Diffractive deep inelastic scattering

1. Diffractive deep inelastic scattering Cyrille MarquetRIKEN BNL Research Center

2. Contents • Inclusive deep inelastic scattering (DIS): e h  e Xthe structure functions F2, FT and FL Diffractive deep inelastic scattering • Inclusive Diffraction: e h  e X h the structure functions F2D, FTDand FLD • Exclusive vector meson production: e h  e  h, e h  e J/ hDeeply virtual Compton scattering (DVCS): e h  e  h momentum transfer and impact parameter • Diffactive jet production

3. lh center-of-mass energyS = (l+P)2*h center-of-mass energyW2 = (l-l’+P)2photon virtualityQ2 = - (l-l’)2 > 0 transverse size resolution 1/Q P hadron Deep inelastic scattering (DIS) x ~ momentum fraction of the struck parton y~ W²/S

4. Deep inelastic scattering (DIS) FTand FL correspond to the scattering of a transversely (T) or longitudinally (L) polarized virtual photon off the hadron experimental data are often shown in terms of

5. e p  e X experimental data measurements performed at the HERA collider by the H1 and ZEUS collaborations over a broad kinematic range at moderate x: bjorken scaling  F2(x) scaling violations: evidence for gluons about 15 % of the events are diffractive

6. Geometric scaling in DIS When plotting the same cross-section as a function of the variable Q² x one obtains a scaling curve: Stasto, Golec-Biernat and Kwiecinski (2001) x < 10-2 with Q0 1 GeV and  0.3 this scaling is called geometric scaling it identifies an intrinsic scale of the proton which rises as x decreases: Q0x-/2 Can we understand that scale/scaling from QCD? It should also have consequences in diffraction

7. Inclusive diffraction

8. momentum transfert = (P-P’)2 < 0diffractive mass of the final stateMX2 = (P-P’+l-l’)2 P hadron P Diffractive DIS when the hadron remains intact ~ momentum fraction of the struck parton with respect to the Pomeron xpom = x/ rapidity gap :  = ln(1/xpom) xpom~ momentum fraction of the Pomeron with respect to the hadron

9. experimental data are often shown in terms of Diffractive DIS in terms of photon-hadron diffractive cross-section:

10. Diffractive DIS without proton tagging e p  e X Y with MY cut H1 LRG data MY < 1.6 GeV ZEUS FPC data MY < 2.3 GeV Inclusive diffraction measurements Diffractive DIS with proton tagging e p  e X p H1 FPS data ZEUS LPS data

11. e p  e X p experimental data measurements performed at the HERA collider by the H1 and ZEUS collaborations over a broad kinematic range

12. perturbative • perturbative evolution of  with Q2 : Dokshitzer-Gribov-Lipatov-Altarelli-Parisi Collinear factorization in the limit Q²   withx fixed • For inclusive DIS a = quarks, gluons not valid if x is too small non perturbative

13. for instance at the Tevatron: predictions obtained with diffractive pdfs overestimate CDF data by a factor of about 10 a very popular approach: use collinear factorization anyway, and apply a correction factor called the rapidity gap survival probability Factorization in DDIS ? collinear factorization for F2Dsimilar with diffractive parton densities but: you cannot do much with the diffractive pdfs factorization does not hold for diffractive jet production at low Q² diffractive jet production in pp collisions factorization also holds for diffractive jet production at high Q²

14. k’ k r : dipole size p in diffraction: at large Nc, 1 dipole emitting N-1 gluons = N dipoles The dipole picture of DIS valid in the small-x limit

15. p p’ Elastic/inelastic components elas: involves the quark-antiquark final state, dominant for small diffractive mass (large  ) same object for inclusiveand diffractive cross-section dissoc: involves higher order final states: qqg, …dominant for large diffractive mass (small  ) can also be expressed in the dipole picture

16. Measuring FLD Contributions of the different final states to the diffractive cross-section: at small  : quark-antiquark-gluon at intermediate  : quark-antiquark (T) at large  : quark-antiquark (L) large  measurements FLD FLD is higher twist: it cannot be predicted from pdfs

17. x < 10-2  0.3 What about geometric scaling geometric scaling can be easily understood as a consequence of large parton densities what does the proton look like in (Q², x) plane: lines parallel to the saturation line are lines of constant densities along which scattering is constant

18. Geometric scaling in diffraction At fixed  , the scaling variable should be C.M. and L. Schoeffel (2006)  0.3 consistent with the HERA data diffractive cross-section in bins of  xpom < 10-2

19. MX=30 GeV MX=20 GeV MX=11 GeV MX=6 GeV MX=3 GeV MX=1.2 GeV Success of the dipole model CGC = saturation model Iancu, Itakura and Munier (2003) Forshaw and Shaw have not been able to find a good fit without saturation effects

20. Ratio diffractive/inclusive saturation naturally explains the constant ratio

21. Exclusive vector meson productionandDeeply virtual Compton scattering

22. in the dipole picture: with the overlap function: sensitive to instead of  access to impact parameter Exclusive vector-meson production measurements: lots of data from HERA (especially J/Psi) - collinear factorization with generalized parton densities - determination of the t slope:

23. rho production S. Munier, A. Stasto and A. Mueller (2001) the S-matrix (S=1-T ) is extracted from the  data yellow band: cannot be trusted, too sensitive to large t region where there is no data S(1/r 1Gev, b  0, x  5.10-4)  0.6 HERA is entering the saturation regime

24. J-Psi production H. Kowalski and D. Teaney (2003) E. Gotsman, E. Levin, M. Lublinsky,U. Maor and E. Naftali (2003)

25. What about geometric scaling t integrated cross-sections d/dt cross-sections C.M., R. Peschanski and G. Soyez (2005) saturation scale form factor with B = const need data at fixed t for different values of x and Q²

26. Diffractive tri-jet production

27. model independent model dependent model independent 1/k² k² k 0 k0 Diffractive tri-jet production C.M. and K. Golec-Biernat (2005) final state configuration: tri-jet + gap + proton k0: typical unitarization scale idea: measure the transverse momentum spectrum of the gluon jet k the gluon jet is the most forward in the proton direction other configurations are suppressed by ln(1/ ) k : gluon transverse momentum • observable strongly sensitive to unitarity effects

28. kmax/QS = independent of Q², QS  1.5 Can we experimentally test this? extract QS? important limitation: at HERA QS< 1 Gev and k > 3 Gev one does not have access to the whole bump Study of with a saturation model marked bump for k = kmax

29. In the HERA energy range Predictions of the GBW model with and the parameters  andx0 taken from the F2 fits: • = 0.288 andx0 = 3.10-4 for full lines (no charm)  = 0.277 andx0 = 4.10-5 for dashed lines (charm included) need points in different bins ZEUS did measure 4 points for

30. Conclusions • Inclusive diffractionmeasure FLD • Exclusive vector meson production/DVCSmeasurements in different t bins with large Q² and x ranges • Diffractive tri-jet productionpotential to bring evidence for saturation?