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Saturation at hadron colliders. Cyrille Marquet SPhT, Saclay. hep-ph/0312261 t o a pp ear in PLB. in collaboration with Robi Peschanski. Contents. Introduction gluon-initiated processes and saturation Framework the color dipoles, the GBW model and its extension

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Saturation at hadron colliders

Saturation at hadron colliders

Cyrille Marquet

SPhT, Saclay


to appear in PLB

in collaboration with Robi Peschanski


  • 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

Gluon initiated processes

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 processes

Saturation and the gbw model

DIS: the Golec-Biernat and Wüsthoff (GBW) model (1998) forthe dipole-proton cross-section

Saturation 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 f actori z ation for hard cross sections
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

Exten s ion of the gbw model

  • thethree models exhibit color transparency

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

Extension of the GBW model

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.

Forward jet i n terms of dip o les

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

The dip o le distribution in a forward jet

larg interpretation in the dipole formalism; e-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 withare positive

The dipole distribution in a forward jet

Peschanski (2000), C.M. and R. P. (2003)

Formul ae for the hard total cross sections
Formul interpretation in the dipole formalism; ae for the hard total cross-sections

C.M. and R. Peschanski (2003)

for the different models :

  • the cross-sections are positivei > 0

  • however2’s high-Q limit (no saturation) does not behave as 1/Q2

Sa turate d cross sections
Sa interpretation in the dipole formalism; turated cross-sections

  • model 3 withQ1= Q2  Q

  • the plot shows theexpected trend: a suppression of3in the domain Q<Qs 1/R0()

Q0 = 1 GeV

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

A suitable measurement
A suitable measurement interpretation in the dipole formalism;

  • 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 int eresting signal
An potentially interpretation in the dipole formalism; interesting signal

  • thevalue of Rgoes downfrom the transparency limit towards the saturation regime whereR1

  • 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 configuration s
Other interpretation in the dipole formalism; configurations

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

Q0 = 1 GeV

  • alternatives to jets: heavy vector mesonsJ/ orD mesons withc quarks or B mesons with b quarks in asymmetric configurations?

Conclusion and outlook
Conclusion interpretation in the dipole formalism; 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