KL π ± e νe + e - (Ke3ee)
Ke3ee ν e + e - Ke3 K 0 γ e + π - Ke3 KL ; 40.67(%)
Ke3ee K 0 ν γ e + π - Ke3 KL ; 40.67(%)
Me + e - 10 4 10 3 10 2 : MC Ke3γ : data K L real γ e detector matter e e 10 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Mee Me + e - (GeV/c2 )
Ke3ee MC
Ke3 ν e + K 0 π - Ke3 KL (0.4067±0.0011) ; 40.67(%)
Ke3 K 0 ν e + e + - ν current π - M kl3 = G F 2 < e + ν (J µ ) + 0 >< π (p π ) J µ K 0 (p K ) >
Ke3 K 0 ν e + π - e + - ν current K 0 -π - current M kl3 = G F 2 < e + ν (J µ ) + 0 >< π (p π ) J µ K 0 (p K ) >
Ke3 ν e + CKM Vus K 0 s π ū - K 0 -π - current Model
K-π current Vus form factor K-π current Γ Kl3 = G 2 F M 5 K 192π 3 S EW (1 + δ l K)C 2 V us 2 f 2 +(0)I l K K 0 ν t = Pw 2 π - e + f + (t) = ( f + (0) 1 + λ + t M 2 π + 1 2 λ + t 2 M 4 π )
Ke3ee form factor Γ Kl3 = G 2 F M 5 K 192π 3 S EW (1 + δ l K)C 2 V us 2 f 2 +(0)I l K ɛ µ e q 2 ūγµ v Gauge invariance MC K-π current
Chiral Perturbation Theory (ChPT) Tune (Ke3ee) ChPT QCD
ChPT (Chiral symmetry) Chiral symmetry Gauge symmetry ψ L = e iβ ψ L, } 1 2 (1 γ 5)ψ = ψ L 1 2 (1 + γ 5)ψ = ψ R ψ R = e +iβ ψ R
ChPT (Chiral symmetry) Dirac eq. γ µ i µ ψ R mψ L = 0 γ µ i µ ψ L mψ R = 0 mass
ChPT (Chiral symmetry) Dirac eq. γ µ i µ ψ R mψ L = 0 γ µ i µ ψ L mψ R = 0 mass m = Chiral symmetry =
ChPT (Spontaneously symmetry breaking) Chiral symm. quark Mass Mass less Pseudo scaler meson (Higgs Gauge symm. Mass less pseudo scaler ) <qq>=0 <qq>=0 http://www.riken.go.jp/r-world/ research/results/2004/040309/ Mass less pseudo scaler meson =Nambu-Goldston Boson (NGB) NGB
Chiral for ChPT exp u, d, s flavor symmetry [ i ] 8 λ i θ Li i 1 γ 5 2 u d s, exp [ i ] 8 λ i θ Ri i 1 + γ 5 2 u d s SU(3)L SU(3)R SU(3)V SU(3)A symmetry symmetry
NGB -- π, K, η pseudo scaler messon NGB [ m = 0 (Higgs ) u, d, s.] U = exp [ i 8 i ] 1 λ i φ i F π 8 λ i φ i = 2 i L 2 = 1 4 F 2 tr{ µ U µ U + 2B 0 M(U + U )} 1 2 π 0 + 1 6 η 8 π + K + π 1 2 π 0 + 1 6 η 8 K 0 K0 2 6 η 8 K p µ p µ /4πF 1
Why Ke3ee? K 0 ν π e + γ(q) - γ : K-π current ( Brems.) Eγ spectrum Brems. ν K energy Vertual γ* e+e- Mee q µ q µ 0
Ke3ee - Ke3ee Ke3 - Ke3 Vus - K-π current form factor - Ke3 form factor Ke3ee - ChPT MC (Tune ) - Ke3ee ChPT (QCD) - Massive radiation Ke3γ
!"#$%&#'#(')*+%,-..%/)01234*5'2)0 KTeV experiment 1.5 10 11 KL 0.2GeV kick
Event selection 1) Four track event with good Vertex quality 2) PID (π ± e e + e - )
PID by E/p 10 5 π e 10 4 10 3 10 2 10 1 0 0.2 0.4 0.6 0.8 1 1.2 Energy on CsI / Momentum of track
Particle ID by TRD e π Transition Radiation Depends on relativistic parameter γ radiator x ray detector 8 modules 10 4 10 3 10 2 10 e π 1 0 0.2 0.4 0.6 0.8 1 e like probele π like TRD parameter
Backgrounds KL π + π - π 0 D (π0 e + e - γ) One π ± fakes e ± KL π ± e + ν π 0 D (π0 e + e - γ) Important π-e rejection! KL π ± e + ν γ (γ e + e - : external conversion) KL π + π - π 0 4e (π 0 e + e - e + e - )
One more cut to reject KL π + π - π 0 D pp0kine Assuming : KL π + π - π 0 : missing π 0 P 0 P + - We have P// 0 π + e - e + e - Kaon =± pp0kine 1000 800 600 400 200 0 : MC KL π + π - π 0 D : MC Ke3ee : Data -0.06-0.04-0.02 0 0.02 0.04 0.06 0.22 * pp0kine pp0kine (GeV 2 /c 2 )
Comparison between Data/MC Pν *2 : Squared longitudinal momentum of neutrino in Kaon rest frame. 10 3 10 2 10 1 BG sample ID Entries Mean RMS UDFLW OVFLW ALLCHAN 987102 987103 1004 4468 216 852 0.1257E-01 0.7718E-02 0.3606E-02 0.1614E-01 0.7070E-02 0.5093E-02 0.5079E-02 0.4095E-02 0.0000E+00 0.0000E+00 457.0 258.7 176.0 184.3 : Data : Ke3ee : KL π + π - π 0 D : π ± e + ν π 0 D : π + π - π 0 4e : Ke3γ 0 0.005 0.01 0.015 0.02 0.025 0.03 Pν *2 (GeV 2 /c 2 ) (Data-BG)/MC data/mc 10 4 10 3 10 2 10 1 Pv *! 2 /dof = 55.7 / 29 Ppieee * Pv// * Kaon 0 0.005 0.01 0.015 0.02 0.025 0.03 (((()-(0.910389 *))-(1.6297 *))-(0.1158 P *2 n *))-(0.4327 (GeV 2 /c 2 )*) 2 60.07 / 26 1.8 A0 1.008 0.1001E-01 1.6 A1-3.606 1.986 1.4 1.2 1 0.8 0.6 0.4 0.2 Slope=-3.9±2.2 Scale factor =0.2572±0.0020 0 0 0.005 0.01 0.015 0.02 0.025 0.03 (((()-(0.910389 *))-(1.6297 *))-(0.1158 P *2 n *))-(0.4327 (GeV 2 /c 2 )*) Pν *2 (GeV 2 /c 2 )
LO vs. Next to LO(t/Mπ 2,min) 1000 data/mc 800 600 400 200 " 2 /dof = 71.3 / 32 0 0 1 2 3 4 5 6 (((()-(0.910389 *))-(1.6297 *))-(0.1158 t/m! *))-(0.4327,min(LO) *) 2 31.90 / 31 1.8 A0 0.8913 0.1841E-01 1.6 A1 0.3889E-01 0.6265E-02 1.4 1.2 1 0.8 0.6 0.4 0.2 Scale factor =0.3199±0.0025 Slope=(3.9±0.6)x10-2 0 0 1 2 3 4 5 6 (((()-(0.910389 *))-(1.6297 *))-(0.1158 t/m! *))-(0.4327,min(LO) *) 1000 LO (p 2 ) NLO (p 4 ) 800 : MC : data-bg data/mc 600 400 200 " 2 /dof = 35.4 / 32 0 0 1 2 3 4 5 6 (((()-(0.910389 *))-(1.6297 *))-(0.1158 *))-(0.4327 t/m!,max *) 2 33.81 / 31 1.8 A0 0.9754 0.1946E-01 1.6 A1 0.7913E-02 0.6418E-02 1.4 1.2 1 0.8 0.6 0.4 0.2 Scale factor =0.2566±0.0021 Slope=(7.9±6.4)x10-3 0 0 1 2 3 4 5 6 (((()-(0.910389 *))-(1.6297 *))-(0.1158 *))-(0.4327 t/m!,max *) t/mπ 2 t/mπ 2 : MC : data-bg
Comparison between Data/MC 10 4 10 3 10 2 10 1 Energy of electron (of pair) Ee - ID Entries Mean RMS UDFLW OVFLW ALLCHAN 987103 987102 2870 158 156 52 10.93 9.405 9.046 12.45 9.191 6.480 5.415 9.321 0.0000E+00 0.0000E+00 128.7 71.01 11.25 166.2 : Data : Ke3ee : KL π + π - π 0 D : π ± e + ν π 0 D : π + π - π 0 4e : Ke3γ 0 10 20 30 40 50 60 70 (GeV) (Data-BG)/MC data/mc 10 4 10 3 10 2 10 1! 2 /dof = 30.7 / 31 Pν *2 < 0.005 GeV 2 /c 2 BG sample Slope=(0.8±1.0) 10-3 GeV -1 0 10 20 30 40 50 60 70 (((()-(0.910389 *))-(1.6297 *))-(0.1158 Ee - *))-(0.4327 (GeV) *) 2 33.25 / 30 1.8 A0 0.9894 0.1260E-01 1.6 A1 0.8429E-03 0.1021E-02 1.4 1.2 1 0.8 0.6 0.4 0.2 Scale factor =0.2571±0.0020 0 0 10 20 30 40 50 60 70 (((()-(0.910389 *))-(1.6297 *))-(0.1158 Ee - *))-(0.4327 (GeV) *) Ee - (GeV)
Comparison between Data/MC Invariant mass of e + e - 10 4 10 3 10 2 10 1 ID Entries Mean RMS UDFLW OVFLW ALLCHAN 987103 987102 1610 138 110 14 0.2642E-01 0.1164E-01 0.1884E-01 0.2064E-01 0.2228E-01 0.1370E-01 0.1882E-01 0.1947E-01 0.0000E+00 0.0000E+00 93.22 112.4 3.029 50.07 : Data : Ke3ee : KL π + π - π 0 D : π ± e + ν π 0 D : π + π - π 0 4e : Ke3γ 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Me + e - (GeV/c 2 ) (Data-BG)/MC data/mc 10 4 10 3 10 2 10 1! 2 /dof = 27.0 / 26 Pν *2 < 0.005 GeV 2 /c 2 BG sample Slope=1.10±0.55 (GeV/c 2 ) -1 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 (((()-(0.910389 *))-(1.6297 *))-(0.1158 Me + e - *))-(0.4327 (GeV/c 2 ) *) 2 20.44 / 24 1.8 A0 0.9788 0.1305E-01 1.6 A1 1.103 0.5608 1.4 1.2 1 0.8 0.6 0.4 0.2 Scale factor =0.2573±0.0023 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 (((()-(0.910389 *))-(1.6297 *))-(0.1158 Me + e - *))-(0.4327 (GeV/c 2 ) *) Me + e - (GeV/c 2 )
Significance of slopes Slope/δslope E Kaon,max E Kaon,min Z vertex E π E e±(ke3) E e-(pair) Me + e - Me±e + e - Mπ±e e + e -
Observed events and estimated BG (Normalization mode KL π + π - π 0 D) without Pν *2 cut Pν *2 <0.005(GeV 2 /c 2 ) Ke3ee(with BG) 19466 evts 14080 evts KL π + π - π 0 D 356.1 evts 34.3 evts KL π ± e + ν π 0 D 256.0 evts evts 88.2 evts KL π ± e + ν γ 132.0 evts 84.7 evts KL π + π - π 0 4e 182.2 evts 2.6 evts Ξ Λ π 0 D 1.7 evts 0.3 evts Double Ke3 39.5 evts 29.1 evts N/S 5.0% 1.7% BR[Ke3ee] (1.673±0.052) 10-5 (1.663±0.053) 10-5
Statistic 0.84 Systematic Correction and error(%) cut variation 0.82 π ineff. (E/p) δ=0.72 0.05 π loss in TRD δ=2.91 (2.24,Signal ) (2.58,norm.) error(%) 0.59 e ineff.(e/p) δ= 0.39 0.10 Radiative corr. δ= 2.1 0.1 Systematic Total(internal) 1.02 Systematic (external) 2.84 Systematic Total 3.02
Summary Ke3ee ChPT - ChPT Ke3ee event - ChPT NLO - Me + e - Preriminary - BR(Ke3ee)=1.673±0.014(stat)±0.051(sys) 10-5
Event Selection Pick up π± e + - e + e -...ke3ee - EKaon < 200 GeV (Both soln.) 95 < Z vertex < 150 m Vertex 2 < 125 0.93 < E/p < 1.15 for electron tracks E/p < 0.9 for pion tracks TRD probability < 0.06 for electron tracks for Ke3ee Ee (pair) > 3 GeV Me+e- > 0.005 GeV/c 2 for pm0d Mπ ± e + e + e - < 0.5 GeV/c 2 0.492 < Mpm0 < 0.504 GeV/c 2-0.127 >Me + e - g> 0.143 GeV/c 2 pp0kine < - 0.002 (GeV/c) 2 pp0kine > - 0.002 (GeV/c) 2 Ee (Ke3) > 10 GeV - π + π - e + e -..pm0d Eπ ± > 10 GeV Eπ ± > 8 GeV (for one π ± )