Lund model 1.T. Sjostrand, ``The Lund Monte Carlo For Jet Fragmentation,'' Comput. Phys. Commun. 27, 243 (1982). 2.T. Sjostrand, ``The Lund Monte Carl

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Lund 模型 http://home.thep.lu.se/~torbjorn/pythia.html B. Andersson, G. Gustafson, G. Ingelman and T.

1 Lund 模型 B. Andersson, G. Gustafson, G. Ingelman and T. Sjostrand, ``Parton Fragmentation And String Dynamics,'' Phys. Rept. 97, 31 (1983). PYTHIA6.4 Physics and Manual 489pages 国際教養大学 (Akita International University) 奈良寧 2008 ICRR 10/4

2 Lund model 1.T. Sjostrand, ``The Lund Monte Carlo For Jet Fragmentation,'' Comput. Phys. Commun. 27, 243 (1982). 2.T. Sjostrand, ``The Lund Monte Carlo For E+ E- Jet Physics,'' Comput.\ Phys. Commun.\ {\bf 28}, 229 (1983). 3.T.Sjostrand, ``The Lund Monte Carlo For Jet Fragmentation And E+ E- Physics: Jetset Version 6.2,'' Comput.\Phys.Commun.39, 347 (1986). 4.T.Sjostrand and M.Bengtsson, ``The Lund Monte Carlo For Jet Fragmentation And E+ E- Physics. Jetset Version 6.3 : An Update,'' Comput. Phys. Commun. 43, 367 (1987). 5.H. U. Bengtsson and T. Sjostrand, ``The Lund Monte Carlo for Hadronic Processes: Pythia Version 4.8,'' Comput. Phys. Commun. 46, 43 (1987). 6.T. Sjostrand, ``High-energy physics event generation with PYTHIA 5.7 and JETSET 7.4,'' Comput. Phys. Commun. 82}, 74 (1994). 7.M.~Bertini, L.~Lonnblad and T.~Sjostrand, ``Pythia version 7-0.0: A proof-of-concept version,'' Comput. Phys. Commun. 134, 365 (2001) 8.T. Sjostrand, P. Eden, C. Friberg, L. Lonnblad, G. Miu, S. Mrenna and E. Norrbin, ``High-energy-physics event generation with PYTHIA 6.1,'' Comput. Phys. Commun. 135, 238 (2001) 9.T. Sjostrand, S. Mrenna and P. Skands, ``A Brief Introduction to PYTHIA 8.1,'' Comput. Phys. Commun. 178, 852 (2008)

3 Pythia project was begun in Pythia versions Double precision Pythia 4.8 (1987) Pythia (1993) Pythia 6.1 (1997) String fragmentation Jetset 6.3 (1986) Jetset (1993) Pythia 6.2 (2001) Pythia 6.3 (2003) C++ is now a slandered tool for scientific activities. Fortran is obsolete. Migrate pythia to C++ Pythia 8 (2008) C++ Pythia 6.4 (2006) C++ Pythia 7 ( 挫折 ) Generic administrative structure ThePEG (adopted by the Herwig++)

4 Massless relativistic string Lorentz 共変因果律 (causality) 閉じ込め半古典的 x p 1 but because y= p/ E x y 0 約 1fm

5 1+1D Motion of relativistic string H =p 1 2 m 1 2 p 2 2 m 2 2 x 1 x 2 dx i dt = H p i = p i E i, dp i dt = H x i =± m/ 一定の力 (linear potential) による運動 (Lorentz invariant) pt=t 0 t, E t= x 0 x x 0, t 0 m 2 =E 2 p 2 = 2 [ x 0 x 2 t 0 t 2 ] 時空座標における双曲線運動 yo-yo motion

6 String breaking E A = x A x 0, E B = x 0 x B p A =t A t 0, p B =t 0 t B m 2 2 = x A x B 2 t A t B 2 m 2 O x O,t O 質量は実数であるから Vertex A と B の間は空間的でありなんの因果関係もない特別な vertex はない. B x B,t B qbar A x A,t A q

7 Fragmentation function 破砕過程が quark と antiquak のどちらから行っても同じである (left-right symmetry) と要請すれば破砕関数の形は一意に決まる Lund symmetric fragmentation function: f z 1 z z a 1 1 z z a2 exp bm 2 z f z 1 z 1 za exp bm 2 z

8 String breaking procedure summary 1.Generate q-qbar pair: flavor u,d,s selection (uu, dd, ud) u u :d d : ss : c c=1:1:0.3: Gaussian transverse momentum 3. Selection of hadron state (L=0 S=0, or 1 for mesons) statistics solving Schreodinger eq. 4. Transverse mass fix dp d 2 k exp m 2 / S 3 : S 1 =3:1 dynamical effect should be taken into account 0.5, 5. Determine light cone momentum (longitudinal momentum) according to the Lund fragmentation function. K K K 0.6 D D D 0.75

stepwise で現れるモデル Wrong color field fluctuation Suppression of

9 Baryon production Diquak production model Popcorn model diquark のような non-fundamental quanta を導入せずに quark production だけでバリオン生成を記述 quak pair が stepwise で現れるモデル Wrong color field fluctuation Suppression of diquark-antidiquark pair production for 0.4 GeV diquark mass case: b P qq P q =0.1 b r r r g g r

10 Lund popcorn Mesons can produced between baryon and antibaryon production vertex.

11 T. Sjostrand and M. van Zijl, Phys. Rev. D36 (1987)2019 Pythia hadronic collisions Hard scattering (pqcd) + soft interaction (longitudinal excitation) + hadronization via string fragmentation. =K dx 1 dx 2 dt f 1 x 1, Q 2 QCD f 2 x 2, Q 2

12 Here pqcd means that partons are independent. パートンの平均密度があまり大きくないときを想定している 2 プロセス p T ~Q s に対する相互作用領域の横方向の面積 /Q s に対して全相互作用面積がハドロンサイズ 2 R h より小さくなくてはならない : ~ jet inel R h, ~ p s 2, 1 jet inel 1 p s 2 R h 2 1 jet p s R h 2 inel PQCD jet の断面積がこの条件を満たさないときはパートン同士の相互作用を考慮したモデルが必要

13 Parton Distributions EHLQ set 1 and 2 (kept for backwards compatibility.) DO sets 1 and 2 (kept for backwards compatibility.) GRV 92L CTEQ 3L, CTEQ3M, CTEQ 3D GRV 94L, GRV 94M, GRV94D CTEQ5L, CTEQ5M1 Parton distributions in neutron are obtained by isospin conjugation f u n = f d p a n d f d n = f u p

14 Initial-Final-State Radiation q qg, g g g, q q q, q q, leptonlepton DGLAP evolution equation Leading-log shower: energy-momentum conservation, coherence (different from NLO/NLL) also different from LL analytical calculations (energy-momentum conservation is a next-to-leading-log correction).

15 String-drawing issues Color flow については Matrix element の干渉項は無視 (1/N_c^2) g g g g Process in proton-proton collision

16 Eikonal Formulation for pqcd (HIJING) HIJING はすべての入射エネルギーで p0=2gev を使っているがそれは古い D0 を使っていてその PDF は small-x での gluon をカットしているからである

17 What to do? Soft Pomerons, strings Hard standard pqcd DEGLAP Semihard nonlinear interactions, BK, JIMWRK eq.

nenmatsu5c19_web.key

nenmatsu5c19_web.key KL π ± e νe + e - (Ke3ee) Ke3ee ν e + e - Ke3 K 0 γ e + π - Ke3 KL ; 40.67(%) Ke3ee K 0 ν γ e + π - Ke3 KL ; 40.67(%) Me + e - 10 4 10 3 10 2 : MC Ke3γ : data K L real γ e detector matter e e 10 1 0 0.02