1. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk WGA Theory Low x BFKL and DGLAP BK Structure functions Diffraction

2. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk L.N. Lipatov presented the talk “DGLAP and BFKL equations in supersymmetric gauge theories”. Next-to-leading corrections to the BFKL kernel and to anomalous dimension matrix in N=4 SUSY are calculated. The DGLAP equation The BFKL equation for the gluon distributions at small x BFKL and DGLAP

3. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk The eigenvalues of the kernel

4. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

5. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

6. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

7. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

8. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

9. ’ ’ ’ Dmitry Colfefrai Gluon Evolution at small-x: Extending the PT Domain of QCD

10. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk ; Scale change: h’ h G’ G h’ h

11. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk Resummed splitting function is independent of : important check of RG factorization Evolution eqn. Gluon density High-energy exponent  c (  s )

12. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk 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, …

13. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

14. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

15. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

16. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk Improved Small-x Evolution with Running Coupling Effects The talk was presented by Guido Altarelli. The talk was devoted to construction of a relatively simple, closed form, improved anomalous dimensions  I ( ,N)

17. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk It was shown that BFKL with running coupling is fully compatible with RGE, factorisation and duality. In the Airy approximation the splitting functions are completely free of unphysical oscillations. An improved anomalous dimension that reduces to the perturbative result at large x and incorporates BFKL with running coupling effects at small x was constructed. The running coupling effects in the LO softens the asymptotic small x behaviour as indicated by the data.

18. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk Mellin transf. (MT) Inverse MT (  >0)

19. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk  M  s =0.2  0 +  2  1  0 The minimum value of  0 at M=1/2 is the Lipatov intercept: 0 =  0 (1/2)=  c 0 =  4n c /  log2~2.65  ~0.5 It corresponds to (for x->0): xP(x)~x - 0 Too hard not supported by data

20. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk The effect of running on  in the Airy model Is a softer small-x behaviour xP ~ x - xP ~ x - N 0

21. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

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25. DIS’03 St.Petersburg April 23-27, 2003 V. Fadin Institute of Nuclear Physics, Novosibirsk

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