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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-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 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
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 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
Formulae 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
Saturated cross-sections
  • model 3 withQ1= Q2  Q
  • the plot shows theexpected trend: a suppression of3in the domain Q

Q0 = 1 GeV

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

a suitable measurement
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 int eresting signal
An potentially 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 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 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