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强子对撞机上的 B物理研讨会

Hadronic Production of Bc(B*c) Meson Induced by the Hadronic Production of Bc(B*c) Meson Induced by the Heavy Quarks inside the Collision HadronsHeavy Quarks inside the Collision Hadrons

吴兴刚 吴兴刚 ( ( Xing-Gang Wu Xing-Gang Wu ))(ITP)(ITP)

In colarboration with Profs. Z.X. Zhang, C.F. Qiao and J.X. Wang

hep-ph/0509040

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• Calculation Technology---GM-VFN SchemeCalculation Technology---GM-VFN Scheme

• Results Under the GM-VFN and Comparison with Results Under the GM-VFN and Comparison with the Original FFN resultsthe Original FFN results

• BackgroundBackground

• A Simple Discussion and SummaryA Simple Discussion and Summary

Contents

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Bc Meson Experimental observation (CDF & D0) Lifetime τ, mass mBc Decays and Production (hadronic)

Special Interests The decay possibilities for the two heavy flavor comparable Vcb

2 mb

5/Vcs2

mc5~O(1) (annihilation~fBc

2Vcb2 )

To study two flavor simultaneously (Vcb, Vcs) To be a source of precisely tagged Bs mesons, to observe χc0, χc1, χc2 and hc etc via Bc weak decay etc.

1. Background

2005A) Why we need to study Bc

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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 pt regions

Our main concern is the hadronic production

BCVEGPY

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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 BCVEGPY2.0 ( High efficiency ! )efficiency ! )

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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.

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2. Calculation Technology---GM-VFN Scheme

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Subtraction method in GM-VFN schemeIntrinsic mechanism

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Comparison of evolved PDF and perturbative PDF (SUB)

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

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Subtraction method

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

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Total cross-section for Bc

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Total cross-section for Bc*

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Pt distributions at LHC

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Pt distributions at TEVATRON

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Comparison between GM-VFN and FFN at LHC

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Comparison between GM-VFN and FFN at TEV

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VFNGMt

FFNt

dpddpd

A Rough comparison of GM-VFN and FFN

%25

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GM-VFN

Strict FFN

Extended FFN

LHC 1S0 LHC 3S1

TEV 3S1TEV 1S0

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GM-VFN

GM-VFN gluon only

FFN

LHC 1S0 LHC 3S1

TEV 3S1TEV 1S0

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4. A Simple Discussion and Summary

• GM-VFN: consistent treat the mass effects and deal well with the double GM-VFN: consistent treat the mass effects and deal well with the double counting problem.counting problem.

• Intrinsic production may give sizable contribution in comparison with ntrinsic production may give sizable contribution in comparison with the gluon-gluon fusion mechanism.the gluon-gluon fusion mechanism.

• Intrinsic production is sizable in small pntrinsic production is sizable in small ptt region (< ~7GeV) and then region (< ~7GeV) and then drops fast.drops fast.• GM-VFN and FFN results are very close to each other at large pt region. Main difference is in small pptt region.

• The old FFN results still are reliable, especially in the large pThe old FFN results still are reliable, especially in the large p tt regions. regions.

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Thanks !

Backup Slides For BCVEGPY

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Y

New GRADE

I<=NEV

PYDUMP()

BEGIN

VEGASOPEN

IT=0 ； IT=IT+1

IGRADE==1

Read existed GRADEN

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

YN

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 BC

VEGPY

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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,GRV98MRST2001

Generate More Precise Grade with

Existed Grade Color-Octet Mechanism

Light Quark-Antiquark Annihilation

Eight Typical States for

Gluon-Gluon

TWO MORE:

IMIX

IMIXTYPE

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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 li

nes.

Our improved Helicity approach

First Great improvement By Z.Xu et

al.

S-Wave ProductionHelicity Amplitude

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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-li

ke 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 h

elicity amplitudes in a proper order for easy programming.

Choose proper way to calculate the fermion line

Schematic Steps For the Improved Helicity Approach

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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 FD

C 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