1. 2 and 3-jet Analysis in Flux-tube Model J.B.Choi, M.Q.Whang, S.K.Lee (Chonbuk National University, Korea)

2. 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

3. I. Generals  Purpose of LC  Production Processes  Factorization  Hadronization into Jets  Jet Overlapping

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

5. Production Processes 4 jets

6. 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)

7. 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 !

8. 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 …

9. 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)

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

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

12. 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

13. 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

14. 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

15. 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

16. Mesons

17. Baryons Proton Neutron

18. 4-quark States (1) square

19. 4-quark States (2)

20. Pentaquarks-1

21. Pentaquarks-2

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

23. 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

24. 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

25. 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

26. 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

27. Angular Ordering

28. Momentum Distributions  2-jet case P1P1 P2P2 P θ

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

30. Parameters – k,d,e

31. Fits

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

34. ◎. Phase space 2 ◦ gluonic effect f

35. Analysis  3 jet

36. (A)(B)

37. Fits

38. ◎. Phase space 3 aa

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

40. Parameters - a

41. Parameters – A0

42. Parameters - e

43. Parameters - d

44. Parameters - f

45. Parameters - k

46. Fits 1

47. Fits 2

48. Fits 3

49. Fits 4

50. Fits 5

51. Fits 6

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