π + e + ν e

π + e + ν e 2 2013 2 5

π + e + ν e π + µ + ν µ R = Γ(π + e + ν e )/Γ(π + µ + ν µ ) 0.1% PIENU 2009 TRIUMF R 0.01% 10 R 0.1% 1000TeV PIENU 0.1% 1980 TRIUMF π + e + ν e π + µ + ν µ KEK COPPER 500MHz Flash ADC(FADC) PMT π + e + ν e 69.8 MeV π + µ + ν µ (µ + e + ν µ ν e ) 0 52.8 MeV R R

1 8 1.1 π +............................. 8 1.2......................... 9 1.3 -............................. 9 1.4............................. 10 2 PIENU 11 2.1........................................ 11 2.2................................... 12 2.3 PIENU...................................... 16 2.3.1................................ 16 2.3.2........................................ 18 2.3.3.................................... 21 2.3.4.................................. 23 3 π + 26 3.1 COPPER 500 MHz FADC..................... 26 3.1.1............................. 26 3.1.2.............. 27 3.2........................................ 28 3.2.1................................ 28 3.2.2................................ 29 3.2.3................................. 31 3.2.4.............................. 33 3.2.5...................... 33 3.2.6.................................. 34 3.3................................... 36 4 37 4.1........................... 39 4.1.1 π + µ + e +.................................... 39 4.1.2.................... 39 4.1.3 PDIF........................... 40 4.2........................... 40 4.2.1 π + e + ν.................................... 40 1

4.2.2 NaI CsI...... 40 4.2.3 µ +....................... 40 4.2.4 π + µ + e +.. 41 4.2.5................................. 44 4.3................................. 46 5 T1 49 5.1..................... 49 5.2............................ 52 5.2.1.................... 53 5.2.2........................... 56 6 60 2

1.1 π + l + ν l g e g µ............................ 8 1.2 Λ........................ 9 2.1 PIENU...... 11 2.2 π + e + ν e π + µ + e + (MC)... 12 2.3 ( ) ( ) π + e + ν e 10 4.......................... 12 2.4 TRIUMF 1980............ 13 2.5 TINA............... 14 2.6 3400ch........... 14 2.7 π + µ + e + TINA PDIF.......................... 16 2.8 M13 F3 PIENU............................ 17 2.9 M13............. 18 2.10 PIENU NaI(Tl) CsI.................................. 19 2.11 PDIF............................... 19 2.12 NaI(Tl) WC3 CsI....................................... 20 2.13 S2..................... 20 2.14 S3 T1 T1 4 PMT 500MHz FADC....................... 21 2.15................................ 22 2.16 COPPER................................. 24 2.17 COPPER 500 MHz FADC FINESSE.................. 24 2.18 COPPER 500 MHz FADC............ 25 3

3.1 1 N 1 N 3 3 3 PH t..................................... 26 3.2 COPPER........... 27 3.3 B1.. 27 3.4 :B1 TOF(43.3ns) :B2................................. 28 3.5 WC1 WC2..................................... 29 3.6 NaI..................................... 30 3.7 T1.............. 30 3.8 B1 B2 T1 PMT PMT1 PMT2 PMT3 PMT4.......................... 31 3.9 B1 B2 RF B1 B2.......................... 32 3.10 :B1 1 Q Qw (Q/Qw) :Q Qw................. 32 3.11 : : E NaI + E CsI < 50 MeV.... 33 3.12 WC3......... 34 3.13 E NaI + E CsI............................ 35 3.14.......................... 35 3.15 : (E NaI + E CsI 50 MeV) : (E NaI + E CsI < 50 MeV)................ 36 4.1 : :............................ 39 4.2 γ y = 2E γ m µ E γ γ m µ [11]........ 41 4.3 π + µ + e + (case2a) π + µ + e + NaI CsI................. 42 4

4.4 π + µ + e + (case2b) π + µ + e + NaI CsI..... 42 4.5 MC π + µ + e + ( :NaI :CsI).............. 43 4.6 NaI CsI π + µ + e + 1............... 44 4.7 π + e + ν e γ γ........... 45 4.8 :NaI :CsI π + µ + ν µ γ 1........ 45 4.9 χ 2 47 5.1 :T1 : T reso....... 49 5.2 2 T1 y x π + µ + e + T1 y = x y = x± T reso.......................................... 50 5.3 :t < T reso : T reso < t < 0 0 t + T reso ( ) :t > 0 T reso < t < 0 t t + T reso ( ) 3 T1 t..................................... 51 5.4 : ( T) 45ns 1 2 2 ( ) 2 1 T : 45ns T1 PMT1(T1 1) 1 ( 3.1.2) 1 2 t[0] t[1](3.1.1) 1 2 1 2 T1...... 52 5.5 : 225 ns 15 ns 225 ns : T1 225 ns................... 53 5

5.6 5.5 3 (5.2) (5.4) ε π eνe (t) 3 5.5 54 5.7 54 5.8 A + B 4..... 56 5.9 t < 0 t > 0.................................... 57 5.10 F U (t) F L (t).............. 58 5.11 f g R...................................... 59 6

1.1 -........................ 10 4.1................... 37 4.2.................. 37 4.3 (µ + e + ν µ ν e ) π + µ + e + b e + i 3.12 o Reject (3.2) NoTrig 2.15 Trigger t e +..... 38 4.4 c d.............. 47 5.1 ndf........................... 55 5.2 F U (t) F L (t) Br....... 57 7

1 π + π + µ + ν µ π + e + ν e π + µ + ν µ 99% π + e + ν e 10 4 π + R = Γ(π + e + ν e )/Γ(π + µ + ν µ ) R (SM) R SM = 1.2352(1) 10 4 [1] (1.1) TRIUMF PSI R TRIUMF = (1.2352±0.0034(stat)±0.0044(syst)) 10 4 [2] (1.2) R PSI = (1.2346±0.0035(stat)±0.0036(syst)) 10 4 [3] (1.3) 10 1.1 π + 1.1 π + l + ν l g e g µ π + R 1 1.1 π + l + ν l (l = e, µ) W + R 0 R 0 = g2 e m 2 ( e m 2 π m 2 ) 2 e gµ 2 m 2 µ m 2 π m 2 = 1.28336(2) 10 4 (1.4) µ m e m µ g e g µ g 2 e = g 2 µ m µ m e 200 m 2 e/m 2 µ π + e + ν e 10 4 (1.4) (1.1) 8

1.2 1.1 R 1.2 R R R R SM R EXP 1 R EXP 2π 1 m 2 π ± R SM G Λ m e (m d + m u ) ( 1T ev ) 2 10 3 Λ (1.5) G m π m d m u Λ 1.2 0.1% 1000 TeV Λ 1.2 Λ 1.3 - g e = g µ W (e, µ, τ) - - 1.1 9

g e /g µ π 0.9985±0.0016 [4] K 0.9960±0.005 [5] τ 0.9999±0.0021 [6] W 0.997±0.010 [4] 1.1 - g e g µ R R - 1.4 π + R R R 0.1% PIENU TRIUMF π + e + ν e π + µ + ν µ R 2010 2 PIENU 3 4 5 10

2 PIENU 2.1 PIENU π + e + ν π + µ + ν µ R 0.1% TRIUMF PIENU 2.1 π + 2.1 PIENU π + π + µ + ν µ µ + 1mm e + π + e + ν e µ + 4.1 MeV ( 2.2) π + e + ν e 2 69.8 MeV π + µ + ν µ µ + e + ν µ ν e (π + µ + e + ) µ + 3 0 52.8 MeV ( 2.3 ) ( 2.3 ) π + e + ν e : ε π eν (t) = exp( t τ π ) τ π (2.1) π + µ + e + : ε π µ e (t) = exp( t τ µ ) exp( t τ π ) τ µ τ π (2.2) R τ π τ µ R R 11

2.2 π + e + ν e π + µ + e + (MC) 2.3 ( ) ( ) π + e + ν e 10 4 2.2 1980 TRIUMF R (TRIUMF-E248) 2.4 83±1 MeV/c π + (B3) π 4 2 46cm 51cm NaI(Tl) (TINA) TINA 12

90 B3 e + 2% 2.4 TRIUMF 1980 13

2.5 TINA 2.5 TINA π + e + ν e π + µ + e + 56.4 MeV(3400 channel) 2.6 2.6 3400ch π + e + ν e (2.1) π + µ + e + 14

(2.2) exp( t τ µ ) F πeν (t) F πeν (t) = A π [R ε π eν (t) + A πµe ε π µ e (t)]h(t) + A BG1 exp( t τ µ ) + C BG1 (2.3) H(t) t < 0 H(t) = 0 t > 0 H(t) = 1 t = t t 0 t t 0 A π R A πµe π µ e A BG1 C BG1 t 0 A π R A πµe A BG1 C BG1 π + µ + e + (2.2) exp( t τ µ ) F πµe (t) F πµe (t) = A π [(1 A πµe )ε π µ e (t)]θ(t) + A BG2 exp( t τ µ ) + C BG2 (2.4) A BG2 C BG2 2.6 2 F πeν (t) F πµe (t) R 1 2.5 π + e + ν e π + µ + e + 2.7 π + µ + e + π + e + ν e TRIUMF-E248 1 10 5 π + e + ν e 0.45% ( (1.2)) R 2.7 π + µ + e + π µ + (pion decay-in-flight:pdif) 15

(pion decay-at-rest:pdar) π + µ + e + 2.7 π + µ + e + TINA PDIF 2.3 PIENU 2.3.1 PIENU TRIUMF M13 2.8 M13 TRIUMF 100 µa 500 MeV Be 1 cm (T1) 2 TRIUMF RF(Radio Frequency) 23.1 MHz M13 3 (B1,B2,B3) 10 (Q1 10) F1 4 16

2.8 M13 F3 PIENU T1 2 π + µ + e + π + B1 F1 77 MeV/c F1 π + B2 F3 µ + e + π + F3 F3 γ π + B3 80% π + 60 khz FWHM 75±1 MeV/c 2.9 B3 17

2.9 M13 2.3.2 PIENU TRIUMF-E248 TRIUMF-E248 2.10 PIENU 75 MeV/c π + 2 (B1,B2) 8mm (Tg) π + T1,T2 (WC3) NaI(Tl) TRIUMF-E248 10 NaI(Tl) NaI CsI π + (WC1,2) (S1,2) TRIUMF-E248 PDIF 2.11 PDIF 18

2.12 2.14 500MHz FADC NaI CsI 60MHz FADC 1.6GHz TDC 2.10 PIENU NaI(Tl) CsI 2.11 PDIF 19

2.12 NaI(Tl) WC3 CsI 2.13 S2 20

2.14 S3 T1 T1 4 PMT 500MHz FADC 2.3.3 NIM π + e + ν e 2.15 PIENU B1 B1 B2 Tg T1 T2 Tg ( ) -300 500ns PIE π + e + ν e 3 1. Prescale trigger π + µ + e + PIE 1/16 2. BinaH trigger NaI CsI 45 MeV 21

PIE BinaH trigger ( π + e + ν e ) 3. Early trigger 800 ns 40 ns 4 40 ns Early trigger 2197 ns 26 ns 70% π + e + ν e 2.15 BinaH trigger Early trigger π + e + ν e π + e + ν e π + µ + e + π + e + ν e BinaH trigger Early trigger 22

Prescale trigger 1/16 500ns 3 π + µ + e + 1/100 2.3.4 Trigger t π +( ) COPPER Trigger t e +( ) VME (VF48 VT48) 2.3.4 COPPER 500 MHz FADC PMT 500 MHz FADC(Flash Analog to Digital Convertar) FADC COPPER(The COmmon Pipelined Platform for Electronics Readout) COPPER Belle J-PARC KEK 2.16 COPPER COPPER 9U VME 4 (FINESSE:Front-end INstrumentation Entity for Sub-detector Specifit Electronics) 2.17 500 MHz FADC FINESSE 1 500 MHz FADC FINESSE 2 2 250 MHz FADC 500 MHz 500 MHz FADC FINESSE 8-bit ±500 mv PIENU PMT -950 50 mv 1 4000 (8 µs) 2.18 COPPER 500 MHz FADC 2 FADC ADC1 ADC2 23

2.16 COPPER 2.17 COPPER 500 MHz FADC FINESSE 24

2.18 COPPER 500 MHz FADC 60 MHz FADC(VF48) NaI CsI PMT VF48 60 MHz FADC VME 6-U 2004 10 bit ±250 mv 48 PIENU 404 (NaI:19 CsI:97 :288) 10 VF48 TDC(VT48) PMT VT48 1.6 GHz TDC VT48 VME 6-U 2006 TRIUMF 1 48 11 VT48 25

3 π + 2010 11 6 10 8 NaI CsI COPPER 500 MHz FADC 3.1 COPPER 500 MHz FADC 3.1.1 3.1 COPPER -6.4µs +1.35µs DAQ (7.75 µs) (2.3.3) Trigger t π + 7.75 µs 1 COPPER -6.4 µs -2.15 µs -2.15 µs 1.35 µs 3.2 t PH t ±20 ns Q t -20 80 ns Qw ( N ) N 3.1 1 N 1 N 3 3 3 PH t 26

3.2 COPPER 3.1.2 T1 B1 COPPER 2 ns T1 B1 PMT 3.3 3.3 B1 27

3.2 3.2.1 π + µ + e + π + B1 B2 Time-Of-Flight(TOF) TOF 2.3.1 RF(23.1 MHz 43.3 ns) B1 TOF B1 1 43.3 ns 3.4 B1 TOF 3.4 B2 3.4 :B1 TOF(43.3ns) :B2 2011 TOF TOF 3.4 WC1 WC2 WC1 WC2 3.5 WC1 28

3.5 WC1 WC2 3.2.2 π + π + µ + PDIF µ + T1 B1 B2 TOF T1 π + (π + + p + π + + p + :p + ) NaI 100 MeV 3.6 NaI S3 T1 T2 T1 T1 (0.3 MeV ) ( 3.7) 29

3.6 NaI 3.7 T1 30

3.2.3 60 khz -300 500 ns 30% B1 B2 PMT N ( ) π + 1 PMT B1 PMT 1 B1 π + T1 B1 B2 T1 PMT 3.8 B1: {(N P MT 1 = 1) (N P MT 2 = 1) (N P MT 3 = 1) (N P MT 4 = 1)}&& {(N P MT 1 > 0) (N P MT 2 > 0) (N P MT 3 > 0) (N P MT 4 > 0)} B2: {(N P MT 1 = 1) (N P MT 2 = 1) (N P MT 3 = 1) (N P MT 4 = 1)} T1: {(N P MT 1 = 1) (N P MT 2 = 1) (N P MT 3 = 1) (N P MT 4 = 1)}&& {(N P MT 1 > 0) (N P MT 2 > 0) (N P MT 3 > 0) (N P MT 4 > 0)} 3.8 B1 B2 T1 PMT PMT1 PMT2 PMT3 PMT4 3.9 (E NaI + E CsI ) 50 MeV π + µ + e + B1 B2 31

3.9 B1 B2 RF B1 B2 2 Q Qw Q/Qw B1 B2 PMT 3.10 B1 PMT1( B1 1) Q Qw Q Qw 3.10 3.10 :B1 1 Q Qw (Q/Qw) :Q Qw 32

3.2.4 PIENU µ + 2.2 µs π + µ + 30% µ + π ( -6.4 µs -2.15 µs( 3.1)) µ + 3.11 π + µ + e + t < 0 1/10 t > 0 70% π + µ + e + B1,B2,Tg,T1,T2: (N P MT 1 = 0) (N P MT 2 = 0) (N P MT 3 = 0) (N P MT 4 = 0) 3.11 : : E NaI + E CsI < 50 MeV 3.2.5 (S3 T1 T2 WC3) NaI WC3 3.12 WC3 60 mm 33

3.12 WC3 3.2.6 75% (3.2.1) 30% ( (3.2.3)) ( (3.2.4)) 60% 3.2.5 35% NaI CsI 3.13 π + e + ν e π + µ + + e 70 MeV T1 B1 3.14 34

3.13 E NaI + E CsI 3.14 35

3.3 3.13 E NaI + E CsI 50 MeV E NaI + E CsI <50 MeV 3.15 TRIUMF-E248 ( (2.2)) π + e + ν π + µ + e 3.15 t < 0 π + e + ν e (2.1) 2.3 150 ns 3.15 t > 150 ns t > 0 3.15 : (E NaI + E CsI 50 MeV) : (E NaI + E CsI < 50 MeV) 36

4 3.15 t = 0 B1 B2 ( 3.2.2) t < 0 : -250-20 ns t > 0 : 20 520 ns t = 0 ( ) t < 0 t > 0 TRIUMF- E248 TRIUMF-E248 4.1 4.2 PIENU 4.2 π + µ + e + PDIF µ + e + ν µ ν e π + µ + µ + e + ν µ ν e 4.1 NaI CsI π + µ + e + µ + e + ν µ ν e µ + µ + e + ν µ ν e γ µ + e + ν µ ν e π + µ + e + π + µ + e + π + π + µ + ν µ γ µ + µ + e + ν µ ν e 4.2 37

µ π e + ν µ ν e + µ + e + T1-T2i T1-T2o T1b-T2i T1b-T2o T1-T2b T1b-T2b T1-T2i case1 case1 case2b case2b case1 case2b T1-T2o case1 Reject case3 Reject Reject Reject T1b-T2i case2a case3 NoTrig NoTrig case4 Reject T1b-T2o case2a Reject NoTrig NoTrig Reject NoTrig T1-T2b case1 Reject case4 Reject NoTrig NoTrig T1b-T2b case2a Reject NoTrig NoTrig NoTrig NoTrig 4.3 (µ + e + ν µ ν e ) π + µ + e + b e + i 3.12 o Reject (3.2) NoTrig 2.15 Trigger t e + case1: T1 (3.2.3) T1 case2a B: T1 T2 Trigger t e + T1 NaI CsI A (µ + e + ν µ ν e ) B π + µ + e + Trigger t e + case3: WC3 WC3 WC3 case4: T1 T2 100 ns T1 T2 100 ns π + e + ν e π + µ + e + 4.1 2011 C.Malbrunot [7] 4.1 π + e + ν e π + µ + e + π + µ + e + µ + NaI CsI π + 4.1 π + µ + e + PDIF 38

4.1 4.3 case2a C.Malbrunot C.Malbrunot case1 4.1 : : 4.1 4.1.1 π + µ + e + t > 0 π + µ + e + π + µ + (2.2) π + e + ν e π + µ + e + π + e + ν e 10 4 π + e + ν e 10% π + e + ν e π + µ + e + 0.001% 4.1.2 t < 0 (µ + e + ν µ ν e ) ε µ e νµ ν e (t) = exp( t τ µ ) τ µ (4.1) t > 0 39

4.1.3 PDIF PDIF 1.2% µ + 4.1.2 ε µ e νµ ν e (t) PDIF t > 0 4.2 π + e + ν e π + µ + e + 10 4 4.2.1 π + e + ν t > 0 π + e + ν e π + (2.1) 4.2.2 NaI CsI NaI CsI π + µ + e + π + H(t)(t < 0 H(t) = 0 t > 0 H(t) = 1) H(t) ε π µ e (t) µ + (ε µ e νµ ν e (t)) t < 0 t > 0 4.2.3 µ + µ + µ + e + ν µ ν e γ γ NaI CsI ( ) π + µ + e + µ + ε π µ e (t) ε µ e νµ ν e (t) 4.2 γ 40

4.2 γ y = 2E γ m µ E γ γ m µ [11] 4.2.4 π + µ + e + NaI CsI π + µ + e + 2 I T1 T2 π µ + e + T1 T2 ( 4.3) 4.3 case2a II I π µ + e + ( 4.4) 4.3 case2b 41

4.3 π + µ + e + (case2a) π + µ + e + NaI CsI 4.4 π + µ + e + (case2b) π + µ + e + NaI CsI µ + e + ν µ ν e π + µ + e + ε π µ νµ ν e (t) ε π µ e (t) T1 (MC) NaI CsI π + µ + e + µ + e + ν µ ν e 4.5 NaI CsI 1 2011 C.Malbrunot casea 42

MC casea B 4.5 MC π + µ + e + ( :NaI :CsI) CsI -80 ns CsI 670 ns -80 ns π + µ + e + NaI CsI 4.5 t = 200 π + µ + e + 4.6 1 43

4.6 NaI CsI π + µ + e + 1 4.2.5 π + µ + ν µ γ 2 10 4 γ NaI CsI (µ + e + ν µ ν e ) (4.2.4) NaI CsI π + µ + e + π + µ + ν µ γ (γ 4.7 ) MC C.Malbrunot π + µ + ν µ γ NaI 2.3% CsI 1.8% (4.2.4) NaI CsI NaI CsI π + e + ν e 0.5% 0.17% 4.8 44

4.7 π + e + ν e γ γ 4.8 :NaI :CsI π + µ + ν µ γ 1 45

4.3 PIMUE(t) PIMUE(t) = H(t)[a(1 r)ε π µ e (t)] + bε µ e νµ ν e (t) (4.2) PIENU(t) PIENU(t) = ah(t)[br{ε π eνe (t) + cg 1 (t) + dg 2 (t)} + rε π µ e (t)] +ef(t) + b ε µ e νµ ν e (t) (4.3) Br π + e + ν e π + µ + e + a π + µ + e + r a(1 r) π + µ + e + a r π + µ + e + b b F(t) 4.2.4 NaI CsI π + µ + e + e G 1 G 2 4.2.5 NaI CsI π + µ + ν ν ν e γ c d G 1 G 2 (4.2.5) t = t t 0 t t 0 ( ) Br a r b b e t 0 PIENU(t) PIMUE(t) Br PIENU(t) b b = b a(1 r) a r b a r = b r (4.4) a PIENU(t) Br{ε π eνe (t) + cg 1 (t) + dg 2 (t)} { } Brε π eνe (t) + c G 1 (t) + d G 2 (t) (4.5) c = c Br = 6.15 10 7 (4.6) d = d Br = 2.09 10 7 (4.7) Br (1.1) PIENU(t) PIENU(t) = ah(t)[brε π eνe (t) + c G 1 (t) + d G 2 (t) + rε π µ e (t)] 46 +ef(t) + b rε µ e νµ ν e (t) (4.8)

PIENU(t) PIMUE(t) 3.15 4.9 4.4 4.9 χ 2 ± a (3.5805±0.0005) 10 9 r (1.0022±0.003) 10 3 t 0 1.387±0.012ns b (1.8194±0.0049) 10 7 Br (1.2215±0.0036) 10 4 c d (6.15±0) 10 7 (2.09±0) 10 7 e (1.2737±0.0360) 10 5 4.4 c d 47

±0.0036 10 4 (ndf) 582 χ 2 =672.54 χ 2 /ndf=1.156 48

5 T1 2.3.3 T1 T1 T2 π + µ + e T1 T1 ( 3.2.3) ( 5.1 ) T1 2 T1 ( 5.1 ) T1 T reso ( T1 15 ns ) E NaI + E CsI 50 MeV 5.1 :T1 : T reso ε π µ νµ ν e (t) ε π µ e (t) π + µ + e T1 T2 5.1 5.1 f(x) π + µ + e + g(y) x y 5.2 x y T1 49

( T reso = 0 ns) T1 2 T reso y = x± T reso T1 5.2 2 T1 y x π + µ + e + T1 y = x y = x± T reso 5.2 y > x T1 y < x T1 π + µ + e + f(x) g(y) f(x) g(y) T1 t y > x ( ) F U (t) t+ Treso F U (t) = f(t) g(y)dy (5.1) t π + µ + e + t > 0 5.3 F U (t) 0 t < T reso F U (t) = f(t) t+ T reso g(y)dy T 0 reso < t < 0 f(t) t+ T reso g(y)dy t > 0 t (5.2) 50

5.3 :t < T reso : T reso < t < 0 0 t+ T reso ( ) :t > 0 T reso < t < 0 t t + T reso ( ) 3 T1 t y < x ( π + µ + e + ) F L (t) t+ Treso F L (t) = g(t) f(x)dx (5.3) t t < 0 F L (t) F L (t) = { 0 t < 0 g(t) t+ T reso t f(x)dx t > 0 (5.4) T1 F (t) F (t) = F U (t) + F L (t) = f(t) t+ Treso t t+ Treso g(y)dy + g(t) f(x)dx (5.5) t f(t) (4.1) g(t) (2.2) t F U (t) = 0 t < T reso t+ Treso τ µ 0 τµ ) t+ Treso τ µ t τµ ) exp( t τπ ) t+ Treso exp( t τµ ) exp( t + exp( t τ µ τ π exp( y τµ ) exp( y τπ ) τ µ τ π dy T reso < t < 0 exp( y τµ ) exp( y 0 τπ ) τ µ τ π exp( x dy τµ ) τ µ dx t > 0 (5.6) 51

5.2 F L (t) t = 0 4.3 case3,4 π + µ + e + T1 F L (t) F L (t) F U (t) (5.2) T reso F U (t) i T1 T reso T1 T1 ( 3.2.3) ii T1 ± T T ( 5.4) iii T T1 5.4 : ( T) 45ns 1 2 2 ( ) 2 1 T : 45ns T1 PMT1(T1 1) 1 ( 3.1.2) 1 2 t[0] t[1](3.1.1) 1 2 1 2 T1 52

5.2.1 5.5 15 ns ( 5.5 ) 5.5 T1 π + e + ν e 100 ns τ N N exp( t/τ) τ = 1059±151.2 ns 5.5 : 225 ns 15 ns 225 ns : T1 225 ns (5.2) (5.4) π + e + ν e ε π eνe (t) 3 (5.2) (5.4) 1 F U (t) F L (t) AF U(t) + BF L(t) + Cε π eνe (t) (5.7) A B C 5.6 5.5 (5.7) 53

5.6 5.5 3 (5.2) (5.4) ε π eνe (t) 3 5.5 5.7 54

5.7 F U (t) F L (t) A B A + B A 5.7 T= 0 T= T reso A + B 1 9 5.1 n χ 2 /ndf ± 1 385.7/11 (2.50±0.03) 10 4 2 30.30/10 (3.71±0.07) 10 4 3 15.32/9 (3.19±0.15) 10 4 4 11.73/8 (3.77±0.34) 10 4 5 10.66/7 (4.45±0.74) 10 4 6 10.42/6 (3.67±1.77) 10 4 7 9.364/5 (7.98±4.56) 10 4 8 6.929/4 (2.71±1.31) 10 5 9 6.602/3 (5.15±4.44) 10 5 5.1 ndf 5.7 χ 2 /ndf 6 1 2 3 4 5.8 4 p4 T 4 +p3 T 3 +p2 T 2 +p1 T+p0(p0 p4 ) 55

5.8 A + B 4 5.2.2 F U (t) UL 5.8 UL = (3.77±0.34) 10 4 (5.8) 4.8 T1 (5.2) (5.4) PIENU(t) = ah(t){brε π eνe (t) + cg 1 (t) + dg 2 (t) + rε π µ e (t)} +ef(t) + b rε µ e νµ ν e (t) + ff U(t) + gf L(t) (5.9) f (5.8) F L (t) t = 0 Case3 4 π + µ + e + T1 g 5.9 5.10 5.2 56

5.9 t < 0 t > 0 Br F U (t) F L (t) (1.2215±0.0036) 10 4 f g f (1.2179±0.0052) 10 4 (1.2192±0.0039) 10 4 5.2 F U (t) F L(t) Br 57

5.10 F U (t) F L(t) 5.9 χ 2 /ndf χ 2 /ndf 1.156 F U (t) F L (t) Case3 4 5.2 f 1.3 2 (5.8) (5.2) (5.4) (5.9) f g f = UL R (5.10) g = UL (1 R) (5.11) R 0 R 1 f g f g R 5.11 0.3% R Br R = 0 R = 1 Br 0.4% R 0 1 2010 2012 13 R Br 0.1% 58

5.11 f g R 59

6 PIENU π + e + ν e π + µ + e + 0.1% R π + µ + e + T1 T1 T F U (t) F L (t) 0.4% 13 0.1% F U (t) F L (t) Case3 Case4 60

TRIUMF Douglas Andrew Bryman PIENU JP-PIENU KEK Tran Nam Hoai Nguyen Duy Thong Izyan Hazwani Hashim Nguyen Minh Truong 61

[1] Vincenzo Cirigliano and Ignasi Rosell. Physical Review Letters. 99,231801. 2007 [2] D.I.Britton etal. Phys. Rev. Lette. 68,3000. 1992 [3] G.Czapec etal. Phys.Rev.Lette. 70,17. 1993 [4] A. Pich. Tau Physics: Theory Overview. Nucl. Phys. Proc. Suppl., 181-182:300 305, 2008. [5] C. Lazzeroni et al. Test of Lepton Flavour Universality in K + l + +ν Decays. 2011. [6] Alberto Lusiani. Measurements of V us and Searches for Violation of Lepton Universality and CPT in Tau Decays at BaBar. PoS, ICHEP2010:251, 2010. [7] Chloé Malbrunot. Study of π + e + ν e decay. PhD thesis. The University of British Columbia. 2011. [8] Kaoru Yamada. Search for Massive Neutrinos in π + e + ν Decay. PhD thesis. Dept of Physics, Graduate School of Science, Osaka University. 2010. [9].... 2007. [10] Naosuke Ito. Improvement of COPPER 500-MHz Flash ADC for PIENU experiment. Master thesis. Dept of Physics,Osaka University. 2010. [11] Feng Xiao. Measurement of the Radiative Muon Decay Branching Fraction in the MEG Experiment. PhD thesis. Univercity of California. 62