Some problems of diffraction at high energies.

1. Some problems of diffraction at high energies. A.B. Kaidalov ITEP, Moscow

2. Contents: • Pomeron, odderon and reggeons: perturbative versus nonperturbative dynamics. • Unitarity effects for diffractive processes and the role of triple-pomeron interactions.

3. Pomeron in QCD is usually related to gluonic states in the t-channel. In QCD perturbation theory: ladder type diagrams with exchange by reggeized gluons – BFKL pomeron. αP(0)=1+(12ln2/π)αs –C2αs ² . Large NLO corrections 1. Pomeron, odderon, and reggeons: perturbative versus nonperturbative dynamics.

4. The pomeron has the vacuum quantum numbers:signature σ=+, parity P=+, C-parity=+.The odderon has σ=-, P=-, C=-. In QCD the odderon is due to exchange by at least 3 gluons in the t-channel and its Intercept in PQCD is close to unity. What is the role of large distance dynamics and of the nonperturbative effects? In general the pomeron (odderon) is determined by both small and large distance dynamics.

5. In the NLO approximation there is a sequence of poles in the j-plane ( ω=j-1 ) . The rightmost pole is the softest one and depends on large distance dynamics. L.P.A. Haakman et al. M.Ciafaloni et al. J-plane structure of the BFKL- pomeron in NLO.

6. Pomeron, odderon Regge trajectories and the spectrum of glueballs. The role of large distance dynamics has been studied using the nonperturbative Wilson loop approach and the method of vacuum correlators. A.Kaidalov, Yu.Simonov This method allows to calculate usual Regge trajectories and predicts spectrum of glueballs in a good agreement with lattice calculations.

7. String Hamiltonian

8. The spectrum for C=+ gluons is well approximated by the formula: M²=2πσ(J-2n+C) Set of linear Regge trajectories Spectra from the string Hamiltonian

11. Mixing with quark-antiquark Regge trajectories. In the region of “crossing” of gg and quark-antiquark Regge trajectories f0, f0’ (t< 1 GeV²) there is a strong mixing between them. These effects lead to a strong curvature for the leading (Pomeron) trajectory.

12. Rich dynamical structure of the Pomeron: both large and small distance effects, mixing with light quarks, influence of light pions. Mixing with light quarkonia

13. 3g-Regge trajectories in nonperturbative approach have low intercepts. Two types of 3g-comfigurations: Δ and Υ. They have the intercepts: • αΔ(0)= -1.0 • αΥ(0)= -1.9 Very different from the perturbative value +1. Critical test : experimental search for “odderon”. No sign of “odderon” exchange in the reactions γpπºN(N*), γpfºN(N*) at HERA( H1).

14. Quark-antiquark Regge trajectorieswith I=1 (ρ, A2). In PQCD such trajectories are predicted to have α(t) > 0 and α(t)  0 for (-t)  ∞. R. Kirschner, L. Lipatov Nonperturbative, string-like dynamics leads to linear Regge trajectories. The leadingρ, A2 – trajectories are well determined experimentally at t > 0 from the spectrum of resonances and at t < 0 from analysis of the reactionsπ־pπºN(X), π־pηºN(X).

15. Linearity of the effective ρ-trajectory up to t ≈ -2 GeV² . Where is the PQCD contribution?

16. Conclusion: • In the high-energy Regge limit nonperturbative effects play an important role up to rather large (-t).

17. Unitarity effects for hard diffractive processes and the role of triple-pomeron interactions. • Example of hard diffraction

18. Importance of multipomeron exchanges Both Regge and QCD factorizations of the lowest order diagrams are strongly broken due to multipomeron exchanges (unitarity effects).

19. Same effects for double gap configurations.

20. Calculation of “survival probability” For single channel diffraction (elastic scattering only) : Where Ω(b,s) is the eikonal. S² is the probability of not to produce particles (not to fill the gap). In the eikonal model Ω(b,s) is the Fourier transform of the Pomeron and it increases with energy for αP(0) > 1.

21. For several diffractive channels same formula (with Ωi(b,s)) for each eigen state i. With a proper choice of the eigen state – reasonable description of the CDF data on diffractive jets. KKMR Account of inelastic diffraction

22. Existence of large mass diffraction. In Regge approach corresponds to 3P, 4P,.. interactions. How to account for extra shadowing effects due to these interactions? KKMR Interactions between pomerons.

23. Interactions between pomerons (continuation). This problem in the framework of PQCD has been discussed recently by J. Bartels et al. KKMR conclusion: for jets at Tevatron and for Higgs at LHC :there is not enough phase space for these effects. However for many processes (especially soft ones) interactions between pomerons can be important.

24. Fan-type diagrams are summed. Schwimmer model.

25. Schwimmer model (cont.). Thus the suppression factor in this model S²Schw= (1+ε(τ-1))־¹(1+2ε(τ-1))־¹ For differential cross section: Yu.V.Kovchegov, E.Levin, K. Boreskov + KKMR

26. The eikonalized Schwimmer model.

27. The eikonalized Schwimmer model. In this case St²=S² S²Schw , where

28. Bounds on 3P-contributions to S². From analysis of CDF data on diffractive dijets one can conclude that effects due to 3P-interactions do not exceed 30%. Same conclusion follows from recent analysis of HERA data on spectra of leading neutrons. KKMR (2006)

29. Conclusions. • Cross sections of inelastic diffractive processes are strongly suppressed at high energies in the small impact parameter region. Only large b~ln(s) contribute. In this region nonperturbative effects are important. A method to account for interactions between pomerons in hadronic interactions should be developed for realistic calculations of diffractive processes.