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Saturation at hadron colliders

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This paper examines saturation effects in gluon-initiated processes using the GBW model and its extensions, focusing on Mueller-Navelet jets and forward-jet production. We discuss the dipole formalism and its implications for understanding cross-sections at hadron colliders like the Tevatron and LHC. Also addressed are the criteria for experimentally accessing saturation through specific ratios and observable changes at high energy scales. The study aims to enhance the comprehension of gluon dynamics and the transition towards saturation in high-energy particle collisions.

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Saturation at hadron colliders

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  1. Saturation at hadron colliders Cyrille Marquet SPhT, Saclay hep-ph/0312261 to appear in PLB in collaboration with Robi Peschanski

  2. 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

  3. 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

  4. 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)

  5. 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

  6. 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.

  7. 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

  8. 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)

  9. 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

  10. Saturated 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

  11. 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?

  12. 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

  13. 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?

  14. 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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