- factorization and ccfm: the solution for describing the hadronic … · 2002-10-23 · j.c....

� - 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


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 !


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 �

� � � � ��


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


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 �




E

E

i

i−1

θ

θ q

i

i−1 i−1x

z xq

i � � �� , �

� ��

� � � �� , ☛� ��

� � � ��

� �� with: � � � �� ☛

� � � �� and

� � ��

in lab. frame

☛with






E

E

i

i−1

θ

θ q

i

i−1 i−1x

z xq

i

,

, ☛

with: ☛ and

in lab. frame

� � � � �

☛ � � � � ��

with

� � ��




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 ...


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)


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



status in 1999




The End of small ?

Much progress since then....Small workshops in Lund


Small Collaboration



status in 1999




The End of small ?

Much progress since then....Small workshops in Lund


Small CollaborationDESY-seminar 22.Oct 2002 – p.13/36

CCFM equation: small and large �

� �� "� � � � � �� "��

� � �� "� � � �� "��

��

��

�

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


Basic idea - Collinear factorisation

� � � � � � � ��

� � � � � � � ��

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

.

.

.

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 !!!


Basic idea - Collinear factorisation

� � � � � � � ��

� � � � � � � ��

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

.

.

.

DGLAP

BGF matrix elementon mass shell


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 !!!


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


� � � �

��

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

� � � � � � � ��

� � � � � � � ��

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

.

.

.

CCFM

BGF matrix elementoff mass shell


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)


Basic idea - � factorisation

� � � � � � � ��

� � � � � � � ��

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

� � � � � � � � �

.

.

.

CCFM

BGF matrix elementoff mass shell


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)


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):



Splitting Fct:

�� !#" $ $

! " � �� % � $ �

ns

��


non-Sudakov log

�

ns

� � "��

� !� � � �

� ��

� � ��

��


naive solution:

log

�

ns � � �� log

� � �

log

��

consistency constraint (CC):� ��

�




log ns log log

withvalid in full phase space




Splitting Fct:

�� !#" $ $

! " � �� % � $ �

ns

��


non-Sudakov log

�

ns

� � "��

� !� � � �

� ��

� � ��

��


naive solution:

log ns log log

consistency constraint (CC):




log

�

ns

� � "�� log� ��

log

% ��

with � � � � ��

valid in full phase space


� � 3 : � � 3 . � � � 3 : � � . � � � � � � � � � � � 3


Non-Sudakov and all - loop resummation

Splitting Fct:

�� ! " $ $

!#" � �� % � $ �

ns

��

Non - Sudakov form factor ➤ all loop resummation:

�

ns

� � � ��

� "��

� !� � � �

� ��

� � ��

��

�

�

ns

� � � � "��

� � � �

� ��

! � !� � � "��

� � � �

� ��

��

+ + + ... +

�� .�

� � ��

�

� ��

� � �� .� � ��

� ��

� � ��

� � ��


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

� �


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


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 � ��


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!!!


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


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: � �


�

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 ???


Solution to the problem:�

production at Tevatron

Test universality of


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:�


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)


Why does �-factorization helpfor

�


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 � � ???


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


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


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


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


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


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


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


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 ...


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


� ��

��

☛ from forward evolution


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


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


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 ?


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


� � �

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

$� �� ? � �


� � �

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


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


� - 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


- factorization and ccfm: the solution for describing the hadronic … · 2002-10-23 · j.c....

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