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### Saturation at hadron colliders

Cyrille Marquet

SPhT, Saclay

hep-ph/0312261

to appear in PLB

in collaboration with Robi Peschanski

Contents

- Introductiongluon-initiated processes and saturation
- Frameworkthecolor dipoles, the GBW model and its extension
- Forward-jet production in terms of dipoles
- Mueller-Navelet cross-sectionswith saturation effects
- Conclusion and outlook

Mueller-Navelet jets (1987): considered to test the BFKL evolution at the TevatronQ1, Q2 » QCD exp()» 1prediction: (>()2)

Production of heavy-flavored and vector mesons

Can we reach saturation inthese processes?atthe Tevatron or LHC ?

How does one formulatesaturation in such processes?

Gluon-initiated processesDIS: the Golec-Biernat and Wüsthoff (GBW) model (1998) forthe dipole-proton cross-sectionSaturation and the GBW model

- photon-photon with an extension of the GBW model: a model for the dipole-dipole cross-section

Tîmneanu, Kwiecinski and Motyka (2002)

Dipole factorization for hardcross-sections

- equivalent to BFKL+kT-factorization
- in the present work, we assume this factorization property to hold in the presence of saturation

thethree models exhibit color transparency

- the model 3 correspondsto the two-gluon exchange betweenthe dipoles

TKM (2002)

- the saturation radius iswe use the same parameters as those of dipole-proton = 0.288, 0 = 8.1 for Q0 1 GeV(universal saturation scale)
- thethree scenarios we consider are

1. 2.3.

the onium allows a perturbative calculation and the interpretation in the dipole formalism; in the collinear limitr0Q »1, f factorizes:Forward-jet in terms of dipoles

Munier (2001), C.M. and R. P. (2003)

collinear factorization

dipole factorization

large-size dipoleshave a contribution to ; this is not the casefor in a photon-initiated process

cannot be seen as a probability distribution

the BFKL cross-sectionscalculated withare positive

The dipole distribution in a forward jetPeschanski (2000), C.M. and R. P. (2003)

Formulae for the hard total cross-sections

C.M. and R. Peschanski (2003)

for the different models :

- the cross-sections are positivei > 0
- however2’s high-Q limit (no saturation) does not behave as 1/Q2

Saturated cross-sections

- model 3 withQ1= Q2 Q
- the plot shows theexpected trend: a suppression of3in the domain Q

Q0 = 1 GeV

The rapidityintervals for the different curves are: = 4, 6, 8, 10

A suitable measurement

- a ratio studiedto test theBFKL evolution at the Tevatron (DØcollaboration, 1999)
- shows the influence of saturation in a more quantitative way
- experimentally, Rwas obtained working at fixed andusing the factorization of the structure functionsinthe totalcross-sections:
- R at LHC?

An potentially interesting signal

- thevalue of Rgoes downfrom the transparency limit towards the saturation regime whereR1
- one can observeasharper transition in the case of the gluon-initiated process
- thevalues of Q at the transition are weak for jet cuts at the Tevatron
- along with BFKL studies, the signal deserves to be studied at the LHC
- alternatives to bypass the small-Q problem?

Q0 = 1 GeV

R 4.6/2.4 : ratiostudied attheTevatronR 8/4 : ratio realistic forthe LHC

Other configurations

- asymmetric configurations ? the transition towards saturation becomesreallysteep more interesting: the transition isshiftedtowardshigher Q

Q0 = 1 GeV

- alternatives to jets: heavy vector mesonsJ/ orD mesons withc quarks or B mesons with b quarks in asymmetric configurations?

Conclusion and outlook

- Introduction of the dipole formalismin the description of hadron-induced hard processes, such as Mueller-Navelet jets
- Studies of saturation effects in these processes using an extension ofthe Golec-Biernat and Wüsthoff model
- Proposal and predictions for an observable at hadron colliders

To do

- Studies of feasabilityforthe Tevatron and LHC:can we access the ratioR experimentally? for which values of Q? using jets or alternativelyheavy vector mesons, heavy flavors?

Theoretical extensions

- Improve our description of gluon-initiated processes in termsof dipoles:taking into account saturation effects in the emission vertex and kT-factorization breaking
- StudyingpQCD saturation beyond GBW models

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