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 03 St. Petersburg, 23-27 April 2003

2. Outline Definition of the RGI approach Green’s function Extension of PT domain Splitting function

3. vs picture BFKLDGLAP ’ ’ ’

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

5. What have we learnt? Position of collinear   -poles of evolution kernels depends on s 0 Origin of cubic poles in  1 (  ) : expansion around  = 0 of shifted poles ~1/(  +  /2) Non-singular part A(  ) of anomalous dimension  gg (  )  A(  ) can be taken into account by a subleading kernel in 2 ways: (remember )

6. Definition of RG Improved Approach Adapting the procedure for running  s and with s 0 = Q 1 Q 2 : resums scale dependent terms of a pure BFKL approach resums exact 1-loop gluon anomalous dimension (note  -dependence of A ) includes left-over exact NL BFKL infos This procedure implements kinematical constraints

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

8. Domain of applicability of perturbative QCD

9. Resummed splitting function is independent of : important check of RG factorization Evolution eqn. Gluon density High-energy exponent  c (  s )

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:  *-  *, forward jets, Mueller-Navelet jets, …