Post on 09-Jan-2016
description
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
Leonardo Bertora, 2004 April 14
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
Leonardo Bertora, 2004 April 14
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
Leonardo Bertora, 2004 April 14
)()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
Leonardo Bertora, 2004 April 14
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
Leonardo Bertora, 2004 April 14
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)
Leonardo Bertora, 2004 April 14
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
Leonardo Bertora, 2004 April 14
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
Leonardo Bertora, 2004 April 14
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
Leonardo Bertora, 2004 April 14
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
Leonardo Bertora, 2004 April 14
Data from Di-Jet Production in photon-photon collisions at sqrt(s) from 189 to 209 GeV,
OPAL coll., hep-ex/0301013
Leonardo Bertora, 2004 April 14
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
Leonardo Bertora, 2004 April 14
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!
Leonardo Bertora, 2004 April 14
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