Transcription

1 CCD A simulation study of a vertex detector system using fine-pixel CCD for the ILC

2

3 (International Linear Collider; ILC) - GeV( 1TeV) ILC CERN LHC b c b c 4 µm 1 3 µm ILC 214 ILC CCD (FPCCD : Fine Pixel CCD) FPCCD µm µm CCD ILC FPCCD 1 2 ILC 3 FPCCD 4 (ILCSoft) 6 7 FPCCD 8

4 1 (International Linear Collider ; ILC) ILC ILC ILD (VXD) (TPC) Particle Flow Algorithm (PFA) ILC CCD (FPCCD) FPCCD FPCCD FPCCD i

5 ii 4 ILCSoft FPCCD FPCCDDigitizer FPCCDClustering ILD SiliconTracking ζ FPCCD FPCCDTrackFinder (FPCCDTrackFinder ) FPCCDTrackFinder CPU Z-pole

6 iii Z b b, c c, q GeV CPU A 86 B 87 C ζ ξ 9 17

7 1.1 ILC ILD ILD TPC ECAL SiECAL( ) ScECAL( ) Detector Slab HCAL AHCAL SDHCAL LumiCal BeamCal BeamCal GeV PFA V e + e HZ e + e ZHH e + e t th FPCCD iv

8 v 4.1 FPCCDDigitizer ILD Kalman Filter ξ ζ t t 6 jets@ 3 GeV ζ t t BG z ζ d (p = 1 GeV/c θ = 8 ) (A) (C) FPCCD + FPCCDTrackFinder FPCCD + ( BG ) FPCCD + FPCCDTrackFinder FPCCD + (cos θ BG ) FPCCD + FPCCDTrackFinder ( ) FPCCD + FPCCDTrackFinder (cos θ) (Z-pole ) (Z b b, c c, q GeV BG ) (Z b b, c c, q GeV BG ) b-jet (FPCCD BG ) b-jet (FPCCD BG ) b-jet (CMOS BG ) b-jet (CMOS BG )

9 vi 8.8 (Z b b, c c, q GeV BG )( (8.6) ) (Z b b, c c, q GeV BG )( (8.6) ) B.1 x-y B.2 s-z C.1 ζ ( GeV) C.2 ζ (3 GeV) C.3 ζ ( GeV) C.4 ζ (1 GeV) C. ζ ( GeV ) C.6 ζ (3 GeV ) C.7 ζ ( GeV ) C.8 ζ (1 GeV ) C.9 ζ ( GeV ) C.1 ζ (3 GeV ) C.11 ζ ( GeV ) C.12 ζ (1 GeV ) C.13 ξ ( GeV) C.14 ξ (3 GeV) C. ξ ( GeV) C.16 ξ (1 GeV) C.17 ξ ( GeV ) C.18 ξ (3 GeV ) C.19 ξ ( GeV ) C.2 ξ (1 GeV ) C.21 ξ ( GeV ) C.22 ξ (3 GeV ) C.23 ξ ( GeV ) C.24 ξ (1 GeV ) C. ξ ( GeV) C.26 ζ ( GeV) C.27 ξ ( GeV ) C.28 ζ ( GeV ) C.29 ξ ( GeV ) C.3 ζ ( GeV ) C.31 1 ξ ( GeV) C.32 1 ζ ( GeV)

10 C.33 1 ξ ( GeV ) C.34 1 ζ ( GeV ) C.3 1 ξ ( GeV ) C.36 1 ζ ( GeV ) C.37 2 ξ ( GeV) C.38 2 ζ ( GeV) C.39 2 ξ ( GeV ) C.4 2 ζ ( GeV ) C.41 2 ξ ( GeV ) C.42 2 ζ ( GeV ) C.43 3 ξ ( GeV) C.44 3 ζ ( GeV) C.4 3 ξ ( GeV ) C.46 3 ζ ( GeV ) C.47 3 ξ ( GeV ) C.48 3 ζ ( GeV ) C.49 4 ξ ( GeV) C. 4 ζ ( GeV) C.1 4 ξ ( GeV ) C.2 4 ζ ( GeV ) C.3 4 ξ ( GeV ) C.4 4 ζ ( GeV ) C. ξ ( GeV) C.6 ζ ( GeV) C.7 ξ ( GeV ) C.8 ζ ( GeV ) C.9 ξ ( GeV ) C.6 ζ ( GeV ) C.61 ξ (3 GeV) C.62 ζ (3 GeV) C.63 ξ (3 GeV ) C.64 ζ (3 GeV ) C.6 ξ (3 GeV ) C.66 ζ (3 GeV ) C.67 1 ξ (3 GeV) C.68 1 ζ (3 GeV) C.69 1 ξ (3 GeV ) C.7 1 ζ (3 GeV ) C.71 1 ξ (3 GeV ) C.72 1 ζ (3 GeV ) vii

11 viii C.73 2 ξ (3 GeV) C.74 2 ζ (3 GeV) C.7 2 ξ (3 GeV ) C.76 2 ζ (3 GeV ) C.77 2 ξ (3 GeV ) C.78 2 ζ (3 GeV ) C.79 3 ξ (3 GeV) C.8 3 ζ (3 GeV) C.81 3 ξ (3 GeV ) C.82 3 ζ (3 GeV ) C.83 3 ξ (3 GeV ) C.84 3 ζ (3 GeV ) C.8 4 ξ (3 GeV) C.86 4 ζ (3 GeV) C.87 4 ξ (3 GeV ) C.88 4 ζ (3 GeV ) C.89 4 ξ (3 GeV ) C.9 4 ζ (3 GeV ) C.91 ξ (3 GeV) C.92 ζ (3 GeV) C.93 ξ (3 GeV ) C.94 ζ (3 GeV ) C.9 ξ (3 GeV ) C.96 ζ (3 GeV ) C.97 ξ ( GeV) C.98 ζ ( GeV) C.99 ξ ( GeV ) C.1 ζ ( GeV ) C.11 ξ ( GeV ) C.12 ζ ( GeV ) C.13 1 ξ ( GeV) C.14 1 ζ ( GeV) C. 1 ξ ( GeV ) C.16 1 ζ ( GeV ) C.17 1 ξ ( GeV ) C.18 1 ζ ( GeV ) C.19 2 ξ ( GeV) C.11 2 ζ ( GeV) C ξ ( GeV ) C ζ ( GeV )

12 C ξ ( GeV ) C ζ ( GeV ) C.1 3 ξ ( GeV) C ζ ( GeV) C ξ ( GeV ) C ζ ( GeV ) C ξ ( GeV ) C.12 3 ζ ( GeV ) C ξ ( GeV) C ζ ( GeV) C ξ ( GeV ) C ζ ( GeV ) C.1 4 ξ ( GeV ) C ζ ( GeV ) C.127 ξ ( GeV) C.128 ζ ( GeV) C.129 ξ ( GeV ) C.13 ζ ( GeV ) C.131 ξ ( GeV ) C.132 ζ ( GeV ) C.133 ξ (1 GeV) C.134 ζ (1 GeV) C.13 ξ (1 GeV ) C.136 ζ (1 GeV ) C.137 ξ (1 GeV ) C.138 ζ (1 GeV ) C ξ (1 GeV) C.14 1 ζ (1 GeV) C ξ (1 GeV ) C ζ (1 GeV ) C ξ (1 GeV ) C ζ (1 GeV ) C.14 2 ξ (1 GeV) C ζ (1 GeV) C ξ (1 GeV ) C ζ (1 GeV ) C ξ (1 GeV ) C. 2 ζ (1 GeV ) C.1 3 ξ (1 GeV) C.2 3 ζ (1 GeV) ix

13 x C.3 3 ξ (1 GeV ) C.4 3 ζ (1 GeV ) C. 3 ξ (1 GeV ) C.6 3 ζ (1 GeV ) C.7 4 ξ (1 GeV) C.8 4 ζ (1 GeV) C.9 4 ξ (1 GeV ) C.16 4 ζ (1 GeV ) C ξ (1 GeV ) C ζ (1 GeV ) C.163 ξ (1 GeV) C.164 ζ (1 GeV) C.16 ξ (1 GeV ) C.166 ζ (1 GeV ) C.167 ξ (1 GeV ) C.168 ζ (1 GeV )

14 ( GeV) (3 GeV) ( GeV) (1 TeV) ( GeV) (3 GeV) ( GeV) (1 TeV) ζ ζ CMOS FPCCD CPU xi

15 1 (International Linear Collider ; ILC) CERN LHC(Large Hadron Collider) 4 % 2 % LHC LHC (LHC TeV) (International Linear Collider ; ILC) ILC 1

16 1. 国際リニアコライダー計画 (International Linear Collider ; ILC) 2 速器を用いた次世代の高エネルギー実験である 加速器は 全長が約 3 km で電子と 陽電子を直線的に加速し正面衝突させる 重心系エネルギーは ECM = GeV の間で調整ができ アップグレードで 1 TeV まで向上する ピークルミノシティは GeV と 1 TeV のビームランでそれぞれ cm 2 s 1 と cm 2 s 1 を目指 している 電子 陽電子のエネルギーや偏極を指定することができるので 崩壊モー ドによってはバックグラウンド事象を抑制し シグナルの結合定数の高精度での測定 が可能である バックグラウンド事象が少ない環境でヒッグス粒子やトップクオーク の精密測定 標準理論を超える物理の検証 暗黒物質の候補となる粒子の探索などが 期待されている 以下では ILC の加速器と測定器について述べる 1.2 ILC の加速器 加速器は大きく分けて電子 陽電子源 (Electron Positron Source) 減衰リング (Damping Ring) 主線形加速器 (Main Linac) の 3 つの要素から構成される 図 1.1 はその全 体図である 第一に電子 陽電子源で電子 陽電子を生成 これをビームとして利用 し 第二に減衰リングにおいてビームの広がりを抑える 最後に主線形加速器でビー ムを一気に加速する 以下では これら 3 つの要素それぞれについて説明する [1] [2] [4] [] Damping Rings IR & detectors e+bunch compressor e- source e+source e- bunch compressor positron main linac 11 km 2 km central region km electron main linac 11 km 2 km 図 1.1: ILC の全体図 ILC の電子源 図 1.2 に示す電子源では 電子銃の中にある GaAs フォトカソードに偏極したレー ザーを照射し 偏極した電子ビームを生成する そしてこのビームは常伝導の加速管 を用いて 7 MeV まで加速させ 同時にバンチ化される (バンチについては 1.3 節を参

17 1.2 ILC 3 ) GeV 9 % 1.2: MeV 3 MeV.4 (1.4 cm ) Ti 4 MeV GeV 3 % 6 % GeV 3.2 km 2 ms

18 4 1. 国際リニアコライダー計画 (International Linear Collider ; ILC) 図 1.3: 陽電子源 電子は制動放射によりエネルギーを失うが 進行方向には一定の割合で加速される 結果としてビームの横方向の運動量が減衰されビームの拡がりを抑えることができる 減衰リングから取り出されたビームは GeV まで加速された後 主線形加速器に入 射される 主線形加速器 ILC の主線形加速器は減衰リングから取り出されたビームを GeV から GeV まで加速させる (ECM = GeV の場合) このビーム加速を実現するには平均加速勾 配が 31. MV/m 必要である これを実現するため 各主線形加速器に図 1.4 に示す 9 個のセルから成り立つ約 1 m のニオブ製超電導加速空洞を約 74 個用いる この加 図 1.4: ニオブ製超伝導加速空洞 速空洞は 1.3 GHz の高周波を生成し 絶対温度 2 K で動作する 低温環境を構築する クライオモジュールは図 1. のように設計されている なお 図 1. の中心部の四重 極磁石はビームを収束させる目的で設置する

19 1.3 1.: 1.3 ILC ms 199 ms 1 ms GeV TeV 24 1 train (1ms) rest (199ms) 1.6: ILC [1] 2

20 1. 国際リニアコライダー計画 (International Linear Collider ; ILC) 6 ILD detector (on beamline) SiD detector (parked) Access to damping ring Beam delivery system (Accelerator tunnel) ILD garage 図 1.7: プッシュプル方式の概要 ループ間競争による技術開発促進のためである また ガレージに置かれる検出器はそ の間にメンテナンスを行い ビームライン上の検出器はデータを取り続けられるため 効率的にデータを貯められる この 2 つの検出器は ILD(International Large Detector) SiD(Silicon Detector) と呼ばれている 以降のページでは 私は ILD 検出器の開発を しているので ILD についてだけ記述する [1][3] [4] [] ILD 検出器 ILD 検出器 (図 1.8 図 1.9) は汎用型衝突実験検出器であり Particle Flow Algorithm (PFA) と呼ばれるジェットエネルギー再構成アルゴリズムを最適化するように設計され ている ILD 検出器内の主な構成要素は衝突点に近いものから 崩壊点検出器 (Vertex Detector; VXD) シリコン内部飛跡検出器 (Silicon Inner Tracker; SIT) 中央飛跡検出 器 (Time Projection Chamber; TPC) 電磁カロリメータ (Electromagnetic Calorimeter; ECAL) ハドロンカロリメータ (Hadronic calorimeter; HCAL) である これらの検出 器は 3. T のソレノイド内に格納されている 以下 ILD 検出器を構成する各検出器 について説明する

21 1.4 検出器 7 図 1.8: ILD 検出器の全体像 崩壊点検出器 (VXD) ILC 実験の多くの物理解析で要求される高精度の b c クォークの同定 (フレーバー タグ) は粒子の崩壊点の測定精度に大きく依存する 高精度なフレーバータグの実現 のため 崩壊点検出器 (VXD) は粒子の崩壊点を精度よく測定する重要な役割を果た す 崩壊点を精度良く測定するために ILD 測定器の構成要素の内 衝突点に最も近 い場所に設置され 位置分解能の高いピクセル型のシリコン半導体が有感層に用いら れる 図 1.1 は VXD 全体の断面図 (４分の１) で 左図がビーム軸に平行な方向 右 図がビーム軸に垂直な方向から見た図である 図中の赤い線が粒子に有感な層であり 1 3 の各レイヤーの表裏に有感層が設置されることが分かる このように設置された 有感層をダブレットレイヤーと呼ぶ ダブレットレイヤーの利点は 粒子がダブレッ トレイヤーを通過したときに残す２つの通過点をベクトルとしてみなすことができ 粒子の飛跡再構成に有用なことである 以後 本論文ではダブレットレイヤーの表裏 にあるレイヤーを別々のレイヤーとみなし 内側からレイヤー, 1, 2, 3, 4, と呼ぶこ とにする 崩壊点の検出原理の基本は 崩壊してできた多数の粒子の飛跡を再構成し その内 ２つ以上の飛跡が重なる点を崩壊点として測定する このため崩壊点分解能は 再構 成された飛跡の精度を表すインパクトパラメータ分解能に大きく依存する ILC で探 索する物理のために要求される飛跡のインパクトパラメータ分解能 (σrϕ ) は次式で表

22 8 1. (International Linear Collider ; ILC) 1.9: ILD 1.1:

23 : a [µm] b [µm (GeV/c)] LEP 7 LHC 12 7 ILC 1 σ rϕ = a b pβ sin 3/2 θ [µm] (1.1) β = V c p [GeV/c] θ ILC a =, b = VXD VXD ( 1.1) 16 mm ( µm 2 ) 1 1 % 2 3 % 2 (1). (2). (1) (2) CCD CCD (FPCCD; Fine Pixel CCD) 3 [6]

24 1 1. (International Linear Collider ; ILC) ILD (SIT) (SET) (FTD) (ETD) 1.11 TPC VXD SIT SET R ϕ 7 µm 1.11 SIT SET FTD ETD ETD TPC 2 ETD R ϕ 7 µm FTD 7 VXD 2 R ϕ 3 6 µm 7 µm 1.11: 1.4. (TPC) TPC 3 ( 1.12) TPC

25 TPC micro-pattern gaseous detector (MPGD) MPGD 3 TPC TPC TPC de/dx TPC σ(1/p T ) 1 4 /(GeV/c) (1.2) % de/dx P T P 2 x + P 2 y (x-y ) 1.12: TPC ILD (ECAL) (HCAL) ECAL HCAL

26 12 1. (International Linear Collider ; ILC) Particle Flow Algorithm (PFA) PFA PFA ECAL HCAL (ECAL) 1.13: ECAL ECAL 1.13 ECAL ECAL ECAL ( X = 3. mm R M = 19 mm) 1/e ( e ) 9 % 2 cm 24X ECAL 1.14 (SiECAL) (ScECAL) Detector Slab( 1.13 ) SiECAL 2 ScECAL x y SiECAL mm 2 ScECAL mm 4 mm

27 : SiECAL( ) ScECAL( ) Detector Slab SiECAL SiECAL ScECAL (Hybrid ECAL) (HCAL) HCAL 1. HCAL PFA HCAL 17 cm 1.8 cm HCAL 2 (analogue HCAL; AHCAL) (semi-digital HCAL; SDHCAL) 1.16 AHCAL 1. mm 3 mm 2 mm ASIC LED SDHCAL 2. mm 1. cm

28 14 1. (International Linear Collider ; ILC) 1.: HCAL TFE(93%) CO2(%) SF6(2%) TFE (8 /mm) CO2 SF ILD 3. T 3 GeV/c Registive Plate Chamber (RPC)

29 1.4 検出器 図 1.16: AHCAL オプションにおけるモジュール内の構成 図 1.17: SDHCAL オプションにおけるガス検出器の構造 前方検出器 ビーム軸近傍に設置される検出器はまとめて前方検出器と呼ぶ 図 1.18 は前方検出 器の全体図である 前方検出器は測定器全体の検出可能立体角の向上 ルミノシティ 測定 ビームサイズの測定の役割を果たす 以下では主な前方検出器とその役割につ いて説明する

30 16 1. (International Linear Collider ; ILC) 1.18: LumiCal LumiCal Bhabha (e + e e + e ) σ B σ B L = N B σ B (1.3) L N B LumiCal Bhabha LumiCal BeamCal BeamCal Bhabha BeamCal 1.2 BeamCal BeamCal

31 1. Particle Flow Algorithm (PFA) : LumiCal BeamCal LumiCal 1.19 GaAs Particle Flow Algorithm (PFA) ILD PFA PFA ILC VXD

32 18 1. (International Linear Collider ; ILC) 1.2: BeamCal PFA 1. VXD 2. ECAL 3. HCAL VXD ECAL HCAL ECAL HCAL 1.21 PFA

33 1. Particle Flow Algorithm (PFA) : 1 GeV PFA

34 2 ILC ILC ( ) ZH( ) ZHH( ) t th( ) 2.1 ILC ILC b b- c c- LCFIPlus [7] LCFIPlus Boosted Decision Trees (BDTs) [8] b- c- b 4 µm c 1 3 µm 2

35 [4] [9] ϕ(x) 1 (ϕ 1 + iϕ 2 ) (ϕ 1, ϕ 2 ) 2 ϕ(x) ϕ 2 V( ϕ 2 ) ϕ 1, ϕ 2 L = µ ϕ µ ϕ V( ϕ 2 ) (2.1) L = 1 2 ( µϕ 1 µ ϕ 1 + µ ϕ 2 µ ϕ 2 ) V ϕ2 1 + ϕ2 2 (2.2) 2 ϕ = e iθ ϕ U(1) V ϕ 1 -ϕ 2 V V + µ 2 (ϕ ϕ2 2 ) + λ(ϕ2 1 + ϕ2 2 )2, µ 2 (T T c ), λ > (2.3) T c λ ϕ V (T > T c ) µ 2 > V ϕ = ( 2.1a) (T < T c ) V ϕ = ( 2.1b) V = µ 4 /4 V = λ(ϕ ϕ2 2 v2 ) 2 (v 2 = µ2 2λ, µ2 < ) (2.4) ϕ ϕ2 2 = v2 (v > : ) (2.) ( ) L H = d 3 x L ϕ = i i d 3 x 1 [ 2 ϕ i + ( ϕ i ) 2 + V ] 2 (2.6) i ϕ i (x) V V V U(1) ϕ vac1 (x) = v ϕ vac2 (x) = (2.7)

36 22 2. ILC V ϕ= ϕ U(1) ϕ vac = 1 2 v ϕ 1 (x) = v + χ(x) ϕ 2 (x) = η(x) χ η (2.8) L = 1 2 ( µχ µ χ + µ η µ η) λ [ (v + χ) 2 + η 2 v 2] 2 (2.9) = 1 2 ( µχ µ χ + µ η µ η) λ(2vχ + χ 2 + η 2 ) 2 (2.1) = 1 2 ( µχ µ χ + µ η µ η) 4v 2 λχ 2 + 4vλχ 3 + λχ 4 + 4vλχη 2 + 2λχ 2 η 2 + λη 4 (2.11) = ( 1 2 µχ µ χ 4µ2 2 χ2 ) µη µ η + L int (2.12) χ 4µ 2 η (2.1) 1 A µ L = (D µ ϕ) (D µ ϕ) V( ϕ 2 ) 1 4 F µνf µν (2.13) D µ µ + iea µ, F µν ν A µ µ A ν (2.14) (a) (b) 2.1: V

37 U(1) ϕ = e ieλ(x) ϕ, A µ(x) = A µ (x) + µ Λ(x) (2.) Λ(x) x ϕ(x) A µ (x) ϕ (x) A µ(x) ϕ(x) ϕ(x) = 1 2 (ϕ 1 + iϕ 2 ) ρ(x)e iθ(x) (ρ(x) >, θ(x) : ) (2.16) Λ(x) ϕ (x) x ϕ (x) = e iθ(x) ϕ(x) (2.17) ϕ (x) ϕ(x) ϕ 2 = (2.4) V = λ(ϕ 2 1 v2 ) 2 (2.18) ϕ 1 = v (2.13) ϕ 1 = v + χ(x) (v, χ : ) (2.19) L = 1 2 ( µχ µ χ + 4µ 2 χ 2 ) 1 4 F µνf µν + e2 v 2 2 A µa µ + e2 2 A µa µ (2vχ + χ 2 ) + (χ 3 ) (2.2) 1 4µ ev 4 U(1) ( U(1) ) ( ±1, ±1) U(1) 2 ϕ ( ϕ+ ϕ ) ( 2 1 (ϕ +1 + iϕ +2 ) ) (ϕ +i, ϕ i (i = 1, 2) : ) (2.21) 1 (ϕ 1 + iϕ 2 ) 2

38 24 2. ILC (ϕ +, ϕ 1 2 (v + χ) S U(2) U(1) (W Z) ( A (A.1)) m l ll m v vv m l v χ( ll) m v χ( vv) (2.22) v 1 2 (m l m v ) (A.1) ( ) 2 2vχ + χ2 2mW + 4 W v +µw µ + ( 1 2mZ 2 v ) 2 Z µ Z µ m2 H 2v χ3 m2 H 8v 2 χ4 (2.23) 1 (W Z) [4] 2.3 LHC ILC [4] [1] H b b

39 : H c c b c E CM = GeV ILC H b b H c c BR BR 2.7% 7.3% HHH LHC ILC

40 26 2. ILC 2.3: e + e HZ 2 1 ZHH (2.23) λ HHH = m2 H 2v (2.24) 2.4 GeV e + e ZHH 3 ZHH e + e ZHH l l( b b) + b bb b 4 6 b b 2 (2.24) m H 2 λ HHH ILC E CM = GeV e + e t th ( (2.)) t b W b

41 : e + e ZHH 2.: e + e t th e + e t tz t th 3 b- g t th 1%

42 3 CCD (FPCCD) ILC µm µm 1 µm 1 µm CCD (Fine Pixel CCD; FPCCD) 6 µm 6 µm FPCCD ( 3.1) FPCCD 3.1: FPCCD 28

43 3.1 FPCCD FPCCD FPCCD FPCCD CCD FPCCD, 1 µm µm 2, 3, 4, 1 µm 1 µm (, 1,..., ) 4 µm µm FPCCD FPCCD FPCCD 3 (1). (a) (b) (c) (2). (3). (1) (2) (1) 3.2 (a) 3.3 (energy deposit) energy deposit (b) P T 3.4

44 3 3. CCD (FPCCD) 3.2: 3.3: (

45 3.1 FPCCD 31 P T 3.4: P 2 x + P 2 y (x-y )) (c) 1 VXD TPC ( ) ILD :

46 32 3. CCD (FPCCD) (2) 2 2 2

47 4 ILCSoft FPCCD ILCSoft [11] ILCSoft FPCCD ILD 4.1 Mokka [12] Geant4 [13] Mokka ILD Mokka ( ) FPCCD FPCCDDigitizer [14] FPCCDClustering [] ILC 4.2 FPCCD FPCCDDigitizer FPCCDDigitizer [14] Mokka FPCCD 4.1 Mokka ( ) ( mm) 33

48 34 4. ILCSoft 4.1: FPCCDDigitizer FPCCDClustering FPCCDClustering [] FPCCDDigitizer energy deposit FPCCD ILD ILD SiliconTracking ILD 4.2 VXD, SIT, FTD SiliconTracking TPC CLUPATRA

49 4.3 ILD 3 TPC TPC ( ) (vertexing) 4.2: ILD SiliconTracking FPCCD SiliconTracking FPCCD SiliconTracking SiliconTracking Kalman Filter SiliconTracking VXD, SIT, FTD VXD 6 VXD 1.1

50 36 4. ILCSoft R Φ x y ( z ) R z 3 R Φ R z (1) : 4.3 Φ 8 ( 4. ) R z θ 8 ( 2. ) 64 A. 3 B. 3 χ 2 /ndf C. d, z P T ( 1 µm 1 µm. GeV/c) A , 4, 3 3, 2, 1 2, 1, 3 ILD VXD 6, 8 SIT 2 B. ( ) N.I. Chernov, G.A. Ososkov Effective Algorithms For Circle Fitting [16] C++ d, z, ω, ϕ, tan λ C. d, z, ω R Φ R z B (2) :

51 4.3 ILD : χ 2 /ndf 4. (1) 3

52 38 4. ILCSoft 4.4: (3) : (2) 4. ϕ, tan λ χ 2 /ndf (4) : (3) χ 2 /ndf 4.6

53 4.3 ILD 39 4.: () Kalman Filter : Kalman Filter Kalman Filter Kalman Filter KalTest [17] Kalman Filter Keisuke Fujii, The ACFA-Sim-J Group Extended Kalman Filter [17] 4.7 Kalman Filter SiliconTracking SiliconTracking 7 SiliconTracking 7

54 4 4. ILCSoft 4.6:

55 4.3 ILD : Kalman Filter

56 VXD 2 3 % 3 FPCCD CCD, 3,, 1 GeV.1.1 Guinea Pig [18] Mokka 3 GeV 1 1 TeV FPCCDDigitizer energy deposit.7 kev 1ADC.91 kev ADC 7bit BeamCal BeamCal 2 VXD BeamCal VXD.1 nsec VXD 42

57 :.1: ( GeV) (%) (%) (%) : (3 GeV) (%) (%) (%)

58 44..3: ( GeV) (%) (%) (%) : (1 TeV) (%) (%) (%) : [hits/cm 2 /BX]( GeV) : [hits/cm 2 /BX](3 GeV) GeV 2 % 1 TeV 12.8%

59 .1 4.7: [hits/cm 2 /BX]( GeV) : [(hits/cm 2 /BX)](1 TeV) FPCCD 1 TeV (1)., 1 (2). (3). BeamCal (4). (1) (2) 4 µm 4 µm µm /16 = 1.6 (3)1 TeV 1.1 % 3.7 % 3 BeamCal BeamCal (4)

60 46. FPCCDClustering.2 ζ ξ C C.1 C.24 (ζ ξ C.2.2 ).1.3 FPCCD GeV 1 TeV 12.8% BeamCal.2 t t 6 jets (E CM = 3 GeV) 6 VXD.2.1 t t 6 jets (E CM = 3 GeV) Physsim [19] Mokka 1 FPCCDDigitizer FPCCDClustering

61 ξ 3. ζ ξ ζ ( ) ξ-ζ ζ ξ ζ ( ζ z ζ z ).4 FPCCD ξ ζ (1).2:.2 t t 6 jets 2 t t (2) ξ

62 48..3: ξ.3 ξ ( ) ξ 1 t t (3) ζ.4 ζ ( ) ζ t t (1) (3) 2 (1) (3) %

63 : ζ.9: ξ ζ ( :µm) < 2 < 1 < 2(1µm) < < 6 < 8.1: [%] BG [%] ( :µm) (1µm)

64 ..11: [%] BG [%] ( :µm) (1µm) ( ) 2. z ζ (ζ ) (1) VXD. FPCCD. ζ, ξ +ζ, +ξ ( energy deposit ). O Minor Area.6. Minor Area Minor Area 37% 4% ξ ζ < Z par : (Z par > ) (.1)

65 .2 1.: t t 6 jets@ 3 GeV.6:.7 Z par Z par Z par

66 2..7: 98%, 1 Z par = 9 mm 2 2, 3 Z par = 28 mm 2 4, Z par = 6 mm 2.13 (2)ζ ζ z ζ.12: + Z par [mm 2 ] [%] BG [%] ( :µm) (1µm)

67 : + Z par [mm 2 ] [%] BG [%] ( :µm) (1µm) ζ ζ.8 η ζ η ξ ζ ( ).8: ζ energy deposit

68 4. θ ( ) z ( ) z = (.2) tan θ z ζ.9 t t ( ) ( ) z (mm) ζ.9: t t BG z ζ t t z ζ t t z ζ 4 energy deposit 2 2 B par = 4 C par = 4 8 % tan λ VXD ( tan λ B )

69 .2.9 y 1 = tan θ B par (.3) y 2 = C par (.4) (.) 2 B par C par C par = 4 2 C par = 2 B par.14 ( + ζ ).14: + ζ B par [ ] [%] BG [%] ( :µm) (1µm) %, 1 B par = 2 µm, C par = 4 µm 2 B par = 1 1 µm, C par = 2 1 µm ζ ( ) 3 FPCCDClustering.: + ζ B par [ ] [%] BG [%] ( :µm) (1µm)

70 6..16: [%] BG [%] ( :µm) (µm) (1µm) (1µm) (1µm) (1µm) : [%] BG [%] ( :µm) (µm) (1µm) (1µm) (1µm) (1µm)

71 6 FPCCD FPCCD 6.1 single µ + µ d ( B ) (1.1) d single µ + d d σ d ( 6.1) ILD VXD VXD CMOS CMOS 6.1 CMOS 6.1 FPCCDDigitizer FPCCD FPCCDDigitizer FPCCDClustering ( )

72 : d (p = 1 GeV/c θ = 8 ) ILC ( (1.1)) FPCCD CMOS µ (1.1) θ [GeV/c] [mm] 6.2 CMOS FPCCD CMOS FPCCD 1 µm FPCCD CMOS 6.1: CMOS [µm] [µsec.]

73 : FPCCD [µm] σ rφ (mm) -2 1 θ=2 (Requirement) θ=8 (Requirement) θ=2 (CMOS) θ=8 (CMOS) θ=2 (FPCCD) θ=8 (FPCCD) Momentum(GeV/c) 2 6.2: FPCCDDigitizer FPCCDClustering 6.2 θ = 8 p = 1 GeV/c.6 µm FPCCD FPCCDDigitizer FPCCDClustering FPCCD Mokka.1 mm FPCCD.1 mm

74 FPCCDDigitizer FPCCDClustering CMOS FPCCD ( ) FPCCDDigitizer FPCCDClustering energy deposit Mokka FPCCDDigitizer FPCCDDigitizer FPCCDClustering 2 1 energy deposit CMOS FPCCDDigitizer FPCCDClustering.2 FPCCDDigitizer FPCCDClustering

75 7 FPCCD 7.1 FPCCD 1 FPCCD t t 6 jets 2 1. VXD 2. track purity 7% track purity track purity (7.1) 61

76 62 7. (1) VXD 1 VXD SiliconTracking χ 2 /ndf VXD χ 2 /ndf χ 2 /ndf VXD VXD 4 VXD (2) Good Track 1. VXD ( 6 ) 1 2. SIT ( 2 ) 1 Good Particle Good Particle Good Track Good Particle Good Track Good Particle (7.2) t t 6 jets (E CM = 3 GeV) 6

77 FPCCD FPCCDDigitizer FPCCDClustering z CMOS CMOS (7.2) [GeV/c] FPCCD CMOS 7.1: P T > 1.7GeV/c 98% Good Particle Good Track P T = 1.7GeV/c P T =.4GeV/c P T < 1.7GeV/c Good Particle Good Track CMOS FPCCD 7.2 P T > 1.7GeV/c 99% TPC VXD

78 64 7. P T < 1.7GeV/c TPC Good Track CMOS FPCCD 7.2 FPCCDTrackFinder FPCCDTrackFinder FPCCDTrackFinder Refitting/FPCCDSiliconTracking_MarlinTrk.cc Refitting/FPCCDFullLDCTracking_MarlinTrk.cc SiliconTracking (1). (2). χ 2 (3). (1) SiliconTracking Φ 8 ( 4. ) θ 8 ( 2. )

79 , 4, 3 1, 2, ( 4.4) ( 4.) 2 ( 4.6) ( ) 7.2 (A) %.18 GeV/c ( ) (B)

80 : (A) (A) FPCCD 1 FPCCD

81 VXD SIT 1% 4 3 VXD (2) (C) ( 7.3) 4 Kalman Filter FPCCD FPCCD (D) Kalman Filter (C) (2) SiliconTracking χ 2 track purity 1% χ 2 /ndf 1 single µ + χ 2 /ndf P T = 1GeV/c SIT VXD SIT 8 6 SIT 2 VXD 1 SIT P T = 1 GeV/c 1 χ 2 /ndf 1 ( 3 ) χ 2 /ndf CMOS FPCCD 7.1 CMOS FPCCD FPCCD SIT χ 2 /ndf CMOS

82 : (C) SIT (1)-(B) 4 3 VXD 3 χ 2 /ndf ( χ 2 /ndf ) (3) ϕ, tan λ t t ϕ, tan λ

83 d, z, ω χ 2 /ndf χ 2 /ndf (E) FPCCD FPCCD CMOS FPCCD 7.4 FPCCD (F) t t@3 GeV. 1 % (.4) 2 1 µm 2, 3, 4, 2 1 µm FPCCD

84 : χ 2 /ndf 1 1 χ 2 /ndf 1 χ 2 /ndf 3 GeV OFF GeV 1TeV FPCCDTrackFinder FPCCD FPCCDTrackFinder

85 7.3 (FPCCDTrackFinder ) 71 FPCCD FPCCDTrackFinder (A) (F) FPCCDTrackFinder (A) (B) (C) (D) Kalman Filter (F) ( 3 GeV FPCCDTrackFinder 7.3 (FPCCDTrackFinder ) FPCCDTrackFinder FPCCD FPCCDTrackFinder 7. 7.: FPCCD + FPCCDTrackFinder FPCCD + ( BG )

86 72 7. FPCCDTrackFinder 98% 99.% 98.% 99% P T =.4 GeV/c 98% P T =.6 GeV/c 98.% 7.6 cos θ P 1 GeV/c θ cos θ <.9 P > 1 GeV/c P > 1 GeV/c 7.6: FPCCD + FPCCDTrackFinder FPCCD + (cos θ BG ) 96.% 99.8% 97% 99.% cos θ >.9 SIT cos θ <.9 cos θ > GeV 7.7 BG P T =.6 GeV/c 7.8 cos θ P 1 GeV/c cos θ < FPCCDTrackFinder CPU FPCCD CPU

87 7.3 (FPCCDTrackFinder ) : FPCCD + FPCCDTrackFinder ( ) P > 1 GeV/c P > 1 GeV/c 7.8: FPCCD + FPCCDTrackFinder (cos θ) 24 CMOS FPCCD FPCCDTrackFinder CPU t t 6 3 GeV FPCCD FPCCDTrackFiner CPU GB CPU : = : 1 FPCCDTrackFinder CPU CPU

88 8 FPCCD Z b b, c c, q 91.2 GeV (Z-pole) Z b b, c c, q GeV 8.1 Z-pole Z b b, c c, q 91.2 GeV(Z-pole) FPCCDTrackFinder FPCCD Z b b, c c, q 91.2 GeV ( ) 2 single µ + Z-pole FPCCD FPCCDDigitizer FPCCDClustering ζ CMOS FPCCDTrackFinder 1 1. Particle Flow Algorithm ILD PFA LCFIPlus [7] LCFIPlus Boosted Decision Trees [8] Z b b, c c, q 91.2 GeV LCFIPlus b-jet c-jet q-jet (q u, d, s 74

89 8.1 Z-pole 7 ) b-jet b-jet b-jet b- b-jet (b-tag purity ) b-jet b-tag (b-tag efficiency ) b-tag efficiency b-tag purity b-tag efficiency b-tag b-jet b-jet (8.1) b-tag purity b-tag b-jet b-tag (8.2) b-tag c-tag q-tag purity Z b b, c c, q q Particle Data Group Z [2] BR(Z b b) =.12 (8.3) BR(Z c c) =.123 (8.4) BR(Z q q) =.428 (8.) efficiency purity b-tag c-tag CMOS + CMOS + FPCCDTrackFiner FPCCD + FPCCDTrackFiner FPCCDTrackFinder FPCCDTrackFinder c-tag ( purity 7% c-tag efficiency 2.% ) b-tag CMOS FPCCD FPCCD b-tag c-tag ( purity 9% b-tag efficiency 2% purity 7% c-tag efficiency 4% ) FPCCDTrackFinder FPCCD

90 : (Z-pole ) 8.2 Z b b, c c, q GeV Z b b, c c, q GeV FPCCDTrackFinder FPCCD ILD Z-pole Z b b, c c, q GeV 2 Z-pole 2 ( FPCCDTrackFinder CPU ) Z-pole 2 ILC GeV Z-pole

91 8.2 Z b b, c c, q GeV : FPCCD CMOS FPCCD CMOS CMOS FPCCD 1 CMOS CMOS 8.1 Z-pole b-tag c-tag efficiency purity b-tag c-tag CMOS + CMOS + FPCCDTrackFiner FPCCD + FPCCDTrackFiner 8.2 Z b b, c c, q GeV FPCCDTrackFinder c-tag CMOS FPCCD b-tag c-tag ( purity 7% c-tag efficiency 2.% ) b-tag CMOS FPCCD FPCCD

92 : (Z b b, c c, q GeV BG ) 8.3: (Z b b, c c, q GeV BG ) b-tag c-tag 8.3

93 8.2 Z b b, c c, q GeV 79 FPCCD FPCCD ( 8.1) CMOS FPCCDTrackFinder ( ) 8.4 FPCCD + FPCCDTrackFinder b-jet track purity >.7 track purity <.7 ( ) : b-jet (FPCCD BG ) 8.: b-jet (FPCCD BG ) b-jet FPCCDTrackFinder

94 8 8. track requirement : SIT 1 TPC 1 cos θ >.9 (8.6) SIT SIT SIT 1 TPC TPC TPC 1 SIT SIT cos θ <.9 SIT cos θ >.9 (8.6) b-jet (8.6) 1% : b-jet (CMOS BG ) 8.7: b-jet (CMOS BG ) CMOS + FPCCDTrackFinder b-jet

95 8.2 Z b b, c c, q GeV ( ) 8.7( ) track requirement b-jet FPCCD CMOS FPCCD 8.7 track requirement track requirement( (8.6)) : (Z b b, c c, q GeV BG )( (8.6) ) 8.8 (8.6) CMOS + FPCCDTrackFinder purity 8 % b-tag efficiency % purity 6 % c-tag efficiency % FPCCD + FPCCDTrackFinder purity 8 % b-tag efficiency % purity 6 % c-tag efficiency % track requirement FPCCD CMOS

96 : (Z b b, c c, q GeV BG )( (8.6) ) 8.2: CPU VXD BG CPU [sec/event] [MB/evt] SiliconTracking CMOS CMOS CMOS FPCCDTrackFinder CMOS FPCCDTrackFinder FPCCD FPCCDTrackFinder FPCCD FPCCDTrackFinder FPCCD 8. (8.6) CPU Z b GeV CPU CPU (SiliconTracking) CMOS

97 8.2 Z b b, c c, q GeV 83 CPU FPCCDTrackFinder 1 1 CPU FPCCD FPCCDTrackFinder CMOS CMOS FPCCD FPCCD Z b GeV t t 6 3 GeV 3. GB CMOS FPCCDTrackFinder CPU FPCCD FPCCDTrackFinder SiliconTracking CPU FPCCDTrackFinder CPU

98 9 ILC FPCCD FPCCD CCD FPCCD GeV 1 TeV FPCCD ζ FPCCDClustering 2 % 2 % FPCCD CCD 1µm ILD FPCCD (P T < 1.7 GeV/c) FPCCD FPCCDTrackFinder FPCCDTrackFinder CPU 84

99 8 FPCCDTrackFinder P T >.6 GeV/c 99 % P T >.6 GeV/c FPCCD FPCCDTrackFinder FPCCDTrackFinder Refitting/FPCCDSiliconTracking_MarlinTrk.cc Refitting/FPCCDFullLDCTracking_MarlinTrk.cc ILC Higgs FPCCD FPCCDTrackFinder FPCCD Z-pole FPCCDTrackFinder c-tag (purity 7% c-tag efficiency 2.% ) FPCCD b-tag c-tag (purity 9% b-tag efficiency 2% purity 7% c-tag efficiency 4% ) Z b b, c c, q GeV CMOS FPCCDTrackFinder SIT Z b b@ GeV CPU CMOS FPCCDTrackFinder CPU 1/1 (342. sec/event 34. sec/event) FPCCD FPCCDTrackFinder 47.6 sec/event FPCCDTrackFinder CPU

100 A ϕ + ϕ 1 2 (v + χ) S U(2) U(1) L = ν(i/ m ν )ν + l(i/ m l )l ( µχ µ χ m 2 H χ2 ) 1 4 F µνf µν + m 2 W W +µw µ G µνg µν + m2 Z 2 Z µz µ + ea µ ( lγ µ l) g 2 [ W+µ ( νγ µ P L l) + c.c ] ḡz µ [ νγ µ (s νl P L + s νr P R )ν + lγ µ (s ll P L + s lr P R )l ] ( ) 2 2vχ + χ2 2mW + 4 W v +µw µ ( ) 2 2mZ Z µ Z µ 2 v m l v χ( ll) m ν v χ( νν) m2 H 2v χ3 m2 H 8v 2 χ4 (A.1) m H = 4µ 2, m W = vg 2, m Z = vḡ 2, e = g sin θ W, ḡ = g 2 + g 2, sin θ W = g ḡ, cos θ W = ḡ g 86

101 B [21] z z x x,z y P r = (P r x, P r y, P r z) (ω, ϕ, d, z, tan λ) x-y P = (P x, P y, P z ) P r = B.1: x-y d, ϕ, ω x-y B.1 d, ϕ, ω R ϕ ω ω = 1 R (B.1) ω + ω > ω < 87

102 88 B. d x-y impact parameter d P P r ( ) sin ϕ n pca cos ϕ n pca d d n pca d n pca d = (P x P r x) sin ϕ + (P y P r y) cos ϕ (B.2) n pca = 1 d x-y P r P d d > d < P r sgn(ω) = sgn(d ) P r sgn(ω) = sgn(d ) ω P r B.2: s-z z, tan λ s-z B.2 z, tan λ s x-y P

103 89 tan λ s-z dz ds θ tan λ = p z p 2 x + p 2 y = cot θ (B.3) z s-z impact parameter z z P z P r z (B.4)

104 C ζ ξ ζ ξ ζ ξ ( ) ξ ζ ζ ξ ζ ( ζ z ζ z ). ξ ζ C. C.168 ϕ = 9 +ϕ 1, 2,... 9

105 layer Entries Mean.762 RMS layer1 Entries Mean.96 RMS layer2 Entries Mean RMS layer3 Entries Mean RMS layer4 Entries 9796 Mean RMS layer Entries 8344 Mean RMS C.1: ζ ( GeV) layer Entries Mean -.21 RMS layer1 Entries Mean.322 RMS layer2 Entries Mean -.33 RMS layer3 Entries 3333 Mean RMS layer4 Entries Mean.1881 RMS layer Entries 188 Mean.8662 RMS C.2: ζ (3 GeV)

106 92 C. ζ ξ layer Entries Mean.96 RMS layer1 Entries Mean.1664 RMS layer2 Entries Mean.424 RMS layer3 Entries Mean.3172 RMS layer4 Entries Mean 1.2 RMS layer Entries Mean.876 RMS C.3: ζ ( GeV) layer Entries e+7 Mean RMS layer1 Entries 1.737e+7 Mean.1331 RMS layer2 Entries Mean.3176 RMS layer3 Entries Mean.9 RMS layer4 Entries Mean RMS layer Entries Mean RMS C.4: ζ (1 GeV)

107 layer Entries Mean.48 RMS layer1 Entries Mean.1926 RMS layer2 Entries 3 Mean RMS layer3 Entries 9127 Mean -.69 RMS layer4 Entries Mean -.28 RMS layer Entries 7831 Mean RMS C.: ζ ( GeV ) 4 4 layer Entries Mean RMS layer1 Entries Mean.9933 RMS layer2 Entries Mean RMS layer3 Entries Mean.3374 RMS layer4 Entries 1146 Mean.392 RMS layer Entries 9832 Mean.273 RMS C.6: ζ (3 GeV )

108 94 C. ζ ξ 8 layer Entries Mean.1291 RMS 37.6 layer1 Entries Mean.136 RMS layer2 Entries Mean.479 RMS layer3 Entries Mean.3938 RMS layer4 Entries 1979 Mean 1.99 RMS layer Entries 172 Mean.9 RMS C.7: ζ ( GeV ) layer Entries Mean RMS layer1 Entries Mean RMS layer2 Entries 8198 Mean RMS layer3 Entries Mean.182 RMS layer4 Entries Mean RMS layer Entries 2178 Mean 1.89 RMS C.8: ζ (1 GeV )

109 9 4 4 layer Entries Mean.876 RMS 37. layer1 Entries Mean RMS layer2 Entries 1666 Mean RMS layer3 Entries Mean RMS layer4 Entries 67 Mean 2.2 RMS layer Entries 13 Mean RMS C.9: ζ ( GeV ) 7 6 layer Entries Mean RMS layer1 Entries Mean RMS layer2 Entries 2437 Mean RMS layer3 Entries 223 Mean RMS layer4 Entries 927 Mean RMS layer Entries 76 Mean RMS C.1: ζ (3 GeV )

110 96 C. ζ ξ layer Entries 169 Mean RMS layer1 Entries 6436 Mean.3677 RMS layer2 Entries 6794 Mean.6192 RMS layer3 Entries 86 Mean -.44 RMS layer4 Entries 191 Mean.1397 RMS layer Entries Mean.8912 RMS C.11: ζ ( GeV ) layer Entries e+7 Mean RMS layer1 Entries e+7 Mean.179 RMS layer2 Entries Mean RMS layer3 Entries Mean.497 RMS layer4 Entries Mean RMS layer Entries Mean.4239 RMS C.12: ζ (1 GeV )

111 layer Entries Mean RMS 3.9 layer1 Entries Mean RMS layer2 Entries Mean RMS layer3 Entries Mean 1.46 RMS layer4 Entries 9796 Mean 2.22 RMS layer Entries 8344 Mean RMS C.13: ξ ( GeV) layer Entries Mean 1.43 RMS layer1 Entries Mean RMS layer2 Entries Mean RMS layer3 Entries 3333 Mean RMS layer4 Entries Mean 2.29 RMS layer Entries 188 Mean RMS C.14: ξ (3 GeV)

112 98 C. ζ ξ 9 8 layer Entries Mean 1.4 RMS 3.62 layer1 Entries Mean RMS layer2 Entries Mean RMS layer3 Entries Mean RMS layer4 Entries Mean 2.47 RMS layer Entries Mean 2. RMS C.: ξ ( GeV) layer Entries e+7 Mean 1.33 RMS layer1 Entries 1.737e+7 Mean 1.41 RMS layer2 Entries Mean 1.46 RMS layer3 Entries Mean 1.48 RMS layer4 Entries Mean 2.21 RMS layer Entries Mean RMS C.16: ξ (1 GeV)

113 layer Entries Mean RMS layer1 Entries Mean RMS layer2 Entries 3 Mean RMS layer3 Entries 9127 Mean RMS layer4 Entries Mean RMS layer Entries 7831 Mean RMS C.17: ξ ( GeV ) 4 4 layer Entries Mean RMS 3.64 layer1 Entries Mean RMS layer2 Entries Mean 1.4 RMS layer3 Entries Mean RMS layer4 Entries 1146 Mean 2.26 RMS layer Entries 9832 Mean RMS C.18: ξ (3 GeV )

114 1 C. ζ ξ layer Entries Mean RMS layer1 Entries Mean RMS layer2 Entries Mean RMS layer3 Entries Mean 1.48 RMS layer4 Entries 1979 Mean 2.4 RMS layer Entries 172 Mean RMS C.19: ξ ( GeV ) layer Entries Mean 1.43 RMS layer1 Entries Mean 1.4 RMS layer2 Entries 8198 Mean 1.43 RMS layer3 Entries Mean 1.43 RMS layer4 Entries Mean RMS layer Entries 2178 Mean RMS C.2: ξ (1 GeV )

115 layer Entries Mean RMS layer1 Entries Mean 1.4 RMS layer2 Entries 1666 Mean RMS 6.41 layer3 Entries Mean RMS layer4 Entries 67 Mean RMS layer Entries 13 Mean 2.31 RMS C.21: ξ ( GeV ) 6 layer Entries Mean RMS layer1 Entries Mean 1.47 RMS layer2 Entries 2437 Mean 1.77 RMS layer3 Entries 223 Mean.9844 RMS layer4 Entries 927 Mean 2.69 RMS layer Entries 76 Mean RMS C.22: ξ (3 GeV )

116 12 C. ζ ξ 14 layer Entries 169 Mean 1.44 RMS layer1 Entries 6436 Mean 1.49 RMS layer2 Entries 6794 Mean 1.16 RMS layer3 Entries 86 Mean RMS layer4 Entries 191 Mean 2.43 RMS layer Entries Mean 2. RMS C.23: ξ ( GeV ) layer Entries e+7 Mean RMS layer1 Entries e+7 Mean RMS layer2 Entries Mean 1.36 RMS layer3 Entries Mean 1.7 RMS layer4 Entries Mean 2.99 RMS layer Entries Mean 2.26 RMS C.24: ξ (1 GeV )

117 13 4 ladder Entries 3119 Mean 1.47 RMS Entries Mean 1.46 RMS Entries Mean RMS Entries Mean 1.44 RMS Entries Mean RMS Entries 328 Mean RMS Entries Mean 1.47 RMS Entries 376 Mean 1.37 RMS Entries Mean RMS Entries Mean RMS C.: ξ ( GeV) 4 ladder Entries 3119 Mean.3916 RMS 37.2 Entries Mean.133 RMS Entries Mean 1.1 RMS Entries Mean.2 RMS Entries Mean.147 RMS Entries 328 Mean.1162 RMS Entries Mean RMS Entries 376 Mean RMS Entries Mean -.7 RMS Entries Mean RMS C.26: ζ ( GeV)

118 14 C. ζ ξ 4 4 ladder Entries 281 Mean RMS Entries Mean RMS Entries Mean RMS Entries Mean RMS Entries 2823 Mean RMS Entries Mean RMS Entries Mean RMS Entries Mean RMS Entries Mean RMS Entries Mean RMS C.27: ξ ( GeV ) 4 ladder Entries 281 Mean.686 RMS Entries Mean.427 RMS Entries Mean RMS Entries Mean.1493 RMS Entries 2823 Mean.1968 RMS Entries Mean RMS Entries Mean -1.7 RMS Entries Mean RMS Entries Mean RMS Entries Mean RMS C.28: ζ ( GeV )

119 ladder Entries 2818 Mean RMS Entries 222 Mean 1.93 RMS Entries Mean 1.42 RMS Entries 173 Mean RMS Entries Mean 1.16 RMS Entries 2661 Mean 1.26 RMS Entries 3467 Mean RMS Entries 4943 Mean RMS Entries 79 Mean 1. RMS Entries 3963 Mean 1.66 RMS C.29: ξ ( GeV ) ladder Entries 2818 Mean RMS Entries 222 Mean RMS Entries Mean -.48 RMS Entries 173 Mean RMS Entries Mean RMS Entries 2661 Mean RMS Entries 3467 Mean 1.2 RMS Entries 4943 Mean RMS Entries 79 Mean -1.7 RMS Entries 3963 Mean.23 RMS C.3: ζ ( GeV )

120 16 C. ζ ξ ladder Entries Mean RMS Entries Mean RMS Entries Mean RMS Entries 1848 Mean RMS Entries Mean RMS Entries Mean RMS Entries Mean RMS Entries Mean 1.39 RMS Entries 2871 Mean RMS Entries Mean RMS C.31: 1 ξ ( GeV) ladder Entries Mean.4617 RMS 37.3 Entries Mean -. RMS Entries Mean 1.3 RMS Entries 1848 Mean RMS Entries Mean.91 RMS Entries Mean RMS Entries Mean -.27 RMS Entries Mean RMS Entries 2871 Mean.92 RMS Entries Mean.1877 RMS C.32: 1 ζ ( GeV)

121 17 ladder Entries Mean RMS Entries Mean RMS Entries Mean 1.43 RMS Entries 17 Mean 1.4 RMS Entries Mean RMS 3.17 Entries Mean RMS Entries 177 Mean RMS Entries Mean RMS Entries 1777 Mean RMS Entries Mean RMS C.33: 1 ξ ( GeV ) ladder Entries Mean.487 RMS Entries Mean RMS Entries Mean.9984 RMS Entries 17 Mean RMS Entries Mean.3324 RMS Entries Mean.134 RMS Entries 177 Mean RMS Entries Mean -.38 RMS Entries 1777 Mean.994 RMS 37. Entries Mean.1232 RMS C.34: 1 ζ ( GeV )

122 18 C. ζ ξ 3 3 ladder Entries 172 Mean RMS Entries Mean RMS Entries 1471 Mean RMS Entries 96 Mean 1.29 RMS Entries Mean 1.27 RMS Entries Mean RMS Entries Mean RMS Entries Mean RMS Entries 3294 Mean 1.7 RMS Entries Mean RMS C.3: 1 ξ ( GeV ) 4 3 ladder Entries 172 Mean 1. RMS 36.2 Entries Mean -.93 RMS Entries 1471 Mean 1.66 RMS Entries 96 Mean -1.7 RMS Entries Mean RMS Entries Mean -2.4 RMS Entries Mean RMS Entries Mean.344 RMS Entries 3294 Mean RMS Entries Mean.649 RMS C.36: 1 ζ ( GeV )

123 ladder Entries 3196 Mean 1.6 RMS Entries 316 Mean RMS Entries 3884 Mean 1.38 RMS 6.19 Entries Mean 1.78 RMS Entries 343 Mean.9393 RMS 6.13 Entries 316 Mean 1.42 RMS 6.29 ladder Entries 3196 Mean RMS 72.3 Entries 316 Mean RMS 73.9 Entries 3884 Mean 1.99 RMS 7.87 Entries Mean RMS Entries 343 Mean 2.33 RMS Entries 316 Mean RMS Entries 3894 Mean RMS Entries 3 1 Mean RMS Entries 3742 Mean RMS Entries 2934 Mean 1.6 RMS Entries 3143 Mean 1.2 RMS Entries 3894 Mean RMS 73.4 Entries 31 Mean.618 RMS Entries 3742 Mean.33 RMS Entries 2934 Mean 4.8 RMS 73.8 Entries 3143 Mean -1.6 RMS C.37: 2 ξ ( GeV) C.38: 2 ζ ( GeV)