2 and 3-jet analysis in flux-tube model
DESCRIPTION
2 and 3-jet Analysis in Flux-tube Model. J.B.Choi, M.Q.Whang, S.K.Lee (Chonbuk National University, Korea). Ⅰ. Generals Ⅱ. Flux-tubes in Coordinate Space Ⅲ. Momentum Space Flux-tube Model Ⅳ. 2-jet Analysis Ⅴ. 3-jet Analysis Ⅵ. Look forward. I. Generals. Purpose of LC - PowerPoint PPT PresentationTRANSCRIPT
2 and 3-jet Analysis in Flux-tube 2 and 3-jet Analysis in Flux-tube ModelModel
J.B.Choi, M.Q.Whang, S.K.LeeJ.B.Choi, M.Q.Whang, S.K.Lee(Chonbuk National University, Korea)(Chonbuk National University, Korea)
ⅠⅠ. Generals. Generals
ⅡⅡ. Flux-tubes in Coordinate Space. Flux-tubes in Coordinate Space
ⅢⅢ. Momentum Space Flux-tube Model. Momentum Space Flux-tube Model
ⅣⅣ. 2-jet Analysis. 2-jet Analysis
ⅤⅤ. 3-jet Analysis. 3-jet Analysis
ⅥⅥ. Look forward. Look forward
I. GeneralsI. Generals
1.1. Purpose of LCPurpose of LC
2.2. Production ProcessesProduction Processes
3.3. FactorizationFactorization
4.4. Hadronization into JetsHadronization into Jets
5.5. Jet Overlapping Jet Overlapping
Purpose of LCPurpose of LC
Higgs → 2, 4 jets Higgs → 2, 4 jets
→ → 4, 6 jets4, 6 jets
→ → 8, 10 jets8, 10 jets
6 jets6 jets
SUSYSUSY
Extra-dimExtra-dim
H
ZHHtt
tt
ZWWWWWW ,,
Production ProcessesProduction Processes
ZH
WW
Z
HWW
4 jets4 jets
QQqq ggqq
e
e SUSY
Htt
tt
ZH
Loop correctionsLoop corrections
no. of loops no. of diagrams drawings calculationsno. of loops no. of diagrams drawings calculations
00 ~10 ~1000 H H H H1 1 ~10 ~1011 H H H H22 ~10 ~1022 H H H/CH/C33 ~10 ~1033 H/C H/C H/CH/C44 ~10 ~1044 C C C C55 ~10 ~1055 C C66 ~10 ~1066 C C
(H : Hand)(H : Hand)
(C : Computer)(C : Computer)
FactorizationFactorization
11stst rule rule
; perturbative expansion in ; perturbative expansion in
; non-perturbative models; non-perturbative models
CorrectionsCorrections asymptotic expansionsasymptotic expansions exponentiation + resummationexponentiation + resummation
Uncertainty exists !Uncertainty exists !
)()(~~ F)(~ )( F
s
Hadronization into JetsHadronization into Jets : 2 jets: 2 jets
2 or 4 jets2 or 4 jets : 4 or 6 jets: 4 or 6 jets : 6 jets: 6 jets : 8 or 10 jets: 8 or 10 jets models based on local models based on local parton-hadron dualityparton-hadron duality
cluster → HERWIGcluster → HERWIG
string → JETSETstring → JETSET
… …
qqH
ZZ
WW
ZHttHtt
Jet OverlappingJet Overlapping
4 jets 4 jets Consider the coneConsider the cone
overlap solid angle ;overlap solid angle ;
∴ ∴ probability to overlapprobability to overlap (maybe OK.)(maybe OK.)
5 jets 5 jets for fixed 4 jetsfor fixed 4 jets
; (difficult to check); (difficult to check)
6
2
41d )(~
16
943 2
2
1
64
2743
169
P4
2
1
16
944
169
P5
ProcessesProcesses 6 jets6 jets
8 jets 8 jets BG :BG :
Htttt ,
3
2
64
4545
169
P6
gttZtt ,
64
6347
169
P8
bbW
ttW
b
b
; ; nearly always overlapnearly always overlap need new methodneed new method
II. Flux-tubes in Coordinate II. Flux-tubes in Coordinate SpaceSpace
1.1. Flux-Tube ClassificationFlux-Tube Classification
2.2. Connection AmplitudeConnection Amplitude
3.3. Gluon DensityGluon Density
4.4. MesonsMesons
5.5. BaryonsBaryons
6.6. 4-quark States4-quark States
7.7. Pentaquarks Pentaquarks
Flux-tube ClassificationFlux-tube Classification a : no. of quarks (sources)a : no. of quarks (sources) b : no. of antiquarks (sinks)b : no. of antiquarks (sinks)baF ,
glueballglueball
mesonmeson
baryonbaryon
pentaquarkpentaquark
hexaquarkhexaquark
0F
11F ,
3F
22F ,
14F ,
6F
qqqq
Connection AmplitudeConnection Amplitude
AA : The amplitude for a quark to be connected: The amplitude for a quark to be connected to another one through given flux-tube.to another one through given flux-tube. M(A)M(A) : measure of A: measure of A ▫▫. . assumptionsassumptions
(1) M(A) decreases as A increases.(1) M(A) decreases as A increases. (2) M(A(2) M(A11) + M(A) + M(A22) = M(A) = M(A11AA22))
((when Awhen A11 and A and A22 are independent) are independent) SolutionSolution
AA0 0 : normalization constant : normalization constant k : parameterk : parameter
)( AMk1
0eAA
Form of MForm of M For M ∝ For M ∝ || x-yx-y || νν , flux-tube shape is determined by , flux-tube shape is determined by || x-yx-y || ν ν = = || x-zx-z || νν + + || z-yz-y || νν
General A becomesGeneral A becomes
For and For and
xx yyzz
shapesphere2
shapeline1
:
:
10
weightdrF
k
1AAA )(exp)(
: Weight : Weight factorfactor
: Integration : Integration limitlimit
)(F
,,)( 21F ArA
r
rr
k
1 2
er
1A ln
Gluon DensityGluon Density
Overlap functionOverlap function probability amplitude to have quark pairsprobability amplitude to have quark pairs For a mesonFor a meson
We can assumeWe can assume probability to have quark pair ∝ gluon densityprobability to have quark pair ∝ gluon density
fiAA
2
222
1
121
230
2
222
1
1212
0f
2
0i
r
rr
r
rr
r
rr
k
1A
r
rr
r
rr
k
1AA
r
rr
k
1AA
lnlnlnexp
lnlnexp
lnexp
z1r 2r
x yr
MesonsMesons
0
50.
BaryonsBaryonsProtonProton
NNeutroeutronn
4-quark States (1)4-quark States (1)squaresquare
4-quark States (2)4-quark States (2)
Pentaquarks-1Pentaquarks-1
Pentaquarks-2Pentaquarks-2
-2 -1 0 1 2-0.002
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
Pro
babi
lity
y
x=0 x=0.5 x=1.0
a=1.0, z=0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
P : 1.0000e-2 ~ 1.0010e-2 P : 1.0000e-3 ~ 1.0010e-3 P : 1.0000e-4 ~ 1.0010e-4 P : 1.0000e-5 ~ 1.0010e-5 P : 1.0000e-6 ~ 1.0010e-6 P : 1.0000e-7 ~ 1.0010e-7 P : 1.0000e-8 ~ 1.0010e-8
y
x
a=1.0, z=0
-1-0.5
00.5
1
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
ⅢⅢ. Momentum Space Flux-tube . Momentum Space Flux-tube ModelModel
1.1. Momentum Space ConnectionMomentum Space Connection
2.2. Definition of JetsDefinition of Jets
3.3. Phase SpacePhase Space
4.4. Angular OrderingAngular Ordering
5.5. Momentum Distributions Momentum Distributions
Momentum Space Momentum Space ConnectionConnection
Final particles are connected in Final particles are connected in momentum!momentum!
→ → momentum space flux-tube modelmomentum space flux-tube model
10 dpG
k
1AA )(exp
Definition of JetsDefinition of Jets
Fragmentation processFragmentation process by quark pair creationsby quark pair creations .. .. .. gluonic flux-tube descriptionsgluonic flux-tube descriptions
(1) (1) Probability amplitude ∝ overlap functionProbability amplitude ∝ overlap function ( in mementum space)( in mementum space) (2) (2) Phase space Phase space ; parton model assumptions; parton model assumptions
A
Phase Space Phase Space
Parton model assumptions about quark fragmentationParton model assumptions about quark fragmentation
(1) Longitudinal momentum components(1) Longitudinal momentum components ∝ ∝ total jet (parton) energytotal jet (parton) energy
(2) Transverse momentum components(2) Transverse momentum components from soft processes (small uncertainty)from soft processes (small uncertainty) → → parametersparameters → → TrapezoidTrapezoid
ee dd PPLL ∝ E (jet) ∝ E (jet)
PPTT : two parameters : two parameters d, ed, e
Angular OrderingAngular Ordering
Prediction of gluon jet direction ?Prediction of gluon jet direction ?
A = AA = A11AA22
(1) for fixed P(1) for fixed P22 (p (p11≡1.0),≡1.0),
vary Pvary P33 and θ and θ
(2) vary P(2) vary P22 and angle and angle
between between PP11 and and PP22
P1
P2
P3
A1
A2
θθ
Angular OrderingAngular Ordering
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
eve
nt
momentum
p2 = 0.1
= /12
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
eve
nt
momentum
p2=0.1
=/3
0.0 0.1 0.2 0.3 0.4 0.52.0
2.2
2.4
2.6
2.8
3.0
3.2
even
t
angle(rad)
p2=0.3
=/6
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
even
t
angle(rad)
p2=0.6
=/4
Momentum Momentum DistributionsDistributions
2-jet case2-jet case
P1P2
Pθθ
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
= 0angle = 0.001
even
t
momentum
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
even
t
momentum
= 0angle = 7
ⅣⅣ. 2-jet Analysis. 2-jet Analysis
PP11 PP22
q q
eedd
hh
L1L1 L2L2
p ln
pk1
-expp1
A 2 p
dpp)A(θ,Ph
0
2
Connection Connection amplitudeamplitude
ProbabilityProbability
Phase Phase SpaceSpace
Parameters – k,d,eParameters – k,d,e
FitsFits
ⅤⅤ. 3-jet Analysis. 3-jet Analysis
I.I.
II.II.
III.III.
Phase SpacePhase Space
◎◎. Phase space 2. Phase space 2
h
q
g
q
dd
ee
◦ ◦ gluonic effectgluonic effect ff
df df
efef
AnalysisAnalysis 3 jet3 jet
(A)(A)
(B)(B)
)
lnccc
lnbbb
lnaaa
(k1
-exp)cb(a
)(AC
1
121
1
121
1
121
111
30
1
)
lnccc
lnbbb
lnaaa
(k1
-exp)cb(a
)(AC
2
222
2
222
2
222
222
30
2
dpCCP
2h
0
21
q
q
g1a
2b
1c
2a
1b
2c q
g
q
FitsFits
◎◎. Phase space 3. Phase space 3
aa aa
◎◎
1. A0, a, e, k, d, f1. A0, a, e, k, d, f
2. Data Analysis2. Data Analysis
lnppp
k1
expp
AA
20
ParametParametersers
Parameters - aParameters - a
Parameters – A0Parameters – A0
Parameters - eParameters - e
Parameters - dParameters - d
Parameters - fParameters - f
Parameters - kParameters - k
Fits 1Fits 1
Fits 2Fits 2
Fits 3Fits 3
Fits 4Fits 4
Fits 5Fits 5
Fits 6Fits 6
ⅥⅥ. Look Forward. Look Forward
1.1. 3-dim. Structures3-dim. Structures
2.2. Momentum DistributionsMomentum Distributions
3.3. Jet Parameter CalculationsJet Parameter Calculations
4.4. Discrimination of Overlapped Discrimination of Overlapped
JetsJets
5.5. PossibilitiesPossibilities