LHCb calorimeter electronics. Photon identification. Calorimeter calibration

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HAL Id: tel-00583998

https://tel.archives-ouvertes.fr/tel-00583998

Submitted on 7 Apr 2011

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LHCb calorimeter electronics. Photon identification.

Calorimeter calibration

F. Machefert

To cite this version:

F. Machefert. LHCb calorimeter electronics. Photon identification. Calorimeter calibration. Physique des Hautes Energies - Expérience [hep-ex]. Université Paris Sud - Paris XI, 2011. �tel-00583998�

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β

β β

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300mrad bb b¯b 2.0 ≤ η ≤ 5.5 L = 2 × 1032_cm−2_s−1 3 × 1011 _bb

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µ σ_bb/σinelastic

z

7TeV bb

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P t 1cm 1034_cm−2_s−1 2 × 1032_{− 5 × 10}32_cm−2_s−1 n = 0 cm−2_s−1 3.5TeV ≈ 400 β∗ 2.5m 2.7

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z pp

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pp

z _−50cm 1m

n+ _n

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3cm 8mm z 1.5cm z r φ r− 45◦ 45◦ r− 8.2mm 41.9mm 38µm 102µm φ− 8mm 17.25mm ±20◦ _17.25mm _41.9mm _±10◦ φ− r− 39µm 97µm

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z 2.5m 27cm ±5◦ _{U − V} K0 s p+ _n % B

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|B| 1.1T y z 4.7m _{x − z} ! B.dl ≈ 4Tm 200GeV x 11 22cm 4m2 ±5◦ p+ _n _198µm 6.0×4.9m2 ±5◦

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4.9mm

CO2 O2 50ns

190µm

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2.5 × 2.5mm2 25ns 60GeV n = 1.03 10GeV C4F10 n = 1.0014 10GeV 60GeV 15GeV 100GeV 120mrad CF4 n = 1.0005 C4F10 CF4 5mrad

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6.2 × 7.6 m2 6.3 × 7.8 m2 6.8 × 8.4 m2 180mm 2.5X0 0.1λI 25X0 1.1λI 5.6λI 10%/√E ⊕ 1.5% 80%/√E ⊕ 10% ET ET

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2 mm _{12 × 12 cm}2 _{6 × 6 cm}2 _{4 × 4 cm}2

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12 × 12 6 × 6 4 × 4cm2

26.2 × 26.2 cm2 _{13.1 × 13.1 cm}2

5.6λI 1.2m

4mm

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2 × 1032_cm−2_s−1 _pp _16MHz 12MHz b¯b Pt 1.1MHz 4µs

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2 ×2

Et

π0

Pt

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Pm

Buffer Integrator

Vss Vdd

Analog Chip

BICMOS 0.8 um Integrated circuit 4 channels per chip

+ -5 ns 25 Ω 65 Ω 27 Ω 45 Ω 12 M Ω 33 Ω 37 Ω 51.1 Ω 33 Ω 330 Ω 3.3 k Ω 1.5 K Ω 25 ns 110 Ω 2.2 nF 470 pF 27 Ω 22 nF 1.07kΩ ADC 12 bits 40 Mhz 4 pF 2.7 k Ω 4.7 k Ω 1 nF 1 nF 4.7 k Ω 4.7 nF +3 V 10kΩ 20 kΩ 20mA 25Ω 1V 250Ω 250µV Et = 2.5M eV 10GeV 25ns 2% ±2ns B → K⋆_γ Pt

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4pF 20MHz 25ns 25ns _{25ns ± 0.5ns} 100Ω 4.7nF ≈ 2µs 4pF 2kΩ ≈ 22ns ≈ 4ns 0 _{≈ 25ns} 300Ω 51Ω 250Ω 1.07kΩ 10kΩ 20kΩ 250Ω

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! !

(fit−signal)/signal ±1%

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! ! 1.5% A B A = m events " j #_{n channels} " i xij − ¯x $2 = m%n2_σ2 coh+ nσincoh2 & B = m events " j n channels " i (xij− ¯x)2 = m × n%σ2coh+ σincoh2 & σcoh σincoh A B

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ns 25ns n × 25ns √ t 0ns σ2_incoh_{= 0.60 + 0.02 × t in ADC}2 σcoh = 0.08 + 0.5 × 10−2× t in ADC 25 50ns ≈ 1.3

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3 × 3 3.5 2.4 _{∼ 8.8MeV} _{∼ 6.0MeV} Pt 4pF 2pF ±2ns ! ! (25 + 50)/2 = 37.5ns

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∆t(500/333Ω) ∆t(500/333Ω) ∆t(500/333Ω) VIL VIH ns 500 333Ω 333V Et 2 × 2

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{5 "} : , ' , : , ' , # $ : , ' , : , ' , # $ : , ' , : , ' , G % B N % # $ : , ' , : , ' , % & ' ( 4 5 6 7 + + 3 % & ' ( 4 5 6 7 + + 2 % & ' ( 4 5 6 7 + + : % & ' ( 4 5 6 7 + + 8 % & ' ( 4 5 6 7 + + 3 % & ' ( 4 5 6 7 + 2 % & ' ( 4 5 6 7 + + : K ) # ! " # $ % & ' ! ( " ) * + , - " ; 7 6 - . & ! " " # $ % & ' ( ) . # " . / & % # . # " . / & % # 2 < = 8 F C . 4 E 7 / $ > ? @ / 5 " 5 " 5 " G / G / G / G / O N L ' P $ , 3 Q A 4 1 # 8 $ - H+ 3 > ? @ / > ? @ / > ? @ / I H 6 ' 2 & B ' A 2 I H 6 ' 2 & B ' A 2 I H 6 ' 2 & B ' A 2 I H 6 ' 2 & B ' A 2

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±2ns

I2_C

25ns

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25ns cos θ Pt Pt [5, 16] ns n n cos θ

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! !

!"#$

±2 ns

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±1 %

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≈ 1.1

17

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2 × 25ns

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◦ ≤ 49◦ ≥ 54◦ _{≤ 60}◦ ≤ 49◦ ≤ 49◦ ≤ 49◦ ≥ 60◦ _{≤ 65}◦ ≥ 60◦ _{≤ 65}◦

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148 × 1012 66 × 1012 130 × 1012 15 × 1012 30 × 1012 350 × 1012 350 × 1012 2.8db/km 100m 9db 1014

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L

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z

nF

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t0 − 1 t0

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t0 − 1 t0

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pp L = 5 × 1032_cm−2_s−1 2 × 1032_cm−2_s−1 π cm−2_year−1 z 12.30m 13.32m 3.5m

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f + f ′ → f + f′ f + ¯_{f → f′ + ¯}_{f ′} f + ¯_{f → g + g} f + g → f + g g + g → f + ¯f g + g → g + g pt 107_s π z = 12.30meters 3.7 × 106_s

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−2 −1 _{z = 12.30m} z = 13.32m x y 100MeV f (x) = Ae−Bx_{+ Cx}D z = 12.30m z = 13.32m cm−2_year−1_MeV−1 _{2.2 × 10}9 _{1.8 × 10}9 MeV−1 _0.27 _0.28 0.43 × 109 _{0.49 × 10}9 −0.87 −0.89 z 12.30 13.32m

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all particles Neutrons Protons K mesons π mesons Fit (z=12.30m) Fit (z=13.30m) cm−2_year−1_MeV−1 z = 12.30m z = 12.30m z = 13.30m 4.2 × 109 108_cm−2_s−1 _200MeV 4cm 200MeV 4MeV. −1 2 6.5rad. −1

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107

10.7 22.6krad

90MeV/

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10−7_µm−1

58MeV/

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−2 µ . −1 2 2.4 × 107 _{2.4 × 10}7 2.4 × 107 _{3.0 × 10}7 2.4 × 107 _{2.3 × 10}7 2.4 × 107 _{2.4 × 10}7 43mA 52mA 6MeV.mg−1_cm2 _{∼ 1.5MeV.µm}−1 dE/dx

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100 -1 1 10 102 103 2 4 6 8 10 12 14 _H He Li Be B C N O F Ne Na Mg Al Si dE/dx (MeV.cm2.mg-1) E (MeV) 6MeV.mg−1_cm2 _1.5MeV.µm−1 15MeV.mg−1_cm2 10-1 1 10 102 103 10-11 10-10 10-9 10-8 10-7 10-6 10-5 H He Li Be B C N O F Ne Na Mg Al Si Probability (um-1) E (MeV) µ −1 1 1 2MeV 10−7_µm−1 10µ

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2 × 10−6 10µ 10µ µ sSEL sKr 1 − sSEL− sKr [sSEL, sKr] sKr > 10−8 LET ≤ 15MeV. −1 2 sKr < 10−8 sLimit sLimit = 8.9 × 10−9 8.9 × 10−7_% 8.9 × 10−9 6MeV. −1 2 _{2 × 10}−6 1.8 × 10−14 30MeV _{4.2 × 10}9_years−1 −2 N14 Si28 _{∆Q = 29MeV} _30MeV 30MeV 1GeV

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 s SEL sKr 10 -11 10 -10 10 -9 10 -8 10 -11 10 -10 10 -9 10 -8 [sSEL, sKr] [sSEL, sKr] 14 sLimit smin year.chip−1₎ 8.9 × 10−9 3.9 × 10−8 1.3 × 10−7 _{4.0 × 10}−8 5.0 × 10−7 _{1.3 × 10}−7 3.1 × 10−7 _{5.7 × 10}−8 8.1 × 10−5 _{2.7 × 10}−5 sLimit smin 2 × 10−6 _{4.2 × 10}9_cm−2_year−1

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γ

s sion

1 − s − sion

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[s, sion]

sion > 6.2 × 10−8

sion < 6.2×10−8

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f (ELET) = σ0 # 1 − e ! ELET −EL0 W "s$

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σ0 L0

3.5 × 10−8_cm2 _1.44MeV.cm2_/mg _15MeV.cm2_/mg

1.0 × 10−6_cm2 _3.00MeV.cm2_/mg _30MeV.cm2_/mg

' ∞

0

φneutron(E) × σ(E)dE

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φi(E) =

' ∞

0

φneutron(E′)pi(E, E′)tdE′

pi(E, E′) E µ E′ _E′ pi(E, E′) φi(E) µ φi(E) i LETmax i LETmax i

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"

ions

' ∞

0

φi(ELET) × σ(ELET)dELET

2 4 6 8 10 12 14 10-17 10-16 10-15 10-14 10-13 H He Li Be B C N O F Ne Na Mg Al Si SEU rate ) -1 .mg 2 LET (MeV.cm 6.5 × 10−13_s−1

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2 4 6 8 10 12 14 10-17 10-16 10-15 10-14 10-13 H He Li Be B C N O F Ne Na Mg Al Si SEU rate ) -1 .mg 2 LET (MeV.cm cm−2 5.5 × 10−13_s−1 35.5 × 10−13_s−1

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0 2 4 6 8 10 12 14 16 10-10 10-9 10-8 10-7 sram R-Cell ("0" pattern) MeV.cm2.mg−₁ _cm2 10−9 5 × 10−8 10−6 3 × 10−6 10−5 10−5 σ0 L0 10−5_cm2 _5.0MeV.cm2_/mg _20MeV.cm2_/mg (√ N + 1) (√N + 1)

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0 20 40 60 80 100 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4

Clock Upset cross-section

) -1 .mg 2 LET (MeV.cm ) 2 cross-section (cm 2 4 6 8 10 12 14 10-17 10-16 10-15 10-14 10-13 H He Li Be B C N O F Ne Na Mg Al Si ) -1 .mg 2 LET (MeV.cm SEU rate 35.5 × 10−13_s−1 5.5 × 10−13 420s−1_.cm−2 1.2 × 10−9 _{7.3 × 10}−6

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6.5 × 10−13 420s−1_cm−2 16µs 4.4 × 10−15 µ 16 × 2048 2.9 × 105 L0 _{7.9 × 10}−5 _{HLT 1} 1.6 × 107 107_s

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3.5 × 10−12 420s−1_cm−2 1.47 × 10−9 108s−1_.cm−2 109s−1cm−2 ∼ 100◦C ∼ 100◦C

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100krad 100MeV.mg−1_cm2 15MeV.mg−1_cm2 20 − 25krad 30 − 35krad 100◦_C 200rad

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∆E = |E γ Rec− E γ M C| E_Recγ !25% * ∆r ! 10mm ∆z ! 150mm π0 2.5GeV z z

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3 × 3 2 × 2 Pt Pt 20MeV/c 50MeV/c Pt Pt B → π+_π−_π0 200MeV/c 3 × 3 Pt 3 × 3

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%ptr 6X0 z %pcl χ2 2D χ2_2D(%p) = (%ptr− %p)TCtr−1(%ptr− %p) + (%pcl− %p)TScl−1(%pcl− %p) %p Ctr %ptr Scl χ2 min χ2 min (GeV/c) t P 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 f ra ct io n γ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 χ2 min χ2 min Pt χ2 min χ2 min Pt χ2 min

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χ2 min E (MeV) 0 10 20 30 40 50 60 70 80 90 100 3 10 × T ra n s fo rm E 1 2 3 4 5

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ETransformed= ln(1.4 × E(MeV)) − 6.2)

γ

γ → e+_e− _↓ _→ _↓ _→

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1 10 2 10 3 10 4 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 No SPD constrain Signal No SPD constrain 1 10 2 10 3 10 4 10 5 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 Background 1 10 2 10 3 10 4 10 5 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 All 1 10 2 10 3 10 4 10 5 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 Background Photon 1 10 2 10 3 10 4 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7

No SPD hit (no conversion)

Signal

1 10 2 10 3 10 4 10 5 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 Background 1 10 2 10 3 10 4 10 5 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 All 1 10 2 10 3 10 4 10 5 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 Background Photon 1 10 2 10 3 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 SPD hit (conversion) Signal SPD hit (conversion) 1 10 2 10 3 10 4 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 Background 1 10 2 10 3 10 4 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 All 1 10 2 10 3 10 4 10 PRS Energy 0 20 40 60 80 100120140160180200 0 1 2 3 4 5 6 7 Background Photon x y

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1 10 2 10 3 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 No SPD constrain Signal No SPD constrain 1 10 2 10 3 10 4 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 Background 1 10 2 10 3 10 4 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 All 1 10 2 10 3 10 4 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 Background Photon 1 10 2 10 3 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7

Signal

1 10 2 10 3 10 4 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 Background 1 10 2 10 3 10 4 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 All 1 10 2 10 3 10 4 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 Background Photon 1 10 2 10 3 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 SPD hit (conversion) Signal SPD hit (conversion) 1 10 2 10 3 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 Background 1 10 2 10 3 10 4 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 All 1 10 2 10 3 10 2D χ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 Background Photon χ2 min x χ2 min y

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1 10 2 10 3 10 4 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 No SPD constrain Signal No SPD constrain 1 10 2 10 3 10 4 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 Background 1 10 2 10 3 10 4 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 All 1 10 2 10 3 10 4 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 Background Photon 1 10 2 10 3 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7

Signal

1 10 2 10 3 10 4 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 Background 1 10 2 10 3 10 4 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 All 1 10 2 10 3 10 4 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 Background Photon 1 10 2 10 3 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 SPD hit (conversion) Signal SPD hit (conversion) 1 10 2 10 3 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 Background 1 10 2 10 3 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 All 1 10 2 10 3 10 /E seed E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 Background Photon Eseed/ECluster x Eseed/ECluster y

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(MeV) t P 0 1000 2000 3000 4000 5000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 - No conversion γ MC Z (mm) 0 200 400 600 800 1000 1200 -4 10 -3 10 -2 10 MC γ conversion position ±25% ±25% ±25% Eseed/E χ2 min

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∆ log L ∆ log L -10-8 -6 -4 -2 0 2 4 6 8 10 0 10000 20000 30000 40000 50000 60000 70000 -10-8 -6 -4 -2 0 2 4 6 8 10 0 5000 10000 15000 20000 25000 30000 -10-8 -6 -4 -2 0 2 4 6 8 10 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 -10-8 -6 -4 -2 0 2 4 6 8 10 0 2000 4000 6000 8000 10000 ∆ log L Pt 200MeV Pt 500MeV ∆ log L

(113)

B → K∗_{γ B → π}0_π+_π− B → K∗_γ _P t π0 ∆ log L ∆ log L Lγ− Lbackground ∆ log L + ǫ _/γ!ee = Nγ Rec( )/N(γ!ee)M C

ǫ _/γ→ee = N_Rec(γ ₎/N(γ→ee)M C

+ ρ = Nγ Rec( )/(N γ Rec( )+ N bkg Rec( ))

ρ = N_Rec(γ ₎/(N_Rec(γ ₎+ N_Rec(bkg ₎)

N_Rec(γ ₎ N_Rec(γ ₎ Nbkg _N(γ!ee)M C N(γ→ee)M C χ2 min Pt 200MeV B → K∗_γ ∆ log L ≤ 0 χ2 min ≤ 4 Pt ∆ log L −∞ ǫ = NγM C Rec /(Nγ M C₎ _{ρ = N}γM C Rec /(N γM C Rec + N bkg Rec)

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0.45 0.5 0.55 0.6 0.65 0.7 0.75 0 0.2 0.4 0.6 0.8 1 ρ vs ∈ SPD ρ vs ee → γ ∈ SPD ρ vs ee → γ ∈ 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0 0.2 0.4 0.6 0.8 1 ρ vs ∈ SPD ρ vs ee → γ ∈ SPD ρ vs ee → γ ∈ ∆ log L Pt 500(MeV) 50 100 150 200 0 5000 10000 15000 20000 25000 30000 LL Cut Δ No 50 100 150 200 0 2000 4000 6000 8000 10000 12000 LL>-2 Δ 50 100 150 200 0 1000 2000 3000 4000 5000 6000 7000 LL>0 Δ mass (MeV/c) 0 π 50 100 150 200 0 500 1000 1500 2000 2500 LL>2 Δ π0 π0 π0 χ2 min Eseed/E µ = 0.4

(115)

0 50 100 150 200 0 0.1 0.2 0.3 0.4 0.5 0.6 0 50 100 150 200 0 0.1 0.2 0.3 0.4 0.5 0.6 PRS E 0 50 100 150 200 0 0.05 0.1 0.15 0.2 0.25 PRS E 0 50 100 150 200 0 0.05 0.1 0.15 0.2 0.25 0 20 40 60 80 100 0.01 0.02 0.03 0.04 0.05 0.06 0.07 min 2 χ 0 20 40 60 80 100 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0 0.10.20.30.40.50.60.70.80.9 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 /E seed E 0 0.2 0.4 0.6 0.8 1 0 0.02 0.04 0.06 0.08 0.1 0.12 χ2 min Eseed/E β∗ _2.5m

(116)

(117)

(118)

β β β π0 β EP RS = βEScint.

(119)

EP RS EScint.

E = αEECAL+ βEScint.

α β α α β 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 factor β 6.5 7 7.5 8 8.5 9 9.5 10 10.5 EC A L m is c a li b r a ti o n 0.9 0.95 1 1.05 1.1 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 factor β 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 EC A L m is c a li b r a ti o n 0.9 0.95 1 1.05 1.1 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 factor β 7 8 9 10 11 12 EC A L m is c a li b r a ti o n 0.9 0.95 1 1.05 1.1 β z π0 π0 _γ e−7/9×2.5X0 ≈ 14% π0 β EECAL EP RS β δβ β α δα x δβ ≈ 1 − δα(1 − x) x 134.98MeV/c2 (x, y) β

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x x β α x x 0.9 1.0 1.1 1.2 ∆Β 0.98 1.00 1.02 1.04 ∆Α β x x β π0 π0 π0 _{E E} t σE E = 10% √ E ⊕ 1.5% 5 mm

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3 × 3 π0 Et 200 MeV π0 E (GeV) 0 10 20 30 40 50 60 70 80 90 100 (G eV) t E 0 1 2 3 4 5 6 7 8 9 100 50 100 150 200 250 300 350 0 50 100 150 200 250 300 E Et π0 π0 E (MeV) 0 5000 10000 15000 20000 25000 30000 EC_AL /E Scint. E 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 1 10 2 10 3 10 4 10 1 10 2 10 3 10 4 10 EScint. β π0 β β

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α β π0 _β σECAL β β β β δβ β β σβ(β − βtrue) βtrue β β β βσP RS σβ(β −βtrue) β π0 m2 _{= 2(1 − cos θ)E}1E2 θ x = EP RS/ET ot δα δβ δα = α/αtrue δβ = β/βtrue (m − -m.)2 ≈ m2P DG((δα− δβ)σ(x))2 π0 δβ β α π0 δβ ≈ δα x β α α β π0

(123)

correction β 0 0.2 0.40.6 0.8 1 1.2 1.41.6 1.8 2 m a s s (Me V) 0_π 126 128 130 132 134 136 138 140 142 144 correction β 0 0.2 0.40.6 0.8 1 1.2 1.41.6 1.8 2 w id th (Me V) 0_π 0 1 2 3 4 5 6 7 8 9 10 Energy smearing Position smearing PS Energy effect PS Energy/smearing effects All included β π0 β β β mP DG β α x β α β β α α β x y mπ0 δβ π0 _β

(124)

correction β 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.41.5 m a s s (Me V) 0_π 126 128 130 132 134 136 138 140 142 144 correction β 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.41.5 w id th (Me V) 0_π 0 1 2 3 4 5 6 7 All included

ECAL miscalibration factor 0.95 ECAL miscalibration factor 1.05

π0 β π0 π0 β 20 mm π0 π0 β σP RS σP RS σP RS+θ π0 β

(125)

β

σ2(β, βcorr) = σECAL2 + σβ2(β − βcorr)2+ β2σP RS+θ2

! !β σπ σ!"#$ α σ_%&'θ π0 _β σECAL α β β π0 β π0 α β β π0 π0

(126)

β π0 _α β α α β

β

β β β π0 γ β π0 _β π0 _β π0 β β

(127)

π0 π0 π0 ∆ log L π0 _β π0 β 5% π0 β π0 ±2.5 × σ σ β β π0

(128)

reconstructed mass (MeV/c) 0 π 0 100 200 300 400 500 600 700 0 50 100 150 200 250 300 350 3 10 × β = 8.3 αtrue βtrue

δαtrue δβtrue αrec βrec

γMC

γrec

γMC

β

δαtrueEγrec − EγM C δαtrue

δαtrue

δβtrue δαtrue

δαtrue

(δαtrueEγrec+ δβrec × βrecEP RS− EγM C)

(129)

α 1 1.0021.0041.0061.008 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 0.005 / ndf 2 χ 4.891e-08 / 3 p0 -0.9642 ± 0.02027 p1 0.9609 ± 0.02019 / ndf 2 χ 4.891e-08 / 3 p0 -0.9642 ± 0.02027 p1 0.9609 ± 0.02019 Outer α 1.0061.008 1.01 1.0121.014 -0.005 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 / ndf 2 χ 1.695e-07 / 3 p0 -0.9011 ± 0.03796 p1 0.8909 ± 0.03758 / ndf 2 χ 1.695e-07 / 3 p0 -0.9011 ± 0.03796 p1 0.8909 ± 0.03758 Middle α 1.0161.018 1.02 1.0221.024 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 0.005 / ndf 2 χ 3.688e-08 / 3 p0 -0.9291 ± 0.01788 p1 0.9116 ± 0.01753 / ndf 2 χ 3.688e-08 / 3 p0 -0.9291 ± 0.01788 p1 0.9116 ± 0.01753 Inner δαtrueEγrec − EγM C δαtrue correction β 0.90.95 1 1.051.11.151.2 -0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 / ndf 2 χ 2.382e-08 / 5 p0 -0.07265 ± 0.0002752 p1 0.06673 ± 0.0002609 / ndf 2 χ 2.382e-08 / 5 p0 -0.07265 ± 0.0002752 p1 0.06673 ± 0.0002609 Outer correction β 0.90.95 1 1.051.11.151.2 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 / ndf 2 χ 2.061e-08 / 5 p0 -0.05707 ± 0.000256 p1 0.05013 ± 0.0002427 / ndf 2 χ 2.061e-08 / 5 p0 -0.05707 ± 0.000256 p1 0.05013 ± 0.0002427 Middle correction β 0.90.95 1 1.051.11.151.2 -0.008 -0.006 -0.004 -0.002 0 0.002 / ndf 2 χ 6.243e-07 / 5 p0 -0.04292 ± 0.001409 p1 0.03827 ± 0.001336 / ndf 2 χ 6.243e-07 / 5 p0 -0.04292 ± 0.001409 p1 0.03827 ± 0.001336 Inner βMC αMC

β

βtrue

(130)

δαtrue βrec δβrec βtrue

reconstructed mass (MeV

0 π 120 125 130 135 140 145 150 155 70 80 90 100 110 120 130 3 10 × π0

NOuter γγ βOuter γγ NM iddle γγ βM iddle γγ NI nner γγ βI nner γγ

9.40 ± 0.07 9.73 ± 0.09 10.15 ± 0.13

β π0

π0

(131)

correction β 0.5 1 1.5 2 (Me v) σ 6 8 10 12 14 ) γ γ → 0 π ( σ Fitted correction β 0.5 1 1.5 2 Ma ss (Me V) 128 130 132 134 136 138 140 142 144 146 148 ) γ γ → 0 π Fitted mass ( correction β 0.5 1 1.5 2 (Me v) σ 8 9 10 11 12 13 14 15 16 ) -e e -e + e → 0 π ( σ Fitted correction β 0.5 1 1.5 2 Ma ss (Me V) 115 120 125 130 135 140 145 150 ) -e + e -e + e → 0 π Fitted mass ( β π0 β π0 β β σ β βrec β β β β

(132)

Entries 16 Mean 9.281 RMS 0.2364 β 8.5 9 9.5 10 10.5 0 1 2 3 4 5 Entries 16 Mean 9.281 RMS 0.2364 Outer - Photon Entries 16 Mean 9.923 RMS 0.5144 β 9 9.5 10 10.5 11 0 1 2 3 4 5 Entries 16 Mean 9.923 RMS 0.5144 Middle - Photon Entries 16 Mean 10.33 RMS 0.6425 β 10 11 12 0 0.5 1 1.5 2 2.5 3 3.5 4 Entries 16 Mean 10.33 RMS 0.6425 Inner - Photon Entries 16 Mean 9.825 RMS 0.3363 β 9 9.5 10 10.5 0 0.5 1 1.5 2 2.5 3 3.5 4 Entries 16 Mean 9.825 RMS 0.3363 Outer - Electron Entries 16 Mean 10.07 RMS 0.4423 β 9 10 11 0 0.5 1 1.5 2 2.5 3 Entries 16 Mean 10.07 RMS 0.4423 Middle - Electron Entries 16 Mean 11.08 RMS 0.5945 β 10 11 12 0 0.5 1 1.5 2 2.5 3 Entries 16 Mean 11.08 RMS 0.5945 Inner - Electron β β

NOuter ee βOuter ee NM iddle ee βM iddle ee NI nner ee βI nner ee

9.85 ± 0.08 9.80 ± 0.10 10.76 ± 0.11

β π0

π0

(133)

β β π0 _MeV/c π0 _α true β π0 π0 αtrue β π0 αtrue β π0 β

β

β β π0

(134)

β correction β 0.5 1 1.5 2 (Me v) σ 6 8 10 12 14 16 ) γ γ → 0 π ( σ Fitted correction β 0.5 1 1.5 2 Ma ss (Me V) 130 135 140 145 150 ) γ γ → 0 π Fitted mass ( correction β 0.5 1 1.5 2 (Me v) σ 6 8 10 12 14 16 ) -e e -e + e → 0 π ( σ Fitted correction β 0.5 1 1.5 2 Ma ss (Me V) 120 125 130 135 140 145 150 ) -e + e -e + e → 0 π Fitted mass ( π0 β π0 _β β 0.2% 1.0% β

(135)

Entries 10 Mean 8.76 RMS 0.17 Underflow 0 Overflow 0 β 8.5 9 0 0.5 1 1.5 2 2.5 3 _Entries ₁₀ Mean 8.76 RMS 0.17 Underflow 0 Overflow 0 Outer - Photon Entries 10 Mean 9.68 RMS 0.2002 Underflow 0 Overflow 0 β 9 9.5 10 10.5 0 0.5 1 1.5 2 2.5 3 Entries 10 Mean 9.68 RMS 0.2002 Underflow 0 Overflow 0 Middle - Photon Entries 10 Mean 11.15 RMS 0.405 Underflow 0 Overflow 0 β 10.5 11 11.5 12 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Entries 10 Mean 11.15 RMS 0.405 Underflow 0 Overflow 0 Inner - Photon Entries 10 Mean 9.39 RMS 0.102 Underflow 0 Overflow 0 β 9.2 9.4 9.6 9.8 0 1 2 3 4 5 6 Entries 10 Mean 9.39 RMS 0.102 Underflow 0 Overflow 0 Outer - Electron Entries 10 Mean 10.67 RMS 0.419 Underflow 0 Overflow 0 β 10 10.5 11 11.5 12 0 0.5 1 1.5 2 2.5 3 Entries 10 Mean 10.67 RMS 0.419 Underflow 0 Overflow 0 Middle - Electron Entries 10 Mean 12.98 RMS 0.3926 Underflow 0 Overflow 0 β 12 12.5 13 13.5 14 0 0.5 1 1.5 2 2.5 3 3.5 4 Entries 10 Mean 12.98 RMS 0.3926 Underflow 0 Overflow 0 Inner - Electron β Nzone π0

NOuter γγ βOuter γγ NM iddle γγ βM iddle γγ NInner γγ βInner γγ

8.69 ± 0.08 9.46 ± 0.09 10.95 ± 0.11

β

(136)

β

NOuter ee βOuter ee NM iddle ee βM iddle ee NInner ee βInner ee

9.40 ± 0.07 10.43 ± 0.08 12.79 ± 0.08

β

NOuter NM iddle NOuter π0

βOuter βM iddle βInner

γγ _{8.69 ± 0.43 ± 0.08} _{9.46 ± 0.47 ± 0.09} _{10.95 ± 0.55 ± 0.11}

e+_e− _e+_e− _{9.40 ± 0.47 ± 0.07 10.43 ± 0.52 ± 0.08 12.79 ± 0.64 ± 0.08}

π0 _β

Outer) π0 βM iddle π0 βInner

γγ

e+_e− _e+_e−

(137)

(138)

(139)

cos(θ)

π0

2.7

(140)

(141)

(142)

(143)

(144)

(145)

(146)

(147)

(148)