Workshop on Top-Row CKM Unitarity Texas A&M University 8 January 2019 In recognition of the achievements of Prof. John Hardy The status of V us Matthew Moulson INFN Frascati Istituto Nazionale di Fisica Nucleare moulson@lnf.infn.it Laboratori Nazionali di Frascati
V us , CKM unitarity, gauge universality Standard-model coupling of quarks and leptons to W : Single gauge Unitary ≈ 2 × 10 − 5 coupling matrix Most precise test of CKM unitarity Universality: Is G F from µ decay equal to G F from π , K , nuclear β decay? ? = Physics beyond the Standard Model can break gauge universality: u ℓ u ℓ u ℓ Z ′ W + H + + ⋅⋅⋅ ⋅⋅⋅ W + s,d ν s,d ν s,d ν The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 2
Experimental paths to V us 1. Kaon decays Γ ( K → πℓν ) ( K ℓ 3 ) Γ ( K → µ ν ) / Γ ( π → µ ν ) ( K µ 2 / π µ 2 ) Most precise method: 0.3% on V us 2. Tau decays Inclusive tau decays: Γ ( τ → X S ν τ ) Exclusive tau decays: Γ ( τ → K ν τ ) / Γ ( τ → πν τ ) ( τ K 2 / τ π 2 ) Good precision: 0.8% on V us Discrepancy between inclusive/exclusive results? 3. Hyperon decays Γ ( Λ → p ℓν ) etc. > 2% uncertainty Not actively pursued at the moment The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 3
V us from kaon decays Based on CKM2018 update in collaboration with Emilie Passemar
V us from kaon decays: A modern history Old K ℓ 3 data give 1 − | V ud | 2 − | V us | 2 = 0.0035(15) → 2002 (2004 PDG) A 2.3 σ hint of unitarity violation? BNL 865 measures BR( K + → π 0 e + ν ) = 5.13(10)% 2003 Value for V us consistent with unitarity 2004-2008 Many new measurements from KTeV, ISTRA+, KLOE, NA48 (mostly) • BRs, lifetimes, form-factor slopes • Much higher statistics than older measurements • Importance of radiative corrections • Proper reporting of correlations between measurements 2008- Much progress on hadronic constants from lattice QCD beyond Value of V us used in precision tests of the Standard Model New wave of K ℓ 3 measurements imminent? 2018? NA62, OKA, KLOE-2, LHCb, TREK… The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 5
Experiment, theory, and evaluation ~100 measurements of ~10 experimental parameters V us from 50+ (and counting!) lattice results for 2 hadronic matrix elements K ℓ 3 & K ℓ 2 Radiative and SU(2)-breaking corrections, ChPT results, etc. Experimental averages, fits, etc Selection of results (experiments, corrections) Evaluation, discussion and intepretation Final report: EPJC 69 (2010) 399 2006-2010 (EU 6FP) This talk is an attempt at an update to 2018 Corresponding effort to synthesize results from lattice QCD: Flavor Lattice Participation by all major lattice collaborations Averaging Group Biannual review of lattice results for π , K , B , D physics (FLAG): 2016 review: EPJC 77 (2017) 112 http://itpwiki.unibe.ch/flag The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 6
Determination of V us from K ℓ 3 data with K ∈ { K + , K 0 }; ℓ ∈ { e , µ }, and: C K 2 1/2 for K + , 1 for K 0 S EW Universal SD EW correction (1.0232) Inputs from theory: Inputs from experiment: K 0 π − (0) f + Γ ( K ℓ 3( γ ) ) Hadronic matrix element Rates with well-determined (form factor) at zero treatment of radiative decays: momentum transfer ( t = 0 ) • Branching ratios Δ K SU (2) Form-factor correction for • Kaon lifetimes SU (2) breaking I K ℓ ({ λ } K ℓ ) Integral of form factor over phase space: λ s parameterize Δ K ℓ EM Form-factor correction for evolution in t long-distance EM effects • K e 3 : Only λ + (or λ + ′ , λ + ″ ) • K µ 3 : Need λ + and λ 0 The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 7
Modern experimental data for V us from K ℓ 3 Experiment Measurement Year BR( K + → π 0 D e + ν )/BR( K + → π 0 D X + ) BNL865 2003 τ ( K S ) KTeV 2003 BR( K Le 3 ), BR( K Lµ 3 ), λ + ( K Le 3 ), λ +,0 ( K Lµ 3 ) 2004 λ + ( K − e 3 ), λ +,0 ( K − ISTRA+ e 3 ) 2004 τ ( K L ) KLOE 2005 BR( K Le 3 ), BR( K Lµ 3 ), BR( K Se 3 ), λ + ( K Le 3 ) 2006 λ +,0 ( K Lµ 3 ) 2007 τ ( K ± ), BR( K Le 3 ), BR( K Lµ 3 ) 2008 τ ( K S ) NA48 2002 BR( K Le 3 /2 tracks), λ + ( K Le 3 ) 2004 Γ ( K Se 3 / K Le 3 ), λ +,0 ( K Lµ 3 ) 2007 BR( K + e 3 / π + π 0 ), BR( K + µ 3 / π + π 0 ) NA48/2 2007 Above data set used for 2010 FlaviaNet review (fits, averages, etc.) The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 8
Fit to K S rate data 6 input measurements: Parameter Value KLOE BR π 0 π 0 / π + π − BR( π + π − ( γ )) 69.20(5)% KLOE BR π e ν / π + π − BR( π 0 π 0 ) 30.69(5)% NA48 Γ ( K S → π e ν )/ Γ ( K L → π e ν ), τ S BR( K e 3 ) 7.05(8) × 10 − 3 KLOE ’11 τ S BR( K µ 3 ) 4.69(6) × 10 − 3 KTeV ’11 τ S τ S 89.58(4) ns 2 constraints: χ 2 /ndf = 0.20/3 (Prob = 98%) • Σ BR = 1 ρ (BR( π + π − ), BR( π 0 π 0 )) = − 0.998 • BR( K e 3 )/BR( K µ 3 ) = 0.66492(137) Little freedom in fit From ratio of phase-space integrals from current fit to Largest effect of 2011 τ S data: dispersive K ℓ 3 form factor parameters FlaviaNet 2010 Update τ S = 89.59(6) ps τ S = 89.58(4) ps The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 9
Fit to K L rate data S 21 input measurements: Parameter Value 5 KTeV ratios BR( K e 3 ) 0.4056(9) 1.3 NA48 BR( K e 3 / 2 track) BR( K µ 3 ) 0.2704(10) 1.5 4 KLOE BRs BR( 3 π 0 ) 0.1952(9) 1.2 with dependence on τ L BR( π + π − π 0 ) 0.1254(6) 1.3 KLOE , NA48 BR( π + π − / K ℓ 3 ) BR( π + π − ( γ IB )) 1.967(7) × 10 − 3 1.1 KLOE , NA48 BR( γγ /3 π 0 ) BR( π + π − γ ) 4.15(9) × 10 − 5 1.6 BR( 2 π 0 / π + π − ) from K S fit, Re ε ′ / ε BR( π + π − γ DE ) 2.84(8) × 10 − 5 1.3 KLOE τ L from 3 π 0 BR( 2 π 0 ) 8.65(4) × 10 − 4 1.4 Vosburgh ’72 τ L BR( γγ ) 5.47(4) × 10 − 4 1.1 KTeV BR( π + π − γ / π + π − ( γ )) τ L 51.16(21) ns 1.1 E731, 2 KTeV BR( π + π − γ DE / π + π − γ ) χ 2 /ndf = 19.8/12 (Prob = 7.0%) 1 constraint: Σ BR = 1 Essentially same result as 2010 fit Current PDG (’09): 37.4/17 (0.30%) The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 10
Comparison: K L fit result vs. input data K ℓ 3 3 π 0 π + π − π 0 π + π − 2 π 0 τ L Ke 3/ 2 track π + π − π 0 / Ke 3 π + π − / Kµ 3 π + π − / Ke 3 Kµ 3 /Ke 3 3 π 0 / Ke 3 K S fit Ke 3 Kµ 3 3 π 0 π + π − π 0 π + π − / Ke 3 2 π 0 / 3 π 0 6 inputs not shown K S fit Measurement pulls for KTeV KLOE NA48 Vosburgh ’72 The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 11
Updates: K ± BRs and lifetimes BR( π + π + π − ) = 0.05565(31)(25) KLOE-2 (0.7%) PLB 738 (2014) • No good measurements of BR( π + π + π − ) in 2010 fit • Reconstruct 2 tracks in small fiducial volume near interaction region; evaluate missing mass for 3 rd track • Fully inclusive of radiation, but radiative corrections handled differently from other KLOE measurements • Significant impact on value of BR( µ ν ) from fit Correlation between BR( µ ν ), BR( π + π + π − ) = − 0.75 BR( K − e 3 / π − π 0 ) = 0.2423(15)(37) ISTRA+ (1.6%) PAN 77 (2014) • Claimed to be fully inclusive for K e 3 γ • No mention of radiative corrections • Many cuts, mainly topological • 3 different selections, at least 1 may be largely inclusive • Included in PDG ’15 fit • Treated as preliminary here (not in K ± BR fit) The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 12
Updated fit to K ± rate data 17 input measurements: S Parameter Value 3 old τ values in PDG BR( µ ν ) KLOE τ 63.58(11)% 1.1 KLOE BR µ ν , ππ 0 BR( ππ 0 ) 20.64(7)% 1.1 KLOE BR K e 3 , K µ 3 BR( πππ ) 5.56(4)% 1.0 with dependence on τ BR( K e 3 ) 5.088(27)% 1.2 NA48/2 BR K e 3 / ππ 0 , K µ 3 / ππ 0 BR( K µ 3 ) 3.366(30)% 1.9 E865 BR K e 3 / K Dal BR( ππ 0 π 0 ) 3 old BR ππ 0 / µ ν 1.764(25)% 1.0 KEK-246 K µ 3 / K e 3 τ ± 12.384(15) ns 1.2 KLOE BR πππ , ππ 0 π 0 χ 2 /ndf = 25.5/11 (Prob = 0.78%) (Bisi ’65 BR ππ 0 π 0 / πππ removed) compare PDG ’16: 53/28 (0.26%) 1 constraint: Σ BR = 1 With ISTRA+ ’14 BR( K − e 3 / π − π 0 ) • BR( K e 3 ) = 5.083(27)% Much more selective than PDG fit • Negligible changes in other PDG ’16: 35 inputs, 8 parameters parameters, fit quality The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 13
Evolution of K ± BRs BR( K ± → π 0 e ν ) BR( K ± → ππ 0 ) PDG ’04 PDG ’04 PDG ’10 PDG ’10 FlaviaNet ’10 FlaviaNet ’10 Update Update BR( K ± → µ ν ) BR( K ± → πππ ) PDG ’04 PDG ’04 PDG ’10 PDG ’10 FlaviaNet ’10 FlaviaNet ’10 Update Update The status of Vus – M. Moulson (Frascati) – Top Row CKM Unitarity Workshop , Texas A&M, 8 January 2019 14
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