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1 KL π ± e νe + e - (Ke3ee)
2 Ke3ee ν e + e - Ke3 K 0 γ e + π - Ke3 KL ; 40.67(%)
3 Ke3ee K 0 ν γ e + π - Ke3 KL ; 40.67(%)
4 Me + e : MC Ke3γ : data K L real γ e detector matter e e Mee Me + e - (GeV/c2 )
5 Ke3ee MC
6 Ke3 ν e + K 0 π - Ke3 KL (0.4067±0.0011) ; 40.67(%)
7 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 ) >
8 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 ) >
9 Ke3 ν e + CKM Vus K 0 s π ū - K 0 -π - current Model
10 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 λ + t 2 M 4 π )
11 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
12 Chiral Perturbation Theory (ChPT) Tune (Ke3ee) ChPT QCD
13 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
14 ChPT (Chiral symmetry) Dirac eq. γ µ i µ ψ R mψ L = 0 γ µ i µ ψ L mψ R = 0 mass
15 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 =
16 ChPT (Spontaneously symmetry breaking) Chiral symm. quark Mass Mass less Pseudo scaler meson (Higgs Gauge symm. Mass less pseudo scaler ) <qq>=0 <qq>=0 research/results/2004/040309/ Mass less pseudo scaler meson =Nambu-Goldston Boson (NGB) NGB
17 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
18 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 η 8 π + K + π 1 2 π η 8 K 0 K0 2 6 η 8 K p µ p µ /4πF 1
19 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
20 Ke3ee - Ke3ee Ke3 - Ke3 Vus - K-π current form factor - Ke3 form factor Ke3ee - ChPT MC (Tune ) - Ke3ee ChPT (QCD) - Massive radiation Ke3γ
21 !"#$%&#'#(')*+%,-..%/)01234*5'2)0 KTeV experiment KL 0.2GeV kick
22 Event selection 1) Four track event with good Vertex quality 2) PID (π ± e e + e - )
23 PID by E/p 10 5 π e Energy on CsI / Momentum of track
24 Particle ID by TRD e π Transition Radiation Depends on relativistic parameter γ radiator x ray detector 8 modules e π e like probele π like TRD parameter
25 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 - )
26 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 : MC KL π + π - π 0 D : MC Ke3ee : Data * pp0kine pp0kine (GeV 2 /c 2 )
27 Comparison between Data/MC Pν *2 : Squared longitudinal momentum of neutrino in Kaon rest frame BG sample ID Entries Mean RMS UDFLW OVFLW ALLCHAN E E E E E E E E E E : Data : Ke3ee : KL π + π - π 0 D : π ± e + ν π 0 D : π + π - π 0 4e : Ke3γ Pν *2 (GeV 2 /c 2 ) (Data-BG)/MC data/mc Pv *! 2 /dof = 55.7 / 29 Ppieee * Pv// * Kaon (((()-( *))-( *))-( P *2 n *))-( (GeV 2 /c 2 )*) / A E A Slope=-3.9±2.2 Scale factor =0.2572± (((()-( *))-( *))-( P *2 n *))-( (GeV 2 /c 2 )*) Pν *2 (GeV 2 /c 2 )
28 LO vs. Next to LO(t/Mπ 2,min) 1000 data/mc " 2 /dof = 71.3 / (((()-( *))-( *))-( t/m! *))-(0.4327,min(LO) *) / A E A E E Scale factor =0.3199± Slope=(3.9±0.6)x (((()-( *))-( *))-( t/m! *))-(0.4327,min(LO) *) 1000 LO (p 2 ) NLO (p 4 ) 800 : MC : data-bg data/mc " 2 /dof = 35.4 / (((()-( *))-( *))-( *))-( t/m!,max *) / A E A E E Scale factor =0.2566± Slope=(7.9±6.4)x (((()-( *))-( *))-( *))-( t/m!,max *) t/mπ 2 t/mπ 2 : MC : data-bg
29 Comparison between Data/MC Energy of electron (of pair) Ee - ID Entries Mean RMS UDFLW OVFLW ALLCHAN E E : Data : Ke3ee : KL π + π - π 0 D : π ± e + ν π 0 D : π + π - π 0 4e : Ke3γ (GeV) (Data-BG)/MC data/mc ! 2 /dof = 30.7 / 31 Pν *2 < GeV 2 /c 2 BG sample Slope=(0.8±1.0) 10-3 GeV (((()-( *))-( *))-( Ee - *))-( (GeV) *) / A E A E E Scale factor =0.2571± (((()-( *))-( *))-( Ee - *))-( (GeV) *) Ee - (GeV)
30 Comparison between Data/MC Invariant mass of e + e ID Entries Mean RMS UDFLW OVFLW ALLCHAN E E E E E E E E E E : Data : Ke3ee : KL π + π - π 0 D : π ± e + ν π 0 D : π + π - π 0 4e : Ke3γ Me + e - (GeV/c 2 ) (Data-BG)/MC data/mc ! 2 /dof = 27.0 / 26 Pν *2 < GeV 2 /c 2 BG sample Slope=1.10±0.55 (GeV/c 2 ) (((()-( *))-( *))-( Me + e - *))-( (GeV/c 2 ) *) / A E A Scale factor =0.2573± (((()-( *))-( *))-( Me + e - *))-( (GeV/c 2 ) *) Me + e - (GeV/c 2 )
31 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 -
32 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) evts evts KL π + π - π 0 D evts 34.3 evts KL π ± e + ν π 0 D evts evts 88.2 evts KL π ± e + ν γ evts 84.7 evts KL π + π - π 0 4e evts 2.6 evts Ξ Λ π 0 D 1.7 evts 0.3 evts Double Ke evts 29.1 evts N/S 5.0% 1.7% BR[Ke3ee] (1.673±0.052) 10-5 (1.663±0.053) 10-5
33 Statistic 0.84 Systematic Correction and error(%) cut variation 0.82 π ineff. (E/p) δ= π loss in TRD δ=2.91 (2.24,Signal ) (2.58,norm.) error(%) 0.59 e ineff.(e/p) δ= Radiative corr. δ= Systematic Total(internal) 1.02 Systematic (external) 2.84 Systematic Total 3.02
34 Summary Ke3ee ChPT - ChPT Ke3ee event - ChPT NLO - Me + e - Preriminary - BR(Ke3ee)=1.673±0.014(stat)±0.051(sys) 10-5
35 Event Selection Pick up π± e + - e + e -...ke3ee - EKaon < 200 GeV (Both soln.) 95 < Z vertex < 150 m Vertex 2 < < 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- > GeV/c 2 for pm0d Mπ ± e + e + e - < 0.5 GeV/c < Mpm0 < GeV/c >Me + e - g> GeV/c 2 pp0kine < (GeV/c) 2 pp0kine > (GeV/c) 2 Ee (Ke3) > 10 GeV - π + π - e + e -..pm0d Eπ ± > 10 GeV Eπ ± > 8 GeV (for one π ± )
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