Work done in collaboration with Stefano Frixione 1 Leonardo Bertora, 2003 April 8 Jet and di-jet...

Work done in collaboration with Stefano Frixione1

Leonardo Bertora, 2003 April 8

Jet and di-jet production at NLO in Photon – Photon collisions

Leonardo Bertora1,2

1

2

INFN, Sezione di Genova

Università di Genova, DiFi

OPAL, see talk by T. Wengler

L3, see talk by M. Kienzle

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 of QCD

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

Experimental Situation:

As of now only the theoretical prediction by

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

hep-ph/9712256) is available

It is based upon slicing method

Situation


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

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

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



About subtraction method:

1

021

1

0

)()1(

1)()1(

2

1xF

xdxxFxdxF

NLO

1

121

1

021 )1(

)(

)1(

)(

x

xFdx

x

xFdxF

Slicing

R)(

)1(

)1(

)1(

)( 1

121

1

0

Ox

Fdx

x

xFdxF

Slicing

R

)()1(2)1(

)( 21

0

OFx

xFdxF

Slicing

R

)()1()1(

)(1

0

LogFx

xFdxF

Slicing

NLO

1

021

1

021 )1(

)1()1(

)1(

)1()1()(

x

xxFdx

x

xxFxFdxF ccSub

R 10 cx

)log()1()1(

)1()1()(1

0

ccSub

NLOxF

x

xxFxFdxF

1

021)1(

)()1(

2

1 x

xFdxFF

NLO

Neglected O() terms Large-number cancellations

)1(2

1x

dx

d

V

xdx

d

R

1

1

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) the 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 input 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 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

ee

jet

jz

jL

hadrons

hz

hL

jet

jz

jL

sx

pE

pE

pE

x2,1

2,12,1

Try another way…


1x

2x

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

x

x

xdx

d1

0

x

xx

1

0 )1(

)1()(

x

FxFdxF

Sub

NLO)1()(

xxF

dx

d px)1(

xp

Dangerous regions:

Zoom

Failure of the perturbativecomputation

PYTHIA

HERWIG

OPAL

350%

)procession hadronisat theof end At the(

)shower parton"" theof end At the(1

hadr


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

Cuts on the phase spacefor di-jet observables

Phi angle

4

1OpalNLO Limit

1tE

2tE

0

2

1

4

1

21

21

TT

TT

EE

EE

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

2

1NLO

0

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


Et min

min Et

Results:opal

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


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


OPAL coll., preprint

75 JetTE

Results:opalc

75.0 & xx

75 JetTE

75.0 & xx

Work done in collaboration with Stefano Frixione 1 Leonardo Bertora, 2003 April 8 Jet and di-jet...

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