Bc Production at Hadron Colliders Sino-German Workshop Sept. 20-23, 2006 at DESY

1. Bc Production at Hadron CollidersSino-German WorkshopSept. 20-23, 2006 at DESY Chao-Hsi Chang (Zhao-Xi Zhang) ITP, AS, Beijing Collaborators: Y.Q. Chen; J.P.Ma; W.G. Ma; C.F. Qiao; J.-X. Wang; X.-G. Wu etc Sino-German workshop

2. Bc Production at Hadron CollidersSino-German Workshop • Based on: • PRD 46 3845, (1992), Erratum PRD50 6013, (1994); • PRD 48 4086 (1993); • PLB 364 78, (1995); • CPC 159 192, (2004); • EPJC 38 267,(2004); • PRD 70 114019, (2004); • PRD 71 074012, (2005); • PRD 72 114009, (2005); • CPC 174 241, (2006); • PRD 73 094022, (2006); • in preparation • etc Sino-German workshop

3. Outlines • Introduction • Hadronic Production at LHC and Tevatron • Generator for Bc hadronic production (BCVEGPY and upgraded) • Outlook Sino-German workshop

4. I. Introduction • To Understand the Production (S-wave & P-wave etc) under PQCD (NRQCD) Theoretical point of view (double heavy flavored) : Explicitly vs Hidden Bc and excited states vsηc, J/ψ ……& ηb,Υ…… ‘Flavor non-singlet’ object vs‘Flavor singlet’ object Thus Comparison and complement to the production of ηc, J/ψ ……& ηb,Υ…… Sino-German workshop

5. I. Introduction • Hadron colliders: ‘unique place’ to produce numerous events for Expt. Obs. Bc and excited states carry two flavors explicitly i.e. are different from those of ‘flavor hidden’. Its production: i). Pertubatively produce c \bar{c} b \bar{b} first ii). Of them, c \bar{b} form a Bc or excited state It is hard to produce NUMEROUS events if C.M. energy and luminosity are not high enough Hadron colliders are ‘unique’ places. Sino-German workshop

6. I. Introduction • Experimental observations of Bcand excited states (in discovery stage) Theoretical estimates offer references for various experimental observation (discovery) Bc is discovered the latest of the usual meson family (1998), has interesting properties (for QCD, heavy flavor physics and PM theory ect) To pick up the signal from so heavy background,the characters (Pt, y, etc) of the events for the ground state Bc and the excited states such as P-wave etc (indirect source of Bc events too) are important. Sino-German workshop

7. II. Hadronic Production of Bc at LHC and Tevatron • The mechanisms : 1). g-g mechanism: via sub-processes Complete αs4 pQCD calculation is adopted , so as to keep the two jet information associate with Bc in final states which may useful experimentally. Sino-German workshop

8. II. Hadronic Production of Bc at LHC and Tevatron 2). g-\bar{b} mechanism i.e. via the sub-process: 3). g-c mechanism Sino-German workshop

9. II. Hadronic Production of Bc at LHC and Tevatron The g-c mechanism is very similar to g-\bar{b} (not repeat) 4). The other mechanisms: q-\bar{q} (annihilation), c-c etc are small. To avoid ‘double counting’, with the help of GM-VFN scheme to sum up 1),……4). Sino-German workshop

10. II. Hadronic Production of Bc at LHC and Tevatron • GM-VFN scheme to sum up 1) ……4) Namely (equivalent): Sino-German workshop

11. II. Hadronic Production of Bc at LHC and Tevatron (S-wave) • S-wave production (Bc and B*c) I. g-g (fusion) mechanism only (extended FFN scheme). II.g-g (fusion) and g+\bar{b}, g+c mechanisms summed up (GM-VFN scheme). Sino-German workshop

12. II. Hadronic Production of Bc at LHC and Tevatron (S-wave) I. g-g mechanism only (extended FFN scheme): Several uncertainties (LO), the main ones are the energy scale dependence, running and charm mass etc. Sino-German workshop

13. II. Hadronic Production of Bc at LHC and Tevatron (S-wave) running, vs pT and y distribution of Bc: solid-line: ; dished-line: LL dotted-line: NLL . Sino-German workshop

14. II. Hadronic Production of Bc at LHC and Tevatron (S-wave) Energy scale Q2 uncertainty (Bc production) pT -and y-distribution: solid line: dotted line: dashed line: dash-dotted line: Sino-German workshop

15. II. Hadronic Production of Bc at LHC and Tevatron (S-wave) Uncertainty from mC Tevatron: LHC: Sino-German workshop

16. II. Hadronic Production of Bc at LHC and Tevatron (S-wave) II.g-g and g+\bar{b}, g+c mechanisms summed up in GM-VFN scheme. Sino-German workshop

17. II. Hadronic Production of Bc at LHC and Tevatron (S-wave) pT-distribution of the Bc and B*c production (GM-VFN) LHC: Tevatron: Sino-German workshop

18. II. Hadronic Production of Bc at LHC and Tevatron (S-wave) GM-VFN intrinsic + gg-fusion FFN gg-fusion LHC: Tevatron: Estended FFN gg-fusion quite close to GM-VFN intrinsic + gg-fusion, except small Pt region. Sino-German workshop

19. II. Hadronic Production of Bc at LHC and Tevatron (S-wave) GM-VFN scheme: • At large pT( ≥ 5.0 GeV) g-g fusion mechanism is dominant. • Thus at LHC and Tevatron in most pT region the contributions from the other mechanisms cannot be measured at all. • Intrinsic charm and bottom in non-perturbative nature can be measured neither. • …… Sino-German workshop

20. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) • P-wave excited Bc production (PM: Spectrum) ( , ) Color singlet production (as S-wave). Color octet production (scaling rule of NRQCD: may be more important for P-wave Bc state production than for S-wave one). Based on ‘extended FFN scheme’ (g-g fusion mechanism). Sino-German workshop

21. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) • PQCD Factorization LO calculation Sino-German workshop

22. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) Formulation: To match the wave functions correctly (special attention on the spin structure), we start with the Mandelstam formulation on BS solution: Here Sino-German workshop

23. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) Under the non-relativistic approximation (spin structure for color-singlet) S-wave: P-wave: Introduce the definitions: Sino-German workshop

24. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) Under NRQCD framework, the production is factorized For color-singlet components, we prefer to work out the precise connections between the matrix element and the wave functions (when lattice results are not available): and ( ). We would like to start with the Mandelstam formulation which is based on BS solutions (the color singlet components of excited states and ground state of Bc are treated at the same approximation level). Sino-German workshop

25. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) From BS wave functions to the instantaneous (potential model) wave functions . For S-wave, the instantaneous wave function at origin Sino-German workshop

26. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) For P-wave, the instantaneous wave function The derivative at origin Sino-German workshop

27. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) with the definitions: Sino-German workshop

28. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) We have the expansion For S-wave only and contribute The kth term of the amplitude: Sino-German workshop

29. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) For P-wave, the kth term of the amplitude: By straightforward calculation we obtain the cross section: Note: in MS,P : P2=(qb1+qc2)2, mc:qc22=mc2, mb:qb12=mb2, we must have either MP=MS, mcP=m cS and mbP=m bSS-wave, P-wave degenerate or MP ≠ MS, mcP ≠ m cS and mbP ≠ m bS S-wave, P-wave does not degenerate! We take MP=MS, mcP=m cS and mbP=m bS in the estimates mainly. (mb, mc involved) Sino-German workshop

30. 3P2 1P1 1P1 3P1 3P1 3P0 3P2 3P0 II. Hadronic Production of Bc at LHC and Tevatron (P-wave) The subprocess pt and y distributions at Sino-German workshop

31. 3S1 3S1 1S0 1P1 3P2 3P1 1P1 3P1 3P2 3P0 3P0 1S0 II. Hadronic Production of Bc at LHC and Tevatron (P-wave) At LHC, the P-wave & S-wave production, Pt and y distribution (Color-singlet: mc=1.5 GeV, mb=4.9 GeV and M=mc+mb) 1P1 Sino-German workshop

32. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) At TEVATRON, the P-wave & S-wave production, Pt and y distribution (mc=1.5 GeV, mb=4.9 GeV and M=mc+mb) 3S1 1S0 3P2 3P2 3S1 1P1 3P1 3P1 3P0 1P1 1S0 3P0 Sino-German workshop

33. II. Hadronic Production of Bc at LHC and Tevatron (P-wave) At TEVATRON and LHC, the P-wave production, the total cross section (mc=1.5 GeV, mb=4.9 GeV and M=mc+mb) Roughly speaking, summed cross sections for P-wave production can be so great as 60% of the ground state production Sino-German workshop

34. II. Hadronic Production of Bc at LHC and Tevatron (P-wave, color-octet) Formulation is similar (only ‘color-flue’ is different) Nonperturbative matrix element (for color-octet) can be estimated : and Sino-German workshop

35. II. Hadronic Production of Bc at LHC and Tevatron (P-wave, color-octet) LHC: Sino-German workshop

36. II. Hadronic Production of Bc at LHC and Tevatron (P-wave, color-octet) Tevatron: Color-octet contributions are smaller than color-singlet ones. Sino-German workshop

37. III. Generator for Bc hadronic production BCVEGPY Experimental observations of Bcand excited states Theoretical estimates offer references for experimental observation (discovery) Characters of the events, such as Pt, rapidity η etc, not only for Bc the ground state but also the excited states (indirect source of Bc events) such as P-wave etc are important in picking up the signal from backgroud. For experimental feasibility studies, efficient event generator is needed Efficiency and interface for simulations are very important. Sino-German workshop

38. III. Generator for Bc hadronic production BCVEGPY The version BCVEGPY2.0 (PYTHIA): • The amplitudes for the hadronic production of the color-singlet components corresponding to the four P-wave states and are included; • The amplitudes for P-wave production via the two color-octet components and are included; • The integration efficiency over the momentum fractions are improved. Version BCVEGPY2.1 (PYTHIA): Technical improvements are involved. Sino-German workshop

39. III. Generator for Bc hadronic production (versions BCVEGPY2) BCVEGPY2 contains P-wave production additionally. • For comparison, the S-wave ( and ) hadronic production via the light quark-antiquark annihilation mechanism is also included; • For convenience, 24 data files to record the information of the generated events in one run are added; • An additional file, parameter.for, is added to set the initial values of the parameters; • Two parameters, `IOUTPDF' and `IPDFNUM', are added to determine which type of PDFs to use; Sino-German workshop

40. III. Generator for Bc hadronic production (versions BCVEGPY2) • Two new parameters 'IMIX' (IMIX=0 or 1) and 'IMIXTYPE' (IMIXTYPE=1, 2 or 3) are added to meet the needs of generating the events for simulating `mixing' or `separate' event samples for various Bc and its excited states correctly; • One switch, `IVEGGRADE', is added to determine whether to use the existed importance sampling function to generate a more precise importance sampling function or not; • The color-flow decomposition for the amplitudes is rewritten by an approximate way, that is adopted in PYTHIA. Sino-German workshop

41. III. Generator for Bc hadronic production (BCVEGPY2.1) • Available under LINUX system (to meet the needs for most experimental group); • With a GNU C compiler, the events in respect to the experimental environments may simulated very conveniently (better modularity and less dependency among various modules) ; • A special and convenient executable-file run as default is available: the GNU command make compiles the codes requested by precise purpose with the help of a master makefile in the main code directory. Embedded in ATHENA (ATLAS group), Gauss (LHCb group) and SIMUB (CMS group) already. Sino-German workshop

42. IV. Outlook To meet Exp. Needs & better tests of QCD & NRQC • The massive mass effects: • FFN vs GM-VFN etc schemes • Decrease the uncertainties: • NLO calculations • …… Sino-German workshop

43. IV. Outlook Heavy quarks b & c production:below the threshold ‘decoupled’; above (close to) the threshold: effects great; much above the threshold: ‘zero mass’ 4 or 5 flavor FFN. General-mass variable-flavor-number GM-VFN scheme and fixed flavor number FFN scheme : gq-fusion: gg-fusion: `Double counting’ due to structure functions, so one must deduct it when summing up the contributions from the two mechanisms. Sino-German workshop

44. IV. Outlook Uncertainties from quark mass, from energy scale, etc. Suppress the uncertainties NLO PQCD calculations are helpful. Suppress the uncertainties Sino-German workshop

45. LHC TEVATRON Uncertainties in P-wave Bc Production due to different heavy quark masses (color-singlet) Pt distribution of the P-wave production: 1. mc=1.5 GeV, mb=4.9 GeV and M=mc+mb (without S-P wave splitting) ; 2. mc=1.7 GeV, mb=5.0 GeV and M=mc+mb (considering the S-P wave splitting). From LHC and TEVATRON results, it seems that we cannot attribute the effects only to the phase space difference. Sino-German workshop

46. Uncertainties in P-wave Bc Production due to factorization energy scale The summed Pt distribution and y distribution of all the P-wave states for different factorization scale 2Fand renormalization scale 2 at LHC The upper edge of the band corresponds to 2F=4MPt2; 2=MPt2/4; and the lower edge corresponds to that of 2F=MPt2/4; 2=4MPt2. The solid line, the dotted line and the dashed line corresponds to that of 2F=2 =MPt2; 2F=  2= 4MPt2 ; 2F=  2= MPt2/4. Sino-German workshop

47. Uncertainties in P-wave Bc Production due to factorization energy scale The summed Pt distribution and y distribution of all the P-wave states for different factorization scale 2Fand renormalization scale 2 at TEVATRON The upper edge of the band corresponds to 2F=4Mt2; 2=Mt2/4; and the lower edge corresponds to that of 2F=MPt2/4; 2=4MPt2. The solid line, the dotted line and the dashed line corresponds to that of 2F=2 =MPt2; 2F=  2= 4MPt2 ; 2F=  2= MPt2/4. Sino-German workshop

48. Progresses • NLO (αs5) precise calculations suppress the uncertainties from μF. • Improve the connection PQCD factor and NRQCD matrix element. • Non-perturbative ‘intrinsic’ charm and bottom contributions in GM-VFN (not important in preparation). • etc In progress Sino-German workshop

49. Thank you 谢 谢 ！ Sino-German workshop