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Sept. 22, 2006Sino-German workshop1 Bc Production at Hadron Colliders Sino-German Workshop Sept , 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

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Sept. 22, 2006Sino-German workshop2 Based on: PRD , (1992), Erratum PRD , (1994); PRD (1993); PLB , (1995); CPC , (2004); EPJC ,(2004); PRD , (2004); PRD , (2005); PRD , (2005); CPC , (2006); PRD , (2006); in preparation etc Bc Production at Hadron Colliders Sino-German Workshop

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Sept. 22, 2006Sino-German workshop3 Outlines Introduction Hadronic Production at LHC and Tevatron Generator for Bc hadronic production (BCVEGPY and upgraded) Outlook

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Sept. 22, 2006Sino-German workshop4 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 vs η c, J/ψ …… & η b,Υ …… ‘ Flavor non-singlet ’ object vs ‘ Flavor singlet ’ object Thus Comparison and complement to the production of η c, J/ψ …… & η b,Υ ……

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Sept. 22, 2006Sino-German workshop5 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.

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Sept. 22, 2006Sino-German workshop6 I. Introduction Experimental observations of Bc and 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.

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Sept. 22, 2006Sino-German workshop7 II. Hadronic Production of Bc at LHC and Tevatron The mechanisms : 1). g-g mechanism: via sub-processes Complete α s 4 pQCD calculation is adopted, so as to keep the two jet information associate with Bc in final states which may useful experimentally.

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Sept. 22, 2006Sino-German workshop8 II. Hadronic Production of Bc at LHC and Tevatron 2). g-\bar{b} mechanism i.e. via the sub-process: 3). g-c mechanism

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Sept. 22, 2006Sino-German workshop9 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).

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Sept. 22, 2006Sino-German workshop10 II. Hadronic Production of Bc at LHC and Tevatron GM-VFN scheme to sum up 1) …… 4) Namely (equivalent):

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Sept. 22, 2006Sino-German workshop11 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).

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Sept. 22, 2006Sino-German workshop12 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.

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Sept. 22, 2006Sino-German workshop13 II. Hadronic Production of Bc at LHC and Tevatron (S-wave) running, vs p T and y distribution of Bc: solid-line: ; dished-line: LL dotted-line: NLL.

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Sept. 22, 2006Sino-German workshop14 solid line: dotted line: dashed line: dash-dotted line: II. Hadronic Production of Bc at LHC and Tevatron (S-wave) Energy scale Q 2 uncertainty (Bc production) p T -and y-distribution:

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Sept. 22, 2006Sino-German workshop15 II. Hadronic Production of Bc at LHC and Tevatron (S-wave) LHC: Uncertainty from m C Tevatron:

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Sept. 22, 2006Sino-German workshop16 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.

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Sept. 22, 2006Sino-German workshop17 II. Hadronic Production of Bc at LHC and Tevatron (S-wave) p T -distribution of the Bc and B * c production (GM-VFN) LHC: Tevatron:

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Sept. 22, 2006Sino-German workshop18 II. Hadronic Production of Bc at LHC and Tevatron (S-wave) FFN gg-fusion GM-VFN intrinsic + gg-fusion LHC: Tevatron: Estended FFN gg-fusion quite close to GM-VFN intrinsic + gg-fusion, except small P t region.

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Sept. 22, 2006Sino-German workshop19 II. Hadronic Production of Bc at LHC and Tevatron (S-wave) GM-VFN scheme: At large p T ( ≥ 5.0 GeV) g-g fusion mechanism is dominant. Thus at LHC and Tevatron in most p T region the contributions from the other mechanisms cannot be measured at all. Intrinsic charm and bottom in non-perturbative nature can be measured neither. ……

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Sept. 22, 2006Sino-German workshop20 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). II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop21 PQCD Factorization LO calculation II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop22 II. Hadronic Production of Bc at LHC and Tevatron (P-wave) To match the wave functions correctly (special attention on the spin structure), we start with the Mandelstam formulation on BS solution: Here Formulation:

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Sept. 22, 2006Sino-German workshop23 Under the non-relativistic approximation (spin structure for color- singlet) S-wave: P-wave: Introduce the definitions: II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop24 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). II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop25 From BS wave functions to the instantaneous (potential model) wave functions. For S-wave, the instantaneous wave function at origin II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop26 For P-wave, the instantaneous wave function The derivative at origin II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop27 with the definitions: II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop28 We have the expansion For S-wave only andcontribute The k th term of the amplitude: II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop29 For P-wave, the k th term of the amplitude: By straightforward calculation we obtain the cross section: Note: in M S,P : P 2 =(q b1 +q c2 ) 2, m c : q c2 2 =m c 2, m b : q b1 2 =m b 2, we must have either M P =M S, m cP =m cS and m bP =m bS S-wave, P-wave degenerate or M P ≠ M S, m cP ≠ m cS and m bP ≠ m bS S-wave, P-wave does not degenerate ! We take M P =M S, m cP =m cS and m bP =m bS in the estimates mainly. (m b, m c involved) II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop30 The subprocessp t and y distributions at 1P11P1 3P13P1 3P23P2 3P03P0 3P03P0 3P13P1 1P11P1 3P23P2 II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop31 1P11P1 At LHC, the P-wave & S-wave production, P t and y distribution (Color-singlet: m c =1.5 GeV, m b =4.9 GeV and M=m c +m b ) 1P11P1 3P13P1 3P03P0 3P23P2 3S13S1 1S01S0 1P11P1 3P13P1 3P03P0 3P23P2 1S01S0 3S13S1 II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop32 At TEVATRON, the P-wave & S-wave production, P t and y distribution (m c =1.5 GeV, m b =4.9 GeV and M=m c +m b ) 3S13S1 3S13S1 1S01S0 1S01S0 3P23P2 3P23P2 1P11P1 1P11P1 3P13P1 3P13P1 3P03P0 3P03P0 II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop33 At TEVATRON and LHC, the P-wave production, the total cross section (m c =1.5 GeV, m b =4.9 GeV and M=m c +m b ) Roughly speaking, summed cross sections for P-wave production can be so great as 60% of the ground state production II. Hadronic Production of Bc at LHC and Tevatron (P-wave)

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Sept. 22, 2006Sino-German workshop34 Formulation is similar (only ‘ color-flue ’ is different) Nonperturbative matrix element (for color-octet) can be estimated : and II. Hadronic Production of Bc at LHC and Tevatron (P-wave, color-octet)

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Sept. 22, 2006Sino-German workshop35 II. Hadronic Production of Bc at LHC and Tevatron (P-wave, color-octet) LHC:

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Sept. 22, 2006Sino-German workshop36 Color-octet contributions are smaller than color-singlet ones. II. Hadronic Production of Bc at LHC and Tevatron (P-wave, color-octet) Tevatron:

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Sept. 22, 2006Sino-German workshop37 III. Generator for Bc hadronic production BCVEGPY Experimental observations of Bc and 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.

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Sept. 22, 2006Sino-German workshop38 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.

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Sept. 22, 2006Sino-German workshop39 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;

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Sept. 22, 2006Sino-German workshop40 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.

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Sept. 22, 2006Sino-German workshop41 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.

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Sept. 22, 2006Sino-German workshop42 The massive mass effects: FFN vs GM-VFN etc schemes Decrease the uncertainties: NLO calculations …… IV. Outlook To meet Exp. Needs & better tests of QCD & NRQC

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Sept. 22, 2006Sino-German workshop43 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.

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Sept. 22, 2006Sino-German workshop44 Uncertainties from quark mass, from energy scale, etc. Suppress the uncertainties NLO PQCD calculations are helpful. IV. Outlook Suppress the uncertainties

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Sept. 22, 2006Sino-German workshop45 Uncertainties in P-wave Bc Production due to different heavy quark masses (color-singlet) P t distribution of the P-wave production: 1. m c =1.5 GeV, m b =4.9 GeV and M=m c +m b (without S-P wave splitting) ; 2. m c =1.7 GeV, m b =5.0 GeV and M=m c +m b (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. LHC TEVATRON

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Sept. 22, 2006Sino-German workshop46 Uncertainties in P-wave Bc Production due to factorization energy scale The summed P t distribution and y distribution of all the P-wave states for different factorization scale 2 F and renormalization scale 2 at LHC The upper edge of the band corresponds to 2 F =4M Pt 2 ; 2 =M Pt 2 /4; and the lower edge corresponds to that of 2 F =M Pt 2 /4; 2 =4M Pt 2. The solid line, the dotted line and the dashed line corresponds to that of 2 F = 2 =M Pt 2 ; 2 F = 2 = 4M Pt 2 ; 2 F = 2 = M Pt 2 /4.

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Sept. 22, 2006Sino-German workshop47 Uncertainties in P-wave Bc Production due to factorization energy scale The summed P t distribution and y distribution of all the P-wave states for different factorization scale 2 F and renormalization scale 2 at TEVATRON The upper edge of the band corresponds to 2 F =4M t 2 ; 2 =M t 2 /4; and the lower edge corresponds to that of 2 F =M Pt 2 /4; 2 =4M Pt 2. The solid line, the dotted line and the dashed line corresponds to that of 2 F = 2 =M Pt 2 ; 2 F = 2 = 4M Pt 2 ; 2 F = 2 = M Pt 2 /4.

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Sept. 22, 2006Sino-German workshop48 Progresses NLO (α s 5 ) precise calculations suppress the uncertainties from μ F. 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

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Sept. 22, 2006Sino-German workshop49 Thank you 谢 谢 ！

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