ILC

∼A study of analysis methodfor the production and decay of top quark pairs

around the threshold region at the ILC∼

30

ILC (350GeV )

ILC

ILD 200fb−1

toy MC

Vtb αs

1 1

2 3

2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.6 CKM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 11

3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.4 . . . . . . . . . . . . . . . . . . . . . . . 14

3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 ILC(International Linear Collider) 29

4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

i

4.2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 42

5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6 48

6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2 (toy MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.3.1 (Γt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.3.2 (αs) . . . . . . . . . . . . . . . . . . . . . . . . 53

6.4 Γt αs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7 59

7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

7.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

8 67

69

ii

2.1 αs . . . . . . . . . . . . . . . . . . 9

3.1 . . . . . . . . . . . . . . . . . 13

3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3 QCD . . . . . . . . . . . . . . . . . 16

3.4 Vtb . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.5 αs . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.6 . . . . . . . . . . . . . . 19

3.7 . . . . . . . . . . . . . . . 20

3.8 αs . . . . . . . . . . . . . . . . . . . . . . . . 21

3.9 Vtb . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1 ILC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2 ILC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3 ILC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.4 ILC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.5 ILD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.7 (SIT,SET) . . . . . . . . . . . . . . . . . . . . . . 36

4.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.10 . . . . . . . . . 39

4.11 LumiCal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.12 BeamCal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.1 PFA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 LCFIPlus . . . . . . . . . . . . . . . . . . . . . . . 46

iii

5.3

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.1 . 49

6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.4 Vtb χ2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.5 αs χ2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.6 χ2 . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6.7 . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

7.1 Vtb . . . . . . . . . . . . . 59

7.2 Vtb . . . . . . . . . . . . . . . . . . . 60

7.3 . . . . . . . . . . . . 61

7.4 Vtb αs 2 . . . . . . . 64

7.5 . . . . . . . . . . . . . . . . 65

iv

2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 . . . . . . . . . . . . . . . 4

3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5.1 ILD . . . . . . . . . . . . . . . . . . . . . . . . 43

6.1 χ2 . . . . . . . . . . . . . . . . . . . . . . . . 55

7.1 (GeV) . . . . . . . . . . . . . . . . . . . . . . . 63

v

1

3

(

)

1989 CERN LEP(Large Electron Positron collider)

91GeV 209GeV Z

2008

LHC(Large Hadron Collider)

1

−∆E ∝ (E/m)4

R E m R

−∆E ∝ 1m4 1013

2012

LHC

3

( )

1

ILC(International Linear Collider)

ILC

R → ∞

ILC 350GeV

QCD

(αs) QCD

2

3 4 ILC 5

6 7

8

2

2

2.1

18

W ,Z, g, γ,h 6

u,b,c,s,t,b 6 , e, νe, µ, νµ, τ, ντ 6

γ, g, Z

2.1

u d e νe2.2+0.5−0.4MeV 4.7

+0.5−0.3MeV 0.511MeV ∼0MeV

c s µ νµ1.275+0.025−0.035MeV 95

+9−3MeV 105.7MeV ∼0MeV

t b τ ντ173.0 0.4GeV 4.18+0.04−0.03GeV 1776.86 0.12MeV ∼0MeV

γ W , Z g h

massless 80.379 0.012GeV massless 125.18 0.16GeV

91.1876 0.0021GeV

2.1:

4

3

3

2.2

GWS(Glashow-Weinberg-Salam)

SU(2)L U(1)Y SU(2)L(IW ) U(1)Y (YW ) Q

3 IW3 (2.1)

YW ≡ 2(Q− IW3) (2.1)

IW IW3 Q YWνlL 1/2 +1/2 0 -1

l−L 1/2 -1/2 -1 -1

l−R 0 0 -1 -2

uL 1/2 +1/2 +2/3 +1/3

dL 1/2 -1/2 -1/3 +1/3

uR 0 0 +2/3 +4/3

dR 0 0 -1/3 -2/3

ν lR 1/2 -1/2 0 +1

l+R 1/2 +1/2 +1 +1

l+L 0 0 +1 +2

uR 1/2 -1/2 -2/3 -1/3

dR 1/2 +1/2 +1/3 -1/3

uL 0 0 -2/3 -4/3

dL 0 0 +1/3 +2/3

2.2:

4

SU(2)L W U(1)Y B

W = (W1,W2,W3) (2.2)

W W1 W2

W± =1√2(W1 ∓ iW2) (2.3)

Z A W3 B

A = BcosθW +W3sinθW (2.4)

Z = −BsinθW +W3cosθW (2.5)

θW sin2θW = 0.23

Z A

Z A SU(2)L U(1)Y W

ψ eieα(x)ψ (2.6)

Aµ

Aµ Aµ + ∂µα(x) (2.7)

Dµ = ∂µ + igAµ(x) (2.8)

g

5

1

2m2AµAµ

1

2m2(Aµ + ∂µΛ)(Aµ + ∂µΛ) ̸=

1

2m2AµAµ (2.9)

m = 0

W Z

2.3

Φ =

(φ+

φ0

)(2.10)

YW = 1/2 φ+ φ0

φ+ =φ1 + iφ2√

2,φ0 =

φ3 + iφ4√2

(2.11)

L = (DµΦ)†DµΦ− µ2Φ†Φ+ λ(Φ†Φ)2 (2.12)

V = µ2Φ†Φ − λ(Φ†Φ)2 λ < 0 Φ → ∞µ2 > 0 0 (v =

√µ2/λ)

(φ+)2 + (φ0)2 = v2 Φ

Dµ = ∂µ − ig1YW2

− ig2τ⃗

2·Wµ (2.13)

τ⃗

φ eiα⃗(x)·τ⃗/2ψ(x) (2.14)

6

Φ φ3 = v,φ1 = φ2 = φ4 = 0

Φ =1√2

(0

v

)(2.15)

(DµΦ)†(DµΦ) =

(1

2vg2

)2W+µ W

−µ +

1

2

(1

2v√g21 + g

22

)2Z0µZ

µ0 (2.16)

W m2WW+W− (m2ZZµZ

µ)/2+(m2γAµAµ)/2

mW =1

2vg2 (2.17)

mZ =1

2v√

g21 + g22 (2.18)

mγ = 0 (2.19)

2.4

3

L = − yt√2

[(bL, tL)

(0

v

)tR + tR(0, v)

(bLtL

)]

= − yt√2(tLvtR + tRvtL)

= −ytv√2tµµ

yt

mt =1√2ytv

7

2.5

QCD QCD

SU(3)C 3

( )

3

αs

αs(Q2) =

12π

(33− 2Nf )ln( Q2

ΛQCD)

(2.20)

Q q 4 Q2 = −q2

Nf Q2 3 6 ΛQCDQCD αs

αs 2.1

8

9. Quantum chromodynamics 39

They are well within the uncertainty of the overall world average quoted above. Note,however, that the average excluding the lattice result is no longer as close to the valueobtained from lattice alone as was the case in the 2013 Review, but is now smaller byalmost one standard deviation of its assigned uncertainty.

Notwithstanding the many open issues still present within each of the sub-fieldssummarised in this Review, the wealth of available results provides a rather precise andreasonably stable world average value of αs(M2Z), as well as a clear signature and proof ofthe energy dependence of αs, in full agreement with the QCD prediction of AsymptoticFreedom. This is demonstrated in Fig. 9.3, where results of αs(Q2) obtained at discreteenergy scales Q, now also including those based just on NLO QCD, are summarized.Thanks to the results from the Tevatron and from the LHC, the energy scales at whichαs is determined now extend up to more than 1 TeV♦.

QCD αs(Mz) = 0.1181 ± 0.0011

pp –> jetse.w. precision fits (N3LO)

0.1

0.2

0.3

αs (Q2)

1 10 100Q [GeV]

Heavy Quarkonia (NLO)e+e– jets & shapes (res. NNLO)

DIS jets (NLO)

April 2016

τ decays (N3LO)

1000

(NLOpp –> tt (NNLO)

)(–)

Figure 9.3: Summary of measurements of αs as a function of the energy scale Q.The respective degree of QCD perturbation theory used in the extraction of αs isindicated in brackets (NLO: next-to-leading order; NNLO: next-to-next-to leadingorder; res. NNLO: NNLO matched with resummed next-to-leading logs; N3LO:next-to-NNLO).

♦ We note, however, that in many such studies, like those based on exclusive states ofjet multiplicities, the relevant energy scale of the measurement is not uniquely defined.For instance, in studies of the ratio of 3- to 2-jet cross sections at the LHC, the relevantscale was taken to be the average of the transverse momenta of the two leading jets [434],but could alternatively have been chosen to be the transverse momentum of the 3rd jet.

June 5, 2018 19:47

2.1: αs [1]

αs ΛQCD αsΛQCDILC ΛQCD

QCD

9

2.6 CKM

3 3⎛

⎜⎝Vud Vus VubVcd Vcs VcbVtd Vts Vtb

⎞

⎟⎠ =

⎛

⎜⎝0.97420 0.00021 0.2243 0.0005 (3.94 0.36) 10−3

0.218 0.004 0.997 0.017 (42.2 0.8) 10−3

(8.1 0.5) 10−3 (39.4 .23) 10−3 1.019 0.025

⎞

⎟⎠

[1] U D

|VUD|2

10

3

3.1

b W

3.1

(direct measurement) 173.0 0.4 GeV

(cross section measurement) 160 +5−4 GeV

1.41 +0.19−0.15GeV

3.1: [1]

(3.1) QCD (ΛQCD)

Γt ≃GFm3t8√2π

|Vtb|2 ∼ 1.4GeV ≫ ΛQCD(∼ 200MeV) (3.1)

GF mt Vtb CKM ΛQCDQCD QCD

3.2

tbW Vertex

11

Γ(t bW ) =GF

8√2π

m3t (1− x2)[(1 + x2 − 2x4)(f 21L + f 21R)

+ (2− x2 − x4)(f 22L + f 22R) + 6x(1− x2)(f1Lf2R + f2Lf1R)] (3.2)

x = mW/mt f form factor f1 W

t-b f2 W t-b L

R

f1L = Vtb = 1 f1R = f2L = f2R = 0

√s = 8TeV ATLAS Γt = 1.76=0.86−0.76GeV

[2] ILC ILC

[3]

[4] [4]

form factor

form factor

3.1 form factor

12

3.1: [5]

NLO(Next-Leading Order)

NLO αs αs tt Γt

Γt =GFm3t8√2π

|Vtb|2(1− M

2W

m2t

)2(1 + 2

M2Wm2t

)[1− 2αs

3π

(2π2

3− 5

2

)]∼ 1.35|Vtb|2

Vtb CKM

1 1

3.3

J/ψ Υ

13

1S

tt

2

3.4

QCD QCD

Bethe-Salpeter Bethe-Salpeter

Schrödinger [H −

(E + i

Γθ2

)]G = 1

H E Γθ (Γθ ∼ 2Γt) G

σtt ∝ Im < x = 0|G|x = 0 >∼ Im∑

n

|Ψn(0)|2

E− En + iΓn/2

n

dσttd|p| ∼ | < p|G|x = 0 > |

2 ∼∣∣∣∣Σ

φn(p)Ψ∗n(0)

E − En + iΓn/2

∣∣∣∣2

( )

Γt mt yt 1S

(E1S) 1S

E1S ∼ 2mt − α2smt [6]W 2 W qq W lν

3

14

tt bWbW bqqbqq( ) (3.3)

tt bWbW bqqblν( ) (3.4)

tt bWbW blνblν( ) (3.5)

ILC

3.2:

QCD V (r) = −43 sr + kr

tt

σtot(e+e− tt) ∝ −Im

∑

n

|φn(0)|2

E − En + iΓt(3.6)

15

b W

QCD

3.3: QCD [7]

(αs)

VQCD ∼ −4αs3r

αs

16

QCD VQCD(r) ∼ −43 sr + kr

9

3.4: Vtb

3.4 mt = 174GeV αs = 0.12 Vtb

17

3.5: αs

3.5 mt = 174GeV Vtb = 1.00 αs αs 1S

1S 3.3√s1S ∼ 2mt − α2smt

αs

√s = 2mt

1S

(physsim)[8]

18

3.6:

mt = 174GeV,Vtb = 1.0,αs = 0.12,√s = 2mt − 1

: mt = 176GeV,√s = 351GeV

: mt = 175GeV,√s = 349GeV

: mt = 174GeV,√s = 347GeV

: mt = 173GeV,√s = 345GeV

: mt = 172GeV,√s = 343GeV

19

3.7:

3.7

: yt = 0.8

: yt = 0.9

: yt = 1.0

: yt = 1.1

: yt = 1.2

20

3.8: αs

3.6 αs tt V (r) ∼ −43αsr

αs

21

3.9: Vtb

3.7 Vtb

Vtbαs

3.5

( dσd|Pt|)

ILC

W

W

W

6 W 4

22

11 340GeV 350GeV 1GeV

Vtb 0.8 1.2 0.1

Vtb

: Vtb = 0.80

: Vtb = 0.90

: Vtb = 1.00

: Vtb = 1.10

: Vtb = 1.20

(GeV)

√s=340GeV

√s=341GeV

23

√s=342GeV

√s=343GeV

√s=344GeV

√s=345GeV

√s=346GeV

√s=347GeV

24

√s=348GeV

√s=349GeV

√s=350GeV

11 αsαs

: αs = 0.110

: αs = 0.115

: αs = 0.120

: αs = 0.125

: αs = 0.130

(GeV)

25

√s=340GeV

√s=341GeV

√s=342GeV

√s=343GeV

√s=344GeV

√s=345GeV

26

√s=346GeV

√s=347GeV

√s=348GeV

√s=349GeV

√s=350GeV

27

Vtb αs347GeV [2]

28

4 ILC(International LinearCollider)

ILC(International Linear Collider) 20km

250GeV

350GeV

500GeV 1TeV

4.1 4.2 ILD

4.1

ILC 1 1 1

(4.1)

L = frepnbN2

4πσ∗xσ∗y

(4.1)

frep nb 1 ( ) N 1

σ∗x σ∗y

ILC 3

•

•

•

4.1 ILC

29

4.1: ILC [9]

4.1.1

ILC DC GaAs

140 160keV

80% 76MeV

5GeV

4.2

30

4.2: ILC [10]

4.1.2

ILC

10MeV

30%

60%

400MeV

5GeV

4.3

31

4.3: ILC [10]

4.1.3

ILC

σx,y =√βx,y ϵx,y (4.2)

β ϵ

3.2km 5GeV

4.4

32

4.4: ILC [10]

4.1.4

RTML 5GeV 15GeV

250GeV

22km 31.5MV/m TDR 9

2K 1.3GHz

4.2

4.2.1

ILC ILD(International Large Detector) SiD(Silicon Detector) 2

ILD SiD

ILD ILD

ILD

33

4.5: ILD ( mm)[10]

4.2.2

(VTX)

σr ≤ 5⊕10

pβsin3/2θ(µm) (4.3)

34

p, β θ 1

2

16mm

FPCCD CMOS

4.6

4.6: [10]

(SIT,SET)

1 FPCCD 1

4.7

35

4.7: (SIT,SET) [10]

(TPC : Time Projection Chember) 3

TPC

2 3

TPC

σ(1/p) ≥ 9× 10−5(GeV/c)−1 (4.4)

4.2.3

2 (γ )

( )

ILC W

Z

36

σEjet ∼30%

Ejet(GeV)(4.5)

γ

4.8

4.8: [10]

4.9

37

4.9: [10]

4.2.4

ILD /

3.5T

4.10

38

4.10: [9]

4.2.5

LumiCal BeamCal

39

LumiCal

LumiCal

(e+e− e+e−)

L = Nbhabhaσ

(4.6)

Nbhabha σ 0.1%

LumiCal 32∼72mrad 4.11 LumiCal

4.11: LumiCal [10]

BeamCal

BeamCal

BeamCal 5∼40mrad 4.12 BeamCal

40

4.12: BeamCal [10]

41

5

5.1

(DBD) ILC

Physsim[6]

Mokka[11] Geant4

Marlin

5.2

Physsim [6] Physsim

HELAS BASES BASES

SPRING SPRING

JSFHadronizer JSFHadronizer

PYTHIA6.4

TAUOLA

5.3

ILC ILD Mokka

Geant4 Mokka PFA[12]

42

Particle Flow Algorithm

ILC Particle Flow Algorithm(PFA)

ILC

5.1 ILD 5.1 WW ZZ

PFA ZZ WW

σE/E

60% 0.00002 E

30% ECAL 0.2/E

10% HCAL 0.6/E

5.1: ILD

5.1: PFA [10]

5.4

ILD

43

4

b 4

3-jet b

Isolated lepton tagging

W 2

W

15GeV

cosθ > 0.96 0

10GeV 1

2

anti-kT

2 2

dij = min(k2T i , k2T j)∆2ijR2

(5.1)

∆2ij = (yi − yj)2 + (φ2i − φ2j) (5.2)diB = k2Tj (5.3)

kT y φ R

dij diBdij i j 1 diB

i R = 0.7

0.6GeV

44

4-jet tagging

Isolated Lepton Tagging

Y

Yij =2min(Ei,Ej)(1− cosθij)

E2vis(5.4)

Ei Ej θij i, j EvisY

4

b quark tagging

4 jet b b̄ b iLCSoft

LCFIPlus ROOT TMVA

TMVA BDT(Boosted

Decison Trees) √s = 500GeV 6

5.2

45

5.2: LCFIPlus [[10]

W

4 jet b b̄ 2 W

2 W

4 W

W b b jet

b b̄

b W cosθbW

46

5.3 3

5.3:

MC

47

6

6.1

5

1

physsim

toy MC toy MC

6.2 (toy MC)

5.3

5.3

6.1

48

6.1:

6.2 5.3

10GeV 11GeV 2623

49

6.2: 10GeV 11GeV

10GeV 11GeV

0 200GeV 1GeV 200

1GeV 1GeV

200

6.3

50

6.3:

Vtb = 0.8

Vtb =1.0 toy

MC

6.3

Vtb 0.95 1.05 Vtb 0.01 αs 0.115 0.125 0.001

toy MC

χ2

χ2 =200∑

i=0

(yiReco − yipReco)2

σ2yiReco

(6.1)

i 1 200 yiReco yipreco i

σyiReco yiReco

(6.1) χ2

51

αs

6.3.1 (Γt)

LO

|Vtb|2 Vtb

6.5 Vtb χ2

6.4: Vtb χ2

χ2 2

Vtb = 0.9959 0.0027

52

χ2 +1 Vtb|Vtb|2 = 0.9918 0.0054

6.3.2 (αs)

(αs)

αs ILC LHC QCD αsILC

ILC αsVtb χ2 6.6

6.5: αs χ2

2

αs = 0.1189 0.0005

53

χ2 +1 αs

6.4 Γt αsαs 0.11 0.13 0.002 11 Vtb 0.9 1.1 0.02

11 121 χ2 3

Γt αs Vtb αs121 χ2 6.1

54

6.1:

χ2

Vtb

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

0.130

682.501

482.237

378.8

476.142

617.458

880.137

1265.81

1750.55

2347.71

3011.91

3810.18

0.128

778.474

512.713

317.108

268.803

375.603

537.958

884.502

1262.17

1795.98

2395.06

3117.59

0.126

941.823

552.203

330.901

187.915

195.571

387.77

601.948

914.198

1384.56

1944.23

2592.38

0.124

1110.09

673.184

425.322

224.604

160.895

248.467

392.8

676.304

1074.44

1568.32

2149.81

0.122

1326.48

826.104

498.871

234.662

157.085

169.574

292.509

534.932

843.812

1285.49

1853.47

αs

0.120

1547.77

985.248

602.579

305.04

155.013

161.455

215.137

405.156

715.338

1118.4

1625.74

0.118

1703.05

1132.66

717.684

454.427

254.305

125.575

199.967

350.897

601.488

1002.95

1429.1

0.116

1886.76

1360.17

863.847

514.951

293.049

201.524

212.407

547.876

547.876

890.448

1290.18

0.114

2033.24

1418.09

951.635

583.46

343.439

222.923

221.606

318.696

541.542

825.76

1204.21

0.112

2145.43

1518.85

1013.9

634.021

381.818

254.599

230.757

322.836

495.639

762.6

1138.68

0.110

2222.59

1609.01

1073.82

704.662

464.783

323.918

269.758

329.908

505.72

747.591

1112.72

55

x αs y Vtb z χ2 6.7

2 2

6.6: χ2

Vtb 0.96 1.04 αs 0.114 0.126 2 2

F (x, y) = ax2 + by2 + cxy + dx + ey + f ∂F (x, y)/∂x = 0

∂F (x, y)/∂y = 0

Vtb = 0.9933 (6.2)

αs = 0.1199 (6.3)

6.8 3σ(χ2 +9)

56

6.7:

Vtb = 1.00 αs = 0.12 2.55σ αsVtb 1GeV

1GeV

6.9 Vtb 3

: Vtb = 0.96

: Vtb = 1.00

: Vtb = 1.04

57

6.8:

χ2

1GeV

1

58

7

7.1

[2]

physsim

Vtb 7.1 physsim

6.2 toy MC toy

MC Vtb Ppeak ( αs=0.12 ) 7.2

7.1: Vtb

59

7.2: Vtb

7.2 1 2

7.3

Ppeak = 19.84 0.12GeV

60

7.3:

7.1

VtbVtb = 1.143 0.008

|Vtb|2 = 1.306 0.018

Γt ∼ 1.5|Vtb|2GeV

Γt = 1.959 0.027GeV

7.2 1

Vtb = 0.992 0.009

|Vtb|2 = 0.984 0.018

61

Γt = 1.477 0.026GeV

2 Vtb

Vtb = 1.004 0.009

|Vtb|2 = 1.008 0.018

Γt = 1.512 0.027GeV

Γt Vtbαs 2 7.1 2

7.4

62

7.1:

(GeV

)Vtb

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

0.110

17.45

18.02

18.21

18.72

19.01

19.25

19.54

19.73

20.08

20.14

20.70

0.112

17.61

18.12

18.43

18.81

19.03

19.28

19.62

19.90

20.14

20.33

20.74

0.114

17.69

18.15

18.48

18.85

19.18

19.33

19.54

19.96

20.24

20.47

20.85

0.116

17.88

18.24

18.57

18.90

19.16

19.41

19.68

20.26

20.26

20.58

20.88

0.118

18.11

18.41

18.87

19.00

19.36

19.49

19.85

20.07

20.33

20.68

20.92

αs

0.120

18.29

18.55

19.07

19.20

19.44

19.67

19.99

20.25

20.58

20.81

21.06

0.122

18.53

18.68

19.20

19.44

19.60

19.84

20.08

20.50

20.73

21.00

21.17

0.124

18.61

18.96

19.42

19.55

19.79

20.04

20.25

20.61

20.94

21.12

21.28

0.126

18.95

19.30

19.51

19.85

20.10

20.28

20.50

20.79

21.09

21.19

21.42

0.128

19.39

19.57

19.84

20.08

20.43

20.54

20.76

21.02

21.26

21.39

21.60

0.130

19.70

19.90

20.23

20.39

20.67

20.88

21.05

21.27

21.40

21.57

21.79

63

7.4: Vtb αs 2

7.4 Vtbαs 7.5

2

64

7.5:

7.5 Vtb αs

7.2

toy MC 1GeV 1GeV

65

66

8

QCD

QCD

ILC

200fb−1

αs Vtb

αs Vtb

Vtb = 0.9959 0.0027

Vtb αs

αs = 0.1189 0.0005

Vtb αs ,

Vtb = 0.9933

αs = 0.1199

67

2.55

αsαs

e+e− W+W−

1GeV

68

ILC

1

ILC KEK

ILC

ILC

2018 2019 3

ILC

69

[1] Particle Data Group

http://pdg.lbl.gov/

[2] The ATLAS Collaboration, ”Direct top-quark decay width measurement in the tt lep-

ton+jets channel at√s = 8 TeV with the ATLAS experiment”

https://arxiv.org/pdf/1709.04207.pdf

[3] ” ”

http://epx.phys.tohoku.ac.jp/eeweb/paper/2014_Mthesis_horiguchi.pdf

[4] ”

”

http://epx.phys.tohoku.ac.jp/eeweb/paper/2017_Mthesis_ozawa.pdf

[5] P.Agrawal, S.Mitra, A.Shivaji,”Effect of Anomalous Couplings on the Associated Produc-

tion of a Single Top Quark and a Higgs Boson at the LHC”

https://arxiv.org/pdf/1211.4362.pdf

[6] K.Fujii, T.Matsui, and Y.Sumino, ”Physics at tt̄ threshold in e+e− collisions,” Phys. Rev.

D 50, 4341 (1994)

[7] http://www-jlc.kek.jp/jlc/en/node/103

[8] Physsim

http://www-jlc.kek.jp/subg/offl/physsim/

[9] ILC

https://www2.kek.jp/ilc/ja/contents/ILC_Report_2018/

[10] ILC Technical Design Report

http://www.linearcollider.org/ILC/Publications/Technical-Design-Report

70

http://pdg.lbl.gov/https://arxiv.org/pdf/1709.04207.pdfhttp://epx.phys.tohoku.ac.jp/eeweb/paper/2014_Mthesis_horiguchi.pdfhttp://epx.phys.tohoku.ac.jp/eeweb/paper/2017_Mthesis_ozawa.pdfhttps://arxiv.org/pdf/1211.4362.pdfhttp://www-jlc.kek.jp/jlc/en/node/103http://www-jlc.kek.jp/subg/offl/physsim/https://www2.kek.jp/ilc/ja/contents/ILC_Report_2018/http://www.linearcollider.org/ILC/Publications/Technical-Design-Report

[11] Mokka

https://ilcsoft.desy.de/portal/software_packages/mokka/

[12] J.S.Marshall and M.A.Thomson, ”Pandora Particle Flow Algorithm”

https://arxiv.org/pdf/1308.4537.pdf

[13] M.Peter and Y.Sumino, ”Final-State Interactions in e+e− → tt → bl+ bW− Near TopQuark Threshold”

https://arxiv.org/pdf/hep-ph/9708223.pdf

[14] (ILC)

http://www.mext.go.jp/b_menu/shingi/chousa/shinkou/038/

[15] R.K.Ellis, W.J.Strling, and B.R.Webber, ”QCD and Collider Physics” , CAMBRIDGE

UNIVERSITY PRESS

[16] Top Quark Physics

http://acfahep.kek.jp/acfareport/node112.html

[17] M. Jeżabek, J.H. Kühn, and T. Teubner, ”Comment on the average momentmum of top

quarks in the threshold region”

https://arxiv.org/pdf/hep-ph/9311235.pdf

[18] M. Jeżabek, J.H. Kühn, and T. Teubner, ”Physics at tt threshold in e+e− collisions”

https://journals.aps.org/prd/pdf/10.1103/PhysRevD.50.4341

[19] Y.Sumino, K.Fujii, and T.Matsui, ”A Study of the Top Quark Production Threshold at a

Future Electron-Positron Linear Collider”

http://discovery.ucl.ac.uk/19429/

[20] , , =

71

https://ilcsoft.desy.de/portal/software_packages/mokka/https://arxiv.org/pdf/1308.4537.pdfhttps://arxiv.org/pdf/hep-ph/9708223.pdfhttp://www.mext.go.jp/b_menu/shingi/chousa/shinkou/038/http://acfahep.kek.jp/acfareport/node112.htmlhttps://arxiv.org/pdf/hep-ph/9311235.pdfhttps://journals.aps.org/prd/pdf/10.1103/PhysRevD.50.4341http://discovery.ucl.ac.uk/19429/

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