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  Production Processes  Factorization  Hadronization into Jets  Jet Overlapping

Purpose of LC  Higgs → 2, 4 jets → 4, 6 jets → 4, 6 jets → 8, 10 jets → 8, 10 jets  6 jets   SUSY  Extra-dim

Production Processes 4 jets

Loop corrections no. of loops no. of diagrams drawings calculations no. of loops no. of diagrams drawings calculations 0 ~10 0 H H1 ~10 1 H H 2 ~10 2 HH/C 3 ~10 3 H/CH/C 4 ~10 4 C C 5 ~10 5 C 6 ~10 6 C (H : Hand) (H : Hand) (C : Computer) (C : Computer)

Factorization  1 st rule ; perturbative expansion in ; perturbative expansion in ; non-perturbative models ; non-perturbative models  Corrections asymptotic expansions asymptotic expansions exponentiation + resummation exponentiation + resummation Uncertainty exists ! Uncertainty exists !

Hadronization into Jets  : 2 jets 2 or 4 jets 2 or 4 jets  : 4 or 6 jets  : 6 jets  : 8 or 10 jets  models based on local parton-hadron duality cluster → HERWIG cluster → HERWIG string → JETSET string → JETSET …

Jet Overlapping  4 jets Consider the cone Consider the cone overlap solid angle ; overlap solid angle ; ∴ probability to overlap ∴ probability to overlap (maybe OK.) (maybe OK.)  5 jets for fixed 4 jets for fixed 4 jets ; (difficult to check) ; (difficult to check)

Processes Processes 6 jets 6 jets  8 jets BG : BG : ; nearly always overlap ; nearly always overlap need new method need new method

II. Flux-tubes in Coordinate Space  Flux-Tube Classification  Connection Amplitude  Gluon Density  Mesons  Baryons  4-quark States  Pentaquarks

Flux-tube Classification a : no. of quarks (sources) a : no. of quarks (sources) b : no. of antiquarks (sinks) b : no. of antiquarks (sinks)glueballmeson baryon pentaquark hexaquark

Connection Amplitude  A : The amplitude for a quark to be connected to another one through given flux-tube. to another one through given flux-tube.  M(A) : measure of A ▫. assumptions ▫. assumptions (1) M(A) decreases as A increases. (1) M(A) decreases as A increases. (2) M(A 1 ) + M(A 2 ) = M(A 1 A 2 ) (2) M(A 1 ) + M(A 2 ) = M(A 1 A 2 ) ( when A 1 and A 2 are independent) ( when A 1 and A 2 are independent)  Solution A 0 : normalization constant A 0 : normalization constant k : parameter k : parameter

Form of M  For M ∝ ｜ x-y ｜ ν, flux-tube shape is determined by  ｜ x-y ｜ ν = ｜ x-z ｜ ν + ｜ z-y ｜ ν   General A becomes    For and xy z : Weight factor : Weight factor : Integration limit : Integration limit

Gluon Density  Overlap function probability amplitude to have quark pairs probability amplitude to have quark pairs  For a meson We can assume We can assume probability to have quark pair ∝ gluon density probability to have quark pair ∝ gluon density

Mesons

Baryons Proton Neutron

4-quark States (1) square

4-quark States (2)

Pentaquarks-1

Pentaquarks-2

Ⅲ. Momentum Space Flux-tube Model  Momentum Space Connection  Definition of Jets  Phase Space  Angular Ordering  Momentum Distributions

Momentum Space Connection Final particles are connected in momentum! Final particles are connected in momentum! → momentum space flux-tube model → momentum space flux-tube model

Definition of Jets  Fragmentation process by quark pair creations by quark pair creations... gluonic flux-tube descriptions gluonic flux-tube descriptions (1) Probability amplitude ∝ overlap function (1) Probability amplitude ∝ overlap function ( in mementum space) ( in mementum space) (2) Phase space (2) Phase space ; parton model assumptions ; parton model assumptions

Phase Space  Parton model assumptions about quark fragmentation (1) Longitudinal momentum components (1) Longitudinal momentum components ∝ total jet (parton) energy ∝ total jet (parton) energy (2) Transverse momentum components (2) Transverse momentum components from soft processes (small uncertainty) from soft processes (small uncertainty) → parameters → parameters → Trapezoid → Trapezoid e d P L ∝ E (jet) e d P L ∝ E (jet) P T : two parameters d, e P T : two parameters d, e

Angular Ordering  Prediction of gluon jet direction ? A = A 1 A 2 A = A 1 A 2 (1) for fixed P 2 (p 1 ≡1.0), (1) for fixed P 2 (p 1 ≡1.0), vary P 3 and θ vary P 3 and θ (2) vary P 2 and angle (2) vary P 2 and angle between P 1 and P 2 between P 1 and P 2 P1P1 P2P2 P3P3 A1A1 A2A2 θ

Angular Ordering

Momentum Distributions  2-jet case P1P1 P2P2 P θ

Ⅳ. 2-jet Analysis P1P1P1P1 P2P2P2P2 e dhL1 L2 Connection amplitude Probability  Phase Space

Parameters – k,d,e

Fits

Ⅴ. 3-jet Analysis I. II. III.  Phase Space

◎. Phase space 2 ◦ gluonic effect f

Analysis  3 jet

(A)(B)

Fits

◎. Phase space 3 aa

◎ 1. A0, a, e, k, d, f 1. A0, a, e, k, d, f 2. Data Analysis 2. Data Analysis Parameter s

Parameters - a

Parameters – A0

Parameters - e

Parameters - d

Parameters - f

Parameters - k

Fits 1

Fits 2

Fits 3

Fits 4

Fits 5

Fits 6

Ⅵ. Look Forward  3-dim. Structures  Momentum Distributions  Jet Parameter Calculations  Discrimination of Overlapped Jets  Possibilities