CKM Unitary tests with Tau decays

CKM Unitary tests with Tau decays Emilie Passemar Indiana University/Jefferson Laboratory Mini Workshop on Tau physics CINVESTAV, Mexico, May 3, 017

Outline 1. Introduction and Motivation. from inclusive hadronic τ decays 3. from exclusive hadronic τ decays 4. Conclusion and Outlook

1. Introduction and Motivation

1.1 Test of New Physics : Extraction of the Cabibbo-Kobayashi-Maskawa matrix element Ø Fundamental parameter of the Standard Model Check unitarity of the first row of the CKM matrix: Cabibbo Universality V + V + V = 1 ud us ub? Ø Input in UT analysis Negligible (B decays) Look for new physics Ø In the Standard Model : W exchange only V-A structure Emilie Passemar 4

1.1 Test of New Physics : Ø BSM: sensitive to tree-level and loop effects of a large class of models V + V + V = 1+ Δ ud us ub CKM BSM effects : ΔCKM ( Λ) ~ v Emilie Passemar Ø Look for new physics by comparing the extraction of from different processes: helicity suppressed K µ, helicity allowed K l3, hadronic τ decays 5

1. Paths to V ud and From kaon, pion, baryon and nuclear decays V ud 0 + 0 + π ± π 0 eν e n peν e π lν l K πlν l Λ peν e K lν l d V d V s = + θ ud us From τ decays (crossed channel) V ud τ ππν τ τ πν τ τ h NS ν τ τ Kπν τ τ Kν τ τ h S ν τ (inclusive) Emilie Passemar 6

1. Paths to V ud and From kaon, pion, baryon and nuclear decays V ud 0 + 0 + 0 e e n pe e l l K l l pe e K l l From decays (crossed channel) V ud τ ππν τ h NS K K h S (inclusive) Emilie Passemar 7

1. Paths to V ud and These are the golden modes to extract V ud and Only the vector current contributes Normalization known in SU() [SU(3)] symmetry limit Corrections start at nd order in SU() [SU(3)] breaking Ademollo & Gato, Berhands & Sirlin Currently the most precise determination of V ud and V ud (0.0 %) and (0.5 %) Emilie Passemar 8

1. Paths to V ud and From kaon, pion, baryon and nuclear decays V ud 0 + 0 + 0 e e n pe e l l K l l pe e K l l n pe e : Both V and A currents contribute need experimental information on A (e.g. asymmetry (r A = g A /g V )) Free of nuclear uncertainties Probe different combinations of BSM operators (e.g. right-handed currents, etc ) Emilie Passemar 9

1. Paths to V ud and From kaon, pion, baryon and nuclear decays V ud 0 + 0 + 0 e e n pe e l l K l l pe e K l l From decays (crossed channel) V ud τ ππν τ h NS K K h S (inclusive) Emilie Passemar 10

1. Paths to V ud and K l / l and K/ Only the axial current contributes Need to know the decay constants F K, F Lattice QCD Probe different BSM operators than from the vector case Input on F K / F /V ud very precisely Emilie Passemar 11

1. Paths to V ud and From decays (crossed channel) V ud τ ππν τ h NS K K h S (inclusive) Possibility to determine V ud, from inclusive decays Use OPE to calculate the inclusive BRs Different test of BSM operators inclusive vs. exclusive Emilie Passemar 1

. from inclusive hadronic τ decays

.1 Introduction d V d V s = + θ ud us Tau, the only lepton heavy enough to decay into hadrons m τ ~ 1.77GeV > Λ QCD use perturbative tools: OPE Inclusive τ decays : τ ud, us ν fund. SM parameters We consider ( ) ALEPH and OPAL at LEP measured with precision not only the total BRs but also the energy distribution of the hadronic system huge QCD activity! α S ( m τ ),, m s Γ ( τ ν τ + hadrons S=0 ) Γ ( τ ν τ + hadrons S 0 ) τ ( ) Davier et al 13 Observable studied: ( ) R τ Γ τ ν τ + hadrons Γ τ ν τ e ν e ( ) Emilie Passemar 14

. Theory d V d V s = + θ ud us ( ) R τ Γ τ ν τ + hadrons N parton model prediction Γ τ ν τ e C ν e ( ) QCD switch R τ = R τ NS + R τ S V ud NC + NC S = R τ V NS us V R ud τ (α S =0) Figure from M. González Alonso 13 Emilie Passemar 15

. Theory d V d V s = + θ ud us ( ) R τ Γ τ ν τ + hadrons N parton model prediction Γ τ ν τ e C ν e ( ) QCD switch R τ = R τ NS + R τ S V ud NC + NC Experimentally: R τ 1 Be Bµ = = 3.691± 0.0086 B e (α S 0) Emilie Passemar 16

3. Theory d V d V s = + θ ud us ( ) R τ Γ τ ν τ + hadrons N parton model prediction Γ τ ν τ e C ν e ( ) QCD switch R τ = R τ NS + R τ S V ud NC + NC Experimentally: R τ 1 Be Bµ = = 3.691± 0.0086 B e Due to QCD correc1ons: R = V N + V N +Ο τ ( α ) ud C us C S (α S 0) Emilie Passemar 17

. Theory d V d V s = + θ ud us From the measurement of the spectral functions, extraction of α S, ( ) R τ Γ τ ν τ + hadrons N naïve QCD prediction Γ τ ν τ e C ν e ( ) QCD switch Extraction of the strong coupling constant : R NS τ = V NC ud + O ( α S ) α S measured calculated (α S 0) Determination of : S ( ) = R τ V R + O α NS S ud τ Main difficulty: compute the QCD corrections with the best accuracy Emilie Passemar 18

.3 Calculation of the QCD corrections Calcula-on of R τ : m ds s s ( 1 ) ( 0 ( ) 1 1 1 Im ( ) Im ) Rτ mτ = πsew s i + ε Π + + Π ( s+ iε) m m m 0 τ τ τ τ Braaten, Narison, Pich 9 Analy-city: Π is analy-c in the en-re complex plane except for s real posi-ve Cauchy Theorem R τ (m τ ) = 6iπ S EW ds! s =mτ m τ 1 s m τ 1 + s m τ Π ( 1) s ( ) + Π 0 ( ) ( ) s We are now at sufficient energy to use OPE: ( J ) 1 ( J ) Π () s = C (, s µ ) OD( µ ) ( s) D D= 0,,4... dimo= D Wilson coefficients Operators μ: separa-on scale between short and long distances Emilie Passemar 19

.3 Calculation of the QCD corrections Calcula-on of R τ : Braaten, Narison, Pich 9 ( ) = C EW ( 1+ P + NP ) Rτ mτ N S δ δ Electroweak correc-ons: Perturba-ve part (D=0): S = 1.001(3) Marciano &Sirlin 88, Braaten & Li 90, Erler 04 EW δ P = a + a + a + a + 3 4 τ 5.0 τ 6 τ 17 τ... 0% α s( mτ ) aτ = π Baikov, Chetyrkin, Kühn 08 ( ) NS D=: quark mass correc-ons, neglected for R m, m but not for S τ u d Rτ ( ms ) D 4: Non perturba-ve part, not known, fi>ed from the data Use of weighted distribu-ons Emilie Passemar 0

.3 Calculation of the QCD corrections D 4: Non perturba-ve part, not known, fi>ed from the data Use of weighted distribu-ons Exploit shape of the spectral func-ons to obtain addi-onal experimental informa-on Le Diberder&Pich 9 Zhang Tau14 R S τ R R 00 ( m ) s Emilie Passemar 1

.4 Inclusive determination of With QCD on: S ( ) = R τ V R + O α NS S ud τ QCD switch Use OPE: NS R τ ( m τ ) = N C S EW V ud 1 + δ ud P + δ NP ( ) δ R τ R τ,ns R τ,s V ud computed using OPE S R τ ( m τ ) = N C S EW 1 + δ us P + δ NP ( ) SU(3) breaking quan-ty, strong dependence in m s computed from OPE (L+T) + phenomenology δ R τ,th = 0.04(3) (α S 0) Gamiz et al 07, Maltman 11 = R τ,s R τ,ns Emilie Passemar V ud δ R τ,th HFAG 17 R τ,s = 0.1633(8) R τ,ns = 3.4718(84) V ud = 0.97417(1) = 0.186 ± 0.0019 exp ± 0.0010 th 3.1σ away from unitarity!

0.1 0. 0.3 0.4 0.5 From Unitarity Kaon and hyperon decays K l3 decays (+ f + (0)) K l /π l decays (+ f K /f π ) Hyperon decays Flavianet Kaon WG 10 update by Moulson CKM16 τ decays τ -> s inclusive τ -> Kν absolute (+ f K ) τ branching fraction ratio τ -> Kν / τ -> πν (+ f K /f π ) Our result from Belle BR τ -> Kπν τ decays (+ f + (0), FLAG) BaBar & Belle HFAG 17 0.1 0. 0.3 0.4 0.5 NB: BRs measured by B factories are systema-cally smaller than previous measurements Emilie Passemar 3

3.5 using info on Kaon decays and τ Kπν τ (0.713 ± 0.003)% (0.471 ± 0.018)% Antonelli, Cirigliano, Lusiani, E.P. 13 (0.857 ± 0.030)% (.967 ± 0.060)% Longstanding inconsistencies between τ and kaon decays in extraction of seem to have been resolved! R. Hudspith, R. Lewis, K. Maltman, J. Zanotti 17 K l3, PDG 016 0.37 ± 0.0010 K l, PDG 016 0.54 ± 0.0007 CKM unitarity, PDG 016 0.58 ± 0.0009 τ s incl., Maltman 017 0.9 ± 0.00 ± 0.0004 Crucial input: τ Kπν τ Br + spectrum = 0.9 ± 0.00 exp ± 0.0004 theo need new data 0. 0.5 V us τ s incl., HFLAV 016 0.186 ± 0.001 τ Kν / τ πν, HFLAV 016 0.36 ± 0.0018 τ average, HFLAV 016 0.16 ± 0.0015 HFLAV Spring 017 5

3. from exclusive hadronic τ decays : Ø τ Kπν τ decays

3.1.1 Introduction: key ingredients Master formula for τ Kπν τ : ( ) = G F Γ τ Kπν τ γ m τ 5 96π 3 C K τ S EW K 0 π f+ (0) τ I K 1 + δ Kτ EM +! Kπ δ SU() Experimental inputs from HFAG Banerjee et al. 1 Emilie Passemar 7

3.1. Radiative corrections Master formula for τ Kπν τ : ( ) = G F Γ τ Kπν τ γ m τ 5 96π 3 C K τ S EW K 0 π f+ (0) τ I K 1 + δ Kτ EM +! Kπ δ SU() Theoretical inputs : Ø S ew : Short distance electroweak correction S ew = 1.001 Marciano &Sirlin 88, Braaten & Li 90, Erler 04 Emilie Passemar 8

3.1. Radiative corrections Master formula for τ Kπν τ : ( ) = G F Γ τ Kπν τ γ m τ 5 96π 3 C K τ S EW K 0 π f+ (0) τ I K 1 + δ Kτ EM +! Kπ δ SU() Theoretical inputs : τ - Ø S ew : Short distance electroweak correction Ø : Long-distance electromagnetic corrections F.V. Flores-Baez, J.R. Morones-Ibarra 13 K - Antonelli, Cirigliano, Lusiani, E.P. 13 Ø à ChPT to O(p e ) \ 0 Kl δ EM π 0 ν τ ( ) K τ δ EM = 0.15 ± 0. % Emilie Passemar ( ) K τ δ and EM = 0. ± 0. % S ew = 1.001 à Counter-terms neglected based on τ - π π 0 ν τ Cirigliano, Neufeld, Ecker 0 F. Flores-Baez, A. Flores-Tlalpa, G. Lopez Castro, G. Toledo Sanchez 06 9

3.1. Radiative corrections.5 u Dalitz Plot Τ K 0 Π Ν F.V. Flores-Baez, J.R. Morones-Ibarra 13.0 1.5 1.0 Τ K Π 0 Ν 0.5 0.5 1.0 1.5.0.5 3.0 s Emilie Passemar 30

3.1. Radiative corrections Master formula for τ Kπν τ : ( ) = G F Γ τ Kπν τ γ m τ 5 96π 3 C K τ S EW f+ K 0 π (0) I K τ 1 + δ Kτ EM +! Kπ δ SU() Theoretical inputs : Ø S ew : Short distance electroweak correction S ew = 1.001 Ø Kl δ EM : Long-distance electromagnetic corrections 0 ( ) K τ δ EM = 0.15 ± 0. % and ( ) K τ δ EM = 0. ± 0. % Ø! Kπ δ SU()! Kπ δ SU() : Isospin breaking corrections = f K + π 0 0 + K f 0 π + 0 ( ) ( ) 1 δ! Kπ SU() Antonelli, Cirigliano, Lusiani, E.P. 13 = (.9 ± 0.4 mixing ± 0.5)% + IB in the K *- to Kπ coupling 31

3.1.3 Phase space integrals Master formula for τ Kπν τ : ( ) = G F Γ τ Kπν τ γ m τ 5 96π 3 C K τ S EW K 0 π f+ (0) τ I K 1 + δ Kτ EM +! Kπ δ SU() Theoretical inputs : Ø I K : Phase space integral need a parametrization for the normalized form factors to fit the experimental distributions (, ( ), ( ) + 0 ) τ I K = ds F s f s f s Hadronic matrix element: Crossed channel from K πlν l ΔKπ ΔKπ K π sγ µ u 0 = ( pk pπ) + ( pk + p ) f ( s) ( pk p ) f0( s) µ π µ π s + + µ s f vector s= q = ( p scalar K + p ) 0, + () t with π, f 0, + () t = f+ (0) Use a dispersive parametrization to combine with K l3 analysis 3

Form factors Invariant mass spectra: constraints on FF very important for tes-ng QCD dynamics and the SM and new physics: Kπ form factors : τ à Kπν τ Jamin, Pich, Portolés 08 Boito, Escribano, Jamin 09, 10 Bernard, Boito, E.P 11 Bernard 13, Escribano, González-Solis, Jamin, Roig 14 Emilie Passemar 33

3.1.5 Results for phase space integrals From the results of the fit to the Belle + K l3 data : Integral result error exp theo I K 0 0.50418 0.0176 0.01689 0.00501 I e K 0 0.1547 0.000 0.000 0.00000 I K /I e 0 K 0 3.5864 0.11115 0.10634 0.0335 I K + 0.5387 0.01958 0.01889 0.00515 I e K + 0.15909 0.0005 0.0005 0.00000 I K /I e + K + 3.98 0.103 0.11589 0.0335 Precision : I τ 0 3.4%, I τ + 3.7% K K l To be compared to the precision on I : 0.14 % K Should be improved with more precise measurements!! Emilie Passemar 34

3.1.6 Extraction of Result for τ Kπν τ : BR ( τ K 0 π ν ) τ = ( 0.416 ± 0.008)% Belle 14 f + ( 0) = 0.141 ± 0.0014 IK ± 0.001 exp FLAG 16 V with us = 0.1 ± 0.006 f 0 + ( ) = 0.9677( 7) Emilie Passemar 35

3.1.6 Extraction of Result for τ Kπν τ : f + ( 0) = 0.141 ± 0.0014 IK ± 0.001 exp = 0.1 ± 0.006 with f + ( 0) = 0.9677( 7) FLAG 16 To be compared to results for K l3 : FLAVIAnet Kaon WG, talk by M. Moulson @CKM16 FLAG 16 f + ( 0) = 0.165 ± 0.0004 = 0.41 ± 0.0007 = 0.38 ± 0.0004 exp ± 0.0006 theo Not competitive yet but interesting cross check of determination from K l3 and inclusive τ result Emilie Passemar 36

3.1.6 Extraction of Result for τ Kπν τ : f + ( 0) = 0.141 ± 0.0014 IK ± 0.001 exp = 0.1 ± 0.006 with f + ( 0) = 0.9677( 7) FLAG 16 To be compared to results for K l3 : FLAVIAnet Kaon WG, talk by M. Moulson @CKM16 FLAG 16 = 0.38 ± 0.0004 exp ± 0.0006 theo f + ( 0) = 0.165 ± 0.0004 = 0.41 ± 0.0007 Not competitive yet but interesting cross check of determination from K l3 and inclusive τ result Bernard 14 Result of fit to K l3 + τ Kπν τ and Kπ scattering data including Emilie Passemar inelasticities in the dispersive FFs f + 0 ( ) = 0.163 ± 0.0014 37

3. from exclusive hadronic τ decays : Ø τ Kν τ / τ π ν τ decays Ø τ Kν τ decays

3. from τ Kν τ / τ π ν τ Γ( τ Kν [ γ] ) 1 m ± m K τ f V K us = 1+ δ Γ τ πν γ 1 m m f ± V ( [ ]) ( ) ( τ ) π π ud ( ) LD Ø δ LD : Long-distance radiative corrections δ LD = 1.0003 ± 0.0044 Ø Brs from HFAG 17 with update by A.Lusiani Ø F K / F π from lattice average: f K f π = 1.1930 ± 0.0030 FLAG 16 Ø V ud : V ud = 0.97417(1) Towner & Hardy 14 = 0.36 ± 0.0018 1.1σ away from unitarity Emilie Passemar 40

3.3 from τ Kν τ ( ) = G m 3 F τ S EW τ τ BR τ Kν γ 16π h 1 m K ± m τ f K In principle less precise than ratios Ø Inputs from HFAG 17 with update by A.Lusiani Ø F K from lattice average f K = ( 156.3 ± 0.9) MeV FLAG 16 = 0.11 ± 0.000 1.9σ away from unitarity Emilie Passemar 41

0.1 0. 0.3 0.4 0.5 From Unitarity Kaon and hyperon decays K l3 decays (+ f + (0)) K l /π l decays (+ f K /f π ) Hyperon decays Flavianet Kaon WG 10 update by M.Moulson τ decays τ -> s inclusive τ -> Kν absolute (+ f K ) τ branching fraction ratio τ -> Kν / τ -> πν (+ f K /f π ) Our result from Belle BR τ -> Kπν τ decays (+ f + (0), FLAG) BaBar & Belle HFAG update by A.Lusiani 0.1 0. 0.3 0.4 0.5 Emilie Passemar 4

4. Conclusion and Outlook

4.1 Conclusion Studying τ physics very interesting tests of the Standard Model e.g. Inclusive τ decays : = 0.176 ± 0.0019 exp ± 0.0010 th Error dominated by experiment Potentially the more precise extraction of Antonelli, Cirigliano, Lusiani, E.P. 13 Simulated New flavour factory data from Belle data : Same central values but uncertainties rescaled assuming 40 ab -1 luminosity = 0.176 ± 0.0019 exp ± 0.0010 th V = 0.11± 0.0006 ± 0.0010 us exp th Promising! Competitive with kaon physics! = 0.55 ± 0.0005 exp ± 0.0008 th 44

4. Outlook : Experimental challenges : strange τ Brs PDG 014: «Nineteen of the 0 B-factory branching fraction measurements are smaller than the non-b-factory values. The average normalized difference between the two sets of measurements is -1.08» (-1.41 for the 11 Belle measurements and -0.75 for the 11 BaBar measurements) Supported by predictions from kaon X channel Measured modes by the B factories: Mode BaBar Belle Normalized Difference (#σ) π π + π ν τ (ex. K 0 ) +1.4 K π + π ν τ (ex. K 0 ).9 K K + π ν τ.9 K K + K ν τ 5.4 η K ν τ 1.0 φ K ν τ 1.3 Emilie Passemar

4. Outlook : Experimental challenges : strange τ Brs PDG 016: «We find that that BaBar and Belle tend to measure lower τ branching fractions and ratios than the other experiments. The average normalized difference between the two sets of measurements is -0.8σ (-0.8σ for the 16 Belle measurements and -0.9σ for the 11 BaBar measurements)» number of measurements number of measurements 4 3 1 0 4 3 1 0 Emilie Passemar Belle 3 1 0 1 3 standard deviations BaBar 3 1 0 1 3 standard deviations Figure 3: Distribution of the normalized difference between the 7 B-factory measurements and non-b-factory measurements. The list includes 16 measurements of branching fractions and ratios published by the Belle collaboration and 11 by the BaBar collaboration that are used in the fit and for which non-b-factory measurements exist.

4. Outlook Experimental challenges : strange τ BRs: PDG 014: «Nineteen of the 0 B-factory branching fraction measurements are smaller than the non-b-factory values. The average normalized difference between the two sets of measurements is -1.08» Supported by predictions from kaon X channel measurements More precise measurements Theoretical challenges : Ø Having the hadronic uncertainties under control: OPE vs. Lattice QCD or ChPT Ø Isospin breaking Ø Electromagnetic corrections Emilie Passemar 47

Prospects : τ strange Brs Experimental measurements of the strange spectral functions not very precise New measurements are needed! Before B-factories With B-factories new measurements : Smaller τ K branching ratios smaller R τ smaller,s S R τ = 0.1686(47) old R τ S new = 0.1615(8) V = 0.14 ± 0.0031 ± 0.0010 us old exp th new = 0.186 ± 0.0019 exp ± 0.0010 th

7. Back-up

summary K l3, PDG 016 0.37 ± 0.0010 K l, PDG 016 0.54 ± 0.0007 CKM unitarity, PDG 016 0.58 ± 0.0009 τ s incl., Maltman 017 0.9 ± 0.00 ± 0.0004 τ s incl., HFLAV 016 0.186 ± 0.001 τ Kν / τ πν, HFLAV 016 0.36 ± 0.0018 τ average, HFLAV 016 0.16 ± 0.0015 0. 0.5 V us HFLAV Spring 017 Emilie Passemar 50

summary Emilie Passemar 51

.3 Calculation of δr τ δ R th τ R τ,ns R τ,s N C S EW δ ud V ud V us D ( D) ( D) - δ us δ R theo τ 4 m (m s τ ) Δ ( α m S ) τ but perturbatives series for L behave very badly! Δ ( α ) ( ) 3 kl S known to order O αs : transverse contribution computed from theory Gámiz, Jamin, Pich, Prades,Schwab 03, 05 longitudinal contribution divergent determined from data E. Gámiz, CKM 1

.4 Results = R τ,s R τ,ns V ud δ R τ,th δr τ,th determined from OPE (L+T) + phenomenology E. Gámiz, CKM 1 δ R τ,th = ( 0.1544 ± 0.0037) + ( 9.3 ± 3.4)m s + (0.0034 ± 0.008) J=L J=L+T, D= δ R τ,th = 0.039(30) Gamiz, Jamin, Pich, Prades, Schwab 07, Maltman 11 Input : m s m s ( GeV, MS) = 93.8 ±.4 MeV lattice average FLAG 13 Tau data : R τ,s = 0.1615(8) and R τ,ns = 3.4650(84) HFAG 1, update by A. Lusiani V ud : Emilie Passemar V = 0.9745() Towner & Hardy 08 ud

.4 Results = R τ,s R τ,ns V ud δ R τ,th δ = R τ, th 0.39(30) = 0.176 ± 0.0019 exp ± 0.0010 th Determination dominated by experimental uncertainties! Contrary to from K l3, dominated by uncertainties on f + (0) 3.4σ away from unitarity! Emilie Passemar