Work done in collaboration with Stefano Frixione

Work done in collaboration with Stefano Frixione1

Leonardo Bertora, 2004 April 14

Jet and Di-jet production in Photon–Photon collisions

Leonardo Bertora1,2

1

2

INFN, Sezione di Genova

Università di Genova, DiFi


Real photon production

Bremmstrahlung at e e colliders (LEP)-+

Real photon

In this case, the photon virtuality averaged is of order , and we can consider both photons as real.

242 GeV 10Q

If are small, typically below

30 mrad, both the leptons

are “untagged”.

21,

Before interacting a real photon can fluctuate in a hadronic state, revealing a “structure”.

In a high energy domain , QCD has to be able to describe photon hard interactions.

QCDE Λ>>

OPAL, hep-ex/0301013

L3, see Photon2003 proceedings

DELPHI, see Photon2001 proceedings

Future Linear Collider …

Theoretical results:

Photon – Photon Hard Collisions

Motivations: Hard production of jets is a complementary method (with respect to DIS) to study the

“structure” of the photonIt is rich test for QCD

(since the beginning of history…Han-Nambu integer charges model)

Experimental Situation:

As of now only the theoretical prediction by

Klasen, Kleinwort, Kramer (KKK)(hep-ph/9611450 and

hep-ph/9712256) is available

Situation


We are not able to compute differential cross section analytically We fight against large unphysical oscillations and the computer precision

A general method should be adopted in order to cancel out divergences analytically, and finite remainders

can be numerical (MC) integrated We use subtraction method, KKK used slicing one

… double test: a different computation with a different method

ddX

f j (x1,Qi ) fk (x2 ,Qi )d ˆ jk(Qi ,Q f )

d ˆ X F( ˆ X X;Qi ,Q f )

ˆ X

j,k

Factorization theorem

Motivations


)()1()1(

)1()( 1

121

1

0

δOx

Fdx

xxF

dxFδ

ε

δSlicing

R

)()1(2)1(

)( 21

0

δOFε

δxxF

dxFεδ

Slicing

R

)()1()1()(1

0

δLogFxxF

dxFδ

Slicing

NLO

About subtraction method:

1

021

1

0

)()1(

1)()1(

21

xFx

dxxFxδdxε

F εNLO

1

121

1

021 )1(

)()1()(

δε

δ

ε

Slicing

R xxF

dxxxF

dxF

1

021

1

021 )1(

)1()1()1(

)1()1()(ε

cε

cSub

R xxxθF

dxx

xxθFxFdxF

10 cx

)log()1()1(

)1()1()(1

0c

cSub

NLOxF

xxxθFxF

dxF

1

021)1(

)()1(

21

εNLO xxF

dxFε

F

Neglected O() terms Large-number cancellations

)1(21

xδεdx

σd

V

xdxσd

R

11

without any approximation and large-number cancellation (beware of narrow bins)

ppx)1(

Real emission plus virtual correction


We have recalculated and checked (with respect to KKK’s)matrix elements

We implemented a “partons generator”(hep-ph/9512328 and hep-ph/9706545)

divided in three classes of Feynman diagrams: double resolved, single resolved, direct diagrams

…paper in preparation

The structure of the “home made” computation

We have to rely on non-perturbative inputs such as

PDFs and

+ + + … NLO terms

s


A first check: A comparison with OPAL 1997 (one inclusive jet)

Ok, at least we are on the right path…

The first check

Inclusive Jet Production in Photon-Photon Collision at sqrt(s)=130 and 136 GeV, Opal coll., Zeit. Fur Physik(1997)


But we need self consistence tests!!! Unfortunately they are very boring!Let’s try to see their physical meaning:

what about the true point-like photon contribution to the cross section?

Changing the factorizationscheme

Scheme DI-MS

Each class of diagrams is separately divergent:

We have removed analyticallythe infinities modulo

finite, scheme dependent,terms

Thus colored histosdo not have a real physical

meaning


Changing the factorization scale

Changing the PDF

eeγ

jet

jz

j

hadrons

hz

h

jet

jz

j

γ sx

pE

pE

pE

x2,1

2,12,1

Try another way…

1x

2x


Let’s try to understand where our troubles come from

Dangerous regions:

Zoom

Failure of the perturbativecomputation

PYTHIA

HERWIG

OPAL

350%

)process ionhadronisat the of end the At()shower parton"" the of end the At(

1σ

σδhadr


Let’s try to understand where our troubles come from

Recall our simple model to deal with the final state direct contribution in the dangerous region

...)1(

)1(

)1(1

γ

γ

γγ x

xθ

xdxσd

γxxx 1

1

0 )1()1()(

xFxF

dxFSub

NLO)1()( γ

γ

xδxFdx

σd

px )1(

xp p

Cuts on the phase spacefor di-jet observables

Phi angle

41

OpalφNLO Limit1tE

2tE

0φ

31

=φ

Observation:• In NLO computation• In the limit we run into IR divergences!

41

21

21

TT

TT

EEEE

φ-

• Symmetric cuts on Et imply large log corrections • Opal coll. have chosen to impose:

31

NLOφ0φ

… thus even if in principle Opal’s choice could be dangerous, in practice it is far from the singularity sources!

Et min

min Et


Data from Di-Jet Production in photon-photon collisions at sqrt(s) from 189 to 209 GeV,

OPAL coll., hep-ex/0301013


Results:opal2

75 JetTE

75 JetTE

75.0 & xx

Data from Di-Jet Production in photon-photon collisions at sqrt(s) from 189 to 209 GeV,

OPAL coll., hep-ex/0301013

Results:l3

Good shape,but not really good

normalization

Wrong shape andnormalization:

Preliminary data seemto confirm L3-hadron

production discrepancywith NLO prediction


Finally, we analyzed some theoretical QCD (NLO) difficulties to describe well particular exclusive

observables measured by OPAL.Theoretical uncertainties for inclusive observables

are under control.

Conclusions

We implemented a computer code to compute jet and di-jet observables using the subtraction method;

our results are in agreement with the predictions by KKK.

The comparisons of our results with OPAL data are really satisfactory for inclusive observables.

The comparison with L3 data is troublesome!


L. Bertora

Results:opalB

PHYTIA

KKK NLO/(1+hadr)

2511 JetTE

Data from Di-Jet Production in photon-photon collisions at sqrt(s) from 189 to 209 GeV,OPAL coll., hep-ex/0301013

75 JetTE

Results:opalc

75.0 & xx

75 JetTE

75.0 & xx

Data from Di-Jet Production in photon-photon collisions at sqrt(s) from

189 to 209 GeV, OPAL coll., hep-ex/0301013

Work done in collaboration with Stefano Frixione

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