) and CVLL,VRR =1(right), taking ⇤ =1TeV in both cases. Colors are defined as in Fig. 3. 15 30
Figure 5: Same sign di-muon invariant mass spectrum for ⌧ µ µ+µ decays when all operators ! are assumed to vanish with the exception of CVLR,VRL =0.3 (continuous black), CDL,DR =0.1 (long- dashed blue) and CSLL,SRR =1(short-dashed red), taking ⇤ =1TeV.
Prospects for LFV ⌧ decays at a Super Tau-Charm Factory are also encouraging, with an 9 1 estimated sensitivity of BR(⌧ µ ) . 10 with 10 ab [35]. In Figs. 6 and 7 we show future! prospects for the observation of LFV ⌧ decays. The figures show (i) current experimental upper limits on the BRs at 90% CL; (ii) expected future limits assuming an improvement of the sensitivity by a factor of ten; (iii) upper bounds (colored bars) that can be derived on the BRs, within each of the benchmark models for single operator dominance, from the non-observation of LFV ⌧ decays (from Section 4). Among other features, Fig. 6 implies that if the dipole operator dominates, clearly ⌧ µ is the channel to focus on (the other have limits below future sensitivity). However, if other! operators contribute, then hadronic decays o↵er greater discovery potential, so they should be vigorously pursued.
16 Rich structure2.7 Discriminating at dim=6 power of τ → µ(e)ππ decays
Celis-VC-Passemar 1403.5781 Celis , Cirigliano, E.P.’14 τ! Dipole µ! • •Two basic handles: 2) Spectra in > 2 bodyτ decays µ Dominant in SUSY-GUT and SUSY see-saw scenarios
D C D µν Leff ⊃ − 2 mτ µσ PL,Rτ Fµν Λ
Spin and isospin of the hadronic operator leave imprint in the spectrum
Emilie Passemar 31 Celis-VC-Passemar 1403.5781 • Two basic handles: 2) Spectra in > 2 body decays
Spin and isospin of the hadronic operator leave 2.7 Discriminating power of τ → µ(e)ππ decays imprint in the spectrum
Celis-VC-Passemar 1403.5781 • Two basic handles: 2) Spectra in > 2 body decays
D C D µν Leff ⊃ − 2 mτ µσ PL,Rτ Fµν Λ C LS ⊃ − S m m G µP τ qq eff Λ 2 τ q F L,R Spin and isospin of the hadronic operator leave imprint in the spectrum
Emilie Passemar 32 Celis-VC-Passemar 1403.5781 • Two basic handles: 2) Spectra in > 2 body decays
Spin and isospin of the hadronic operator leave 2.7 Discriminating power of τ → µ(e)ππ decays imprint in the spectrum Celis-VC-Passemar 1403.5781 Celis-VC-Passemar 1403.5781 Two basic handles: 2) Spectra in > 2 body decays • • Two basic handles: 2) Spectra in > 2 body decays
D C D µν Leff ⊃ − 2 mτ µσ PL,Rτ Fµν Λ S CS Leff ⊃ − 2 mτ mqGF µPL,Rτ qq Spin and isospin of the Λ hadronic operator leave Spin and isospin of the imprint in the spectrum hadronic operator leave imprint in the spectrum
G CG a µν Leff ⊃ − 2 mτ GF µPL,Rτ GµνGa Λ Different distributions according to the operator!
33 2.8 Non standard LFV Higgs coupling
Goudelis, Lebedev, Park’11
λ i j Davidson, Grenier’10 • Δ L = − ij f i f j H H †H −Y f f h Harnik, Kopp, Zupan’12 Y 2 ( L R ) ij ( L R ) Λ Blankenburg, Ellis, Isidori’12 McKeen, Pospelov, Ritz’12 h m i In the SM: Y SM = δ • High energy : LHC ijv ij Arhrib, Cheng, Kong’12
Hadronic part treated with perturba ve Y QCD τµ
• Low energy : D, S operators
Emilie Passemar 34 2.8 Non standard LFV Higgs coupling
Goudelis, Lebedev, Park’11
λ i j Davidson, Grenier’10 • Δ L = − ij f i f j H H †H −Y f f h Harnik, Kopp, Zupan’12 Y 2 ( L R ) ij ( L R ) Λ Blankenburg, Ellis, Isidori’12 McKeen, Pospelov, Ritz’12 h m i In the SM: Y SM = δ • High energy : LHC ijv ij Arhrib, Cheng, Kong’12
Hadronic part treated with perturba ve Y QCD τµ
Reverse the process
• Low energy : D, S, G operators
Yτµ
+
Hadronic part treated with Emilie Passemar non-perturba ve QCD 35 Constraints in the τµ sector
• At low energy Cirigliano, Celis, E.P.’14 Ø τ → µππ : + h h
Dominated by Ø ρ(770) (photon mediated)
Ø f0(980) (Higgs mediated)
ρ f0
Emilie Passemar 36 14 Constraints in the τµ sector 9 Summary
CMS 19.7 fb-1 (8 TeV) 1 • Constraints from LE: |
µ Ø τ → µγ : best constraints τ τ→ 3µ but loop level |Y τ → µππ sensi ve to UV -1 10 comple on of the theory Ø τ → µππ : tree level τ→ µ γ diagrams -2 ATLAS H→ττ robust handle on LFV 10 |Y µ τ Y observed τ µ |=m • Constraints from HE: µ m expected τ /v H→µτ 2 LHC wins for τ µ! 10-3 • Opposite situa on for µe! BR<0.1% BR<1% BR<10% BR<50% • For LFV Higgs and nothing else: LHC bound 10-4 -4 -3 -2 -1 10 10 10 10 1 −9 BR (τ → µγ ) < 2.2 × 10 |Y | Plot from Harnik, Kopp, Zupan’12 µτ BR τ → µππ < 1.5 × 10−11 updated by CMS’15 ( ) Figure 6: Constraints on the flavour-violating Yukawa couplings, Y and Y . The black | µt| | tµ| dashed lines are contours of (H µt) for reference. The expected limit (red solid line) B ! with one sigma (green) and two sigma (yellow) bands, and observed limit (black solid line) are derived from the limit on (H µt) from the present analysis. The shaded regions are B ! derived constraints from null searches for t 3µ (dark green) and t µg (lighter green). The ! ! yellow line is the limit from a theoretical reinterpretation of an ATLAS H tt search [4]. The ! light blue region indicates the additional parameter space excluded by our result. The purple diagonal line is the theoretical naturalness limit Y Y m m /v2. ij ji i j 9 Summary The first direct search for lepton-flavour-violating decays of a Higgs boson to a µ-t pair, based on the full 8 TeV data set collected by CMS in 2012 is presented. It improves upon previously published indirect limits [4, 26] by an order of magnitude. A slight excess of events with a significance of 2.4 s is observed, corresponding to a p-value of 0.010. The best fit branching +0.39 fraction is (H µt)=(0.84 0.37)%. A constraint of (H µt) < 1.51% at 95% confidence B ! B ! level is set. The limit is used to constrain the Yukawa couplings, p Y 2 + Y 2 < 3.6 10 3. | µt| | tµ| ⇥ It improves the current bound by an order of magnitude.
Acknowledgments We congratulate our colleagues in the CERN accelerator departments for the excellent perfor- mance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus); MoER, ERC IUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Re- Hint of New Physics in h → τ µ ? 13 CMS’16
-1 CMS Preliminary 2.3 fb (13 TeV) 1 | µ
τ τ→ 3µ
|Y τ → µππ 10−1
τ→ µ γ 10−2 expected H→ µτ observed
−3 |Y µ 10 τ Y τµ |=m
µ m BR<0.1% BR<1% BR<10% BR<50% τ /v 2
10−4 −4 −3 −2 −1 10 10 10 10 |Y | 1 µ τ
Figure 5: Constraints on the flavour violating Yukawa couplings, Y and Y . The black | µt| | tµ| Emilie Passemar dashed lines are contours of (H µt) for reference. The expected limit38 (red solid line) with B ! one standard deviation (green) and two standard deviation (yellow) bands, and observed limit (black solid line) are derived from the limit on (H µt) from the present analysis. The B ! shaded regions are derived constraints from null searches for t 3µ (dark green) and t µg ! ! (lighter green). The light blue region indicates the additional parameter space excluded by our result. The purple diagonal line is the theoretical naturalness limit Y Y m m /v2. ij ji i j 9 Conclusions A direct search for lepton flavour violating decays of the Higgs boson in the H µt channel ! is described. The data sample used in the search was collected in proton-proton collisions at ps = 13 TeV with the CMS experiment at the LHC and corresponds to an integrated integrated 1 luminosity of 2.3 fb . No excess is observed. The best-fit branching fraction is (H µt)= +0.81 B ! 0.76 0.84% and an upper limit of (H µt) < 1.20% (1.62% expected) is set at 95% CL. B ! At ps = 8 TeV a small excess was observed, corresponding to 2.4s, with an analysis based on 1 an integrated luminosity of 19.7 fb that yielded an expected 95% CL limit on the branching fraction of 0.75%. More data are needed to make definitive conclusions on the origin of that excess.
References [1] ATLAS Collaboration, “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC”, Phys. Lett. B 716 (2012) 1, doi:10.1016/j.physletb.2012.08.020, arXiv:1207.7214.
[2] CMS Collaboration, “Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC”, Phys. Lett. B 716 (2012) 30, doi:10.1016/j.physletb.2012.08.021, arXiv:1207.7235. Hint of New Physics in h → τ µ ?
CMS’17
Emilie Passemar 39 3. LFC processes: CPV in tau decays 3.1 Introduction
• CP violation measured in K and B decays in agreement with SM
• Not enough CP violation to explain asymmetry matter/anti-matter
• Look elsewhere: – Neutrinos – Charged leptons
– Electric dipole moments
• Aim: pin down new sources of CPV in the lepton sector and discriminating between NP scenarios
• Study of tau decays: – CPV in tau pair production (e+e- → τ+τ-) EDM – CPV in hadronic tau decays • SM source: K-Kbar mixing NP source: In the vertex
FSI Emilie Passemar 41
EDMsEDMs and and T(CP) T(CP) violation violation inin 3.2the the EDM LHC ofLHC the Tau era era The tau g-2 via its radiative leptonic decays: a proposal • Probe to test new sources of CP violation No SM background Tau radiative leptonic decays at LO:
d3 ↵ M 5 G2 yPp andx2 T 4violation:r2 EDMs⌧P andF T violation: as probes of new physics = G0(x, y, cos ✓,r) dx dy d cos ✓ 2⇡(4⇡)6→ → → →d ∝ J Kinoshita & Sirlin PRL2(1959)177;d ∝ KunoJ & Okada, RMP73(2001)151 1 (⌧ 1. e Essentially⌫¯e ⌫⌧ ) free of SM “background”2E (CKM)2E * m ! =1.823% vs 1.75(18)% x = l ,y= ,r= l total M M M E >10MeV ⌧ ⌧ ⌧ CLEO 2000 From V. Cirigliano (⌧ µ ⌫¯ ⌫ ) ! µ ⌧ =0.364% vs 0.361(38)% total E >10MeV • CPV in tau pair production Add the contribution of the effective (e+e- → τ+τ-) EDM coupling and the QED corrections: • Very challenging ↵ measurementG for τG +˜a G + G 0 ! 0 ⌧ a ⇡ RC • Measured using spin
correlations of decay3 product Measure d Γ precisely and get ãτ ! of the taus
• HelpM. ofPassera polarized TAU2012 Nagoya beams? Sep 18 2012 14 Emilie Passemar 42 *1 Observation would signal new physics or a tiny QCD θ-term (< 10-10). Multiple measurements can disentangle the two effects
20 unpolarized electron beam, one could access the imaginary part of the form factor by measuring the polarization of the normal to the scattering plane of a single ⌧, while the real part requires tounpolarized measure the electron correlations beam, between one could the decay access products the imaginary of both ⌧ part. Using of the polarized form factor beams by o↵ measuringers unpolarized electron beam, one could access the imaginary part of the form factor by measuring unpolarizedthethe possibility electron polarization tobeam, study of the one the normal polarization could accessto the of scattering theonly imaginary one ⌧, plane the real part of part a single of being the⌧ form, in while this factor case the determined real by part measuring requires the polarizationto of measure the normal the correlationsto the scattering between plane the of decay a single products⌧, while of both the real⌧. Using part requires polarized beams o↵ers the polarizationby studying of the the transverse normal to and the longitudinal scattering polarizations plane of a of single a single⌧,⌧ while. the real part requires to measure the correlationsthe possibility between to study the the decay polarization products of of only both one⌧.⌧ Using, the real polarized part being beams in this o↵ers case10 determined+ to measureA the study correlations has already between been done the for decay a future products flavour of factory both ⌧ showing. Using that polarized with 10 beams⌧ ⌧ o↵ers the possibility toby study studying the polarization the transverse of only and onelongitudinal⌧, the6 real polarizations part being in of this a single case⌧ determined. the possibilitypairs the to estimated study the sensitivity polarization is of order of only 10 one[15].⌧, the real part being in this case determined10 + by studying the transverseA study and has longitudinal already been polarizations done for a future of a single flavour⌧. factory showing that with 10 ⌧ ⌧ by studying the transverse and longitudinal polarizations6 of a single ⌧. 10 + A study haspairs already the estimated been done sensitivity for a future is of flavour order 10 factory [15]. showing that with 10 ⌧ ⌧ 10 + pairs theA estimated study0.0.2 has sensitivity Electric already Dipoleis been of order Momentdone 10 for6 [15]. of a thefuture⌧ flavour factory showing that with 10 ⌧ ⌧ 6 pairs the estimated sensitivity is of order 10 [15]. Since0.0.2 CP Electric violation hasDipole been Moment discovered of in the the⌧ 1960s, there has been experimental e↵orts to 0.0.2 Electrictry Dipole to measure Moment the electric of the dipole⌧ moments (EDMs) of leptons, neutron, atoms and molecules. 0.0.2 ElectricSince CP Dipole violation Moment has been of discovered the ⌧ in the 1960s, there has been experimental e↵orts to Since CP violationAstry EDMs to has measure violate been discovered boththe electric parity in and dipole the time 1960s, moments reversal there symmetries, (EDMs) has been of leptons, their experimental values neutron, yield e↵ aorts atoms mostly to and model- molecules. try toSince measure CPindependentAs the violation EDMs electric violate measure has dipole been both moments (assuming discovered parity (EDMs) CPT and time symmetry in of the reversal leptons, 1960s, is valid) symmetries, neutron, there of CP-violation has atoms their been and values in experimental molecules. nature. yield Therefore, a mostly e↵orts model- to As EDMstry to violate measurevaluesindependent both for the parity these electric measure EDMs and time dipole place (assuming reversal strong moments constraints CPT symmetries, (EDMs) symmetry upon their of the is leptons, valid)values scale of of yield CP-violation neutron, CP-violation a mostly atoms that model- in extensions nature. and molecules. Therefore, of independentAs EDMs measurethevalues violate SM may (assuming for both these allow. parity EDMs New CPT sources andplace symmetry time strong of CP reversal is violation constraints valid) symmetries, of is CP-violation one upon essential the scaletheir ingredient in ofnature. values CP-violation to yieldTherefore, lead to a a that mostly successful extensions model- of electroweak baryogenesis to account for the baryon asymmetry of the universe. Hence EDMs are valuesindependent for thesethe EDMs SMmeasure place may allow. strong (assuming New constraints sources CPT uponsymmetry of CP the violation scale is valid) of is CP-violation one of essential CP-violation that ingredient extensions in nature.to lead of to Therefore, a successful veryelectroweak interesting baryogenesis quantities to to study account since for if the they baryon are observed, asymmetry that wouldof the universe.be a clear Hence indication EDMs are the SMvalues may allow.for these New EDMs sources place of CP strong violation constraints is one essential upon the ingredient scale of to CP-violation lead to a successful that extensions of electroweak baryogenesisofvery the existence interesting to account of new quantities sources for the to of baryon study CP violation asymmetry since if [17], they the of are the SM observed, universe. prediction that Hence being would EDMsat an be unobservable are a clear indication the SM may allow. New sources of CP violation is one essential ingredient to lead to a successful very interestingrate.of quantities the Indeed, existence to a fundamental study of new since sources EDM if they of in CP are the violation observed,SM can only [17], that be the would generated SM predictionbe aat clear three beingindication loop level at an [20]. unobservable electroweak baryogenesis to account for the baryon asymmetry of the universe. Hence EDMs are of the existencerate. ofWhile new Indeed, sources strong a experimental offundamental CP violation limits EDM [17], have in the the been SM SM placed prediction can on only the be being electron generated at an[18] unobservable and at three muon loop [19] EDMslevel [20]. rate.very Indeed, interesting agiving fundamentalWhile stringent quantities strong EDM constraints experimental to in studythe on SM ND since can limits [17, only if 21], have they be the been generated are measurement placed observed, at on three of the that the electron loop tau would EDM level [18] be [20]. su and a↵ers clear muon the indication same [19] EDMs Whileof the strong existencedigiving experimentalculty stringent of as new the measurement sources limits constraints have of CP been of on its violation ND placed anomalous [17, on 21], [17], the magnetic the electronthe measurement SM moment: [18]prediction and the of muon the tau being tau lifetime [19] EDM at EDMs an is too su unobservable↵ short!ers the same givingrate. stringent Indeed,Thedi constraints bestculty a fundamental current as the on limit ND measurement [17, comes EDM 21], from in the of the the its measurement SM anomalous Belle can collaboration only of magnetic bethe generated tau that moment: EDM has searched su at↵ the threeers tau the for loop lifetime same CP level violating is [20].too short! The best current limit+ comes from+ the Belle collaboration that has searched for CP violating di cultyWhile as thee↵ measurementstrongects in the experimental process of itse anomalouse limits ⇤ have magnetic⌧ been⌧ using placed moment: triple on momentum the the tau electron lifetime and [18] spin is too andcorrelations short! muon [19] of the EDMs e↵ects in the process e+e! ! ⌧ +⌧ using triple momentum and spin correlations of the The bestgiving current stringentdecay limit products. constraints comes from on the ND Belle ! [17, collaboration⇤ 21],! the measurement that has searched of the for tau CP EDM violating su↵ers the same decay products.+ + + + e↵ectsdi in culty the process asIndeed thee measuremente the matrix ⇤ element⌧ of⌧ its forusing anomalous the tripleprocess momentume magnetice ⇤ moment: and⌧ spin⌧ is correlations given the tau by the lifetime offollowing the is too sum: short! Indeed the! matrix! element for the process e+!e ! ⌧ +⌧ is given by the following sum: decayThe products. best current limit comes from the Belle collaboration ! that⇤ ! has searched for CP violating Indeed the matrix element+ for the2 process2 e++e 2 ⌧ +⌧ is given2 by the2 following2 sum: e↵ects in the process e e =2 ⇤ SM 2+Re(d⌧ ⌧ ⌧using) ⇤Re +Im(d triple2 ⌧ momentum) Im + 2d⌧ andd2 2 spin, 2 correlations(2) of the 3.2 EDMM !of Mthe= ! SMTau+Re(d !M⌧ )! Re +Im(dM⌧ ) |Im |+Md⌧ d2 , (2) decay products.2 M M 2 M M | | M 2 2 with SM22 the SM2 contribution, 2 d2 the2 squared2 EDM contribution2 2 and Re(d⌧ ) Re,Im(2d⌧ ) Im 2 withM SM= theSM SM+Re(d contribution,⌧ ) MRe +Im(dd2 the⌧+) squaredIm + EDMd⌧ contribution+d2 , and Re(M d⌧(2)) Re,Im(M d⌧ ) Im Indeedthe the interferenceMM matrixM element between them for theM with processM Re(d⌧ )e theMe real+ part |⇤ - | ofM⌧ the⌧⌧ EDMis given+ and by Im(- thed⌧ ), following theM imag- sum:M 2 the interference• The squared between2 spin them density with matrix Re(d ⌧for) the e!(p real) e!(- partp) → of γ* the → ⌧τ (EDM2k,S+) andτ (-k, Im(S-)2 d⌧ ), the imag- with SM theinary SM contribution, part. These interferenced2 the squared terms EDM contain contribution the following and combinations Re(d⌧ ) Re,Im( of spin-momentumd⌧ ) Im M inary part. These2 M interference2 terms2 contain the following2 combinationsM2 2 ofM spin-momentum the interferencecorrelations: between them with= Re(d+Re(d⌧ ) the real⌧ ) part+Im(d of the ⌧⌧ )EDM and+ d Im(⌧ d⌧ ),2 the, imag- (2) correlations: SM Re Im d inary part. These interference M termsM contain theM following combinationsM | of| spin-momentumM with 2 the SM contribution, 2 2 the squared EDMˆ contribution and Re(d ) 2 ,Im(d ) 2 correlations: SM • Study of spin momentumRed22 (correlations:S+ S ) k, (ˆS+ S ) p,ˆ ⌧ Re (3) ⌧ Im M MM Re/ (⇥S+ S· ) k, ⇥(S+ · S ) p,ˆ M M(3) the interference between them with2M Re(d/⌧ ) the⇥ real part· of the⇥⌧ EDM· and Im(d⌧ ), the imag- 2 (S+ S ) k,ˆ (ˆS+ S ) p,ˆ 2 Im Im ˆ (S+ S ) k, (S+ S ) p,ˆ inary part. These interferenceRe (SM+ termsMS/) contain/k, (S+ the · S following)· p,ˆ combinations · · of spin-momentum(3) M The/ tau g-2⇥ via its· radiative⇥ leptonic · decays: a proposal 2 ˆ ˆ correlations:wherewhereS S isis a ⌧ aIm⌧spinspin vector,( vector,S+ andS andk) andk,kˆ andp ˆ(Sare+p ˆ theareS unit the) p,ˆ unit vectors vectors of the of⌧ theand⌧ e andmomentae momenta in in ± ± M± ± / · · thethe center center of of massTau mass radiative of ofthe the system leptonic system respectively. respectively. decays at These LO: These terms terms are CP-odd are CP-odd since they since change they change sign sign ˆ 2 where S is a ⌧ spin vector, and k andp ˆ are(S the unitS ) vectorsk,ˆ ( ofS theS⌧ )andp,ˆ e momenta in (3) ± underunder± a a CP-transformation. CP-transformation.3 Re Using5 Using2 this+p this2 method method2 the following the+ following limit limitat 95% at confidence 95% confidence level is level is d Mτ spin↵ M/ ⌧vectorGF y ⇥x unit 4 rvectors· of momenta⇥ · of the center of massobtainedobtained of the [23]: [23]: system respectively.2= These termsGˆ- are0(x, y, CP-oddcos ✓,r) since they change sign dx dy d cos ✓Im 2(⇡S(4+⇡)6 τS and) ek, in CMS(S+ S ) p,ˆ Belle’02 under a CP-transformation. UsingM this method/ the following · limit at 95% · confidence level is Kinoshita & Sirlin PRL2(1959)177;16 16 Kuno & Okada, RMP73(2001)151 16 16 obtained [23]: 0.220.22<
M. Passera TAU2012 Nagoya Sep 18 2012 2 14 BaBar measurement: Rate asymmetry
BaBar measures the CP rate asymmetry in the decay
3.3 τ →K 00Kπ(0ν CP ) violating asymmetry S τ 00 ()() KK A SS Observable Cp 00 ()() KK Selection SS + + K 0 − − K 0 Γ (τ → π Sντ ) − Γ (τ → π Sντ ) one• Ks, A =one charged track not identified as Kaon Q Γ τ + → π + K 0ν + Γ τ − → π − K 0ν up to 3 0’(s, tag-sideS τis) e or( S τ ) 000 KpKqKS =+ Observed level22 asymmetry =-pq≈0.36± 0.01 % in the SM ( + ) - 000 Tag-mode N( Ks) N( Ks) Aobs Bigi & Sanda’05 KpKqKL =−
e-tag 99,222 ev. Grossman99,842 &ev Nir’11. (-0.32+/-0.23)% 2 2 K K = p − q ! 2Re ε tag 70,233 ev. 70,369 ev. (-0.05+/ L -S0.27)% ( K )
• Experimental measurement : BaBar’11 CorrectionA = 1- 0.36 ± 0.23 ± 0.11 % 2.8σ from the SM! The Q easymmetryxp ( arises sfromtat the sdifferentyst ) K0 and anti-K0 nuclear cross section The asymmetry is corrected by –(0.07 +/- 0.01) %
• CP violation in the tau decays should be of opposite sign compared to the 2014/10/31 30-31, October, 2014, B2TIP, KEK, Japan 6 one in D decays in the SM Grossman & Nir’11
D+ + K 0 D− − K 0 Γ ( → π S ) − Γ ( → π S ) A = = -0.54 0.14 % Belle, Babar, D + + 0 − − 0 ( ± ) Γ D → π K + Γ D → π K CLEO, FOCUS ( S ) ( S ) Emilie Passemar 44 3.3 τ → Kπντ CP violating asymmetry
• New physics? Charged Higgs, WL-WR mixings, leptoquarks, tensor interactions (Devi, Dhargyal, Sinha’14, Cirigliano, Crivellin, Hoferichter’17)?
Bigi’Tau12
Very difficult to explain!
• Need to investigate how large can be the prediction in realistic new physics models: it looks like a tensor interaction can explain the effect
but in conflict with bounds from neutron EDM and DD mixing Cirigliano, Crivellin, Hoferichter’17
light BSM physics?
Emilie Passemar 45 3.3 τ → Kπντ CP violating asymmetry
• In this measurement, need to know hadronic part form factors
⎡ Δ Kπ ⎤ Δ Kπ Kπ sγ u 0 = p − p + p + p f (s) − p + p f (s) µ ⎢( K π )µ ( K π )µ ⎥ + ( K π )µ 0 s s ⎣ ⎦
2 2 s Q ( p p ) with = = K + π vector scalar
2 2 Δ = M − M Kπ ( K π )
Emilie Passemar 46
3.3 τ → Kπντ CP violating asymmetry
Bernard, Boito, E.P.’11 Antonelli, Cirigliano, Lusiani, E.P.’13
1 dΓKπ NNbevents∝ tot w ΓKπ ds
2 ⎡ s s ∞ ⎤ ( − Δ Kπ ) ds' φ0 (s') f 0 (s) = exp ⎢P2 (s) + 2 ⎥ ∫ m +m 2 π ( K π ) s' s'− Δ s'− s − iε ⎣⎢ ( Kπ )( ) ⎦⎥
Emilie Passemar 3.3 τ → Kπντ angular CP violating asymmetry
• Measurement of the angular CP asymmetry from Belle:
d - K − Γ (τ → π ντ ) 2 2 2 2 2 = ⎡ A(Q ) − B(Q ) 3cos ψ − 1 3cos β − 1 ⎤ f (s) 2 ⎣ ( )( )⎦ + d Q d cosθ d cos β 2 + m 2 f! (s) − C(Q2 )cosψ cos β Re f (s) f! * (s) τ 0 ( + 0 ) CP violating term 2 2 2 – A ( Q ) , B ( Q ) , C ( Q ): kinematic factors S-P interference – Angles: in Kπ rest frame • β: angle between kaon and e+e- CMS frame • Ψ: angle between τ and CMS frame
in τ rest frame • θ: angle between τ direction in CMS and direction of Kπ system (dependence with Ψ) Emilie Passemar 48
3.3 τ → Kπντ angular CP violating asymmetry
• Measurement of the angular CP asymmetry from Belle:
d - K − Γ (τ → π ντ ) 2 2 2 2 2 = ⎡ A(Q ) − B(Q ) 3cos ψ − 1 3cos β − 1 ⎤ f (s) 2 ⎣ ( )( )⎦ + d Q d cosθ d cos β 2 + m 2 f! (s) − C(Q2 )cosψ cos β Re f (s) f! * (s) τ 0 ( + 0 ) CP violating term 2 2 2 – A ( Q ) , B ( Q ) , C ( Q ): kinematic factors S-P interference
Charged Higgs contribution
+
2 Khün & Mirkes’05 ! η s f0 (s) = f0 (s) + 2 fH (s) fs() fs () m with H = 0 Emilie Passemar τ mmus− 49 3.3 τ → Kπντ CP violating asymmetry
• Measurement of theBelle direct contribution (Conti.) of NP in the angular CP violating asymmetry done by CLEO and Belle Belle does not see any asymmetry at the 0.2 - 0.3%Phys. level Rev. Lett. Result Belle’11107,131801 (2011)
• Problem with this measurement? It would be great to have other experimental measurements from Belle II AxatWQGeV (1.8 2.1 1.4) 10 32 1.0 CP Emilie Passemar 50
2014/10/31 30-31, October, 2014, B2TIP, KEK, Japan 11 Phenomenology: Two hadron system
Hadronic Current: (Kp system will only arrow Jp=1- and 0+) QQ jKppV → ()()|(0)|0 FQg ()22 ppFQQ () Qpp 00 3.3 τ KπKVντ CP violating asymmetry 2 kS k Q Full differential cross section in K rest frame. p • The angular CP asymmetry from Belle:
d - K − Γ (τ → π ντ ) 2 2 2 2 2 = ⎡ A(Q ) − B(Q ) 3cos ψ − 1 3cos β − 1 ⎤ f (s) 2 ⎣ ( )( )⎦ + d Q d cosθ d cos β 2 m 2 f! (s) C(Q2 )cos cos Re f (s) f! * (s) + τ 0 − ψ β ( + 0 ) Source of CPV if F CP violatingor term Fs has an S-P interferenceimaginary phase • When integrating on the angle the interference term between scalar and vectorIntegrated vanishes over angular distribution 2 22 3 22 dQQ Gmsin 2 Fc 11 No Vector and 2 32532Qm 2 m 2 dQ Scalar interference
2 term 2222 3 Q 2 qQ() qQ ()|| F | F | 11 VS4 12 Qm22 / 2014/10/31 30-31, October, 2014, B2TIP, KEK, Japan 12 Emilie Passemar 51
How to understand BaBar’s rate asymmetry
A recent paper discuss the possibility about the tensor interaction (H.Devi, L.Dhargyal,N. Sinha, PRD 90,013016(2014). Effective Hamiltonian of Tensor int. How to understandeff BaBar’s rate asymmetry H T Gs'( u )( (1 5 ) ) 3.3 τ → Kπντ CP violating asymmetry A recent paper discuss the possibility about the tensor interactionDevi , Dhargyal, Sinha’14 G’ (isH.Devi an , L.Dhargyal,Nimaginary. Sinha , couplingPRD 90,013016(2014 ). Cirigliano, Crivellin, Hoferichter’17 G 5 • We needGG a',|| tensorR interactionF to getGe somei interference: Effective HamiltonianT of Tensor int. 0.10 2 G i eff F φT uc H Gs'( u )( (1 ) ) with G' = CT , CT = CT e T 5 2 The Vector -Tensor interference term does not vanish after 0.05 τ τ G’ is• anWhen imaginary integrating coupling the interference term between vector and tenson does not 5 angular integration.G GG',|| R F Gei ] vanish: T n 11 T 2 EDM 0.10 c
[ 0.00 D-D, =- /4 uucu Im uc The Vectord -Tensord SM interferenced T d VT term does not vanish after D-D, = /4 angular integration.222 2 FIG. 3: Diagrammatic representation of the electromagnetic dQ dQ dQ dQ |A ,BSM|>10-3 -0.05 CP 0.05 dipole operator contributing to the neutron EDM produced d dτ d d τ by inserting the (¯τσ Rτ)(¯uσµν Ru)operator(left),andthe SM T VT 2 µν dQ222 dQ dQ dQ 2 322 2 2 2 ] contribution to D–D¯ mixing originating from the double in-d VT 223 mmQ 2 2 3 q12 Q n
11 T EDM µν d m ⎛ m2 Q ⎞ q Γ GqRFF2 sin2 322 − 2 Q 2 2c | || || | cos( ) -0.10 [ sertion of the operator (¯τσµν Rτ)(¯cσ Ru)(right,thesecond Vd − T2 FcmmQ τ 32τ q 1 23/2Q 1 0.00 TVT 2 TV dQ2 VT = GF22sin θC 643 21 m 3 (/Q2 )2 m D-D, =- /4 2 uu GqRFF-Fc0.10sin -0.0532 cu0.00⎜ 23/20.05 ⎟ 21 |0.10 TVT || || |2 cos(Im TV ) permutation is omitted). dQdQ 64 32πm m (Q ) 2 m m ⎝ τ ⎠ Q τ D c21 ( ) D- , = /4 Im[ T ] FIG. 3: Diagrammatic representation of the electromagnetic |A ,BSM|>10-3 -0.05 CP × CT FV (s) FT (s) cos δ T (s) − δV (s) + φT involving the τ and the up quark only. The renormaliza-dipole operator contributing to the( neutron21 EDM11 produced) 5 FIG. 4: Allowed regionsµν in the Im cT –Im cT plane from the tion group evolution [41] of this operator then producesby insertingneutron the (¯τσ EDMµν Rτ and)(¯uσD–DRu¯ mixing)operator(left),andthe (for φ = ±π/4andΛ = ¯ 0.10 an up-quark EDM du(µ), contribution1TeV),comparedtothefavoredregionfromthe to D–D mixing originating from the doubleτ → in-KS πντ In conflict with bounds fromµν uc sertion of theCP operatorasymmetry. (¯τσµ Theν Rτ exclusion)(¯cσ Ru regions)(right,thesecond for φ = ±π/4differ -0.10 i µν 2014/10/31permutationneutron due is EDM to omitted). the asymmetricand DD mixing form30-31, of October, the fit 2014, result B2TIP, in [48].KEK, Japan -0.10 -0.05 0.00 14 0.05 0.10 D = du(µ)¯uσ γ5uFµν , (31) τ τ 21 L −2 Im[cT ] ] n Cirigliano, Crivellin, Hoferichter’17 11 T EDM c
[ 0.00 via the diagram shown in Fig. 3. Solving the RG follow- D-D, =- /4 uu11 cu21 Im 52 involving theof [48]τ and and the assuming up quark the only.phase The of Vcd renormaliza-c + Vcsc to be 21 11 D ing [42–44] we find 2014/10/31 30-31,T October,T 2014,FIG. B2TIP, 4: Allowed KEK, regions Japan in the Im cT –Im cT planeD- , = from/4 the 14 3 FIG. 3: Diagrammatic representation of the electromagnetic |A ,BSM|>10-3 tion groupequal evolution to φ = [41]π/ of4, thisthis operator leads to the then situation produces depictedneutron EDM and-0.05 D–D¯ mixing (for φ = ±π/CP4andΛ = 2 ± dipole operator contributing to the neutron EDM produced emτ V Λ in Fig. 4. Since (34) requires the insertion of twoµν effective us an up-quark EDM du(µ), by inserting the (¯τσµν Rτ)(¯uσ Ru)operator(left),andthe1TeV),comparedtothefavoredregionfromthe τ → KS πντ du(µ)= 2 2 Im cT (µ) log contribution to D–D¯ mixing originating from the double in- v π µ operators, the leading contribution here is of dimensionµν 8,CP asymmetry. The exclusion regions for φ = ±π/4differ sertion of the operator (¯τσµν Rτ)(¯cσ Ru)(right,thesecond -0.10 while in an ultravioleti complete model there is in general -0.10 -0.05 0.00 0.05 0.10 Λ −21 permutationµν is omitted). due to the asymmetric form of the fit result in [48]. 3.0 Im c (µ) log 10 e cm. (32) D = du(µ)¯uσ γ5uFµν , (31) c21 ≃ × T µ × alreadyL a dimension-6−2 contribution, making the bounds Im[ T ] ¯ from D–D mixing eveninvolving stronger the thanτ and the up one quark shown only. The in renormaliza- 21 11 u via the diagram shown in Fig. 3. Solving the RG follow- FIG. 4: Allowed regions in the Im cT –Im cT plane from the Using the 90% C.L. bound dn = gT (µ)du(µ) < 2.9 Fig. 4. To evade all bounds,tion group one evolution would [41] thereforeof this operator not then produces neutron EDM and D–D¯ mixing (for φ =11±π/4andΛ21= − × of [48] and assuming the phase of VcdcT + VcscT to be 10 26 e cm [45] and the recent lattice result [46] gingu (µ [42–44]= we find an up-quark EDM du(µ), 1TeV),comparedtothefavoredregionfromthe τ → KS πντ T only have to cancel the cT contribution to the neutron CP asymmetry.3 The exclusion regions for φ = ±π/4differ − equal to φ = π/4, this leads to the situation depicted 2GeV)= 0.233(28) we obtain (µτ =2GeV) 4 i µν due to the asymmetric form of the fit result in [48]. EDM at the2 level of 10 , but also tuneD = thedu( combinationµ)¯uσ γ5uFµν , (31) ± − em11 τ Vus 21 Λ L −2 in Fig. 4. Since (34) requires the insertion of two effective − 5 du(µ)=VcdcT 2+ Vcs2 cTImclosecT (µ to) log purely imaginary to evade the 4.4 10 −5 v π via theµ diagram shown in Fig. 3. Solving theoperators, RG follow- the leading contribution here is of dimension 8, < ¯ of [48] and assuming the phase of V c11 + V c21 to be Im cT (µτ ) × Λ 10 , (33) constraint from D–D mixing.ing [42–44] we find cd T cs T | | ≤ log while in an ultraviolet complete3 model there is in general µτ ∼ Λ − equal to φ = π/4, this leads to the situation depicted 21 2 ± 3.0 Im cT (µ) log 10 emeτcmV . (32) Λ in Fig. 4. Since (34) requires the insertion of two effective d (µ)= us Im c (µ) log already a dimension-6 contribution, making the bounds > ≃ × µ ×u v2 π2 T µ operators, the leading contribution here is of dimension 8, where the last inequality holds for Λ 100 GeV. This CONCLUSIONS from D–D¯ mixing even stronger than the one shown in Λ − while in an ultraviolet complete model there is in general bound is based on the assumption that∼ there are no other u 3.0 Im c (µ) log 10 21 e cm. (32) Using the 90% C.L. bound dn = gT (µ≃)du×(µ) T< 2.9µ × Fig. 4. To evadealready a all dimension-6 bounds, contribution, one would making thereforethe bounds not contributions to the neutron EDM canceling the effect−26 of u × from D–D¯ mixing even stronger than the one shown in 10 e cm [45] and the recent lattice result [46] g (µ = u In this article we examinedUsing the non-standard 90% C.L. bound contributionsT dn = gT (µ)donlyu(µ) < have2.9 toFig. cancel 4. To the evadec allT bounds,contribution one would to therefore the neutronnot cT . However, for values of Im cT (µτ ) 0.1 required to 10−26 e cm [45] and the recent lattice result [46] gu (µ ×= −4 2GeV)= to0 the.233(28)CP asymmetry we obtain in (τµτ =2GeV)K πν .Wefindthatatthe T only have to cancel the cT contribution to the neutron ∼ S τ EDM at the level of 10 , but− also tune the combination explain the tau CP asymmetry, the cT contribution alone − 2GeV)=→ 0.233(28) we obtain (µτ =2GeV) 11 EDM21 at the level of 10 4, but also tune the combination dimension 6 level only the− tensor− operator can lead to di- 11 21 5 − VcdcT + VcscVT c close+ V c toclose purely to purely imaginary imaginary to to evade evade the the would predict a neutron EDM four orders of magnitude 4.4 10 − 5 cd T cs T rect CP violation, with negligible< QED5 corrections4.4 10 from< −5 ¯ ¯ Im cT (µτ ) × 10Im cT (,µτ ) ×(33)Λ 10constraint, (33) fromconstraintD–D frommixing.D–D mixing. larger than the current bound, requiring an extraordinary Λ | | ≤ log ∼ the| scalar operator.| ≤ log However, the effect of theµτ tensor cancellation at the level of one part in 104. µτ ∼ operator is much smallerwhere than the previously last inequality estimated holds for Λ as> 100 a GeV. This Such a cancellation could in principle occur with op- CONCLUSIONS where theconsequence last inequality of Watson’s holdsbound for final-state-interactionΛ is based> 100 on the GeV. assumption This theorem. that∼ there are no other erators related to the flavor structure C in (28), contributions to the neutron EDM canceling the effect of CONCLUSIONS 3311 In this article we examined non-standard contributions bound is basedTherefore, on the a veryassumption large imaginaryc . that However,∼ there part for valuesare of nothe of Im other Wilsonc (µ ) co-0.1 required to since the neutron EDM is sensitive to the combination T T τ to the CP asymmetry in τ K πν .Wefindthatatthe explain the tau CP asymmetry, the c contribution∼ alone S τ 11 21 21 11 contributionsefficient to the of the neutron tensor EDM operator canceling would be the required effect inof T order dimension 6 level only the tensor→ operator can lead to di- VudIm cT + VusIm cT ,wherecT = cT and cT is defined would predict a neutron EDM four orders of magnitude In this articlerect CP weviolation, examined with negligible non-standard QED corrections contributions from cT . However,to account for values for the of current Im clargerT ( tensionµτ than) the between0 current.1 required bound, theory requiring to and ex- an extraordinary analogously to (30). However, yet another combination the scalar operator. However, the effect of the tensor periment. In fact, we findcancellation in a model-independent∼ at the level of one part analy- in 104to. the CP asymmetry in τ KSπντ .Wefindthatatthe appears in D–D¯ mixing, which is very sensitiveexplain to the the tau CP asymmetry, the cT contribution alone operator is much smaller→ than previously estimated as a Such a cancellation could in principle occurdimension with op- 6 level only the tensor operator can lead to di- sis that this is in general in conflict with the bounds from consequence of Watson’s final-state-interaction theorem. imaginary part of the Wilson coefficients (as for examplewould predict a neutron EDM fourerators orders related toof the magnitude flavor structure C in (28), ¯ rect3311 CP violation,Therefore, with a very negligible large imaginary QED part of corrections the Wilson co- from the neutron EDM and Dsince–D themixing, neutron making EDM is sensitive a BSM to ex- the combination defined in [47]) larger than the current bound, requiring an extraordinary efficient of the tensor operator would be required in order planation (realized aboveV theIm c electroweak11 + V Im c21,where breakingc21 = c scale)andthec11 is scalar defined operator. However, the effect of the tensor ud T us4 T T T T to account for the current tension between theory and ex- 2 cancellation at the level of one partanalogously in 10 to. (30). However, yet another combination ′ 1 ′ m Λ 2 operator is muchperiment. smaller In fact, we than find in previously a model-independent estimated analy- as a 2 τ 2 11 21 Such a cancellation could in principleappears in D– occurD¯ mixing, with which op- is very sensitive to the C2 = C3 =4GF 2 log Vus VcdcT + VcscT , (34) sis that this is in general in conflict with the bounds from 2 π µτ imaginary part of the Wilson coefficients (asconsequence for example of Watson’s final-state-interaction theorem. ! "erators related to the flavor structure C in (28), the neutron EDM and D–D¯ mixing, making a BSM ex- defined in [47]) 3311 Therefore, a very large imaginary part of the Wilson co- 3 planation (realized above the electroweak breaking scale) where we have neglected the effect of external momenta,since the neutronIn general, EDM the constraint is sensitive is diluted to the by ! combination| tan2 φ| and therefore 11 21 21 ′ 1 ′ 211mτ Λ 2 11 efficient21 2 of the tensor operator would be required in order i.e. the mass of the charm quark. Using the global fit disappears for φ = ±π/2. C2 = C3 =4GF 2 log Vus VcdcT + VcscT , (34) VudIm cT + VusIm cT ,wherecT = cT2 and cTπ is definedµτ ! to account" for the current tension between theory and ex- analogously to (30). However, yet another combination where we have neglected the effect of externalperiment. momenta, In3 fact,In general, we the find constraint in a is model-independent diluted by !| tan φ| and therefore analy- appears in D–D¯ mixing, whichi.e. is the very mass sensitive of the charm to quark. the Using the global fit disappears for φ = ±π/2. sis that this is in general in conflict with the bounds from imaginary part of the Wilson coefficients (as for example the neutron EDM and D–D¯ mixing, making a BSM ex- defined in [47]) planation (realized above the electroweak breaking scale) 2 ′ 1 ′ m Λ 2 C = C =4G2 τ log V 2 V c11 + V c21 , (34) 2 2 3 F π2 µ us cd T cs T τ ! " where we have neglected the effect of external momenta, 3 In general, the constraint is diluted by !| tan φ| and therefore i.e. the mass of the charm quark. Using the global fit disappears for φ = ±π/2. 3. Three hadron system
References: K. Kiers,K.Little,A. Datta, D. London et al., Phys. Rev. D78, 1130083.4 (2008). Three body CP asymmetries Tau2012 proceeding by K. Kiers e.g: (p123) K (p1) (p2 ) (p3 ) • Ex: → K τ ππντ
Possible Jp states for 0-+0-+0- system 0-, 1+, 1-
4 Hadronic Form Factors e.g., Choi, Hagiwara and 2 • A variety of CPV2 observables can be studied : Tanabashi’98 Axial Vector F1(Q ,s1,s2): K* , F2(Q ,s1,s2); K B1,B2 Kiers, Little, Datta, τ → Kππν , τ → πππν rate, angular asymmetries, 2 τ τ London et al.,’08 Vector F3(Q ,s1,s2) B3 triple products,…. Mileo, Kiers and, Szynkman’14 Pseudo-Scalar F (Q2,s ,s ) B 4 1 Same2 principle as in charm4 , see Bevan’15
Difficulty : Treatement of the hadronic part 2014/10/31 30-31, October,Hadronic 2014, B2TIP, final KEK, state Japan interactions have to be taken17 into account! Disentangle weak and strong phases
• More form factors, more asymmetries to build but same principles as for 2 bodies
Emilie Passemar 53
Belle does not see any asymmetry at the 0.2 - 0.3% level
4. Other interesting topics with tau decays Charged4.1 Lepton Current Universality Universality
• Test of µ/e universality: gg / e
BB e 1.0018 0.0014 BB e 1.0021 0.0016Charged Current Universality
BBKK e 0.9978 0.0018 gg / e BBKK e 1.0010 0.0025 BB e 1.0018 0.0014 gg/ BBWW e 0.996 0.010 BB e 1.0021 0.0016
B BB e 1.0011 0.0015 • Tested at 0.14%KK from Tau leptonice 0.9978 Brs! (0.28% 0.0018 in Z decays) gg / e BBKK e 1.0010 0.0025 0.9962 0.0027 Emilie Passemar 55 gg/ B 1.0029 0.0015BBWW e 0.996KK 0.010 0.9858 0.0070 B BBWW e 1.031 0.013 BBWW 1.034 e 0.013 1.0011 0.0015 gg / e 0.9962 0.0027
A. Pich B Physics 1.0029 0.0015 KK 4 0.9858 0.0070
BBWW e 1.031 0.013 BBWW 1.034 0.013
A. Pich Physics 4 Charged4.1 Lepton Current Universality Universality
• Test of µ/e universality: gg / e
BB e 1.0018 0.0014 BB e 1.0021 0.0016Charged Current Universality
BBKK e 0.9978 0.0018 gg / e BBKK e 1.0010 0.0025 BB e 1.0018 0.0014 gg/ BBWW e 0.996 0.010 BB e 1.0021 0.0016
B BB e 1.0011 0.0015 • Tested at 0.14%KK from Tau leptonice 0.9978 Brs! (0.28% 0.0018 in Z decays) gg / e • What about the third family? BBKK e 1.0010 0.0025 0.9962 0.0027 Emilie Passemar 56 gg/ B 1.0029 0.0015BBWW e 0.996KK 0.010 0.9858 0.0070 B BBWW e 1.031 0.013 BBWW 1.034 e 0.013 1.0011 0.0015 gg / e 0.9962 0.0027
A. Pich B Physics 1.0029 0.0015 KK 4 0.9858 0.0070
BBWW e 1.031 0.013 BBWW 1.034 0.013
A. Pich Physics 4 4.1 Lepton Universality
• What about the third family?
1.0010 ± 0.0015
0.9961 ± 0.0027
0.9860 ± 0.0070 1.0029 ± 0.0015
1.0000 ± 0.0014
Updated with HFAG’17 Updated with HFAG’17
• Universality tested at 0.15% level and good agreement except for – W decay old anomaly – B decays See talks on Thursday Emilie Passemar 57
Measured σWW / YFSWW Measured σWW / RacoonWW
17/02/2005 17/02/2005
1.034 ± 0.023 1.033 ± 0.023
0.986 ± 0.013 0.987 ± 0.013
1.000 ± 0.029 1.003 ± 0.029
1.003 ± 0.019 1.006 ± 0.019
0.985 ± 0.018 0.987 ± 0.018
0.995 ± 0.024 0.998 ± 0.024
0.980 ± 0.018 0.983 ± 0.018
1.000 ± 0.015 1.004 ± 0.015
0.994 ± 0.009 0.996 ± 0.009
0.9 1. 1.1 0.9 1. 1.1
Figure 5.2: Ratios of LEP combined W-pair cross-section measurements to the expectations according to YFSWW [84] and RACOONWW [85] The yellow bands represent constant relative→ errors of 0.5% on4.1 the twoLepton cross-section Flavour predictions. Universality anomaly W τ ντ
Winter 2005 - LEP Preliminary • Old LEPWinter anomaly 2005 - LEP Preliminary W Leptonic Branching Ratios 23/02/2005 W Hadronic Branching Ratio ALEPH 10.78 ± 0.29 DELPHI 10.55 ± 0.34 23/02/2005 L3 10.78 ± 0.32 OPAL 10.40 ± 0.35 LEP W→eν 10.65 ± 0.17 ALEPH 67.13 ± 0.40 ALEPH 10.87 ± 0.26 DELPHI 10.65 ± 0.27 DELPHI 67.45 ± 0.48 L3 10.03 ± 0.31 OPAL 10.61 ± 0.35 L3 67.50 ± 0.52 LEP W→µν 10.59 ± 0.15 OPAL 67.91 ± 0.61 ALEPH 11.25 ± 0.38 DELPHI 11.46 ± 0.43 L3 11.89 ± 0.45 OPAL 11.18 ± 0.48 LEP 67.48 ± 0.28 2 LEP W→τν 11.44 ± 0.22 χ /ndf = 15.4 / 11 χ2/ndf = 6.3 / 9 LEP W→lν 10.84 ± 0.09 χ2/ndf = 15.4 / 11 66 68 70 10 11 12 Br(W→hadrons) [%] Br(W→lν) [%]
Figure 5.3: Leptonic and hadronic W branching fractions, as measured by the experiments, and the EmilieLEP Passemar combined values according to the procedures described inthetext. 58
55 Measured σWW / YFSWW Measured σWW / RacoonWW
17/02/2005 17/02/2005
1.034 ± 0.023 1.033 ± 0.023
0.986 ± 0.013 0.987 ± 0.013
1.000 ± 0.029 1.003 ± 0.029
1.003 ± 0.019 1.006 ± 0.019
0.985 ± 0.018 0.987 ± 0.018
0.995 ± 0.024 0.998 ± 0.024
0.980 ± 0.018 0.983 ± 0.018
1.000 ± 0.015 1.004 ± 0.015
0.994 ± 0.009 0.996 ± 0.009
0.9 1. 1.1 0.9 1. 1.1
Figure 5.2: Ratios of LEP combined W-pair cross-section measurements to the expectations according to YFSWW [84] and RACOONWW [85] The yellow bands represent constant relative→ errors of 0.5% on4.1 the twoLepton cross-section Flavour predictions. Universality anomaly W τ ντ
Winter 2005 - LEP Preliminary • Old LEPWinter anomaly 2005 - LEP Preliminary W Leptonic Branching Ratios 23/02/2005 W Hadronic Branching Ratio ALEPH 10.78 ± 0.29 DELPHI 10.55 ± 0.34 23/02/2005 L3 10.78 ± 0.32 OPAL 10.40 ± 0.35 LEP W→eν 10.65 ± 0.17 2.8ALEPHσ away from SM! 67.13 ± 0.40 ALEPH 10.87 ± 0.26 DELPHI 10.65 ± 0.27 DELPHI 67.45 ± 0.48 L3 10.03 ± 0.31 • New physics? OPAL 10.61 ± 0.35 L3 67.50 ± 0.52 LEP W→µν 10.59 ± 0.15 SomeOPAL models: 67.91 ± 0.61
ALEPH 11.25 ± 0.38 Li & Ma’05, Park’06, Dermisek’08 DELPHI 11.46 ± 0.43 L3 11.89 ± 0.45 OPAL 11.18 ± 0.48 TryLEP to explain with SM EFT 67.48 approach ± 0.28 χ2/ndf = 15.4 / 11 LEP W→τν 11.44 ± 0.22 5 χ2/ndf = 6.3 / 9 with [U(2)xU(1)] flavour symmetry LEP W→lν 10.84 ± 0.09 Very difficult to explain without χ2/ndf = 15.4 / 11 modifying66 any 68 other 70 observables 10 11 12 Filipuzzi, Portoles, Gonzalez-Alonso'12 Br(W→hadrons) [%] Br(W→lν) [%] • Would be great to have another measurement by LHC Figure 5.3: Leptonic and hadronic W branching fractions, as measured by the experiments, and the EmilieLEP Passemar combined values according to the procedures described inthetext. 59
55 The CKM Mechanism 4.2 Probing the CKM mechanism: extraction of Vus
The CKM Mechanism• The CKM Mechanism source source of ofCharge C hargeParity PViolationarityV iniolation SM in SM
• Unitary 3x3 Matrix• Unitary, parametrizes 3x3 Matrix, parametrizes rotation rotation between between mass mass and and weakweak interaction interaction eigenstates in Standardeigenstates Model in Standard Model
d0 Vud Vus Vub d
s0 = V V V s 0 1 0 cd cs cb 1 0 1 b0 Vtd Vts Vtb b @ A @ A @ A The |Vus| element of CKM Matrix Weak Eigenstates CKM Matrix Mass Eigenstates
Vij: Mixing between Weak and Mass Eigenstates • Fully parametrized by four parameters if unitarity holds: three real parameters 1 λ λ3 and one complex phase that if non-zero results in CPV λ 1 λ2 • Unitarity can be visualized usingλ triangle3 λ2 equations,1 e.g. Emilie Passemar 60
V V † = 1 V ⇤ V + V ⇤ V + V ⇤V =0 CKM CKM ! ub ud cb cd tb td • |Vud| = 0.97417 ± 0.00021 (from nuclear β decays) J.C.Hardy & I.S. Towner, PRC 91 (2015) 025501 -3 University• |Vub |of = Zurich, (4.09 2016,± 0.39) May x 910 (from BFlavour → Xu anomaliesℓ ν decays) & Belle II's impact on the physics landscape 14 Particle Data Group 2016 CKM ⇒ |Vus| = 0.22582 ± 0.00091
Precision measurement of |Vus| is a test of CKM unitarity Overview Swagato of τ physics 10 Banerjee
4.2 Paths to Vud and Vus
• From kaon, pion, baryon and nuclear decays
0+ 0+
Vud ± 0 n peνe π lνl π π eνe
Vus K πlνl Λ peνe K lνl
dVdVs=+ud us θ
• From τ decays (crossed channel)
V ud τ ππντ τ πντ τ hNSντ
τ hSντ Vus K K τ πντ τ ντ (inclusive)
Emilie Passemar 61
4.2 Paths to Vud and Vus
• From kaon, pion, baryon and nuclear decays
0+ 0+
Vud ± 0 n peνe π lνl π π eνe
Vus K πlνl Λ peνe K lνl
dVdVs=+ud us θ
• From τ decays (crossed channel)
V ud τ ππντ τ πντ τ hNSντ
τ hSντ Vus K K τ πντ τ ντ (inclusive)
Emilie Passemar 62
4.2 Vus determination
0.21 0.22 0.23 0.24 0.25 From Unitarity Kaon and hyperon decays K decays (+ f (0)) Flavianet l3 + Kaon WG’10 K / decays (+ f /f l2 πl2 K π) update by Moulson’CKM16 Hyperon decays
τ decays τ -> s inclusive
τ -> Kν absolute (+ fK) BaBar & Belle HFAG’17 τ branching fraction ratio -> K / -> (+ f /f τ ν τ πν K π) Our result from Belle BR -> K decays (+ f (0), FLAG) τ πντ +
0.21 0.22 0.23 0.24 0.25 NB: BRs measured by B factories are systema cally Vus Emilie Passemar smaller than previous measurements 63 4.2 Vus determination
• Longstanding inconsistencies between inclusive τ and kaon decays in extraction of Vus • Inclusive τ decays:
Rτ ,NS Rτ ,S δ R τ ≡ 2 − 2 V V ud us
SU(3) breaking quantity,
strong dependence in ms computed from OPE (L+T) + phenomenology
δ R = 0.0242(32) τ ,th Gamiz et al’07, Maltman’11
HFAG’17 2 Rτ ,S V = R = 0.1633(28) us τ ,S V 0.2186 0.0019 0.0010 Rτ ,NS us = ± exp ± th R R 3.4718(84) 2 − δ τ ,th τ ,NS = V ud V = 0.97417(21) 3.1σ away from unitarity! ud 64 5. Conclusion and outlook
Emilie Passemar Conclusion and outlook
• Direct searches for new physics at the TeV-scale at LHC by ATLAS and CMS energy frontier
• Probing new physics orders of magnitude beyond that scale and helping to decipher possible TeV-scale new physics requires to work hard on the intensity and precision frontiers
• Charged leptons and in particular tau physics offer an important spectrum
of possibilities:
Ø LFV measurement has SM-free signal
Ø Current experiments and mature proposals promise orders of magnitude sensitivity improvements (Belle II, Tau-Charm factory, etc.)
Ø There is a hint of new dynamics in CPV asymmetries in the tau sector
Ø Progress towards a better knowledge of hadronic uncertainties
Ø New physics models usually strongly correlate the flavours sectors
Emilie Passemar 66 Conclusion and outlook
• We show how CLFV decays offer excellent model discriminating tools giving indications on - the mediator (operator structure) - the source of flavour breaking (comparison τ µ vs. τe vs. µe)
• Interplay low energy and collider physics: LFV of the Higgs boson
• We discussed the possibilities to look for CP violation in the tau sector: BaBar result does not agree with SM expectation but needs to be
confirmed A lot of new measurements possible (ACP, AFB, etc.) to shed light on CP violation in the tau sector: combine strong and weak phase determination
• EDM of the tau also very interesting to study but difficult
• Several topics extremely interesting to study that I just mentioned or had no time to talk about:
– αS, |Vus| and ms from hadronic tau decays – Lepton universality tests, Michel parameters, g-2 of the tau…
• A lot of very interesting physics remains to be done in the tau sector! Emilie Passemar 67 6. Back-up 3.3 → K angular CP violating asymmetry Formτ Factorπντ and Analysis of Babar results
• Belle uses sum of BWs to fit the invariant mass distribution Belle’08 Use Belle results for the Form Factors Fv and Fs. Phys. Lett. 654, 65 (2007). 1
Two best fit solutions: • Can be justified for the vector but not for the scalar! Use a parametrization relying on dispersion relations instead: – Resum all final state Kπ rescattering
K K 2 |T/SM| RT|FT| cos res. Model
0.009 -0.213 -0.82 (a)
– Allow to combine with K 0.018 → πl νl precise-0.303 measurements -0.90 (b)
• Several theoretical parametrizations proposed:They conclude All rely that on analyticity1-2 % tensor and unitarity and crossing symmetry Jamin, Pichcontribution, Portolés’06,’08, could explain Moussallam’08, the BaBar Boito, Escribano, Jamin’09,’10, Bernard, Boito, rate E.P.’11, asymmetry Bernard’14 for both cases. Emilie Passemar2014/10/31 30-31, October, 2014, B2TIP, KEK, Japan 1569
3.3 τ → Kπντ angular CP violating asymmetry
Bernard, Boito, E.P.’11 Antonelli, Cirigliano, Lusiani, E.P.’13
1 dΓKπ NNbevents∝ tot w ΓKπ ds
2 ⎡ s s ∞ ⎤ ( − Δ Kπ ) ds' φ0 (s') f 0 (s) = exp ⎢P2 (s) + 2 ⎥ ∫ m +m 2 π ( K π ) s' s'− Δ s'− s − iε ⎣⎢ ( Kπ )( ) ⎦⎥
Emilie Passemar 3.3 τ → Kπντ CP violating asymmetry
• In this measurement, need to know hadronic part form factors
⎡⎤ΔΔKKππ Kπγ su 0=pp−++ pp fs()− pp+ fs() µ( KKπ)µµ( π) + ( K π) µ0 ⎢⎥ss ⎣⎦
2 2 s Q ( p p ) with = = K + π vector scalar
• Up to now know from decay spectrum but difficult to disentangle scalar and vector form factor consider the FB asymmetry instead
ddΓ−Γ(cosθθ) ( -cos ) Beldjoudi & Truong’94 A = FB ddΓ(cosθθ) +Γ( -cos ) Moussallam, B2TIP
• Formula: can disentangle scalar and vector FF easily K0
K K cos δ 1/2 − δ 1/2 K0 K0 ( 1 0 ) K K K0 K0
Emilie Passemar 71
3.5 Results
Bound:
2 2 Y h + Y h ≤ 0.13 µτ τµ
Emilie Passemar Belle’08’11’12 except last from CLEO’97 72 ττ→→""#### 3.5 What if τ → µ(e)ππ observed? Talk byreinterpreting J. Zupan Celis, Cirigliano, Passemar, 1309.3564;! $$ reinterpreting Celis, Cirigliano, Passemar, 1309.3564;! Reinterpreting Celis, Cirigliano, E.P’14 @ KEK-FF2014FALL see also Petrov, Zhuridov, 1308.6561 ! •• hadronichadronic tautau decaysdecays ττ→→"&"&++&&-,-,ττ→→"&"&00&&00 see also Petrov, Zhuridov, 1308.6561 ! • τ →• µ(sensitivee)ππ sensitive to both to Y Y , and • sensitive to bothµ Yτ τ" τ","τ"τ and but also to Y ! lightu ,dquark,s yukawas Yu,d,s! h h light quark yukawas Yu,d,s! Y poorly bounded ~O(Y )$ • Yu,d,•s• poorlyYu,d,s bounded poorly bounded ~O(Yb )$ u,d,s b
•• forfor YYu,d,s atat theirtheir SMSM valuesvalues thenthen • For Yu,d,s u,d,sat their SM values : + 11 0 0 12 Br (⌧ µ⇡ +⇡ ) < 1.6 10 11,Br(⌧ µ⇡ 0⇡ 0) < 4.6 10 12 Br(⌧ ! µ⇡ ⇡ ) < 1.6⇥ 10 ,Br(⌧ ! µ⇡ ⇡ ) < 4.6⇥ 10 ! + ⇥ 10 ! 0 0 ⇥ 11 Br(⌧ e⇡ +⇡ ) < 2.3 10 10,Br(⌧ e⇡ 0⇡ 0) < 6.9 10 11 Br(⌧ e⇡ ⇡ ) < 2.3 10 ,Br(⌧ e⇡ ⇡ ) < 6.9 10 ! ⇥ ! ⇥ ! ⇥ ! ⇥
• •Butfor for Y Yu,d,su d s atat theirtheir upper present bound: upper bounds • for Yu,d,s, , at their present upper bounds + 8 0 0 8 Br (⌧ µ⇡ +⇡ ) < 3.0 10 8,Br(⌧ µ⇡ 0⇡ 0) < 1.5 10 8 Br(⌧ µ⇡ ⇡ ) < 3.0 10 ,Br(⌧ µ⇡ ⇡ ) < 1.5 10 !! + ⇥⇥ 7 !! 0 0 ⇥⇥ 7 Br (⌧ e⇡ +⇡ ) < 4.3 10 7,Br(⌧ e⇡ 0⇡ 0) < 2.1 10 7 Br(⌧ ! e⇡ ⇡ ) < 4.3⇥ 10 ,Br(⌧ ! e⇡ ⇡ ) < 2.1⇥ 10 below present! experimental⇥ limits! ! ⇥
•• Br(Br(ττ→→"&"&++&&-)-) belowbelow presentpresent exp.exp. limit,limit, ifif discovereddiscovered • If discovered among other things upper limit on Yu,d,s! would (among other things) imply upper limit on Yu,d$ wouldInterplay (among between other high-energy things) and imply low-energy upper constraints! limit on Yu,d$ Emilie Passemar•• similarlysimilarly pseudoscalarpseudoscalar HiggsesHiggses cancan bebe boundedbounded fromfrom ττ→→"&"&((73ηη, ,ηη’),’), ττ→→ee&&((ηη,,ηη’)’)$$ •• cancan saturatesaturate presentpresent experimentalexperimental limitslimits J.J. ZupanZupan CPCP andand flavorflavor violationviolation inin Higgs…Higgs… 1313 KEK-FF2014FALL,KEK-FF2014FALL, OctOct 2929 2012014,4, TsukubaTsukuba 2.5 Constraints from τ → µππ
• Contribution from dipole diagrams
2 2 Yτµ Γ ∝ F (s) Y τ →µπ +π − ∫ V τµ 3.1 Constraints from τ → µππ
• Photon mediated contribution requires the pion Photon mediated contribution requires vector form factor:
the pion vector form factor
• Dispersive parametrization following the properties of analyticity and unitarity −−+ − 00 • Diagram only there in the case of τ → µ ππ absent for τ −−→ µ ππ of the Form Factor ρ(770) neutral mode more model independent Dispersive parametrization Gasser, Meißner ́91 Guerrero, Pich’97 following the properties of analyticity Oller, Oset, Palomar ́01 Emilie Passemar and unitarityρ’’(1700) of24 the Form Factor Pich, Portolés ́08 ’(1465) Gómez Dumm&Roig’13 ρ Gasser, Meißner ´91 ... Guerrero, Pich ´97,
• Determined from a fit Oller, Oset, Palomar ´01 - - 0 to the Belle data on τ → π π ντ Pich, Portolés ´08, … Celis, Cirigliano, E.P.’14 Emilie Passemar 74
Determined from a fit to the Belle data Belle Collaboration, Phys.Rev. D78, 072006 (2008) AC, Cirigliano, Passemar (1309.3564) Determination of FV(s)
• Vector form factor
Ø Precisely known from experimental measurements ee+−+− −−0 → ππ and τππν → τ (isospin rotation)
Ø Theoretically: Dispersive parametrization for FV(s) Guerrero, Pich’98, Pich, Portolés’08 Gomez, Roig’13 2 * 3 - s 1 " s % s ∞ ds' φ (s') F (s) = exp,λ ' + λ '' − λ '2 $ ' + V / V V 2 ( V V )$ 2 ' ∫ 4m2 3 , m 2 m π π s' s'− s − iε / + π # π & ( ). Extracted from a model including
3 resonances ρ(770), ρ’(1465)
and ρ’’(1700) fitted to the data
Ø Subtraction polynomial + phase determined from a fit to the Belle data −−0 τππν→ τ
Emilie Passemar 75 Determination of FV(s)
ρ(770)
ρ’’(1700)
ρ’(1465)
Determination of FV(s) thanks to precise measurements from Belle! Emilie Passemar 76
3.1 Constraints from τ → µππ couplings to the light quarks, `¯(1 )⌧ q¯ 1, q. Finally, the diagram to the right, through ± 5 · { 5} heavy-quarks in the loop generates gluonic operators of the type `¯(1 )⌧ GG and `¯(1 )⌧ GG˜. • Tree level Higgs exchange ± 5 · ± 5 · When considering hadronic LFV decays such as ⌧ `⇡⇡ or ⌧ `P (P = ⇡, ⌘, ⌘0) one Y ! ! needs theτµ matrix elements of the quark-gluon operators in the hadronic states. In particular, h P-even+ operators will mediate the ⌧ `⇡⇡ decay and one needs to know the relevant two- h ! pion form factors. The dipole operator requires the vector form factor related to ⇡⇡ q¯ q 0 3.1 Constraints from τ µππ h | µ | i (photon converting in two pions). The scalar operator requires the scalar form factors related to ⇡⇡ qq¯ 0 . The gluon operator requires ⇡⇡ GG 0 , which we will reduce to a combination of • Tree level Higgsh exchange| | i h | | i 2 the scalar form factors and the two-pion matrixs = elementp + + ofp the− trace of the energy-momentum ( π π ) µ tensor ⇡⇡ ✓µ 0 via the trace anomaly relation: Voloshin’85 h h + | | i h ↵ ✓µ = 9 s Ga Gµ⌫ + m qq¯ . (2) µ 8⇡ µ⌫ a q q=u,d,s X
To impose robust bounds on LFV Higgs couplings from ⌧ `⇡⇡, we need to know the hadronic ! matrix elements with a good accuracy. With this motivation in mind, we now discuss in detail
the derivation of the two-pion matrix elements.
with the form factors: fyh Emilie Passemar 3 Hadronic form factors for( q⌧) `⇡⇡ decays77 ! The dipole contribution to the ⌧ `⇡⇡ decay requires the matrix element ! + 1 ↵ ↵ ↵ ⇡ (p + )⇡ (p ) (¯u u d¯ d) 0 FV (s)(p + p ) , (3) Emilie Passemar ⇡ ⇡ 2 ⌘64 ⇡ ⇡ ⌦ ↵ with FV (s) the pion vector form factor. As for the scalar currents and the trace of the energy- µ momentum tensor ✓µ, the hadronic matrix elements are given by
+ ⇡ (p + )⇡ (p ) muuu¯ + m dd¯ 0 ⇡(s) , ⇡ ⇡ d ⌘ + ⌦ ⇡ (p + ) ⇡ (p ) msss¯ 0↵ ⇡(s) , ⇡ ⇡ ⌘ + µ ⌦ ⇡ (p + )⇡ (p ) ✓ 0↵ ✓⇡(s) , (4) ⇡ ⇡ µ ⌘ ⌦ ↵ µ with ⇡(s) and ⇡(s) the pion scalar form factors and ✓⇡ (s) the form factor related to ✓µ. Here 2 2 s is the invariant mass squared of the pion pair: s =(p + + p ) =(p⌧ p ) . ⇡ ⇡ ` In what follows, we determine the form factors by matching a dispersive parameterization (that uses experimental data) with both the low-energy form dictated by chiral symmetry and the asymptotic behavior dictated by perturbative QCD. Numerical tables with our results are available upon request.
3.1 Determination of the ⇡⇡ vector form factor
The vector form factor F (s) has been measured both directly from e+e ⇡+⇡ [31–35] V ! and via an isospin rotation from ⌧ ⇡ ⇡0⌫ [36, 37]. It has also been determined by several ! ⌧ theoretical studies [38–54].
6 Determination of the form factors : Γπ(s), Δπ (s), θπ (s)
• No experimental data for the other FFs Coupled channel analysis
up to √s ~1.4 GeV Donoghue, Gasser, Leutwyler’90 Inputs: I=0, S-wave ππ and KK data Moussallam’99 Daub et al’13
• Unitarity:
π π π π K K π
Donoghue, Gasser, Leutwyler’90 + Form factors Moussallam’99 π π π π K K • Two channel unitarity condition (ππ, KK) (OK up to √s ~ 1.4 GeV) π
n n == ππππ,, KKKK
Emilie General Passemar solution: 78 •
Polynomials Canonical solution falling as 1/s for large s determined by (obey un-subtracted dispersion relation) matching to ChPT
• Solved iteratively, using input on s- wave I=0 meson meson scattering Determination of the form factors : Γπ(s), Δπ (s), θπ (s) Celis, Cirigliano, E.P.’14 • Inputs : ππ → ππ, KK
Buttiker et al’03
Garcia-Martin et al’09
• A large number of theoretical analyses Descotes-Genon et al’01, Kaminsky et al’01, Buttiker et al’03, Garcia-Martin et al’09, Colangelo et al.’11 and all agree
• 3 inputs: δπ (s), δK(s), η from B. Moussallam reconstruct T matrix Emilie Passemar 79 3.4.4 Determination of the form factors : Γπ(s), Δπ (s), θπ (s)
• General solution:
Canonical solution Polynomial determined from a matching to ChPT + lattice
• Canonical solution found by solving the dispersive integral equations iteratively starting with Omnès functions X (s) = C(s), D(s)
Emilie Passemar 80
Determination of the polynomial
• General solution
• Fix the polynomial with requiring F ( s ) → 1 / s ( Brodsky & Lepage ) + ChPT: P
Feynman-Hellmann theorem:
• At LO in ChPT:
81 Determination of the polynomial
• General solution
• At LO in ChPT:
• Problem: large corrections in the case of the kaons! Use lattice QCD to determine the SU(3) LECs
Dreiner, Hanart, Kubis, Meissner’13 Bernard, Descotes-Genon, Toucas’12 82 Determination of the polynomial
• General solution
• For θP enforcing the asymptotic constraint is not consistent with ChPT The unsubtracted DR is not saturated by the 2 states
Relax the constraints and match to ChPT
83 "σ "
f0
f0
Emilie Passemar 84 "σ "
f0
• Uncertainties:
2 2 - Varying scut (1.4 GeV - 1.8 GeV ) - Varying the matching conditions - T matrix inputs
f0
Emilie Passemar 85 2.4 Comparison with ChPT
• ChPT, EFT only valid at low energy for
It is not valid up to E = !
Emilie Passemar 86