B Physics: QCD Monte Carlo
Model Predictions
Rick Field - University of Florida
and
Keith Ellis - Fermilab
QCD Run II Workshop
http://www.phys.ufl.edu/~rfield/cdf/
Goals:
• Compare the LO parton level predictions of Herwig, Isajet,
and Pythia with the NLO MRSR2 predictions.
• Compare the LO parton level predictions with the LO
hadron level predictions (Herwig, Isajet, Pythia).
• Compare the LO hadron level predictions of Herwig, Isajet,
and Pythia.
Outline:
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New
Integrated Cross Sections (parton level)
Transverse Momentum Distributions (parton level)
Pseudo-Rapidity & Rapidity Distributions (parton level)
Integrated Cross Sections (hadron level)
Transverse Momentum Distributions (hadron level)
PT Distributions Parton/Hadron (fragmentation)
Strange Quark Production fs/(fu+fd) (fragmentation)
Y and η Distributions Hadron versus Parton
Azimuthal ∆φ Correlations Hadron versus Parton
PT Correlations Hadron versus Parton (PT1-PT2)
Pseudo-Rapidity Correlations: dσ
σ/dη
η1dη
η2 & R(η
η1,η
η2)
Comparisons between 1.8 TeV and 2.0 TeV
QCD Monte Carlo Models (default parameters):
Herwig 5.9 (DO1.1, Λ = 0.18 GeV)
Isajet 7.32 (CTEQ3L, Λ = 0.20 GeV)
Pythia 6.115 (GRV94LO, Λ = 0.23 GeV)
Pythia 6.115 (CTEQ3L, Λ = 0.18 GeV)
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 1 of 26
B Physics: Cross Sections
Parton Level: Integrated b-quark Cross Section for PT > PTmin
Integrated b-quark Cross Section for PT > PTmin
σ µb
1.0E+02
1.8 TeV
all y
1.0E+01
1.0E+00
1.0E-01
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
1.0E-02
PythiaC3L b-quark
Pythia b-quark
1.0E-03
5
10
15
20
25
30
35
40
PTmin (GeV)
Plot shows σ(PT>PTmin) (in µb) for b-quarks at 1.8 TeV (all Y).
Parton Level: Integrated b-quark Cross Section for PT > PTmin
Integrated b-quark Cross Section for PT > PTmin
σ µb
1.0E+02
1.8 TeV
all y
1.0E+01
1.0E+00
1.0E-01
MRSR2 b-quark
Herwig b-quark times 2
1.0E-02
Isajet b-quark times 2
Pythia b-quark times 2
1.0E-03
5
10
15
20
25
30
35
40
PTmin (GeV)
Plot shows σ(PT>PTmin) (in µb) for b-quarks at 1.8 TeV (all Y). Herwig, Isajet,
and Pythia have been increased by a factor of two.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 2 of 26
B Physics: Cross Sections
Parton Level: Ratio MRSR2/Monte-Carlos
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)
Plot shows the ratio of σ(PT>PTmin) for b-quarks at 1.8 TeV (all Y) from MRSR2
to Herwig, Isajet, Pythia, and PythiaC3L.
Parton Level: Integrated b-quark Cross Section for PT > PTmin
Integrated b-quark Cross Section for PT > PTmin
σ µb
1.0E+01
1.8 TeV
|y| < 1
1.0E+00
1.0E-01
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
Pythia b-quark
1.0E-02
D0 Data
CDF Data
1.0E-03
5
10
15
20
25
30
35
40
PTmin (GeV)
Plot shows σ(PT>PTmin) (in µb) for b-quarks at 1.8 TeV (|Y|<1).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 3 of 26
B Physics: Cross Sections
Parton Level: Integrated b-quark Cross Section for PT > PTmin
Integrated b-quark Cross Section for PT > PTmin
σ µb
1.0E+02
1.8 TeV
|y| < 1
1.0E+01
1.0E+00
MRSR2 b-quark times 2
1.0E-01
Herwig b-quark times 4
Isajet b-quark times 4
Pythia b-quark times 4
1.0E-02
D0 Data
CDF Data
1.0E-03
5
10
15
20
25
30
35
40
PTmin (GeV)
Plot shows σ(PT>PTmin) (in µb) for b-quarks at 1.8 TeV (|Y|<1). MRSR2 has been
increased by a factor of two and Herwig, Isajet, and Pythia have been increased by a
factor of four.
Parton Level: Ratio MRSR2/Monte-Carlos
Integrated b-quark Cross Section for PT > PTmin
4
1.8 TeV
|y| < 1
3
2
MRSR2/Herwig
MRSR2/Isajet
MRSR2/Pythia
1
5
10
15
20
25
30
35
40
PTmin (GeV)
Plot shows the ratio of σ(PT>PTmin) for b-quarks at 1.8 TeV (|Y| < 1) from MRSR2
to Herwig, Isajet, and Pythia.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 4 of 26
B Physics: Cross Sections
Parton Level: Fraction |Y| < 1 of the b-quark Cross Section
Fraction |y|<1 of the Integrated b-quark Cross Section
70%
60%
50%
40%
1.8 TeV
30%
5
10
15
20
25
30
35
40
PTmin (GeV)
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
Pythia b-quark
Plot shows the fraction |Y| < 1 of the b-quark integrated cross section (PT < PTmin).
Parton Level: Fraction |η
η | < 1 of the b-quark Cross Section
Fraction |eta|<1 of the Integrated b-quark Cross Section
70%
60%
50%
40%
1.8 TeV
30%
5
10
15
20
25
30
35
40
PTmin (GeV)
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
Pythia b-quark
Plot shows the fraction |η
η | < 1 of the b-quark integrated cross section (PT < PTmin).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 5 of 26
B Physics: PT Distributions
Parton Level: Transverse Momentum Distribution (|η
η | < 1)
Transverse Momentum Distribution dσ/dPT
µb/GeV
1.0E+01
1.8 TeV
|eta| < 1
1.0E+00
1.0E-01
1.0E-02
1.0E-03
MRSR2 b-quark
Herwig b-quark
1.0E-04
Isajet b-quark
Pythia b-quark
1.0E-05
5
10
15
20
25
30
35
40
45
50
45
50
PT (GeV)
Plot shows dσ
σ/dPT (in µb/GeV) for b-quarks at 1.8 TeV (|η
η |<1).
Parton Level: Transverse Momentum Distribution (|η
η | < 1)
Transverse Momentum Distribution (b-quark)
4
1.8 TeV
|eta| < 1
3
2
1
5
10
15
20
25
30
35
40
PTmin (GeV)
MRSR2/Isajet
MRSR2/Herwig
MRSR2/Pythia
Plot shows the ratio of dσ
σ/dPT for b-quarks at 1.8 TeV (|η
η | < 1) from MRSR2 to
Herwig, Isajet, and Pythia.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 6 of 26
B Physics: Pseudo-Rapidity Distributions
Parton Level: Pseudo-Rapidity Distributions (PT > 5 GeV)
Pseudo-Rapidity Distribution
dσ/dη (µb)
4
1.8 TeV
PT > 5 GeV
3
2
1
0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
PythiaC3L b-quark
Pythia b-quark
Plot shows dσ
σ/dη
η (in µb) for b-quarks at 1.8 TeV (PT > 5 GeV).
Parton Level: Pseudo-Rapidity Distributions (PT > 5 GeV)
Pseudo-Rapidity Distribution (normalized to 1)
(1/N)dN/dη
0.20
1.8 TeV
PT > 5 GeV
0.15
0.10
0.05
0.00
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
PythiaC3L b-quark
Pythia b-quark
Plot shows (1/N)dN/dη
η (normalized to 1) for b-quarks at 1.8 TeV (PT > 5 GeV).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 7 of 26
B Physics: Rapidity Distributions
Parton Level: Rapidity Distributions (PT > 5 GeV)
Rapidity Distribution
dσ/dY (µb)
4
1.8 TeV
PT > 5 GeV
3
2
1
0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Rapidity Y
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
Pythia b-quark
Plot shows dσ
σ/dY (in µb) for b-quarks at 1.8 TeV (PT > 5 GeV).
Parton Level: Rapidity Distributions (PT > 5 GeV)
Rapidity Distribution (normalized to 1)
(1/N)dN/dY
0.25
1.8 TeV
PT > 5 GeV
0.20
0.15
0.10
0.05
0.00
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Rapidity Y
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
Pythia b-quark
Plot shows (1/N)dN/dY (normalized to 1) for b-quarks at 1.8 TeV (PT > 5 GeV).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 8 of 26
B Physics: Cross Sections
Hadron Level: Integrated B-quark Cross Section for PT > PTmin
Integrated Cross Section for PT > PTmin
σ µb
1.0E+01
B-mesons = (B+,B0,Bs0)
1.0E+00
1.8 TeV
|eta| < 1
1.0E-01
b-quark
Pythia b-quark
Pythia B-mesons
1.0E-02
Isajet b-quark
Isajet B-mesons
1.0E-03
B-mesons
Herwig b-quark
Herwig B-mesons
1.0E-04
5
10
15
20
25
30
35
40
45
PTmin (GeV)
Plot shows σ(PT>PTmin) (in µb) for B-mesons (B+,B0,Bs0) and b-quarks at 1.8 TeV
(|η
η | < 1).
Hadron Level: Integrated B-quark Cross Section for PT > PTmin
Integrated Cross Section for PT > PTmin
σ µb
1.0E+01
B-mesons = (B+,B0,Bs0)
1.0E+00
Isajet at 1.8 TeV
|eta| < 1
1.0E-01
1.0E-02
B-mesons from
bottom quarks
1.0E-03
1.0E-04
B-mesons from
top quarks
1.0E-05
1.0E-06
1.0E-07
5
10
15
20
25
30
35
40
45
PTmin (GeV)
Plot shows σ(PT>PTmin) (in µb) for B-mesons (B+,B0,Bs0) from b and t-quarks 1.8
TeV (|η
η | < 1).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 9 of 26
B Physics: PT Distributions
Parton & Hadron Level: Transverse Momentum Distribution (|η
η | < 1)
Transverse Momentum Distribution dσ/dPT
µb/GeV
1.0E+00
B-mesons = (B+,B0,Bs0)
1.8 TeV
|eta| < 1
1.0E-01
1.0E-02
Pythia b-quark
b-quark
Pythia B-mesons
1.0E-03
Isajet b-quark
Isajet B-mesons
1.0E-04
B-mesons
Herwig b-quark
Herwig B-mesons
1.0E-05
5
10
15
20
25
30
35
40
45
50
PT (GeV)
Plot shows dσ
σ/dPT (in µb/GeV) for B-mesons (B+,B0,Bs0) and for the b-quark at 1.8
TeV (|η
η |<1).
Hadron/Parton Level: Transverse Momentum Distribution (|η
η | < 1)
(B-meson)/(b-quark) Ratio versus PT
100%
B-mesons = (B+,B0,Bs0)
80%
60%
40%
1.8 TeV
|eta| < 1
20%
0%
5
10
15
20
25
30
35
40
45
50
PT (GeV)
Pythia
Herwig
Isajet
Plot shows the ratio of dσ
σ/dPT (|η
η| < 1) for B-mesons (B+,B0,Bs0) to b-quark at 1.8
TeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 10 of 26
B Physics: PT Distributions
Hadron Level: B+ Meson Transverse Momentum Distribution (|Y| < 1)
B+ Meson Transverse Momentum Distribution
µb/GeV
1.0E+00
1.8 TeV
|Y| < 1
1.0E-01
1.0E-02
1.0E-03
1.0E-04
5
10
15
20
25
30
35
40
PT (GeV)
Herwig B+ meson
Isajet B+ meson
Pythia B+ meson
CDF Data
CDF Data
CDF Data
Plot shows dσ
σ/dPT (in µb/GeV) for B+ mesons at 1.8 TeV (|Y| < 1).
Hadron Level: B+ Meson Transverse Momentum Distribution (|Y| < 1)
B+ Meson Transverse Momentum Distribution
µb/GeV
1.0E+00
1.8 TeV
|Y| < 1
1.0E-01
1.0E-02
1.0E-03
1.0E-04
5
10
15
20
25
30
35
40
PT (GeV)
Herwig times 4
Isajet times 4
Pythia times 4
CDF Data
CDF Data
CDF Data
Plot shows dσ
σ/dPT (in µb/GeV) for B+ mesons at 1.8 TeV (|Y| < 1). The QCD
Monte-Carlo predictions have been increased by a factor of four.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 11 of 26
B Physics: Fragmentation
s
fs
d
sbar
fd
K+
dbar
u
sbar
fs
π+
u
ubar
s
fu
Bs0
u
bbar
B+
bbar
CDF Run I
0.408+/-0.068
0.344+/-0.039
0.159+/-0.026
0.089+/-0.029
0.213+/-0.068
fu
fd
fs
fbaryon
fs/(fu+fd)
Old FF
0.4
0.4
0.2
0.0
0.25
Hadron Level: fs/(fu+fd) Ration versus PT (|η
η | < 1)
fs/(fu+fd) Ratio versus PT
40%
1.8 TeV
|eta| < 1
Old FF
30%
20%
10%
0%
5
10
15
20
25
30
PT (GeV)
Herwig
Isajet
Pythia
CDF Data
Plot shows the ratio fs/(fu+fd) at 1.8 TeV (|η
η | < 1), where fs = dσ
σ/dPT(Bs0), fu =
dσ
σ/dPT(B+), and fd = dσ
σ/dPT(B0).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 12 of 26
B Physics: Y and η Distributions
Parton & Hadron Level: Pseudo-Rapidity Distribution
Pseudo-Rapidity Distribution (normalized to 1)
(1/N)dN/dη
PT > 10 GeV
0.25
Isajet at 1.8 TeV
B-mesons = (B+,B0,Bs0)
0.20
PT > 5 GeV
0.15
0.10
0.05
0.00
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η
Isajet b-quark
Isajet B-mesons
Isajet b-quark
Isajet B-mesons
Plot shows (1/N)dN/dη
η (normalized to 1) for B-mesons (B+,B0,Bs0) and for the bquark at 1.8 TeV (PT > 5 GeV and PT > 10 GeV).
Parton & Hadron Level: Rapidity Distribution
Rapidity Distribution (normalized to 1)
(1/N)dN/dY
PT > 10 GeV
0.25
Isajet at 1.8 TeV
B-mesons = (B+,B0,Bs0)
0.20
PT > 5 GeV
0.15
0.10
0.05
0.00
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Rapidity Y
Isajet b-quark
Isajet B-mesons
Isajet b-quark
Isajet B-mesons
Plot shows (1/N)dN/dY (normalized to 1) for B-mesons (B+,B0,Bs0) and for the bquark at 1.8 TeV (PT > 5 GeV and PT > 10 GeV).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 13 of 26
B Physics: Y and η Distributions
Parton & Hadron Level: Pseudo-Rapidity Distribution
Pseudo-Rapidity Distribution
(1/N)dN/dη
PT > 10 GeV
0.25
Herwig at 1.8 TeV
B-mesons = (B+,B0,Bs0)
0.20
PT > 5 GeV
0.15
0.10
0.05
0.00
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η
Herwig b-quark
Herwig B-mesons
Herwig b-quark
Herwig B-mesons
Plot shows (1/N)dN/dη
η (normalized to 1) for B-mesons (B+,B0,Bs0) and for the bquark at 1.8 TeV (PT > 5 GeV and PT > 10 GeV).
Parton & Hadron Level: Rapidity Distribution
Rapidity Distribution (normalized to 1)
(1/N)dN/dY
PT > 10 GeV
0.25
Herwig at 1.8 TeV
B-mesons = (B+,B0,Bs0)
0.20
0.15
PT > 5 GeV
0.10
0.05
0.00
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Rapidity Y
Herwig b-quark
Herwig b-quark
Herwig B-mesons
Herwig B-mesons
Plot shows (1/N)dN/dY (normalized to 1) for B-mesons (B+,B0,Bs0) and for the bquark at 1.8 TeV (PT > 5 GeV and PT > 10 GeV).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 14 of 26
B Physics: Y and η Distributions
Parton & Hadron Level: Pseudo-Rapidity Distribution
Pseudo-Rapidity Distribution
(1/N)dN/dη
PT > 10 GeV
0.25
Pythia at 1.8 TeV
B-mesons = (B+,B0,Bs0)
0.20
PT > 5 GeV
0.15
0.10
0.05
0.00
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η
Pythia b-quark
Pythia B-mesons
Pythia b-quark
Pythia B-mesons
Plot shows (1/N)dN/dη
η (normalized to 1) for B-mesons (B+,B0,Bs0) and for the bquark at 1.8 TeV (PT > 5 GeV and PT > 10 GeV).
Parton & Hadron Level: Rapidity Distribution
Rapidity Distribution (normalized to 1)
(1/N)dN/dY
PT > 10 GeV
0.25
Pythia at 1.8 TeV
B-mesons = (B+,B0,Bs0)
0.20
0.15
PT > 5 GeV
0.10
0.05
0.00
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Rapidity Y
Pythia b-quark
Pythia B-mesons
Pythia b-quark
Pythia B-mesons
Plot shows (1/N)dN/dY (normalized to 1) for B-mesons (B+,B0,Bs0) and for the bquark at 1.8 TeV (PT > 5 GeV and PT > 10 GeV).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 15 of 26
B Physics: Azimuthal Correlations
bbar-quark or
Bbar-mesons
∆φ
PT2
PT1
b-quark or B-mesons
Beam Axis
Parton Level: Azimuthal ∆φ Distribution
Azimuthal ∆φ Distribution (normalized to 1)
(1/N)dN/d∆φ
0.040
1.8 TeV
1 = b-quark 2 = bbar-quark
|eta1| < 1 |eta2| < 1
PT1 > 5 GeV
0.030
0.020
0.010
0.000
90
100
110
120
130
140
150
160
170
180
∆φ = |φ2-φ1| (degrees)
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
Pythia b-quark
Plot shows (1/N)dN/d∆φ
∆φ (normalized to 1), where ∆φ = |φ
φ 2-φ
φ 1| for 1 = b-quark and 2
= bbar-quark at 1.8 TeV with |η
η1| < 1, |η
η2| < 1, and PT1 > 5 GeV.
Measures intrensic PT, gluon
radiation, fragmentation.
Hadron Level: Azimuthal ∆φ Distribution
Azimuthal ∆ φ Distribution (normalized to 1)
(1/N)dN/d∆φ
0.040
1.8 TeV
1 = B-meson 2 = Bbar-meson
|eta1| < 1 |eta2| < 1
PT1 > 5 GeV
0.030
0.020
B-mesons = (B+,B0,Bs0)
0.010
0.000
90
100
110
120
130
140
150
160
170
180
∆φ = |φ2-φ1| (degrees)
Herwig B-meson
Isajet B-mesons
Pythia B-meson
Plot shows (1/N)dN/d∆φ
∆φ (normalized to 1), where ∆φ = |φ
φ 2-φ
φ 1| for 1 = B-mesons
(B+,B0,Bs0) and 2 = Bbar-mesons at 1.8 TeV with |η
η 1| < 1, |η
η 2| < 1, and PT1 > 5 GeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 16 of 26
B Physics: Azimuthal Correlations
Parton & Hadron Level: Azimuthal ∆φ Distribution
Azimuthal ∆φ Distribution (normalized to 1)
(1/N)dN/d∆φ
0.030
1.8 TeV
1 = b-quark or B-meson
2 = bbar-quark or Bbar-meson
|eta1| < 1 |eta2| < 1
PT1 > 5 GeV
0.020
B-mesons = (B+,B0,Bs0)
0.010
0.000
90
100
110
120
130
140
150
160
170
180
∆φ = |φ2-φ1| (degrees)
Herwig b-quark
Herwig B-meson
Plot shows (1/N)dN/d∆φ
∆φ (normalized to 1), where ∆φ = |φ
φ 2-φ
φ 1| for 1 = b-quark and 2
= bbar-quark and for 1 = B-mesons (B+,B0,Bs0) and 2 = Bbar-mesons at 1.8 TeV
with |η
η1| < 1, |η
η2| < 1, and PT1 > 5 GeV.
Parton & Hadron Level: Azimuthal ∆φ Distribution
Azimuthal ∆φ Distribution (normalized to 1)
(1/N)dN/d∆φ
0.040
1.8 TeV
1 = b-quark or B-meson
2 = bbar-quark or Bbar-meson
|eta1| < 1 |eta2| < 1
PT1 > 5 GeV
0.030
0.020
B-mesons = (B+,B0,Bs0)
0.010
0.000
90
100
110
120
130
140
150
160
170
180
∆φ = |φ2-φ1| (degrees)
Pythia b-quark
Pythia B-meson
Plot shows (1/N)dN/d∆φ
∆φ (normalized to 1), where ∆φ = |φ
φ 2-φ
φ 1| for 1 = b-quark and 2
= bbar-quark and for 1 = B-mesons (B+,B0,Bs0) and 2 = Bbar-mesons at 1.8 TeV
with |η
η1| < 1, |η
η2| < 1, and PT1 > 5 GeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 17 of 26
B Physics: PT Correlations
bbar-quark or
Bbar-mesons
∆φ
PT2
PT1
b-quark or B-mesons
Beam Axis
Parton Level: Transverse Momentum Correlations
Transverse Momentum Correlations dσ/d∆PT
dσ/d∆PT (µb/Gev)
1.0E+00
1.0E-01
1.8 TeV
1 = b quark 2 = bbar quark
|eta1|< 1 |eta2|<1 |phi1-phi2|>90 deg
PT2 > 5 GeV
1.0E-02
1.0E-03
1.0E-04
-20
-15
-10
-5
0
5
10
15
20
∆P T = P T 1 - P T 2 ( G e V )
Herwig b-quark
Isajet b-quark
Pythia b-quark
Plot shows dσ
σ/d∆
∆ PT (µ
µb/GeV), where ∆ PT = PT1-PT2 for 1 = b-quark and 2 =
bbar-quark at 1.8 TeV with |η
η1| < 1, |η
η2| < 1, |φ
φ1-φ
φ 2| > 90o, and PT2 > 5 GeV.
Parton Level: Transverse Momentum Correlations
PT Correlations (normalized to 1)
(1/N)dN/d∆PT
0.20
1.8 TeV
1 = b quark 2 = bbar quark
|eta1|< 1 |eta2|<1 |phi1-phi2|>90 deg
PT2 > 5 GeV
0.15
0.10
0.05
0.00
-15
-10
-5
0
5
10
15
∆PT = PT1 - PT2 (GeV)
Herwig b-quark
Isajet b-quark
Pythia b-quark
Plot shows dσ
σ/d∆
∆ PT (µ
µb/GeV), where ∆ PT = PT1-PT2 for 1 = b-quark and 2 =
bbar-quark at 1.8 TeV with |η
η1| < 1, |η
η2| < 1, |φ
φ1-φ
φ 2| > 90o, and PT2 > 5 GeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 18 of 26
B Physics: PT Correlations
Measures intrensic PT, gluon radiation,
and fragmentation.
Hadron Level: Transverse Momentum Correlations
PT Correlations (normalized to 1)
(1/N)dN/d∆PT
0.20
0.15
1.8 TeV
1 = B-mesons 2 = Bbar-mesons
|eta1|< 1 |eta2|<1 |phi1-phi2|>90 deg
PT2 > 5 GeV
B-mesons = (B+,B0,Bs0)
0.10
0.05
0.00
-15
-10
-5
0
5
10
15
∆PT = PT1 - PT2 (GeV)
Herwig B-mesons
Isajet B-mesons
Pythia B-mesons
Plot shows dσ
σ/d∆
∆ PT (µ
µb/GeV), where ∆ PT = PT1-PT2 for 1 = B-mesons (B+,B0,Bs0)
and 2 = Bbar-mesons at 1.8 TeV with |η
η1| < 1, |η
η 2| < 1, |φ
φ 1-φ
φ 2| > 90o, and PT2 > 5
GeV.
Parton & Hadron Level: Transverse Momentum Correlations
PT Correlations (normalized to 1)
(1/N)dN/d∆PT
0.15
1.8 TeV
1 = b-quark or B-mesons
2 = bbar-quark or Bbar-mesons
|eta1|< 1 |eta2|<1 |phi1-phi2|>90 deg
PT2 > 5 GeV
B-mesons = (B+,B0,Bs0)
0.10
0.05
0.00
-15
-10
-5
0
5
10
15
∆PT = PT1 - PT2 (GeV)
Herwig b-quark
Herwig B-mesons
Plot shows dσ
σ/d∆
∆ PT (µ
µb/GeV), where ∆ PT = PT1-PT2 for 1 = b-quark and 2 =
bbar-quark and for 1 = B-mesons (B+,B0,Bs0) and 2 = Bbar-mesons at 1.8 TeV with
|η
η 1| < 1, |η
η2| < 1, |φ
φ1-φ
φ2| > 90o, and PT2 > 5 GeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 19 of 26
B Physics: Pseudo-Rapidity Correlations
Double-Differential Cross Section
Correlation Functions:
C (η 1 , η 2 ) =
1
1 dσ dσ
dσ
− 2
σ dη 1 dη 2 σ dη 1 dη 2
“Normalized” Correlation Functions:
 1 dσ
1 d σ dσ
− 2
R (η1 ,η 2 ) = 
 σ d η1d η 2 σ d η1 d η 2



 1 dσ dσ
 2
 σ dη1 dη 2



“Integrated” (a < η 2 < b) Normalized Correlation Functions:
 1 dσ
1 dσ dσ
− 2
R (η1 ) = ∫ 
σ d η 1 d η 2 σ d η1 d η 2
a 
b

d η 2

 1 dσ dσ
∫a  σ 2 d η1 d η 2
b

 d η 2

Hadron Level: Pseudo-Rapidity Correlations (|η
η 2| < 0.5)
Pseudo-Rapidity Correlations dσ/dη1dη2
(1/σ )dσ/dη1dη2
0.020
1.8 TeV |eta2|<0.5
1 = B-mesons 2 =Bbar-mesons
|PT1|< 5 GeV |PT2|<5 GeV
|phi1-phi2|>90 deg
0.015
0.010
0.005
eta2
0.000
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η1
Herwig B-mesons
Isajet B-mesons
Pythia B-mesons
Plot shows (1/σ
σ)dσ
σ/dη
η1dη
η2 versus η 1, for 1 = B-mesons (B+,B0,Bs0) and 2 = Bbarmesons at 1.8 TeV with |η
η2| < 0.5, |φ
φ1-φ
φ2| > 90o, PT1 > 5 GeV, and PT2 > 5 GeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 20 of 26
B Physics: Pseudo-Rapidity Correlations
Measures PDF’s,
fragmentation.
Hadron Level: Pseudo-Rapidity Correlations (1 < |η
η 2| < 2)
Pseudo-Rapidity Correlations dσ/dη1dη2
(1/σ )dσ/dη1dη2
0.020
1.8 TeV 1<eta2|<2
1 = B-mesons 2 = Bbar-mesons
|PT1|< 5 GeV |PT2|<5 GeV
|phi1-phi2|>90 deg
0.015
0.010
0.005
eta2
0.000
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η1
Herwig B-mesons
Isajet B-mesons
Pythia B-mesons
Plot shows (1/σ
σ)dσ
σ/dη
η1dη
η2 versus η 1, for 1 = B-mesons (B+,B0,Bs0) and 2 = Bbarmesons at 1.8 TeV with 1 < |η
η2| < 2, |φ
φ1-φ
φ2| > 90o, PT1 > 5 GeV, and PT2 > 5 GeV.
Parton & Hadron Level: Pseudo-Rapidity Correlations
Pseudo-Rapidity Correlations dσ/dη1dη2
(1/σ )dσ/dη1dη2
0.020
Isajet at 1.8 TeV
1 = b-quark or B-mesons
2 = bbar quark or Bbar-mesons
|PT1|< 5 GeV |PT2|<5 GeV
|phi1-phi2|>90 deg
0.015
1 < |eta2| < 2
0.010
|eta2| < 0.5
0.005
0.000
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η1
Isajet b-quark
Isajet b-quark
Isajet B-mesons
Isajet B-mesons
Plot shows (1/σ
σ)dσ
σ/dη
η1dη
η2 versus η 1, for 1 = b-quark and 2 = bbar-quark and for 1
= B-mesons (B+,B0,Bs0) and 2 = Bbar-mesons at 1.8 TeV with |η
η 2| < 0.5 and with 1 <
η2 < 2 and |φ
φ1-φ
φ2| > 90o, PT1 > 5 GeV, and PT2 > 5 GeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 21 of 26
B Physics: Pseudo-Rapidity Correlations
Parton & Hadron Level: Pseudo-Rapidity Correlations
Pseudo-Rapidity Correlations dσ/dη1dη2
(1/σ)dσ/dη1dη2
0.025
Herwig at 1.8 TeV
1 = b-quark or B-mesons
2 = bbar quark or Bbar-mesons
|PT1|< 5 GeV |PT2|<5 GeV
|phi1-phi2|>90 deg
0.020
0.015
1 < |eta2| < 2
0.010
|eta2| < 0.5
0.005
0.000
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η1
Herwig b-quark
Herwig b-quark
Herwig B-mesons
Herwig B-mesons
Plot shows (1/σ
σ)dσ
σ/dη
η1dη
η2 versus η 1, for 1 = b-quark and 2 = bbar-quark and for 1
= B-mesons (B+,B0,Bs0) and 2 = Bbar-mesons at 1.8 TeV with |η
η 2| < 0.5 and with 1 <
η2 < 2 and |φ
φ1-φ
φ2| > 90o, PT1 > 5 GeV, and PT2 > 5 GeV.
Parton & Hadron Level: Pseudo-Rapidity Correlations
Pseudo-Rapidity Correlations dσ/dη1dη2
(1/σ)dσ/dη1dη2
0.020
Pythia at 1.8 TeV
1 = b-quark or B-mesons
2 = bbar quark or Bbar-mesons
|PT1|< 5 GeV |PT2|<5 GeV
|phi1-phi2|>90 deg
0.015
1 < |eta2| < 2
0.010
|eta2| < 0.5
0.005
0.000
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Pseudo-Rapidity η1
Pythia b-quark
Pythia b-quark
Pythia B-mesons
Pythia B-mesons
Plot shows (1/σ
σ)dσ
σ/dη
η1dη
η2 versus η 1, for 1 = b-quark and 2 = bbar-quark and for 1
= B-mesons (B+,B0,Bs0) and 2 = Bbar-mesons at 1.8 TeV with |η
η 2| < 0.5 and with 1 <
η2 < 2 and |φ
φ1-φ
φ2| > 90o, PT1 > 5 GeV, and PT2 > 5 GeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 22 of 26
B Physics: Pseudo-Rapidity Correlations
Hadron Level: Pseudo-Rapidity Correlations
Pseudo-Rapidity Correlations R(η1)
R(η1)
0.0
1.8 TeV |eta2|<0.5
1 = B-mesons 2 =Bbar-mesons
|PT1|< 5 GeV |PT2|<5 GeV
|phi1-phi2|>90 deg
-0.2
-0.4
-0.6
-0.8
eta2
-1.0
-4
-3
-2
-1
0
1
2
3
4
Pseudo-Rapidity η1
Herwig B-mesons
Isajet B-mesons
Pythia B-mesons
Plot shows the normalized correlation function R(η
η 1) versus η 1, for 1 = B-mesons
(B+,B0,Bs0) and 2 = Bbar-mesons at 1.8 TeV with |η
η 2| < 0.5 and |φ
φ 1-φ
φ 2| > 90o, PT1 >
5 GeV, and PT2 > 5 GeV.
Parton & Hadron Level: Pseudo-Rapidity Correlations
Pseudo-Rapidity Correlations R(η1)
R(η1)
0.0
1.8 TeV 1<eta2|<2
1 = B-mesons 2 = Bbar-mesons
|PT1|< 5 GeV |PT2|<5 GeV
|phi1-phi2|>90 deg
-0.2
-0.4
-0.6
-0.8
eta2
-1.0
-4
-3
-2
-1
0
1
2
3
4
Pseudo-Rapidity η1
Herwig B-mesons
Isajet B-mesons
Pythia B-mesons
Plot shows the normalized correlation function R(η
η 1) versus η 1, for 1 = B-mesons
(B+,B0,Bs0) and 2 = Bbar-mesons at 1.8 TeV with 1 < η 2 < 2 and |φ
φ 1-φ
φ 2| > 90o, PT1 >
5 GeV, and PT2 > 5 GeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 23 of 26
B Physics: 2.0/1.8 TeV Cross Section Ratio
Parton Level: Integrated b-quark Cross Section Ratio for PT > PTmin
Ratio 2.0/1.8 TeV for the Integrated b-quark Cross Section
1.4
All y
1.3
1.2
1.1
1.0
5
10
15
20
25
30
35
40
PTmin (GeV)
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
PythiaC3L b-quark
Pythia b-quark
Plot shows the 2.0/1.9 TeV ratio of σ(PT>PTmin) for b-quarks (all Y).
Parton Level: Integrated b-quark Cross Section Ratio for PT > PTmin
Ratio 2.0/1.8 TeV for the Integrated b-quark Cross Section
1.4
|eta| < 1
1.3
1.2
1.1
1.0
5
10
15
20
25
30
35
40
PTmin (GeV)
MRSR2 b-quark
Herwig b-quark
Isajet b-quark
PythiaC3L b-quark
Pythia b-quark
Plot shows the 2.0/1.9 TeV ratio of σ(PT>PTmin) for b-quarks (|eta|<1).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 24 of 26
B Physics: Parton 2-to-2 Cross Section Ratio
Parton Level: All-Parton/b-quark 2-to-2 Cross Section Ratio
All-Parton/b-quark 2-to-2 Cross Section Ratio vs PT(cut-off)
10,000
Isajet 1.8 TeV
Isajet 2.0 TeV
1,000
100
2
4
6
8
10
12
PT(hard cut-off) (GeV)
Plot shows the ratio of the cross sections of all QCD parton 2-to-2 subprocesses to
the 2-to-2 b-quark production subprosesses at 1.8 and 2.0 TeV versus the hardscattering transverse momentum cut-off.
Parton Level: Ratio 2.0/1.8 TeV of the All/b-quark Cross Section Ratio
Ratio 2.0/1.8 TeV of the All/b-quark 2-to-2 Cross Section Ratio
1.050
1.025
1.000
0.975
Isajet
PythiaC3L
0.950
2
4
6
8
10
12
PT(hard cut-off) (GeV)
Plot shows the All/b-quark 2-to-2 subprocess cross section ratio at 2.0 TeV divided
by All/b-quark 2-to-2 subprocess cross section ratio at 1.8 TeV versus the hardscattering transverse momentum cut-off (i.e. background/signal at 2.0 TeV divided by
background/signal at 1.8 TeV).
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 25 of 26
B Physics: Parton Invariant Cross Section Ratio
Parton Level: Integrated Inclusive All/b-quark Cross Section Ratio
All-Parton/b-quark Integrated Inclusive Cross Section Ratio
1,000
Isajet 1.8 TeV
Isajet 2.0 TeV
|eta| < 1
100
5
10
15
20
25
30
35
40
PTmin (GeV)
Plot shows the inclusive cross section σ(PT>PTmin, |eta|<1) for all partons (divided by
2) divided by σ(PT>PTmin, |eta|<1) for b-quarks at 1.8 TeV and 2.0 TeV.
Rick Field & Keith Ellis
B-Group Meeting – December 3, 1999
Page 26 of 26