1. 1 强子对撞机上的 B 物理研讨会 Hadronic Production of Bc(B*c) Meson Induced by the Heavy Quarks inside the Collision Hadrons 吴兴刚 ( Xing-Gang Wu ) (ITP) In colarboration with Profs. Z.X. Zhang, C.F. Qiao and J.X. Wang hep-ph/0509040

2. 2 Calculation Technology---GM-VFN Scheme Results Under the GM-VFN and Comparison with the Original FFN results Background A Simple Discussion and Summary A Simple Discussion and Summary Contents

3. 3  Bc Meson Experimental observation (CDF & D0) Lifetime τ, mass m Bc Decays and Production (hadronic)  Special Interests The decay possibilities for the two heavy flavor comparable V cb 2 m b 5 /V cs 2 m c 5 ~O(1) (annihilation~f Bc 2 V cb 2 ) To study two flavor simultaneously (V cb, V cs ) To be a source of precisely tagged Bs mesons, to observe χ c0, χ c1, χ c2 and h c etc via Bc weak decay etc. 1. Background 2005 A) Why we need to study Bc

4. 4 Mechanisms for the hadronic production A) Gluon-gluon fusion ---------------- dominant color-singlet: S-wave: Bc ( 1), Bc*(~2.6); P-wave: Bc*(~ 0.5) color-octet: S-wave: Bc+Bc* (~0.2) B) Quark-antiquark annihilation -----must be light quark color-singlet: S-wave: Bc+Bc* (<0.1) C) Gluon + c-quark (anti-b) -------- intrinsic c or b---GM-VFN scheme color-singlet: S-wave: Bc, Bc* (~1) in small p t regions Our main concern is the hadronic production BCVEGPY

5. 5 B) Present Status of BCVEGPY ATLAS (ANTNA?) --- in collaboration with Prof. Z.X. Zhang, Chafik Driouichi and P. Eerola (Lund U.) CMS (SIMUB) --- in collaboration with Prof. Z.X. Zhang, G.M. Chen, S.H. Zhang, A.A. Belkov and S. Shulge (IHEP) D0 --- in collaboration with Prof. Z.X. Zhang, Y.Jiang, N. Han and W.G. Ma (CUST) TEVATRON RUN II --- Generated data used in hep-ex/0505076 (new results of CDF) for analyzing data, with Vaia Papadimitriou BCVEGPY2.0 ( High efficiency ! )

6. 6 C) Why studying the intrinsic mechanism ? 1)In most of the present calculations, extended FFN scheme is applied. Including BCVEGPY. 2)Prof.Qiao has studied the intrinsic charm mechanism to the hadronic production of J/\Psi. 3)Interesting to study its function to the hadronic production of Bc. Lower order in  s and the phase space distribution compensate its higher order in PDF. D) Why GM-VFN scheme and not FFN ? 1)The mass effects can be consistent treated in both PDF and hard scattering amplitude. 2)The double counting of gluon-gluon fusion and intrinsic mechanism can be treated well.

7. 7 2. Calculation Technology---GM-VFN Scheme

8. 8 Subtraction method in GM-VFN scheme Intrinsic mechanism

9. 9 Comparison of evolved PDF and perturbative PDF (SUB)

10. 10

11. 11 For hadronic production, we always include a small pt cut, so the fifth term shall be studied here

12. 12 Subtraction method 3. Results Under the GM-VFN and Comparison with the Original FFN results

13. 13 Total cross-section for Bc

14. 14 Total cross-section for Bc*

15. 15 Pt distributions at LHC

16. 16 Pt distributions at TEVATRON

17. 17 Comparison between GM-VFN and FFN at LHC

18. 18 Comparison between GM-VFN and FFN at TEV

19. 19 A Rough comparison of GM-VFN and FFN

20. 20 GM-VFN Strict FFN Extended FFN LHC 1S0LHC 3S1 TEV 3S1 TEV 1S0

21. 21 GM-VFN GM-VFN gluon only FFN LHC 1S0 LHC 3S1 TEV 3S1 TEV 1S0

22. 22 4. A Simple Discussion and Summary GM-VFN: consistent treat the mass effects and deal well with the double counting problem. ntrinsic production may give sizable contribution in comparison with the gluon-gluon fusion mechanism. Intrinsic production may give sizable contribution in comparison with the gluon-gluon fusion mechanism. ntrinsic production is sizable in small p t region (< ~7GeV) and then drops fast. Intrinsic production is sizable in small p t region (< ~7GeV) and then drops fast. p t GM-VFN and FFN results are very close to each other at large pt region. Main difference is in small p t region. The old FFN results still are reliable, especially in the large p t regions.

23. 23 Thanks ! Backup Slides For BCVEGPY

24. 24 Y New GRADE I<=NEV PYDUMP() BEGIN VEGASOPEN IT=0 ； IT=IT+1 IGRADE==1 Read existed GRADE N NUM<=NUMBER NUM=0 ； NUM=NUM+1 I=0 ； I=I+1 PYEVNT PYFILL() END CALL PHPOINT() CALL AMP2UP() CALL PHPOINT() CALL AMP2UP() N Y N Y EVNTINIT ， PYINIT ， UPINIT Y Y N N IT<=ITMX USING PYTHIA SUBROUTINES TO GENERATE FULL EVENTS IMPROVE THE MONTE CARLO EFFICIENCY BASIC INPUT: NEV,NUMBER,ITMX,VEGASOPEN The Whole Flowchart for BCVEGPY

25. 25 BCVEGPY2.0 designed for all the considered color-singlet/octet S-wave and P-wave states. The flow chart is quite the same as that of the first version BCVEGPY1.0. CTEQ6L,GRV98 MRST2001 Generate More Precise Grade with Existed Grade Color-Octet Mechanism Light Quark-Antiquark Annihilation Eight Typical States for Gluon-Gluon TWO MORE: IMIX IMIXTYPE

26. 26 Derivation of Bc Meson Generator BCVEGPY1.0 Divide the whole amplitude into several gauge invariant groups, and simplify each group with proper gauges. Find out all the independent fermion lines “bases” Simplify the fermion lines Expande all the Feynman amplitude over these bases and find out the corresponding coefficients Decompose the diagram Numerical calculation Subtle points ： 1 ： how to choose gauge in each group ； 2 ： stability of numerical calculation ； 3 ： no help for the massive fermion lines. Our improved Helicity approach First Great improvement By Z.Xu etal. S-Wave Production Helicity Amplitude

27. 27 Unit the Same Type Terms As Much As Possible find out all the independent fermion lines without taking into account the color factor and the scalar part of the propagator with these independent fermion lines construct all the necessary QED-like Feynman diagrams using basic QED-like Feynman diagrams, with the help of the gluon-gluon and quark- quark symmetry, construct all the QED-feynman diagrams. And decompose all the QCD- like diagrams to be QED-like and also expand over the basic QED-like diagrams. consider the color factors and the scalar part of the proporgator and get the whole helicity amplitude. Arrange all the different helicity amplitudes in a proper order for easy programming. Choose proper way to calculate the fermion line Schematic Steps For the Improved Helicity Approach

28. 28 The amplitude of the P-wave production involve the derivation over the relative momentum of the constituent quark, so other than taking the helicity approach as has been done in the S-wave case, we take FDC program to do such kind of work for the P-wave production. Amplitudes for color-Octet S-wave states Improved Helicity amplitude approach ! The main difference for color-singlet S-wave is the color flow Derivation of Bc Meson Generator BCVEGPY2.0 Amplitudes for color-Singlet p-wave states