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

Sept. 22, 2006 Sino-German workshop 1

Bc Production at Hadron Colliders

Sino-German Workshop

Sept. 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


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

Bc Production at Hadron CollidersSino-German Workshop


Outlines

Introduction Hadronic Production at LHC and Tev

atron Generator for Bc hadronic productio

n (BCVEGPY and upgraded) Outlook


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 ηc, J/ψ ……& ηb,Υ ……‘Flavor non-singlet’ object vs ‘Flavor singlet’ obje

ct Thus Comparison and complement to the production of ηc, J/ψ ……& ηb,Υ ……


I. Introduction Hadron colliders: ‘unique place’ to pro

duce 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 an

d luminosity are not high enough Hadron colliders are ‘unique’ places.


I. Introduction Experimental observations of Bc and exc

ited states (in discovery stage) Theoretical estimates offer references for various e

xperimental observation (discovery) Bc is discovered the latest of the usual meson famil

y (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.


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 infor

mation associate with Bc in final states which may useful experimentally.



2). g-\bar{b} mechanism

i.e. via the sub-process:

3). g-c mechanism



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).



GM-VFN scheme to sum up 1) ……4)

Namely (equivalent):


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).



I. g-g mechanism only (extended FFN scheme):

Several uncertainties (LO), the main ones are the energy scale dependence, running and charm mass etc.



running, vs pT and y distribution of Bc:

solid-line: ; dished-line: LL

dotted-line: NLL .


solid line: dotted line: dashed line: dash-dotted line:


Energy scale Q2 uncertainty (Bc production) pT -and y-distribution:



LHC:

Uncertainty from mC

Tevatron:



II.g-g and g+\bar{b}, g+c mechanisms summed up in GM-VFN scheme.



pT-distribution of the Bc and B*c production (GM-VFN)

LHC:

Tevatron:



FFN gg-fusion

GM-VFN intrinsic + gg-fusion

LHC:

Tevatron:

Estended FFN gg-fusion quite close to GM-VFN intrinsic + gg-fusion, except small Pt region.



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.• ……


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)


PQCD Factorization LO calculation




To match the wave functions correctly (special attention on the spin structure), we start with the Mandelstam formulation on BS solution:

Here

Formulation:


Under the non-relativistic approximation (spin structure for color-singlet)

S-wave:

P-wave:

Introduce the definitions:



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).



From BS wave functions to the instantaneous (potential model) wave functions .

For S-wave, the instantaneous wave function

at origin



For P-wave, the instantaneous wave function

The derivative at origin



with the definitions:



We have the expansion

For S-wave only

and contribute

The kth term of the amplitude:



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: qc2

2=mc2, mb: qb1

2=mb2,

we must have either MP=MS, mcP=m cS and mbP=m bS S-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)



The subprocess pt and y distributions at

1P1

3P1 3P23P0

3P0

3P1

1P1

3P2



1P1

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)

1P13P1

3P0

3P2

3S1

1S01P1

3P1

3P0

3P21S0

3S1



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

3S1

1S0

1S03P23P21P1

1P1

3P13P1

3P0

3P0



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



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)



LHC:


Color-octet contributions are smaller than color-singlet ones.


Tevatron:


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.


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.


III. Generator for Bc hadronic production (versions BCVEGPY2)

BCVEGPY2 contains P-wave production additionally. For comparison, the S-wave ( and ) hadronic production via t

he 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;


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.


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.


• 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


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.


Uncertainties from quark mass, from energy scale, etc.

Suppress the uncertainties NLO PQCD calculations are helpful.

IV. Outlook

Suppress the uncertainties


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.

LHC TEVATRON


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 2

F and renormalization scale 2 at LHC

The upper edge of the band corresponds to 2F=4MPt

2; 2=MPt2/4;

and the lower edge corresponds to that of 2F=MPt

2/4; 2=4MPt2. The

solid line, the dotted line and the dashed line corresponds to that of 2

F=2 =MPt2; 2

F= 2= 4MPt2 ; 2

F= 2= MPt2/4.


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 2

F and renormalization scale 2 at TEVATRON

The upper edge of the band corresponds to 2F=4Mt

2; 2=Mt2/4; and

the lower edge corresponds to that of 2F=MPt

2/4; 2=4MPt2. The solid

line, the dotted line and the dashed line corresponds to that of 2F=2

=MPt2; 2

F= 2= 4MPt2 ; 2

F= 2= MPt2/4.


Progresses

NLO (αs5) precise calculations suppress the u

ncertainties from μF. Improve the connection PQCD factor and NR

QCD matrix element. Non-perturbative ‘intrinsic’ charm and bo

ttom contributions in GM-VFN (not important in preparation).

etcIn progress


Thank you 谢谢！

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

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