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� - factorization and CCFM:the solution for describingthe hadronic final states
- everywhere ?H. Jung, University of Lund
DESY - seminar 22.Oct 2002
where is the problem ?hadronic final states - jets, heavy quarks - even at Tevatronapproximations
doing it better !CCFM equation in one - loop (DGLAP) and all - loop, solutionimplementation into new hadron level MC CASCADE
solve problems, also for heavy quarks and even for Tevatron
nobody is perfect
conclusion
DESY-seminar 22.Oct 2002 – p.1/36
The structure function � � ���
��
: DGLAP
0
2
4
6
8
10
12
14
16
1 10 102
103
104
105
Q2 (GeV2)
Fem
+ci(x
)2
ZEUS 96/97 Preliminary
H1 96/97 Prelim. H1 94/97
NMC, BCDMS, E665
ZEUS QCD Fit (Prelim.)
H1 QCD Fit (Prelim.)
Scaling violations perfectlydescribed with DGLAP:��� � � � ��� �� ��� �
�� � ��� � � � � �GeV
�
● adjust input pdf to fit
� � dataBUT different sets: MRS, GRV etc● use extracted pdf to predict
x - sections● even at � ��
BUT for reliable predictions atHERA II/III, THERA, LHC etc
● better understand pdf’s
DESY-seminar 22.Oct 2002 – p.2/36
Where is the problem? Forward Jets
x bj x bj small
from largeevolution
to small x
’forward’ jet
xjet
=Ejet
Eproton= large
0
50
100
150
200
250
300
350
400
450
500
0.001 0.002 0.003 0.004
x
dσ
/ d
x (
nb
)
H1 1994 Data
NLO (DISENT)
pT jet > 3.5 GeV
.
Mueller - Navelet jets in DIS: Jet in � - direction with
� �� � � �
, ���� � large, BUT small �� �
☛ suppress DGLAP evolution allow evolution in �
☛ standard DGLAP � factor 2 too small!DESY-seminar 22.Oct 2002 – p.3/36
Where is the problem? Charm in DIS
c
c _
color string
exp. cuts�� � � � �� �
GeV
�
��� �� � � � ��� � � � �� �GeV
��� � � � � �� �
0
2.5
5
7.5
-5 -4.4 -3.8 -3.2 -2.6 -2
H1
log(x)d
σ vis(
ep→
eD* x)
/dlo
g(x
) [n
b]
HVQDIS
1 10 100
1
0.1
0.01
H1
Q2 [GeV2]
dσ vi
s(ep
→eD
* X)/
dQ
2 [nb
GeV
-2]
HVQDIS
��
production in DIS
☛ standard DGLAP with NLO calculation too small
☛ Problem at small � and small
� �
!
☛ How to determine
�� � ?DESY-seminar 22.Oct 2002 – p.4/36
Where is the problem ?Bottom at HERA and Tevatron
HERA
ZEUS (ZEUS Coll. EPJC (2001))� � � �
GeV
�
,
��� � �� � ���
,
� � � �
GeV,
��� � � � �
� � � � � � ��� �
(stat.)
� ��� �� �� � (syst.)
� ��� �� �� �(ext.) nb
NLO: � � ��� � � � ��� �� �� nb
safe extrapolation fromvisible to total x-section ???
D0 Data
! " !
in photoproduction and hadroproduction:☛ standard DGLAP with NLO calculation☛ � factor 2 - 4 too small !
DESY-seminar 22.Oct 2002 – p.5/36
Approximation in QCD cascade: Factorization
Gluon Bremsstrahlung:
� �� �
� �� � � � �
x
zxk
tp
pt
kt
collinear approximation
1/E
factorizationcollinear factorization
´small x´ approximation
DGLAP:
� collinear singularities
factorized in pdf
� evolution in
� ��� �
, �� or ��
� � � � � � �� � � �� � �� � ����� � � �
BFKL:
� � dependent pdf
� unintegrated pdf
� evolution in �
� � � � �� � � � � � �� � � � �� ����� � �
DESY-seminar 22.Oct 2002 – p.6/36
The problem of Asymptotia...
DGLAP is great
at large
� � � �
But has problems:
➤ Small � processes:
☛ heavy quarks
☛ particle spectra
☛ jets
BFKL is great
at small � � �But has problems:
➤ at finite �:
☛ NLO corrections
☛ predictive power
☛ how to simulate?
But asymptotia still far away
even for THERA or LHC ...DESY-seminar 22.Oct 2002 – p.7/36
Attempts to survive in reality
☛ hack DGLAP and BFKL
prediction ?
☛ introduce new concepts: resolved (virtual) photons
➥evolve with DGLAP from proton and photon side
➥similar to � "�
➥works nicely ( � RAPGAP MC generator)
BUT theoretical questions: which scale etc ???
☛ CCFM - new investigation of color coherence
hacker: person paid to do hardand uninteresting work ...
Oxford Advanced Dictionary
DESY-seminar 22.Oct 2002 – p.8/36
Attempts to survive in reality
☛ hack DGLAP and BFKL
prediction ?
☛ introduce new concepts: resolved (virtual) photons
➥evolve with DGLAP from proton and photon side
➥similar to � "�
➥works nicely ( � RAPGAP MC generator)
BUT theoretical questions: which scale etc ???
☛ CCFM - new investigation of color coherence
hacker: person paid to do hardand uninteresting work ...
Oxford Advanced Dictionary
DESY-seminar 22.Oct 2002 – p.8/36
CataniCiafaloni Fiorani Marchesini (1988 - 1990)
including color coherence effects in multi-gluon emissionsangular ordering of emission angles:
E
E
i
i−1
θ
θ q
i
i−1 i−1x
z xq
i
,
, ☛
with: ☛ and
in lab. frame
☛with
ordering in � (DGLAP) implies also angular orderingunification of DGLAP and BFKL
☛ WOWfor small � no restriction in �: ☛ random walk in �
DESY-seminar 22.Oct 2002 – p.9/36
CataniCiafaloni Fiorani Marchesini (1988 - 1990)
including color coherence effects in multi-gluon emissionsangular ordering of emission angles:
E
E
i
i−1
θ
θ q
i
i−1 i−1x
z xq
i � � ��� �� ��� ��� � , �
� �� � � �
� � � �� � � � � �� � � � � �� � �� , ☛� �� � � �� � � � � �
� � � �� � ��� � � � �� � � � � � �
� �� � � � � � �with: � � � ��� � ☛
� � � �� � � �and
� � �� � � � �� �
in lab. frame
☛with
ordering in � (DGLAP) implies also angular orderingunification of DGLAP and BFKL
☛ WOWfor small � no restriction in �: ☛ random walk in �
DESY-seminar 22.Oct 2002 – p.9/36
CataniCiafaloni Fiorani Marchesini (1988 - 1990)
including color coherence effects in multi-gluon emissionsangular ordering of emission angles:
E
E
i
i−1
θ
θ q
i
i−1 i−1x
z xq
i
,
, ☛
with: ☛ and
in lab. frame
� � � � �
☛ � � � � �� � � �
with
� � ����� �
ordering in � (DGLAP) implies also angular orderingunification of DGLAP and BFKL
☛ WOWfor small � no restriction in �: ☛ random walk in �
DESY-seminar 22.Oct 2002 – p.9/36
CASCADE with CCFM solves the problems
Solve CCFM equationto fit
� � data from HERA
● obtain CCFM un-integrated gluon
CASCADE MC implements CCFM:
● predict fwd jet x-section at HERA ✔
● predict charm at HERA ✔
● predict bottom at HERA ✔ x
dσ/
dx
x
dσ/
dx
x
dσ/
dx
E2T/Q2
dσ/
d(E
2 T/Q
2 )
050
100150200250300350400450500
0.001 0.002 0.003 0.0040
25
50
75
100
125
150
175
200
225
0.001 0.002 0.003 0.004
0
20
40
60
80
100
120
140
10-3
10-2
10-4
10-3
10-2
10-1
10-2
10-1
1 10 102
.
● test universality of un-integratedgluon density from HERA
● predict bottom at Tevatron ✔
● w/o additional free parameters
.
WOW !!!DESY-seminar 22.Oct 2002 – p.10/36
CCFM Monte Carlo - CASCADE
Why is CASCADE doing well
and
why did it take so long
to develop it ???
Or
Why did all the other
brave approaches fail ???
Apologies to my friends in Lund ...
DESY-seminar 22.Oct 2002 – p.11/36
CCFM Monte Carlo - CASCADE
Why is CASCADE doing well
and
why did it take so long
to develop it ???
Or
Why did all the other
brave approaches fail ???
Apologies to my friends in Lund ...
DESY-seminar 22.Oct 2002 – p.11/36
CCFM history
1988 - 1990 Formulation of CCFM
M. Ciafaloni,
Nucl. Phys. B 296 (1988) 49
S. Catani, F. Fiorani, G. Marchesini,
Phys. Lett B 234 (1990) 339
S. Catani, F. Fiorani, G. Marchesini,
Nucl. Phys. B 336 (1990) 18
G. Marchesini,
Nucl. Phys. B 445 (1995) 49
1992 SMALLX- MC programG. Marchesini. B. Webber,
Nucl. Phys. B 386 (1992) 215
1996 - 1998 Formulation of LDC
B. Andersson, G. Gustafson, J. Samuelsson,
Nucl. Phys. B 467 (1996) 443
B. Andersson, G. Gustafson, H. Kharrazhia,
J. Samuelsson, Z. Phys. C 71 (1996) 613
H. Kharrazhia, L.Lönnblad, JHEP 03 (1998) 006
1998 Had. final states in CCFMG. Bottazzi, G. Marchesini, G.P. Salam,
M. Scorletti, JHEP 9812:011 (1998)
DESY-seminar 22.Oct 2002 – p.12/36
CCFM history (cont’d)
status in 1999
CCFM is great !can describe � ��� � � � (
� �)(hm..., DGLAP does it also...)
But fails for hadronic final states: Forward Jets ...
The End of small ?Much progress since then....Small workshops in Lund
(thanks to DESY for support)
Small Collaboration
DESY-seminar 22.Oct 2002 – p.13/36
CCFM history (cont’d)
status in 1999
CCFM is great !can describe � ��� � � � (
� �)(hm..., DGLAP does it also...)
But fails for hadronic final states: Forward Jets ...
The End of small ?
Much progress since then....Small workshops in Lund
(thanks to DESY for support)
Small Collaboration
DESY-seminar 22.Oct 2002 – p.13/36
CCFM history (cont’d)
status in 1999
CCFM is great !can describe � ��� � � � (
� �)(hm..., DGLAP does it also...)
But fails for hadronic final states: Forward Jets ...
The End of small ?
Much progress since then....Small workshops in Lund
(thanks to DESY for support)
Small CollaborationDESY-seminar 22.Oct 2002 – p.13/36
CCFM equation: small and large �
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�� �� � � �
��� � � ��� �
�
CCFM Splitting fct:
� � ��� �� � � � � ����� � !#" $ $
! " � ���� % � $ �
ns
��� �� � � �
Sudakov
� � �'& � ! �
: probablility for no radiation in
(& � ! )
angular ordering:
�� * �,+ �+- �+ * �+ . �+ �- � � �- � . * �0/
small 1 large 1
☛ BFKL limit ( � 2 �
)☛ angular ordering2 no restriction on �43
☛ DGLAP limit ( � 5 �
)☛ DGLAP splitting fct
687
with
9
ns : �
☛ angular ordering 2 �43 ordering
DESY-seminar 22.Oct 2002 – p.14/36
Basic idea - Collinear factorisation
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.
.
.
DGLAP
BGF matrix elementon mass shell
evolution of parton cascade
10-4
10-3
10-2
10-1
10-1
1
10
10 2
Q=10 GeV
x
xG(x
,Q)
one - loop
� - orderedwith DGLAP splitting fct.6 7 � �- �- �� � : ����
.. �� .
��
initial distribution: steep
10-4
10-3
10-2
10-1
10-1
1
10
10 2
x
xG(x
,Q)
Q=1 GeVone - loop
�( � ��� �� ) � ����
� � � �� �� �� � � ���� �� � � � � � ��� � � ���� �� �� �
with
� � � ��� � � ���� �� �� � � ��� � � ���� � � �
( )
with
J.C. Collins, X. Zu JHEP 06 (2002) 018
on shell matrix elementis only assumption withoutproofand is unphysical !!!and not necessary for proofof factorization !!!
DESY-seminar 22.Oct 2002 – p.15/36
Basic idea - Collinear factorisation
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.
.
.
DGLAP
BGF matrix elementon mass shell
evolution of parton cascade
10-4
10-3
10-2
10-1
10-1
1
10
10 2
Q=10 GeV
x
xG(x
,Q)
one - loop
� - orderedwith DGLAP splitting fct.6 7 � �- �- �� � : ����
.. �� .
��
initial distribution: steep
10-4
10-3
10-2
10-1
10-1
1
10
10 2
x
xG(x
,Q)
Q=1 GeVone - loop
( )
with
�( � ��� �� ) � � � � ����
� � � �� �� �� � � ���� �� � � ��� � � ���� �� �� �
with
� � � ��� � � ���� �� �� � � � ��� � � ���� � � �
J.C. Collins, X. Zu JHEP 06 (2002) 018
on shell matrix elementis only assumption withoutproofand is unphysical !!!and not necessary for proofof factorization !!!
DESY-seminar 22.Oct 2002 – p.15/36
DGLAP unintegrated gluon density- integrated -
10-1
1
10
10 2
xG(x
,Q)
Q=1 GeVone-loop
GRV 98 NLO MSBAR
Q=4 GeV
10-4
10-3
10-2
10-1
110
-1
1
10
10 2
Q=6 GeV
x
xG(x
,Q)
10-4
10-3
10-2
10-1
1
Q=10 GeV
x
one-loop gluon integrated over
��� � � � �� � � ��� � �� "� � � � � � ��� "� �
➤ compare to evolved DGLAP gluon
one-loop gluon:
� at starting scale use GRV
� test evolution machinery� full treatment of kinematics
� more than standard DGLAP
� small differences from
special form of
��� � ��� � � � � � �
� small differences since only gluons
DESY-seminar 22.Oct 2002 – p.16/36
� � � �
��
and forward jets (in one-loop)
With � : � � ��� � ��� �� 2 � �� � � � � �� � ���- � ��- �� �
fit
� � � �- � � �
(data from H1 Coll, NPB 470 (1996) 3.)
(fitted for
� � � �
GeV
�
, � � ��� �
)
00.20.40.60.8
11.21.41.61.8
22.2
10-5
10-4
10-3
10-2
10-1
F2
grv-off-shellgrv-on-shell
00.20.40.60.8
11.21.41.61.8
22.2
10-5
10-4
10-3
10-2
10-1
x
0
50
100
150
200
250
300
350
400
450
500
0.001 0.002 0.003 0.004x
dσ/
dx
H1 forward jets
jets pt > 3.5 GeV
grv-off-shell
grv-on-shell
only
� � � and
� � � � � � �
included in
7� �
problem: small � region
But also off-shell ME helps (with �-ordering and
�� � � � ) for rise at small � !!!similar findings with standard NLO splitting kernels
still to small for forward jets... but the same as NLODESY-seminar 22.Oct 2002 – p.17/36
Basic idea - � factorisation
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.
.
CCFM
BGF matrix elementoff mass shell
evolution of parton cascade
10-4
10-3
10-2
10-1
10-1
1
10
10 2
Q=10 GeV
x
xG(x
,Q)
JS (CCFM)
with CCFM splitting fct.6 7 : ��� .. �
� .�
9+ ��
initial distribution: flat
10-4
10-3
10-2
10-1
10-1
1
10
10 2
x
xG(x
,Q)
Q=1 GeVJS (CCFM)
�( � ��� �� ) � ����
� � � �� �� � � � � � � � ���� �� � � ��� � � ���� �� �� �
with
� � � ��� � � ���� �� �� � � ��� � � ���� � � �
( )
with
NEW
angular ordering(instead of ordering)
(non - Sudakov)
DESY-seminar 22.Oct 2002 – p.18/36
Basic idea - � factorisation
� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �
� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
� � � � � � � � �
.
.
.
CCFM
BGF matrix elementoff mass shell
evolution of parton cascade
10-4
10-3
10-2
10-1
10-1
1
10
10 2
Q=10 GeV
x
xG(x
,Q)
JS (CCFM)
with CCFM splitting fct.6 7 : ��� .. �
� .�
9+ ��
initial distribution: flat
10-4
10-3
10-2
10-1
10-1
1
10
10 2
x
xG(x
,Q)
Q=1 GeVJS (CCFM)
( )
with
�( � �� �� ) � ����
� � � �� �� � � � � � � � ���� �� � � �� � � ��� �� �� �
with
� � � ��� � � ���� �� �� � � ��� � � ���� � � �
NEW
angular ordering(instead of �� ordering)9+ � (non - Sudakov)
DESY-seminar 22.Oct 2002 – p.18/36
Splitting Function,non-Sudakov and all that...
Splitting Fct:
�� � ���� � !#" $ $
! " � ��� % � $ �
ns
��� �� � � �
...contains only singular parts....
non-Sudakov log
�
ns
� � "�� � � � ��
� !� � � �
� �� � � � � � � �
� � �� � �
�� � �
reason why others fail:only 1/z termsnon -singular terms
naive solution:
log ns log log
consistency constraint (CC):
CC removes part of phase space
reason why others failed:integrals not properly evaluatedConsistency Constraint !!!
solution for CCFM splitting fct:(Kwiecinski, Martin, Sutton PRD 52 (1995) 1445)
log ns log log
withvalid in full phase space
non - Sudakov depends on non - local (history of cascade):
DESY-seminar 22.Oct 2002 – p.19/36
Splitting Function,non-Sudakov and all that...
Splitting Fct:
�� � ���� � !#" $ $
! " � ��� % � $ �
ns
��� �� � � �
...contains only singular parts....
non-Sudakov log
�
ns
� � "�� � � � ��
� !� � � �
� �� � � � � � � �
� � �� � �
�� � �
reason why others fail:only 1/z termsnon -singular terms
naive solution:
log ns log log
consistency constraint (CC):
CC removes part of phase space
reason why others failed:integrals not properly evaluatedConsistency Constraint !!!
solution for CCFM splitting fct:(Kwiecinski, Martin, Sutton PRD 52 (1995) 1445)
log ns log log
withvalid in full phase space
non - Sudakov depends on non - local (history of cascade):
DESY-seminar 22.Oct 2002 – p.19/36
Splitting Function,non-Sudakov and all that...
Splitting Fct:
�� � ���� � !#" $ $
! " � ��� % � $ �
ns
��� �� � � �
...contains only singular parts....
non-Sudakov log
�
ns
� � "�� � � � ��
� !� � � �
� �� � � � � � � �
� � �� � �
�� � �
reason why others fail:only 1/z termsnon -singular terms
naive solution:
log
�
ns � � ����� �� � log
� � �
log
��� � �� �
consistency constraint (CC):� �� � �
�
CC removes part of phase space
reason why others failed:integrals not properly evaluatedConsistency Constraint !!!
solution for CCFM splitting fct:(Kwiecinski, Martin, Sutton PRD 52 (1995) 1445)
log ns log log
withvalid in full phase space
non - Sudakov depends on non - local (history of cascade):
DESY-seminar 22.Oct 2002 – p.19/36
Splitting Function,non-Sudakov and all that...
Splitting Fct:
�� � ���� � !#" $ $
! " � ��� % � $ �
ns
��� �� � � �
...contains only singular parts....
non-Sudakov log
�
ns
� � "�� � � � ��
� !� � � �
� �� � � � � � � �
� � �� � �
�� � �
reason why others fail:only 1/z termsnon -singular terms
naive solution:
log ns log log
consistency constraint (CC):
CC removes part of phase space
reason why others failed:integrals not properly evaluatedConsistency Constraint !!!
solution for CCFM splitting fct:(Kwiecinski, Martin, Sutton PRD 52 (1995) 1445)
log
�
ns
� � "����� � � � log� ��
log
% �� � � �
with � � � � ��� � �� ��
valid in full phase space
non - Sudakov depends on non - local (history of cascade):
� � 3 : � � 3 . � � � 3 : � � . � � � � � � � � � � � 3
DESY-seminar 22.Oct 2002 – p.19/36
Non-Sudakov and all - loop resummation
Splitting Fct:
�� � ���� � ! " $ $
!#" � ��� % � $ �
ns
��� �� � � �
Non - Sudakov form factor ➤ all loop resummation:
�
ns
� � � ��
� "�� � � � ��
� !� � � �
� �� � � � � � � �
� � �� � �
�� � �
�
�
ns
� � � � "�� � � � ��
� � � �
� �� �
! � !� � � "�� � � � ��
� � � �
� �� �
�� � �
+ + + ... +
��� � �� � .�
� � ��� � � �
�
� �� � � � � �
� � �� �� � .� � ���� � � ��
� �� � � � � �
� � �� �� � �
� � ��
DESY-seminar 22.Oct 2002 – p.20/36
Structure Function � � ���
��
together with G.P. Salam, EPJC 19, 351 (2001)
With � : � � � �� � �� � ��- � ��- �� � � ��� �� � 2 � �� �
fit
� � � �- � � �
(data from H1 Coll, NPB 470 (1996) 3.)
F2
CASCADE
x
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
10-5
10-4
10-3
10-2
10-1
Parameters in fit(fitted for
� � � �
GeV
�
, � � ��� �
)
collinear cut-off
� / : � � �
GeV
initial gluon � / � �- � �� / �
freezing of � �� �� �
for�� 2 �
�� not constrained ...
light quark masses:
�� : ��� � � �
GeV,
��� : � � � GeV
unintegrated gluon density
� � �- � ��- �� �obtained from fit to
� �
DESY-seminar 22.Oct 2002 – p.21/36
Unintegrated gluon density
10-410
-310
-210
-110-5
10-4
10-3
10-2
10-1
1
k2⊥=10 GeV2
x
xA(x,k2 ⊥,q_2) JS(CCFM)
oneloopKMR
10-410
-310
-210
-1
k2⊥=30 GeV2
x10
-410
-310
-210
-11
k2⊥=50 GeV2
x
10-1
1 10 102
10-6
10-5
10-4
10-3
10-2
10-11
10
x=0.001
k2⊥ (GeV2)
xA(x,k2 ⊥,q_2) JS(CCFM)
oneloopKMR
10-1
1 10 102
x=0.01
k2⊥ (GeV2)
10-1
1 10 102
103
x=0.1
k2⊥ (GeV2)
JS (CCFM) gluonH. Jung, G.P. Salam, EPJC 19, 351 (2001)
constrained from
� � fit only for��� � ��� ��
Compare JS (CCFM) toother unintegrated gluonsat �� � � �
GeV:
➤ DGLAP (one-loop) gluon
with GRV at start (NEW !!!)➤ BFKL+DGLAP gluon from
KMR with MRST at startM. Kimber, A. Martin, M. RyskinPRD 63 (2001) 114027
DESY-seminar 22.Oct 2002 – p.22/36
CCFM unintegrated gluon density- integrated -
10-1
1
10
10 2
xG(x
,Q)
Q=1 GeVJS (CCFM)one-loopGRV 98 NLO MSBAR
Q=4 GeV
10-4
10-3
10-2
10-1
110
-1
1
10
10 2
Q=6 GeV
x
xG(x
,Q)
10-4
10-3
10-2
10-1
1
Q=10 GeV
x
CCFM gluon integrated over
��� � � � �� � � ��� � �� "� � � � � � ��� "� �
➤ compare to DGLAP gluon
CCFM gluon:
at starting scale � � �
GeV
flat !!!small � rise of gluononly for DGLAP needed
in CCFM small � risegenerated perturbatively
Remember: gluon density is no observable, only cross sections !!!DESY-seminar 22.Oct 2002 – p.23/36
The Monte Carlo Generator CASCADE
❀ Implement CCFM backward evolution into NEW MC generatorCASCADE (http://www.quark.lu.se/ hannes/cascade)
❀ hard scattering processes included:
☛ � � � 2 � ��, � �� � 2 � � �
, � � � 2 � �� � for � � scattering
☛ � �� � 2 � ��, � �� � 2 � � �
for � �� scattering
❀ initial state parton cascade acc. to CCFM with angular ordering
❀
7
-remnant treatment like in PYTHIA ( �-di- �, primordial
�� )❀ final state parton showers added to quarks, hadronization via
JETSET/PYTHIA
CASCADE is MC implementation of CCFMfor �� and also for � ��
DESY-seminar 22.Oct 2002 – p.24/36
Backward evolution of initial state radiation
10-5
10-4
10-3
10-2
0 0.2 0.4 0.6 0.8 1 z
1/N
dN
/dz
10-5
10-4
10-3
10-2
0 5 10 15 20 25 kt [GeV]
1/N
dN
/dk t [
1/G
eV]
10-5
10-4
10-3
10-2
0 5 10 15 20 25 qt [GeV]
1/N
dN
/dq
t [G
eV]
10-4
10-3
10-2
0 1 2 3 4 5 (kt/qt)
1/N
dN
/d(k
t/qt)
❀ Compare forward withbackward evolution
❀ NEW backwardevolution for small �
processes possible
❀ backward evolution:parton kinematics ofevolution equation withangular ordering repro-duced !!!
forward - backward evolution comparisonnever shown for DGLAP type MC’s!!!
DESY-seminar 22.Oct 2002 – p.25/36
Solution to the problem: Forward Jets
x bj x bj small
from largeevolution
to small x
’forward’ jet
xjet
=Ejet
Eproton= large
x
dσ/
dx
x
dσ/
dx
x
dσ/
dx
E2T/Q2
dσ/
d(E
2 T/Q
2 )
050
100150200250300350400450500
0.001 0.002 0.003 0.0040
25
50
75
100
125
150
175
200
225
0.001 0.002 0.003 0.004
0
20
40
60
80
100
120
140
10-3
10-2
10-4
10-3
10-2
10-1
10-2
10-1
1 10 102
require jets with � � ��
� � ��
� �GeV and
��
� � � ��
� � � � �
(H1 Coll. NPB 538 (1999) 3)
� CASCADE well in shape and normalization !!!
� RAPGAP off as expected from DGLAP type evolution
DESY-seminar 22.Oct 2002 – p.26/36
Solution to the problem: charm in DIS
c
c _
color string
0
2.5
5
7.5
-5 -4.4 -3.8 -3.2 -2.6 -2
H1
log(x)
dσ vi
s(ep
→eD
* x)/d
log
(x)
[nb
]
CASCADEHVQDIS
1 10 100
1
0.1
0.01
H1
Q2 [GeV2]
dσ vi
s(ep
→eD
* X)/
dQ
2 [nb
GeV
-2]
CASCADEHVQDIS
� �
production in DIS
☛ standard DGLAP with NLO calculation too small
☛ CASCADE � perfect even at low � and
� �
☛ free parameter: � �
DESY-seminar 22.Oct 2002 – p.27/36
�
production at HERA: H1 and ZEUS
H1(H1 Coll. PLB 467 (1999) 156)
� � � �
GeV
�
,
��� � �� � ���
,
�� � �
GeV,
� � � � � � � � � � �
visible x-section � � � �� �� �
:
��� � � � � � � � � � � � �� � � ��� � � �� � �� �
pb
NLO: � � � � ��
pb
CASCADE
� � � � � � �� � � � � � � ��� �
��� � �H1
� � ���� ��� � � � � � ��� � � � ��� �� �� ��
ZEUS (ZEUS Coll. EPJC (2001))
� � � �
GeV
�
,
��� � �� � ���
,
�� � �
GeV,
��� � � � �
� � � � � � ��� � � � � � �� � � ��� �� ��� �� �� � �� � � ��� �� �� �� � �� �
nb
NLO: � � ��� � � � ��� �� �� nb
CASCADE
� � � � � � �� � � ��� � ��� � �� �
��� � �ZEUS
� � ���� ��� � � � � � � � ��� � � � �� � � ��� � �
Measurements rely on large extrapolationfrom visible to total x-section
difference in visible x-sections !?!DESY-seminar 22.Oct 2002 – p.28/36
Solution to the problem at HERA:�
ZEUS (ICHEP (2002) Abstract 785)
� � � �
GeV
�
,
��� � � � � ���
,
two jets + muon with � � �
GeV, � � � � � � � � � � �
ZEUS: � � � � � � � � �� � � � � � � � � � � � � � � � �
pb
CASCADE: � � � � � � � � � � � � � � � � � � � �
pb NLO: � � � �
pb
0
5
10
15
20
25
30
35
40
-1.5 -1 -0.5 0 0.5 1 1.5 2
ηµ
dσ/
d η
µ (p
b)
ZEUS (prel) 96-00CASCADE
0
500
1000
1500
2000
2500
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
xγ (GeV)
dσ/
d x
γ (p
b)
ZEUS (prel) 96-00
CASCADE
CASCADE agrees for �’s, extrapolation to jets ???
DESY-seminar 22.Oct 2002 – p.29/36
Solution to the problem:�
production at Tevatron
Test universality of
unintegrated gluon density
from HERA
➤ use unintegrated gluon asbefore (from
� � fit at HERA)
➤ use of shell matrix elementfor � �� � 2 � � � with �� : ��
���
GeV.
NOTE NLO off by factor 2
CASCADE w/o additional free parametersDESY-seminar 22.Oct 2002 – p.30/36
Solution to the problem:�
production at Tevatron
data from: D0 Collaboration B. Abbott et al., Phy.Rev.Lett 84 (2000) 5478
� CASCADE describes � spectrum over huge range well
� NLO fails by factor � 2 (central) and � 4 (forward)
DESY-seminar 22.Oct 2002 – p.31/36
Why does �-factorization helpfor
�
production at Tevatron
Ng (ptg > pt
bb )
Ph(N
g)
= 1/
N d
N/d
Ng
µ2 = pt2
µ2 = pt2 + m2
estimate higher order corrections
Nr of gluons with � � � � ��
LO:� � � �� � � �
� � �
NLO:
� � � �� � � �� � �
NNLO:
� � � �� � � �� � �
.....
CASCADE � � � ���
�
CASCADE with� factorization for estimation of
higher order correctionsDESY-seminar 22.Oct 2002 – p.32/36
Nobody is perfect ...
fwd �’s and fwd jets with
��� - algo are less well described☛ only gluons included, need to worry about quarks also ?
bottom production at HERA: what about difference between H1 and ZEUS ?☛ need to care about fragmentation issues ?
jets in DIS and charm☛ x-section seems to be at high end....☛ think about fine tuning and re-fitting of CCFM unintegrated gluon ?
BUT also:improve CCFM splitting function
�� � to be valid for all �
☛ non-singular terms☛ scale �
�� in �� also for small � part
CCFM unintegrated gluon density also for diffraction at HERA☛ better suited because of angular ordering - rapidity gap - angle☛ 1st attempts look promising
unintegrated gluon density for photon (M. Hansson (Lund) started ... )
☛ solve also
� �in � � ???
DESY-seminar 22.Oct 2002 – p.33/36
What has been achieved ???
important to go beyond DGLAP: treat kinematics properly.....
full machinery for MC evolution developed:suitable for DGLAP - reproduces standard evolutionreliable for small � evolution with
factorization and CCFM
MC solution of CCFM evolution equation obtained
full hadron level CCFM MC generator developed: CASCADE
resolves nearly all discrepancies with data at s mall �
forward jetsheavy quarks: charm (open charm and
� ��
) and bottom
solves
� � �
crisis at Tevatron with unintegrated gluon fromHERA
DESY-seminar 22.Oct 2002 – p.34/36
The Beginning, Not the End
��� - factorization has reached new phase
☛ precision tests☛ fine tuning possible and necessary
��� - factorization is now at comparable level with DGLAP
many new items are opened up:☛ more studies with high statistics at HERA II☛ more studies in small angle region at HERA III☛ � � - physics at TESLA☛ new perspectives for THERA
new theoretical interest in
�� - factorization generated:
☛ Lund small � workshops☛ Small � collaboration
DESY-seminar 22.Oct 2002 – p.35/36
The Beginning, Not the End
Even if there is still a bit to go for a
Theory of Everything
we are facing the beginning of an
interesting, bright and challenging future
in small � physics
DESY-seminar 22.Oct 2002 – p.36/36
Problems in small � evolution: scale of ���together with G.P. Salam
Splitting Fct:����� �� �� ���� � � ��� � � � ���� �� ���� ���! " # � $
%'&( �)�� � * +-,� � # .� $
/�0 1 � 2� 2 / 1 3 3 4 � # � * " $ 4 � " * � 5 " � $
Splitting Fct:����� � 6 �� ��� � � ���� � � � 6 �� �� �)�� � �! " # � $
%'&( � �� � * /�0 1 � 2� 2/ 1 3 3 ,� � " $ 4 � # � * " $ 4 � " * � 5 " � $
%'&( � �� � 7 7 7 /� 3� � � 2 � � 3 1 3 3 �8:9; �� <=�> ?@ �
worry: lower limit � 5 " � A BDCE F :introduce cutoff " 0 .
z
∆n
s
q0=1.4
αs(q) q=k=Qgstandard ∆ns
z
∆n
s
q0=1.4
αs(q) q=k=5standard ∆ns
z
∆n
s
q0=1.4
αs(q) q=5,k=10standard ∆ns
z
∆n
s
q0=1.4
αs(q) q=10,k=5standard ∆ns
DESY-seminar 22.Oct 2002 – p.37/36
Problems in small � evolution
� only singular terms in
splitting function
���
� � +,��� �
� � �� � ��� ��
� similar in BFKL
� conceptual problems with
non-singular terms
�� � � + ,��
� � � � �� * � � � � * � $ � ���� ��
� study � values in forward jet
events with CASCADE
� at HERA � values � ��
� need to consider non - singular
terms in splitting function z
dσ/
dz
fwd jet 7o 30x920
10-1
1
10
10-2
10-1
DESY-seminar 22.Oct 2002 – p.38/36
CCFM including full splitting fucntiontogether with G.P. Salam
� improve splitting function
�� � � +-,�
� � � ��� � ���� ��
� to include non-singular terms
�� � � +-,�
� � � ���� * � � � � * � $ � ��� ��
� new attempt (G. Salam):
��� + ,�� ��� � �� � � * � $ � � * � $ � �)��
� +-,�� ��� � � �� � * � $ �
� need also new Sudakov:
%'&( �� � * /�0 1 2 3 2 3 �� 5 + ,�
� � 2��� � 2 � � ��� � �.�
and new non-Sudakov
%'&( � �� �
* +,� � # $ / / �� 5 1 2 3 2 3 � ��� �� 2 � � * � $ � � * � $ �
z
∆n
s
old ∆ns q/k=1fullold ∆ns q/k=0.5fullold ∆ns q/k=2full
z
∆n
s
old ∆ns q/k=1fullold ∆ns q/k=0.5fullold ∆ns q/k=2full
DESY-seminar 22.Oct 2002 – p.39/36
MC solution of CCFM eq: Forward Evolutionfollowing SMALLX of G. Marchesini and B. Webber NPB 349 (1991) 617, NPB 386 (1992) 215
1.select starting ��� ��� � from
�� � � ��� � �
x 0
2.select ��� from Sudakov (incl. angular ordering)
Sudakov gives probability for non-radiationbetween
� � and ���
x 0
q1
3.
select � � from
�
calculate � � , and finally � � � ��� �� � � � �
and
�� �
x 0
qx 1 1 0xz=
1−=
z1
t1p
1
4.
select � � from Sudakov��
�� � � � � �� �
repeat step 2 and 3until next step would result in
��� � � (max. angle) x 0
qx 1 1 0xz=
1−=
z1
t1p
q2
1
DESY-seminar 22.Oct 2002 – p.40/36
Forward or backward evolutionwhere is the problem ?
SMALLX Monte Carlo:☛ forward evolution used to
solve CCFM equation☛ obtain unintegrated
gluon density☛ produces also partons☛ weighted events produced☛ large fluctuations☛ difficult to extend to
Betterbackward evolution☛ starting from hard scattering☛ use unintegrated
gluon density☛ parton and hadron level☛ very efficient☛ unweighted events☛ easy to extend to
... Only need to formulate backward evolution for CCFM ...
DESY-seminar 22.Oct 2002 – p.41/36
CCFM backward evolutiontogether with G.P. Salam, EPJC 19, 351 (2001)
Backward evolution needs differential form of CCFM eq.(G. Marchesini NPB 445 (1995) 49)
☛
��� � ����� . � � �� �� ��� �
�� ��� � 0 � � �����
���
��� �� �� ��� � �
�� ��� � 0 � � � � � �� � �
��� � � �
☛ similar form to DGLAP
BUT angular ordering complicates things
☛
��� � � instead of ��� in DGLAP
And non-Sudakov also plays a role
unintegrated gluon density
� �� �
��� �
☛ from forward evolution
DESY-seminar 22.Oct 2002 – p.42/36
The CCFM Backward Evolution
1.
starting with quark - box: � ��� ��� � � � � �
select � � ��� � from
� � � ��� �� �
with
� given by quark box:
�� �� � ��
_q
nx k tn
}
2.
select ��� from bwd evolution Sudakov:� � � ���� �� � � �� � � � � � �
� � ��� 2
� � 3� 3 �� ���
��� � � � � � � � ���
� 2! " 2$# % 2� # � &(' )
! " # %� # � )with
� from previous step, � � � � � ��q p
nx k tn
tnn
3.
select � � from � ��* " �,+ " �.- ' + ) )
�.- ' + �* " %� + )' +
�� �
� � � ��� � � �� �
with
�� � � �� already known
calculate � � - � , andfinally � � � �� �� � � �
�
and
�� � - � x n−1 k tn−1
q pnx k tn
tnn
DESY-seminar 22.Oct 2002 – p.43/36
The CCFM Backward Evolution (cont’d)
4.
repeat step 2 and 3 until ...stopping condition is reached:
x n−1 k tn−1
q
q
p
p
nx k tn
tn
tn−1
n
n−1
5.
Stop evolution with probability:
�
�� � � � ��� � �� �
� � � � ��� � �� � �
�� � � � ��� �
� ��
� � � � � �
� � � � ��� � �� �
☛ construct �� and
�� �
☛ construct
�
-remnant system☛ add on primordial
��� to � di- � system x n−1 k tn−1
x 0 t0k
q
q
q
p
p
p
nx k tn
tn
tn−1
t1
n
n−1
1
DESY-seminar 22.Oct 2002 – p.44/36
Parton dynamics at small �: Forward Jets I
x bj x bj small
from largeevolution
to small x
’forward’ jet
xjet
=Ejet
Eproton= large
DIS :
GeV
.�� � .� �
GeV
.
forward jet (incl.
# algorithm)��
� �� ��� � ���
�
� � � ��
�
��
� 3� ����C 3 � � 0
50
100
150
200
250
0.001 0.002 0.003 0.004
H1 Forward Jet Data
H1 data, prel.RG(DIR)CASCADE
pT,JET>3.5 GeV
DGLAP too small, need
factorisation with CCFM
why CASCADE too large ? quarks ?
DESY-seminar 22.Oct 2002 – p.45/36
Parton dynamics at small �: Forward�
I
π 0’forward’
x bjx bj x smallbj
evolution from largeto small x
xπ= Eπ
Eproton= large
DIS : forward � 0 (instead of jet)
�� ��� � � �
�
� � � ��
DGLAP too small, need:
� resolved virtual photons ?!?
� CCFM too small at small � !?!
� WHY ?!?
0
200
400
600
10-4
10-3
H1 Forward π0
dσπ/
dx [n
b] ● H1 preliminary DIR + RES, Q2+4pt
2
CCFM (CASCADE) DIR (LO DGLAP)
2.0 < Q2 < 8.0 GeV2
0
20
40
60
80
10-4
10-3
8.0 < Q2 < 20.0 GeV2
0
5
10
15
20
10-4
10-3
20.0 < Q2 < 70.0 GeV2
x
pT,*π > 3.5 GeV
5o < θπ < 25o
DESY-seminar 22.Oct 2002 – p.46/36
� � �
production in DIS at HERA: H1 and ZEUS
H1(prel.)
�� � .�
GeV
.
,
��
� �� ��
�
,
� � � �
GeV,
� �� � �� � �
visible x-section � � � � 5� +� �
:
�� �� � ��� ��� ��
$ � � �� ��
$�� �
NLO: �� �
pb
CASCADE
� � � � � � 5� +� $� � �
��� E �
H1
$� ��� � � � �� ��� ? � ��
�
ZEUS(prel.) ICHEP 2002
� . � �
GeV
.
,
��
� �� ��
�
,
� "! # $&% � � �
GeV, * �� ' (*) +� � ��
� � � �
GeV,� �� � �� � �
x-section � � � � 5� +� � � 5, � �
:
�� � ��
� ��
� ��� ��� ��
$ -/. �10. 0 ��� �� ��
$ � �
NLO: �� � ��
�
pb
CASCADE
� � � � � � 5� +� $� � � �
�2� E �
ZEUS
$� �� � � � �� ��� ? � �
DESY-seminar 22.Oct 2002 – p.47/36
� � �
production in DIS at HERA: ZEUS
10-3
10-2
10-1
1
10 102
103
ZEUS
Q2 (GeV2)
dσ/
dQ
2 (p
b/G
eV2 )
ZEUS (prel.) 99-00
O(αs) QCD⊗CCFM (CASCADE)
O(αs) QCD⊗DGLAP (RAPGAP)
σ(e+p → e+ bb- X → e+ µ± Jet X)
0.05 < y < 0.7
Pµ > 2 GeV, 30o < θµ < 160o
Et,Jet
Breit > 6 GeV, -2 < ηJet
Lab < 2.5
1
10
10 2
-4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1
ZEUS
log10(x)
dσ/
dlo
g10
(x)
(pb
)
ZEUS (prel.) 99-00
O(αs) QCD⊗CCFM (CASCADE)
O(αs) QCD⊗DGLAP (RAPGAP)
σ(e+p → e+ bb- X → e+ µ± Jet X)
Q2 > 2 GeV2, 0.05 < y < 0.7
Pµ > 2 GeV, 30o < θµ < 160o
Et,Jet
Breit > 6 GeV, -2 < ηJet
Lab < 2.5
DESY-seminar 22.Oct 2002 – p.48/36
Resolved - , NLO and � - factorization
k = 0t|
k = 0tk = 0t k = 0t
tk − factorization
resolved photon(heavy quark excitation)
NLOLO # factorization
➤ NLO corrections
➤ anomalous �
➤ even in NLO
➤includes NNLO
➤includes NNNLO
➤includes NNNNLO
# factorization has
no problem with:
➤ negative weights....
➤ matching to PS
➤ matching to
hadronsiation
DESY-seminar 22.Oct 2002 – p.49/36
� - and collinear factorization
k = 01
k = 01 |
k = 01
k = 01
k = 01 |
k = 01 |
k = 01 |
k = 01 |
BFKLCCFM
} off − shell ME
}
off - shell matrix element
➤ 1-loop correction to
Born approximation
➤ high energy limit of NLO !!!
�� / 1 �� � . # � � � �� # $ � ��� # $
� ���! # $� / 1 ��� � � � ���! # � � 0 $ +��0 � �! � 0 $
factorize
# dependence in
�
and insert in �
➤ improved coefficient and splitting functions to all order
DESY-seminar 22.Oct 2002 – p.50/36
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