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Gluon Evolution at small-x : Extending the PT Domain of QCD

This research explores the extension of the perturbative domain of Quantum Chromodynamics at small momentum fractions. It delves into the BFKL and DGLAP evolutions, their scale changes, and implications for high-energy phenomena in QCD. By developing an improved approach that considers subleading corrections and running coupling effects, this study aims to provide reliable predictions in the high-energy regime.

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Gluon Evolution at small-x : Extending the PT Domain of QCD

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  1. Gluon Evolution at small-x:Extending the PT Domain of QCD Dimitri Colferai University of Firenze M. Ciafaloni G.P. Salam A.M. Stasto { In collaboration with: DIS 03St. Petersburg, 23-27 April 2003

  2. Outline

  3. vs picture BFKL DGLAP ’ ’ ’ ’ ’ ’

  4. h’ hG’ Gh’ h Scale change: BFKL vs DGLAP kernel in the collinear limit k >> k’ ; Simplified case:

  5. What have we learnt? • Position of collinear g-poles of evolution kernels depends on s0 • Origin of cubic poles in c1(g ): expansion around w= 0 of shifted poles ~1/(g+ w/2) • Non-singular part A(w) of anomalous dimension ggg(w) = 1/w + A(w) can be taken into account by a subleading kernel in 2 ways: (remember )

  6. Definition of RG Improved Approach Adapting the procedure for running asand with s0= Q1Q2 : resums scale dependent terms of a pure BFKL approach includes left-over exact NL BFKL infos resums exact 1-loop gluon anomalous dimension (note w-dependence of A) This procedure implements kinematical constraints

  7. Diffusion corrections: Scheme A Scheme B fixed running numeric Y-evolution of Green’s function Hard Pomeron

  8. Domain of applicability of perturbative QCD

  9. Gluon density Evolution eqn. Resummed splitting function is independent of : important check of RG factorization High-energy exponent wc(as)

  10. Conclusions • 2 main problems of high-energy perturbative QCD: • occurrence of large leading log s contributions and of subleading ones of comparable size and opposite sign • increasing importance of wee partons, whence a strong coupling non-perturbative Pomeron regime • RGI approach tames both problems: • through an understanding and consequent resummation of the most important subleading contributions • Subleading corrections and running coupling effects lower high-energy exponents and diffusion/tunneling into NP region • We expect a large domain of applicability of PT QCD • We have the tools to make reliable physical predictions: g *-g *, forward jets, Mueller-Navelet jets, …

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