The Sources of b-quarks
at the Tevatron
Leading order
“Flavor Creation”
is a factor of four
below the data!
Integrated b-quark Cross Section for PT > PTmin
1.0E+01
1.8 TeV
|y| < 1
1.0E+00
Cross Section (b)
 Important to have good leading (or leadinglog) order predictions of collider
observables.
 If the leading order estimates are within a
factor of two of the data, higher order
calculations might be expected to improve
the agreement.
 On the other hand, if the leading order
estimates are not within roughly a factor of
two of the data, one cannot expect higher
order calculations to improve the situation.
 If a leading order estimate is off by more
than a factor of two, it usually means that
one has overlooked something.
 “Something is goofy” (Rick Field, CDF B
Group Talk, December 3, 1999).
 http://www.phys.ufl.edu/~rfield/cdf/
CTEQ3L
1.0E-01
Pythia Creation
Isajet Creation
1.0E-02
NLO/LO “Flavor
Creation” is
40 roughly a factor
of two.
Herwig Creation
D0 Data
CDF Data
1.0E-03
5
10
15
20
25
30
35
PTmin (GeV/c)
Integrated b-quark Cross Section for PT > PTmin
4
1.8 TeV
all y
3
2
MRSR2/Herwig
MRSR2/Isajet
MRSR2/PythiaC3L
MRSR2/Pythia
1
5
10
15
20
25
30
35
40
PTmin (GeV)
Today’s talk available at my WEBsite.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 1
“Flavor Creation”
“Flavor Creation”
Integrated b-quark Cross Section for PT > PTmin
b-quark
1.0E+01
Proton
AntiProton
Underlying Event
1.8 TeV
|y| < 1
Underlying Event
Initial-State
Radiation
Cross Section (b)
1.0E+00
b-quark
“Flavor Creation” corresponds to
the production of a b-bbar pair
by gluon fusion or by annihilation
of light quarks.
CTEQ3L
1.0E-01
Pythia Creation
Isajet Creation
1.0E-02
Herwig Creation
D0 Data
CDF Data
Leading-Log order “Flavor
Creation” is a factor of four
below the data!

1.0E-03
5
10
15
20
25
30
35
40
PTmin (GeV/c)
Data from CDF and D0 for the integrated b-quark total cross section (PT > PTmin, |y| < 1) for
proton-antiproton collisions at 1.8 TeV compared with the QCD Monte-Carlo model
predictions of HERWIG, PYTHIA, and ISAJET for the “flavor creation” subprocesses. The
parton distribution functions CTEQ3L have been used for all three Monte-Carlo models. .
March 9, 2001
Rick Field - CDF B Group Meeting
Page 2
Other Sources of b-quarks
“Flavor Excitation”
Proton
“Parton Shower/Fragmentation”
b-quark
AntiProton
Underlying Event
Underlying Event
b-quark
Initial-State
Radiation
Proton
AntiProton
Underlying Event
Underlying Event
Initial-State
Radiation
gluon, quark,
or antiquark
b-quark
b-quark
“Flavor Excitation” corresponds to the
scattering of a b-quark (or bbar-quark) out of
the initial-state into the final-state by a gluon
or by a light quark or antiquark.


The b-bbar pair is created within a parton shower or during the
the fragmentation process of a gluon or a light quark or
antiquark. Here the QCD hard 2-to-2 subprocess involves
gluons and light quarks and antiquarks. This includes what is
referred to as “gluon splitting”.
“Flavor excitation” is, of course, very sensitive to the number of b-quarks within the proton (i.e.
the structure functions).
The Monte-Carlo models predictions for the “shower/fragmentation” contribution differ
considerably. This is not surprising since ISAJET uses independent fragmentation, while
HERWIG and PYTHIA do not; and HERWIG and PYTHIA modify the leading-log picture of
parton showers to include “color coherence effects”, while ISAJET does not.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 3
Inclusive b-quark Cross Section
Integrated b-quark Cross Section for PT > PTmin
Integrated b-quark Cross Section for PT > PTmin
1.0E+02
1.0E+02
Pythia CTEQ3L
Pythia GRV94L
Pythia Creation
Pythia Creation
Pythia Excitation
1.0E+01
Pythia Excitation
1.0E+01
Pythia Fragmentation
Pythia Fragmentation
D0 Data
CDF Data
Cross Section (b)
Cross Section (b)
D0 Data
1.0E+00
1.0E-01
1.0E-01
1.8 TeV
|y| < 1
1.8 TeV
|y| < 1
1.0E-02
CDF Data
1.0E+00
1.0E-02
1.0E-03
1.0E-03
5
10
15
20
25
30
35
40
5
10
PTmin (GeV/c)

15
20
25
30
35
40
PTmin (GeV/c)
Data on the integrated b-quark total cross section (PT > PTmin, |y| < 1) for proton-antiproton
collisions at 1.8 TeV compared with the QCD Monte-Carlo model predictions of PYTHIA
(CTEQ3L) and PYTHIA (GRV94L). The four curves correspond to the contribution from
flavor creation, flavor excitation, shower/fragmentation, and the resulting total.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 4
Inclusive b-quark Cross Section
Integrated b-quark Cross Section for PT > PTmin
Integrated b-quark Cross Section for PT > PTmin
1.0E+02
1.0E+02
Herwig CTEQ3L
Isajet CTEQ3L
Herwig Creation
Isajet Creation
Isajet Excitation
Isajet Fragmentation
Herwig Fragmentation
D0 Data
D0 Data
CDF Data
1.0E+00
1.0E-01
1.8 TeV
|y| < 1
1.0E-02
Herwig Excitation
1.0E+01
Cross Section (b)
Cross Section (b)
1.0E+01
CDF Data
1.0E+00
1.0E-01
1.8 TeV
|y| < 1
1.0E-02
1.0E-03
1.0E-03
5
10
15
20
25
30
35
40
5
10

15
20
25
30
35
40
PTmin (GeV/c)
PTmin (GeV/c)
Data on the integrated b-quark total cross section (PT > PTmin, |y| < 1) for proton-antiproton
collisions at 1.8 TeV compared with the QCD Monte-Carlo model predictions of ISAJET
(CTEQ3L) and HERWIG (CTEQ3L). The four curves correspond to the contribution from flavor
creation, flavor excitation, shower/fragmentation, and the resulting total.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 5
Inclusive b-quark Cross Section
Integrated b-quark Cross Section for PT > PTmin
Integrated b-quark Cross Section for PT > PTmin
1.0E+01
1.0E+01
1.8 TeV
|y| < 1
1.8 TeV
|y| < 1
1.0E+00
Cross Section ( b)
Cross Section (b)
1.0E+00
CTEQ3L
1.0E-01
CTEQ3L
1.0E-01
1.0E-02
1.0E-02
Pythia Excitation
Pythia Fragmentation
Isajet Excitation
Isajet Fragmentation
Herwig Excitation
Herwig Fragmentation
1.0E-03
1.0E-03
5
10
15
20
25
30
35
40
5
10
PTmin (GeV/c)

15
20
25
30
35
40
PTmin (GeV/c)
Predictions of HERWIG, PYTHIA, and ISAJET for the integrated b-quark total cross section (PT
> PTmin, |y| < 1) for proton-antiproton collisions at 1.8 TeV resulting from “flavor excitation” and
“shower/fragmentation”. The parton distribution functions CTEQ3L have been used for all three
Monte-Carlo models .
March 9, 2001
Rick Field - CDF B Group Meeting
Page 6
Inclusive b-quark Cross Section
Integrated b-quark Cross Section for PT > 5 GeV/c |Y| < 1
Integrated b-quark Cross Section for PT > 5 GeV/c |Y| < 1
25
12
1.8 TeV
1.8 TeV
10
15
Fragmentation
Flavor Excitation
Flavor Creation
10
Cross Section (b)
Cross Section (b)
20
8
Fragmentation
6
Flavor Excitation
Flavor Creation
4
5
2
0
0
Isajet CTEQ3L



Herwig CTEQ3L Pythia CTEQ3L
Herwig DO1.1
Pythia GRV94L
Isajet CTEQ3L
Herwig CTEQ3L
Pythia CTEQ3L
Predictions of ISAJET (CTEQ3L), HERWIG (CTEQ3L), PYTHIA (CTEQ3L), HERWIG (DO1.1),
and PYTHIA (GRV94L) for the integrated b-quark total cross section (PT > 5 GeV/c, |y| < 1) for
proton-antiproton collisions at 1.8 TeV. The contributions from flavor creation, flavor excitation,
and shower/fragmentation are shown together with the resulting sum (overall height of box).
The differences in the flavor excitation contribution are due to the different ways the models handle
the b-quark mass in this subprocess. However, it seems likely that at the Tevatron the flavor
excitation contribution to the b-quark cross section is comparable to or greater than the
contribution from flavor creation.
The QCD Monte-Carlo predictions differ considerably for the “shower/fragmentation”
contribution. However, at the Tevatron the fragmentation contribution to the b-quark cross section
might be comparable to the contribution from flavor creation.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 7
b-quark Rapidity Distribution
b-quark Rapidity Distribution PT > 5 GeV/c
b-quark Rapidity Distribution PT > 5 GeV/c
8
8
1.8 TeV
1.8 TeV
6
d/dY (b)
d/dY (b)
6
4
2
4
2
0
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
Rapidity Y

0
1
2
3
4
5
Rapidity Y
Pythia CTEQ3L
Pythia Creation
Herwig CTEQ3L
Herwig Creation
Pythia Excitation
Pythia Fragmentation
Herwig Excitation
Herwig Fragmentation
Predictions of PYTHIA (CTEQ3L), and HERWIG (CTEQ3L) for the b-quark rapidity distribution
(PT > 5 GeV/c) for proton-antiproton collisions at 1.8 TeV. The four curves correspond to the
contribution from flavor creation, flavor excitation, shower/fragmentation, and the resulting total.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 8
Simple Correlations
b-quark
direction
b-quark Correlations PT > 5 GeV/c |y|<1
Df
50%
Pythia (CTEQ3L) 1.8 TeV
40%
Percent of Events
“Toward”
“Away”
30%
Away
Toward
20%
10%
bbar-quark
0%
Flavor Creation
Flavor Excitation
Fragmentation
For events with a b-quark (PT > 5 GeV/c
|y|<1), probability of observing a bbar-quark
(PT > 5 GeV/c |y|<1).

Predictions of PYTHIA (CTEQ3L) for the probability of finding a bbar-quark with PT > 5 GeV/c
and |y|<1 for events with a b-quark with PT > 5 GeV/c and |y|<1 for proton-antiproton collisions at
1.8 TeV. The contribution from the “toward” (|Df|<90o) and the “away” (|Df|>90o) region of the bquark are shown for flavor creation, flavor excitation, and shower/fragmentation.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 9
Simple Correlations
b-quark Correlations PT > 5 GeV/c |y|<1
50%
q-quark Correlations PT > 5 GeV/c |y|<1
40%
30%
Away
Toward
20%
Percent of Events
Percent of Events
40%
30%
Away
Toward
20%
10%
10%
0%
0%
Flavor Creation

Isajet (CTEQ3L) 1.8 TeV
50%
Herwig (CTEQ3L) 1.8 TeV
Flavor Excitation
Fragmentation
Flavor Creation
Flavor Excitation
Fragmentation
Predictions of HERWIG (CTEQ3L) and ISAJET (CTEQ3L) for the probability of finding a bbarquark with PT > 5 GeV/c and |y|<1 for events with a b-quark with PT > 5 GeV/c and |y|<1 for
proton-antiproton collisions at 1.8 TeV. The contribution from the “toward” (|Df|<90o) and the
“away” (|Df|>90o) region of the b-quark are shown for flavor creation, flavor excitation, and
shower/fragmentation.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 10
b-quark Inclusive versus
Pair Cross Section
b-quark Inclusive versus Pair Cross Section
b-quark Correlations PT1 > 6.5 GeV/c
35%
100.0
1 = b-quark
2 = bbar-quark
1.8 TeV
30%
CDF Data
Probability of Anti-b Quark
b-quark Inclusive Cross
Section
PT1 > Ptmin |Y1|<1
Cross Section (b)
CDF Data
1.8 TeV
1
10.0
25%
20%
15%
10%
1 = b-quark
2 = bbar-quark
PT1 > 6.5 GeV
PT2 > PT2min
|Y1|<1 |Y2|<1
5%
1.0
0%
Pair Cross Section
PT1 > 6.5 GeV
PT2 > PTmin
|Y1|<1 |Y2|<1
2
0
10
15
20
PT2min
0.1
5
5
10
15
20
Divide the pair cross section 2 by the
single inclusive cross section 1.
PTmin (GeV/c)
 Data from CDF on the single b-quark inclusive cross section and the b-bbar pair cross
section at 1.8 TeV.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 11
Integrated Pair Cross Section
Integrated Pair Cross Section for PT2 > PT2min
b-quark Correlations PT1 > 6.5 GeV/c
1.0E+02
60%
Pythia CTEQ3L
1.8 TeV
1.8 TeV
Pythia Creation
Pythia CTEQ3L
50%
Pythia Creation
Pythia Excitation
Pythia Excitation
Pythia Fragmentation
Probability of Anti-b Quark
Pythia Fragmentation
1.0E+01
Cross Section (b)
CDF Data
1.0E+00
CDF Data
40%
1 = b-quark
2 = bbar-quark
PT1 > 6.5 GeV
PT2 > PT2min
|Y1|<1 |Y2|<1
30%
20%
1.0E-01
10%
1 = b-quark
2 = bbar-quark
PT1 > 6.5 GeV/c
PT2 > PT2min
|y1| < 1 |y2| < 1
1.0E-02
0%
0
5
10
15
20
PT2min
1.0E-03
0
5
10
15
20
PT2min (GeV/c)

Data from CDF on the b-bbar pair cross section and the b-bbar probability at 1.8 TeV compared
with the QCD Monte-Carlo predictions of PYTHIA (CTEQ3L). The four curves correspond to the
contribution from flavor creation, flavor excitation, shower/fragmentation, and the resulting total.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 12
Azimuthal Correlations
b-bbar Correlations: Azimuthal Df Distribution
b-quark
direction
0.07
Df
1.8 TeV
1 = b-quark
2 = bbar-quark
PT1 > 5 GeV
PT2 > 0
|Y1|<1 |Y2|<1
0.06
“Toward”
d/df (b/deg)
0.05
“Away”
0.04
0.03
"Toward"
"Away"
0.02
bbar-quark
0.01
0.00
0
30
60
90
120
150
180
Df (degrees)
Pythia CTEQ3L

Pythia Creation
Pythia Excitation
Pythia Fragmentation
QCD Monte-Carlo predictions of PYTHIA (CTEQ3L) for the b-bbar pair azimuthal cross section
d/df for |y|<1. The four curves correspond to the contribution from flavor creation, flavor
excitation, shower/fragmentation, and the resulting total at 1.8 TeV.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 13
b-quark Inclusive versus
Pair Cross Section
Integrated Pair Cross Section for PT2 > PT2min
Integrated b-quark Cross Section for PT > PTmin
1.0E+02
1.0E+02
Pythia CTEQ3L (fudged)
Pythia CTEQ3L (fudged)
1.8 TeV
Pythia Creation (x2)
Pythia Creation (x2)
1.0E+01
Pythia Excitation
1.0E+01
Pythia Excitation
Pythia Fragmentation
Cross Section (b)
Cross Section (b)
Pythia Fragmentation
D0 Data
1.0E+00
CDF Data
1.0E-01
1.8 TeV
|y| < 1
1.0E-02
CDF Data
1.0E+00
1.0E-01
1 = b-quark
2 = bbar-quark
PT1 > 6.5 GeV/c
|y1| < 1 |y2| < 1
1.0E-02
1.0E-03
1.0E-03
5
10
15
20
25
30
35
40
0

5
10
15
20
PT2min (GeV/c)
PTmin (GeV/c)
Data from CDF on the single b-quark inclusive cross section and the b-bbar pair cross section at
1.8 TeV compared with the QCD Monte-Carlo predictions of PYTHIA (CTEQ3L) where the flavor
creation term has been multiplied by a factor of 2 to take into account higher order corrections.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 14
Summary & Conclusions
“Flavor Creation”
Proton
“Flavor Excitation”
b-quark
AntiProton
Underlying Event
Underlying Event
Initial-State
Radiation
b-quark
Proton
“Parton Shower/Fragmentation”
b-quark
AntiProton
Underlying Event
Underlying Event
Proton
AntiProton
Underlying Event
Underlying Event
b-quark
Initial-State
Radiation
Initial-State
Radiation
gluon, quark,
or antiquark
b-quark
b-quark
All three sources are important at the Tevatron!
 One should not take the QCD Monte-Carlo model estimates of “flavor excitation”
and “shower/fragmentation” too seriously. The contributions from these
subprocesses are very uncertain and more work needs to be done. There are many
subtleties!
 However, it seems likely that all three sources are important at the Tevatron.
 In Run II we should be able experimentally to isolate the individual contributions
to b-quark production by studying b-bbar correlations in detail.
March 9, 2001
Rick Field - CDF B Group Meeting
Page 15