Studies of the hadronic final state with the H1 detector · Studies of the hadronic final state...
Transcript of Studies of the hadronic final state with the H1 detector · Studies of the hadronic final state...
Studies of the hadronic final state with the H1
detectorDaniel Traynor, QMUL
1
Recent Results from H1
• Photoproduction of Dijets with High Transverse Momenta at HERA.
• Multi-jet production in high Q2 neutral current deeply inelastic scattering at HERA and determination of αs
• H1 Search for a Narrow Baryonic Resonance Decaying to K0s p(p)
• Measurements of Forward Jet Production at low x in DIS
2
Recent Results from H1
• Photoproduction of Dijets with High Transverse Momenta at HERA.
• Multi-jet production in high Q2 neutral current deeply inelastic scattering at HERA and determination of αs
• H1 Search for a Narrow Baryonic Resonance Decaying to K0s p(p)
• Measurements of Forward Jet Production at low x in DIS
2
HERA + H1
3
4
electrons
27.6 GeV
4
electrons
27.6 GeV
Protons
920GeV
4
electrons
27.6 GeV
Protons
920GeV
4
electrons
27.6 GeV
Protons
920GeV
4
H1
s.c. Solenoid 1.16 T
Liquid Argon Calorimeter
Instrumented Iron Detector Forward Muon
Spectrometer
GO GG
Forward
Tracker
Central
Tracker
Silicon
Tracker
Spaghetti
Calorimeters
ep
Central
MWPCs
Backward
MWPC
ToF
Scintillators
920 GeV27.6 GeV
5
Forward Jet Production at HERA
6
Inelasticity yy = p.q / p.k`
s = Q2 / xy = 318 GeV
KinematicsFour-momentum transfer
squaredQ2 =-q2 = (k-k`)2
Bjorken x (xbj)x = Q2 / 2p.q
Kinematics overstrainedcalculable from electron or proton side
e+ e’+
!
p
q
Q2
xbj
e+(k)e+(k`)
qP
γ
7
xi = longitudinal momentum fractionkt = transverse momentum
Parton Evolution
8
Monte Carlo and NLO predictions
9
xBj xBj small
evolution from largeto small x
"forward" jet
x =E
= largejet
jet
Eproton
Suppress DGLAP Pt,jet2 ~ Q2
Opens up phase space to BFKL type emissions
xjet >> xbj
kinematic acceptance xbj ~ 10-4, θjet(lab) > 7o, ηjet < 3.0
Forward Jet takes large fraction of proton
momentum
Enhancing non-DGLAP Parton Emmisions
mor
e fo
rwar
d
10
Event selection
Ee′ > 10 GeV156o < θe′ < 175o
0.1 < y < 0.70.0001 < xbj < 0.004
5 GeV2 < Q2 < 85 GeV2
pt,jet > 3.5 GeV7.0o < θjet(lab) < 20o
xjet > 0.035
Inclusive kt jet algorithm in Breit frame
11
H1 prelim.
E scale uncert
NLO di-jet 1+!HAD
0.5!r,f"!
r,f"2!
r,f
PDF uncert.
LO di-jet1+!
HAD
H1 forward jet data
xBj
d"
/ d
xB
j (n
b)
0
250
500
750
1000
0.001 0.002 0.003 0.004
NLO = DISENT
μr2 = ET2 of Jetμf2 = <ET2> = 45 GeV2
PDF = CTEQ6M
NLO significantly below data
Is scale uncertainty large enough?
Large difference from LO to NLO predictions!
Inclusive Forward Jet Production
0.5 < pt,jet2 /Q2 < 5
12
H1 Prelim.
E. scale uncert.
RG-DIR
CDMRG-DIR+RES
CASC set1
CASC set2
H1 forward jet data
xBj
d!
/ d
xB
j (n
b)
0
250
500
750
1000
0.001 0.002 0.003 0.004
Significant improvement in RapGap (DGLAP) description if resolved photon interactions
included
CDM similar model to RG-DIR+RES
Both still too low at low xbj
CASCade shape wrong!Predictions sensitive to proton
PDF used.
Inclusive Forward Jet Production
13
Triple Differential Cross Sections
0
7
14
0
0.5
1
0
0.025
0.05
0
1.1
2.2
0
0.2
0.4
0
0.0115
0.023
0
0.07
0.14
0.0001 0.001
0
0.014
0.028
0.0001 0.002
5!Q2!10
12
.25!p
t2!3
5
H1 prelim.E scale uncertNLO di-jet 1+!
HAD0.5"
r,f!"
r,f!2"
r,f+PDF uncert.
LO
!r#=3.5
a)
10!Q2!20
0.6!r!3.5!r#=1.8
b)
20!Q2!85
0.1!r!1.8!r#=0.8
c)
35!p
t2!9
5
3.5!r!19!r#=8.1
d)
d"
/ d
xd
Q2d
pt2
(n
b G
eV
-4)
1.8!r!9.5!r#=4.2
e)
0.4!r!4.8!r#=1.8
f)
95!p
t2!4
00
9.5!r!80!r#=22.2
g)
xBj
4.8!r!40!r#=11.3
h)
xBj
1.1!r!20!r#=4.9
i)
xBj
0
0.0012
0.0025
0.001 0.004
Good description at high Q2, high
Pt,jet2 and high xbj
Additional emissions needed at low Q2, pt,jet2, xbj
r = ptjet2/Q2
14
0
5.5
11
0
0.475
0.95
0
0.03
0.06
0
1.1
2.2
0
0.18
0.36
0
0.0132
0.0265
0
0.105
0.21
0.0001 0.001
0
0.02
0.04
0.0001 0.002
5!Q2!10
12
.25!p
t2!3
5
RGDIR
CDMRGtot
CAS1CAS2
H1 prelim.E.scale uncert
1.2!r!7
a)
10!Q2!20
0.6!r!3.5
b)
20!Q2!85
0.1!r!1.8
c)
35!p
t2!9
5
3.5!r!19
d)
d!
/ d
xd
Q2d
pt2
(n
b G
eV
-4)
1.8!r!9.5
e)
0.4!r!4.8
f)
95!p
t2!4
00
9.5!r!80
g)
xBj
4.8!r!40
h)
xBj
1.1!r!20
i)
xBj
0
0.0012
0.0023
0.001 0.004
Triple Differential Cross Sections
RG DIR Fails
RG DIR+RES Better
CDM good problems at high
pt,jet2
CAScade wrong shape,
sensitivity to PDF
15
!!"#$"!!
%&
!'()!!"#
"!"
!!"#*
%&
!!"#$
!!"#*
!'()!!"#
"!!
"!"
Forward Jet + Dijet
Two central jets (pt > 6GeV) + Forward Jet
Δη1 < 1, xg small, Δη2 large,
room for BFKL ladder
Δη > 1, Δη2 small, shorter
ladder, less BFKL like
16
!"2
d#
/d!"
2
All !"1
H1 Prelim.
E.scale uncert.
RG-DIR
CDMRG TOT
CASC set1CASC set2
0
0.02
0.04
0.06
0 1.5 3
!"2
d#
/ d!"
2 (
nb
)
!"1!1
0
0.0165
0.033
0 2 !"2
d#
/ d!"
2 (
nb
)
!"1!1
0
0.0175
0.035
0 2
!"1!1
!"2
d#
/ d!"
2 (
nb
)
0
0.01
0.02
0 1.5 3
!"1!1
!"2
d#
/ d!"
2 (
nb
)
0
0.01
0.02
0.03
0 1.25 2.5
H1 prelim.
E scale uncert0.5!
r,f"!
r,f"2!
r,fPDF uncert.
!"2
d#
/d!"
2
All !"1
0
0.035
0.07
0 2
scale uncertainties
large
3 jet predictions from NLOJET++
no model able to work in all phase space
17
Photoproduction of Dijets with high
Transverse Momenta at HERA
18
e
p
y, Q2
x!
xP
ME
Jet
Jet
photon remnant
proton remnant
Q2 <1 GeV2
Photoproduction
xγ < 0.8 → resolved
xγ > 0.8 → direct
Experimentallyno electron seen
19
QCD Models
PYTHIA 6.1Born level QCD matrix elements of hard processes
+ minimum pt cutoff + LO proton (CTEQ5L) PDF
+ photon (GRV-LO) PDF+ leading log parton shower models
+ multiple interactions + string hadronisation
only contain 2→2 photoproduction processeshave to apply scale factor 1.2 (1.55 for HERWIG)
Only PYTHIA shown, HERWIG very simmilar
20
NLO Calculations
Factorisation and renormalisation scale (μf μr) set to sum of pt of outgoing partons /2
pQCD NLO jet cross sections on parton level obtained from programs
by Frixione + Ridolfi
proton PDF = CTEQ6Mphoton PDF = GRV-HO
Hadronisation correction (δhad) from Monte Carlo
21
Event Selection
|ZVTX| < 35 cmpt,miss < 20 GeV
non-ep topological background finder
no identified scattered electronjet mass > 2 GeV
Not (Jet in φ crack and jet size < 0.05)pt,jet > 25 GeVpt,jet2 > 15 GeV
-0.5 < ηjet < 2.750.1 < yJB < 0.9
22
DIR ∝ (1-cosθ)-1RES ∝ (1-cosθ)-2
Mjj >
65
GeV
[pb]
!/d
cos
"d
20
40
60
80
100
120
140
160
[pb]
!/d
cos
"d
20
40
60
80
100
120
140
160 < 0.8#x
H1 prel.NLO
)had$ (1+×NLO 1.2×Pythia
[pb]
!/d
cos
"d
20
40
60
80
100
120
140
160
[pb]
!/d
cos
"d
20
40
60
80
100
120
140
160 > 0.8#x
*!cos 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
[pb]
!/d
cos
"d
0
10
20
30
40
50
60
70
80
90
*!cos 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
[pb]
!/d
cos
"d
0
10
20
30
40
50
60
70
80
90
> 65GeVJJM
*!cos 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
[pb]
!/d
cos
"d0
10
20
30
40
50
60
70
80
90
*!cos 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
[pb]
!/d
cos
"d0
10
20
30
40
50
60
70
80
90
> 65GeVJJM
xγ < 0.8 xγ > 0.8COSθ*
cosθ* = |tanh(η1-η2)/2| Scale+PDFScale
23
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
100
200
300
400
500
600
700
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
100
200
300
400
500
600
700
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
50
100
150
200
250
300
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
50
100
150
200
250
300
< 0.1p
x
H1 prel.
NLO
)had# (1+!NLO
1.2!Pythia
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
50
100
150
200
250
300
350
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
50
100
150
200
250
300
350 > 0.1p
x
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
< 0.8!x
H1 prel.
NLO
)had# (1+!NLO
1.2!Pythia
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310 > 0.8!xphoton - gluon photon - quark
nlo dominated by the scale uncertainty
xγ
24
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
100
200
300
400
500
600
700
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
100
200
300
400
500
600
700
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
50
100
150
200
250
300
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
50
100
150
200
250
300
< 0.1p
x
H1 prel.
NLO
)had# (1+!NLO
1.2!Pythia
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
50
100
150
200
250
300
350
!x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[p
b]
!/d
x"
d
0
50
100
150
200
250
300
350 > 0.1p
x
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
< 0.8!x
H1 prel.
NLO
)had# (1+!NLO
1.2!Pythia
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x"
d
1
10
210
310 > 0.8!x
xp
high xp sensitive to proton PDF
scale uncertainty smallest
high xp - high jet η
25
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-310
-210
-110
1
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-310
-210
-110
1
< 1 1,2"
< 0.8#xH1 prel.
NLO
)had$ (1+!NLO
1.2!Pythia
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-310
-210
-110
1
10
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-310
-210
-110
1
10
> 1 j" < 1,
i"
< 0.8#x
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-210
-110
1
10
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-210
-110
1
10
> 1 1,2"
< 0.8#x
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-310
-210
-110
1
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-310
-210
-110
1
< 1 1,2"
> 0.8#xH1 prel.
NLO
)had$ (1+!NLO
1.2!Pythia
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-210
-110
1
10
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-210
-110
1
10
> 1 j" < 1,
i"
> 0.8#x
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-210
-110
1
[GeV]t,max
p30 40 50 60 70 80
[p
b/G
eV
]t,
ma
x/d
p!
d
-210
-110
1
> 1 1,2"
> 0.8#x
pt,max
26
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
1
10
210
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
1
10
210
< 1 1,2"
< 0.8#xH1 prel.
NLO
)had$ (1+!NLO
1.2!Pythia
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
-210
-110
1
10
210
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
-210
-110
1
10
210
> 1 j" < 1,
i"
< 0.8#x
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
1
10
210
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
1
10
210
> 1 1,2"
< 0.8#x
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
1
10
210
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
1
10
210
< 1 1,2"
> 0.8#xH1 prel.
NLO
)had$ (1+!NLO
1.2!Pythia
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
-210
-110
1
10
210
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
-210
-110
1
10
210
> 1 j" < 1,
i"
> 0.8#x
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
1
10
210
Px
0.1 0.2 0.3 0.4 0.5 0.6 0.7
[p
b]
p/d
x!
d
1
10
210
> 1 1,2"
> 0.8#x
xp
27
)2
(GeV2
Q
310
410
)2
(p
b/G
eV
2 / d
Q!
d
-510
-410
-310
-210
-110
1
Dijets
Trijets)
had"(1+.NLO
< 4.02 / Q2
r,f!0.25 <
> 5 GeVT,jet
BreitE
< 2.5jet
Lab#-1 <
> 25 GeV3jet
, M2jet
M
H1 Preliminary 99-00
-exchange only)$ (
)2
(GeV2
Q
310
410
)2
(p
b/G
eV
2 / d
Q!
d
-510
-410
-310
-210
-110
1
Multi-jet production in high Q2 neutral current deeply inelastic scattering at HERA and determination of αs
H1prelim-05-033
28
)2
(GeV2
Q
310
410
)2
(p
b/G
eV
2 / d
Q!
d
-510
-410
-310
-210
-110
1
Dijets
Trijets)
had"(1+.NLO
< 4.02 / Q2
r,f!0.25 <
> 5 GeVT,jet
BreitE
< 2.5jet
Lab#-1 <
> 25 GeV3jet
, M2jet
M
H1 Preliminary 99-00
-exchange only)$ (
)2
(GeV2
Q
310
410
)2
(p
b/G
eV
2 / d
Q!
d
-510
-410
-310
-210
-110
1
)2
(GeV2
Q
310
410
dijet
! /
trijet
! =
3/2
R
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
H1 Preliminary 99-00
)had"NLO (1+
-exchange only)#(
< 4.02 / Q2r,f!0.25 <
Hadronisation Uncertainty
)2
(GeV2
Q
310
410
dijet
! /
trijet
! =
3/2
R
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
Multi-jet production in high Q2 neutral current deeply inelastic scattering at HERA and determination of αs
H1prelim-05-033
28
)2
(GeV2
Q
310
410
)2
(p
b/G
eV
2 / d
Q!
d
-510
-410
-310
-210
-110
1
Dijets
Trijets)
had"(1+.NLO
< 4.02 / Q2
r,f!0.25 <
> 5 GeVT,jet
BreitE
< 2.5jet
Lab#-1 <
> 25 GeV3jet
, M2jet
M
H1 Preliminary 99-00
-exchange only)$ (
)2
(GeV2
Q
310
410
)2
(p
b/G
eV
2 / d
Q!
d
-510
-410
-310
-210
-110
1
)2
(GeV2
Q
310
410
dijet
! /
trijet
! =
3/2
R
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
H1 Preliminary 99-00
)had"NLO (1+
-exchange only)#(
< 4.02 / Q2r,f!0.25 <
Hadronisation Uncertainty
)2
(GeV2
Q
310
410
dijet
! /
trijet
! =
3/2
R
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
αs(MZ) = 0.1175 ± 0.0017 (stat.) ± 0.0050 (syst.) {+0.0054}{-0.0068} (th.)
)2
(GeV2
Q
310
410
s!
0.1
0.12
0.14
0.16
0.18
0.2
0.22
)2
(GeV2
Q
310
410
s!
0.1
0.12
0.14
0.16
0.18
0.2
0.22
H1 Preliminary 99-00
)2
(Qs!
)Z(Ms!Averaged
World Average (PDG):
0.0020!) = 0.1187 Z(Ms!
Multi-jet production in high Q2 neutral current deeply inelastic scattering at HERA and determination of αs
H1prelim-05-033
28
H1 Search for a Narrow Baryonic Resonance Decaying to K0s p(p)
H1prelim-05-031
1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8
20
30
40
50
60
70
80
90
100
p)[GeV]S
0M(K
N/5
Me
V
H1 preliminary
H1 databgr fit
29
H1 Search for a Narrow Baryonic Resonance Decaying to K0s p(p)
H1prelim-05-031
1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8
20
30
40
50
60
70
80
90
100
p)[GeV]S
0M(K
N/5
Me
V
H1 preliminary
H1 databgr fit
Upper limit on cross section at 1520MeV is
roughly 100pb, does not exclude ZEUS observation
1.45 1.5 1.55 1.6 1.65 1.70
20
40
60
80
100
120
140
160
))[GeV]pp(S
0M(K
))[p
b]
pp
(0
->K
+!(
U.L
."
2<100 GeV
220<Q
low momentum dE/dx selection
H1 prel.
95 % C.L.
10 MeV!int. window = 16 MeV!int. window =
29
Summary
• Studies of Forward Jets show need for additional terms beyond present collinear DGLAP
• New results on the photoproduction of high Et dijets, sesitive to the proton PDF, have been made.
30
JET PRODUCTION IN DIFFERENT EVOLUTION SCHEMES
DGLAP
DGLAP direct photon
DGLAP
DGLAP resolved photon
DGLAP
CCFM or BFKL
DGLAP: strong ordering of parton kTCCFM: angular ordering of parton emissions (“unintegrated” PDF)BFKL: strong ordering in xi (“unintegrated” PDF)
JET PRODUCTION IN DIFFERENT EVOLUTION SCHEMES
DGLAP
DGLAP direct photon
DGLAP
DGLAP resolved photon
DGLAP
CCFM or BFKL
DGLAP: strong ordering of parton kTCCFM: angular ordering of parton emissions (“unintegrated” PDF)BFKL: strong ordering in xi (“unintegrated” PDF)
JET PRODUCTION IN DIFFERENT EVOLUTION SCHEMES
DGLAP
DGLAP direct photon
DGLAP
DGLAP resolved photon
DGLAP
CCFM or BFKL
DGLAP: strong ordering of parton kTCCFM: angular ordering of parton emissions (“unintegrated” PDF)BFKL: strong ordering in xi (“unintegrated” PDF)
Parton Dynamics in DIS
Strong ordering in kt of parton
emissions
angular ordering of parton emissions
31