2 and 3-jet Analysis in Flux-tube Model

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 → 8, 10 jets • 6 jets • SUSY • Extra-dim

5. Production Processes 4 jets

6. Loop corrections no. of loops no. of diagrams drawings calculations 0 ~100 H H 1 ~101 H H 2 ~102 H H/C 3 ~103 H/C H/C 4 ~104 C C 5 ~105 C 6 ~106 C (H : Hand) (C : Computer)

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

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

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

10. Processes • 6 jets • 8 jets BG : ; nearly always overlap 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) b : no. of antiquarks (sinks)

13. Connection Amplitude • A: The amplitude for a quark to be connected to another one through given flux-tube. • M(A): measure of A ▫. assumptions (1) M(A) decreases as A increases. (2) M(A1) + M(A2) = M(A1A2) (when A1 and A2 are independent) • Solution A0 : normalization constant k : parameter

14. z x y 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 : Weight factor : Integration limit

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

16. Mesons

17. Baryons

18. 4-quark States (1)

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! → momentum space flux-tube model

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

25. Phase Space • Parton model assumptions about quark fragmentation (1) Longitudinal momentum components ∝ total jet (parton) energy (2) Transverse momentum components from soft processes (small uncertainty) → parameters → Trapezoid edPL ∝ E (jet) PT : two parameters d, e

26. P1 A1 P3 A2 P2 θ Angular Ordering • Prediction of gluon jet direction ? A = A1A2 (1) for fixed P2 (p1≡1.0), vary P3 and θ (2) vary P2 and angle between P1 and P2

27. Angular Ordering

28. P2 P1 P θ Momentum Distributions • 2-jet case

29. P1 P2 h e d L1 L2 • Phase Space Ⅳ. 2-jet Analysis Connection amplitude Probability

30. Parameters – k,d,e

31. Fits

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

34. ◎. Phase space 2

35. Analysis • 3 jet

36. (A) (B)

37. Fits

38. a a ◎. Phase space 3

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

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