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

Contents:Contents:1.1. Pomeron, odderon and reggeons:Pomeron, odderon and reggeons: perturbative versus nonperturbative perturbative versus nonperturbative

dynamics.dynamics.

2.2. Unitarity effects for diffractive Unitarity effects for diffractive processes and the role of triple-processes and the role of triple-pomeron interactions.pomeron interactions.

1. Pomeron, odderon, and reggeons: 1. Pomeron, odderon, and reggeons: perturbative versus nonperturbative perturbative versus nonperturbative dynamics.dynamics.

Pomeron in QCD is usually Pomeron in QCD is usually related to gluonic states in related to gluonic states in the t-channel.the t-channel.

In QCD perturbation theory: In QCD perturbation theory: ladder type diagrams with ladder type diagrams with exchange by reggeized exchange by reggeized gluons – BFKL pomeron.gluons – BFKL pomeron.

ααPP(0)=1+(12ln2/(0)=1+(12ln2/ππ))ααs s –C–C22 ααs s ² .² .

Large NLO correctionsLarge NLO corrections

The pomeron has the vacuum quantum numbers:The pomeron has the vacuum quantum numbers:signature signature σσ=+, parity P=+, C-parity=+.=+, parity P=+, C-parity=+.The odderon has The odderon has σσ=-, P=-, C=-. =-, P=-, C=-.

In QCD the odderon is due to exchange byIn QCD the odderon is due to exchange byat least 3 gluons in the t-channel and itsat least 3 gluons in the t-channel and itsIntercept in PQCD is close to unity.Intercept in PQCD is close to unity.

What is the role of large distance dynamics and of What is the role of large distance dynamics and of the nonperturbative effects?the nonperturbative effects?

In general the pomeron (odderon) is determined by In general the pomeron (odderon) is determined by both small and large distance dynamics.both small and large distance dynamics.

J-plane structure of the BFKL- J-plane structure of the BFKL- pomeron in NLO. pomeron in NLO.

In the NLO approximation In the NLO approximation there is a sequence of poles there is a sequence of poles

in the j-planein the j-plane ( ( ωω=j-1 ) .=j-1 ) .

The rightmost pole is theThe rightmost pole is thesoftest one and depends on softest one and depends on

large distance dynamics.large distance dynamics. L.P.A. Haakman et al.L.P.A. Haakman et al. M.Ciafaloni et al.M.Ciafaloni et al.

Pomeron, odderon Regge trajectories Pomeron, odderon Regge trajectories and the spectrum of glueballsand the spectrum of glueballs..

The role of large distance dynamics has been The role of large distance dynamics has been studied using the nonperturbative Wilson loop studied using the nonperturbative Wilson loop approach and the method of vacuum approach and the method of vacuum correlators. correlators. A.Kaidalov, Yu.SimonovA.Kaidalov, Yu.Simonov

This method allows to calculate usual Regge This method allows to calculate usual Regge trajectories and predicts spectrum of glueballs trajectories and predicts spectrum of glueballs in a good agreement with lattice calculations.in a good agreement with lattice calculations.

String HamiltonianString Hamiltonian

Spectra from the string HamiltonianSpectra from the string Hamiltonian

The spectrum for C=+The spectrum for C=+ gluons is well gluons is well

approximated by theapproximated by the formula:formula:

M²=2M²=2πσπσ(J-2n+C)(J-2n+C)Set of linear Regge Set of linear Regge

trajectoriestrajectories

Mixing with quark-antiquark Regge Mixing with quark-antiquark Regge trajectories.trajectories.

In the region of “crossing” of gg and quark-antiquark In the region of “crossing” of gg and quark-antiquark Regge trajectories fRegge trajectories f00, f, f00’ (t< 1 GeV’ (t< 1 GeV²) there is a ²) there is a strong mixing between them. strong mixing between them.

These effects lead to a strong curvature for the These effects lead to a strong curvature for the leading (Pomeron) trajectory. leading (Pomeron) trajectory.

Mixing with light quarkoniaMixing with light quarkonia

Rich dynamical Rich dynamical structure of the structure of the

Pomeron:Pomeron:both large and small both large and small

distance effects, distance effects, mixing with light mixing with light

quarks, influence of quarks, influence of light pions.light pions.

3g-Regge trajectories in 3g-Regge trajectories in nonperturbative approach have low nonperturbative approach have low intercepts.intercepts.

Two types of 3g-comfigurations: Two types of 3g-comfigurations: ΔΔ and and ΥΥ..They have the intercepts:They have the intercepts: ααΔΔ(0)= -1.0(0)= -1.0 ααΥΥ(0)= -1.9(0)= -1.9

Very different from the perturbative value +1.Very different from the perturbative value +1.Critical test : experimental search for “odderon”. Critical test : experimental search for “odderon”. No sign of “odderon” exchange in the reactionsNo sign of “odderon” exchange in the reactions

γγppππºN(N*), ºN(N*), γγppfºN(N*) fºN(N*) at HERAat HERA ( H( H11).).

Quark-antiquark Regge trajectoriesQuark-antiquark Regge trajectorieswith I=1 (with I=1 (ρρ, A, A22).).

In PQCD such trajectories are predicted to have In PQCD such trajectories are predicted to have αα(t) (t) > 0 and > 0 and αα(t) (t) 0 for (-t) 0 for (-t) ∞∞..

R. Kirschner, L. LipatovR. Kirschner, L. LipatovNonperturbative, string-like dynamics leads toNonperturbative, string-like dynamics leads to

linear Regge trajectories.linear Regge trajectories.The leadingThe leading ρρ, A2 – trajectories are well determined , A2 – trajectories are well determined

experimentally at t > 0 from the spectrum of experimentally at t > 0 from the spectrum of resonances and at t < 0 from analysis resonances and at t < 0 from analysis of the of the

reactionsreactions ππ־־ppππºN(X), ºN(X), ππ־־ppηηºN(X).ºN(X).

Linearity of the effective Linearity of the effective ρρ-trajectory -trajectory up to t ≈ -2 GeV² . up to t ≈ -2 GeV² .

Where is the PQCD contribution?Where is the PQCD contribution?

Conclusion:Conclusion:

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

Unitarity effects for hard diffractive Unitarity effects for hard diffractive processes and the role of triple-processes and the role of triple-pomeron interactions.pomeron interactions.

Example of hard diffractionExample of hard diffraction

Importance of multipomeron Importance of multipomeron exchangesexchanges

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

Same effects for double gap Same effects for double gap configurations.configurations.

Calculation of “survival probability”Calculation of “survival probability”

For single channel diffraction (elastic scattering For single channel diffraction (elastic scattering only) :only) :

Where Where ΩΩ(b,s) is the eikonal. S² is the probability of(b,s) is the eikonal. S² is the probability of not to produce particles (not to fill the gap). In thenot to produce particles (not to fill the gap). In the eikonal model eikonal model ΩΩ(b,s) is the Fourier transform of the (b,s) is the Fourier transform of the Pomeron and it increases with energy for Pomeron and it increases with energy for ααPP(0) > 1. (0) > 1.

Account of inelastic diffractionAccount of inelastic diffractionFor several diffractive For several diffractive channels same formula channels same formula (with (with ΩΩii(b,s))(b,s)) for each for each eigen state i.eigen state i.With a proper choiceWith a proper choiceof the eigen state –of the eigen state –reasonable descriptionreasonable descriptionof the CDF data on of the CDF data on diffractive jets.diffractive jets. KKMRKKMR

Interactions between pomerons.Interactions between pomerons.

Existence of large Existence of large mass diffraction. In mass diffraction. In Regge approach Regge approach corresponds to 3P, corresponds to 3P, 4P,.. interactions.4P,.. interactions.How to account for How to account for extra shadowing extra shadowing

effects due to these effects due to these interactions?interactions?

KKMRKKMR

Interactions between pomeronsInteractions between pomerons (continuation). (continuation).

This problem in the framework of PQCD has This problem in the framework of PQCD has been discussed recently by J. Bartels et al.been discussed recently by J. Bartels et al.

KKMR conclusion: for jets at Tevatron andKKMR conclusion: for jets at Tevatron andfor Higgs at LHC :there is not enough phasefor Higgs at LHC :there is not enough phasespace for these effects. However for manyspace for these effects. However for many processes (especially soft ones) interactions processes (especially soft ones) interactions between pomerons can be important.between pomerons can be important.

Schwimmer model.Schwimmer model.

Fan-type diagramsFan-type diagrams are summed.are summed.

Schwimmer model (cont.).Schwimmer model (cont.).

Thus the suppression factor in this modelThus the suppression factor in this model SS²²SchwSchw = (1+= (1+εε((ττ-1))-1)) ¹¹־־ ((1+21+2εε((ττ-1))-1)) ¹¹־־For differential cross section:For differential cross section: Yu.V.Kovchegov, E.Levin,Yu.V.Kovchegov, E.Levin, K. Boreskov + KKMRK. Boreskov + KKMR

The eikonalized Schwimmer model.The eikonalized Schwimmer model.

The eikonalized Schwimmer model.The eikonalized Schwimmer model.

In this caseIn this case SStt²=S²²=S² S S²²Schw Schw , where, where

Bounds on 3P-contributions to S².Bounds on 3P-contributions to S².

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

Conclusions.Conclusions. Cross sections of inelastic diffractive processes Cross sections of inelastic diffractive processes

are strongly suppressed at high energies in the are strongly suppressed at high energies in the small impact parameter region. Only large b~ln(s)small impact parameter region. Only large b~ln(s)

contribute. In this region nonperturbative effects contribute. In this region nonperturbative effects are important.are important.

A method to account for interactions between A method to account for interactions between pomerons in hadronic interactions should be pomerons in hadronic interactions should be developed for realistic calculations of diffractive developed for realistic calculations of diffractive processes.processes.