æepx.phys.tohoku.ac.jp/eeweb/paper/2019_mthesis_eda.pdfz q ¨ t s m h z c + î g p ¤ É ç ª g ü...
TRANSCRIPT
-
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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