1. Bernd Löhr, DESY Page 1 DIFFRACTION AT HERA The HERA Collider and the Experiments Luminosity and its Measurement Kinematics of Deep-Inelastic (DIS) and Diffractive Reactions Diffraction in High-Energy Particle Scattering Regge Phenomenology versus pQCD Exclusive Vectormeson Production and Deeply-Virtual Compton Scattering (DVCS) Inclusive Diffraction and Diffractive Structure Functions Exclusive Diffractive Reactions: Jets and Heavy Quarks

2. The HERA Collider Electron - proton collisions 27.5 GeV 920 GeV Bernd Löhr, DESYPage 2 This corresponds to an electron energy in a fixed-target experiment of E e = 26952 GeV electrons protons

3. Bernd Löhr, DESYPage 3 protons electrons protons backward The H1 Experiment Tracking : Liquid-Argon calorimeter : EM section : HAC section : HERA I Configuration

4. A rear view of the H1 detector Bernd Löhr, DESYPage 4

5. Bernd Löhr, DESYPage 5 protons backward The ZEUS Experiment electrons protons Tracking : Uranium-scintillator- calorimeter : EM section : HAC section : HERA I Configuration

6. electrons protons The ZEUS detector seen from above Bernd Löhr, DESYPage 6

7. The Concept of Luminosity Proton and electron beams are not continuous but they consist of bunches. Typically 180 proton bunches and electron bunches collided. Individual bunches from each beam collide What is the probability that a given process happens ? reaction rate ; cross section ; (instantaneous) luminosty The luminosity can be calculated from HERA parameters: where: -beam revolution frequency ; -number of electrons/protons in the i-th bunch - transverse size of interaction region Cross section: L = integrated luminosity Bernd Löhr, DESYPage 7 [cm -2 s -1 ] [cm -2 ]

8. Measurement of the Luminosity Measure the rate of a process whose cross-section is well known: Bremsstrahlung in e- collisions or Bethe-Heitler process proton Measure energy and rate of bremsstrahlung photons in specialized photon detector under very small angles w.r.t. the electron beam very well known cross-section (universal) integrated luminosity, for all cross-section calculations Bernd Löhr, DESYPage 8 initial state radiationfinal state radiation ZEUS interaction point about 100m away from interaction point photon detector e - - beam p- beam

9. Optical diffraction High energetic elastic scattering Generalization in high energy particle interactions : Diffraction is the exchange of an object with vacuum quantum numbers. elastic single dissociation double dissociationdouble Pomeron exchange Hypothetical object : Pomeron IP Bernd Löhr, DESYPage 9 From Optical Diffraction to High Energy Particle Scattering

10. Kinematics of DIS and Diffraction Bernd Löhr, DESYPage 10 virtuality, size of the probe center of mass energy squared - proton cms energy squared x : fraction of the proton carried by the struck parton y : inelasticity, fraction of the electron momentum carried by the virtual photon q = k - k’ kk’ mass of the diffractive system x four-momentum transfer squared at the proton vertex For diffractive events in addition 2 variables Inclusive nondiffr. DIS events : Diffractive DIS events : momentum fraction of the proton carried by the Pomeron fraction of the Pomeron momentum which enters the hard scattering

11. DIS- and Diffractive Events Bernd Löhr, DESYPage 11 kk’ Inclusive DIS events : Diffractive DIS events : Considerable energy flow in the very forward direction Large rapidity gap in forward direction   ln tan(  2) Pseudo-Rapidity  is the angle w.r.t. proton direction.

12. Regge Phenomenology vs. pQCD Bernd Löhr, DESYPage 12 e e’ p P’ IP, R X Regge Phenomenology Peripheral (soft) processes I P = Pomeron trajectory t shrinkage From fit to hadronic data : (Donnachie, Landshoff) =Reggeon trajectory R I Diffraction I 0.16

13. Diffractive DIS in pQCD In pQCD the simplest way to describe the exchange of vacuum quantum numbers is the exchange of a colour neutral system of two gluons. This is realized in the colour dipole picture. + higher orders + Bernd Löhr, DESYPage 13 The wave function of the incoming virtual photon can be calculated from QED. The outgoing wave function might be known for some exclusive Final states, like e.g. vector mesons.

14. Exclusive Vectormeson Production I Bernd Löhr, DESYPage 14 VDM+Regge p P’ VM ** Shrinkage ; pQCD p P’ VM ** r z 1-z r 2 small if Q 2 large or M V large Ryskin : fast rise with W and no or little shrinkage Do pQCD models describe the data ? Which variables can provide a hard scales ?

15. PHP DIS Exclusive Vectormeson Production II Bernd Löhr, DESYPage 15

16. Can the Vectormeson Mass be a Hard Scale ? I Bernd Löhr, DESYPage 16 Photoproduction ; Q 2 =0 The w-dependence of the “light” vector-meson (  production is described by Regge phenomenology For higher mass vector mesons the rise of the production cross section with W gets steeper. This indicates the onset of hard diffractive scattering

17. Can the Vectormeson Mass be a Hard Scale ? II Bernd Löhr, DESYPage 17 Photoproduction : Q 2 =0 Still some shrinkage seen in J/  photoproduction but compatible with pQCD models. 50 100 200 W[GeV] pQCD models can describe photoproductionof J/  mesons. [GeV] W dependence Shrinkage  from H1 alone

18. Can Q 2 be a Hard Scale ? I Bernd Löhr, DESYPage 18 For  –production the W-dependence gets steeper with Q 2.  -electroproduction pQCD models can describe exclusive production -electroproduction The rise with W is essentially independent of Q 2 for production J/ . ZEUS

19. Can Q 2 be a Hard Scale ? II Bernd Löhr, DESYPage 19 Slopes of the t-distributions The b-slope of  -production decreases with Q 2. At high Q 2 it reaches the value of -production. The b-slope of -production is independent of Q 2. It is a hard process already at Q 2 =0. Q 2 provides a hard scale

20. Can |t| be a Hard Scale ? I Bernd Löhr, DESYPage 20 Complication : at high |t|, the vector-meson production proceeds predominantly through proton-dissociative processes. e e’ p VM t Y Low mass M Y : particles of system Y disappear undetected through the beampipe hole in the detector. High mass M Y : a fraction of the particles from system Y are detected in the calorimeter. We have to assume vertex factorization : The ratio should not depend on Q 2. Within experimental uncertainties : vertex factorization holds.

21. Can |t| be a Hard Scale ? II Bernd Löhr, DESYPage 21 pQCD models Ivanov et al. Bartels et al. not exponential at high |t|, predicted by pQCD models. t-dependence of p-dissociative vector-meson production can be described by pQCD models. Large |t| may provide a hard scale to apply pQCD.

22. Bernd Löhr, DESYPage 22 The Pomeron Trajectory I e e’ pP’ IP t Measure W-dependence separately for different t-bins Pomeron trajectory  IP (t)=  IP (0)+  ’t 1.198 + 0.115. t DIS  1.14 + 0.04. t  photoproduction 1.096+0.125. t  photoproduction 1.081+0.158. t Soft pomeron (DL) 1.08+.25. t VM

23. The Pomeron Trajectory II Bernd Löhr, DESYPage 23 Slope of the Pomeron trajectory at higher |t| : depends on t for high |t|, proton diffractive processes dominate. In Regge language : is not linear in t However :

24. Decay Matrix Density and Ratio of Longitudinal to Transverse Cross-Section for    Production The    is a spin 1 particles. It decays into two pions:        The angular distribution ofthe decay particles   and    is  described by a function of 3 angles: In total 15 density matrix elements describe the decay angular distribution, which depend on the helicity amplitudes for spin non-flip, single spin-flip, and double spin-flip: T 00, T 01, T 10, T 11, T 1-1 S-channel helicity conservationOnly non-flip amplitudes T 00 and T 11 are non-zero ; Notation: Bernd Löhr, DESYPage 24

25. Measured Decay Matrix Elements for    Production I If S-channel helicity conservation (SCHC) is valid only the following matrix elements should be different from zero: Bernd Löhr, DESYPage 25

26. Measured Decay Matrix Elements for    Production II Bernd Löhr, DESYPage 26 If S-channel helicity conservation is valid only the following spin density matrix elements should be zero: r 1 00 = r 1 11 = r 5 00 = r 5 11 = 0 At very small |t| SCHC holds, as |t| grows SCHS is increasingly violated. A pQCD based model (I.Royen and J.Cudell) is able to describe the SCHC violation.

27. Bernd Löhr, DESYPage 27 A virtual photon has two polarization states: transverse: helicity 1 (normal light) longitudinal: helicity 0 (only for Q 2 >0) Ratio of longitudinal to transverse cross-section is function of the photon virtuality: If SCHS holds  R is qualitatively described by pQDC models Ratio of longitudinal to transverse cross-section

28. Bernd Löhr, DESYPage 28 Deeply Virtual Compton Scattering I Probably cleanest test of pQCD, no hadrons in the final state. Bethe-Heitler processes lead to the same final state Interference between QCD and QED gives access to DVCS-QCD amplitude : DVCS Bethe-Heitler Difficult to disentangle experimentally Generalized parton distributions GPD -> information on transverse distribution of partons Interference term can be derived from asymmetries, e.g. Beam-Spin-Asymmetry:  skewedness

29. Bernd Löhr, DESYPage 29 Deeply Virtual Compton Scattering II Q 2 = 8 GeV 2 :  = 1.0  ~ W  DVCS is a hard process NLO-QCD calculations can describe DVCS qualitatively, magnitude of the predicted cross-section depends on used parton-density functions

30. Deeply Virtual Compton Scattering III Bernd Löhr, DESYPage 30 t-dependence of DVCS measured at several Q 2 and W values For Q 2 > 5 GeV 2 : b ~ 5 -6 GeV -2 Compatible with b values for hard production of vector mesons

31. Summary of Exclusive Vectormeson Production Bernd Löhr, DESYPage 31 A high vectormeson mass provides a hard scale. Photoproduction of  is described by sof Pomeron exchange, whereas J/  photoproduction is a hard process, it can be described by pQCD models. Vectormeson production at high Q 2 is a hard process, pQCD can be applied. The vertex factorization holds. Vectormeson production at high |t| is a hard process. The |t| -n dependence is in agreement with pQCD expectations. The Pomeron trajectory for  photoproduction is compatible with the soft Pomeron trajectory : and shrinkage is observed. DIS  and J/  trajectories are not compatible with a soft Pomeron, little shrinkage is observed. pQCD based models are able to describe the features of exclusive hard-production of vector mesons

32. At high Q 2 the W-dependence of the DVCS cross-section and the slope of the t-distribution are compatible with a hard production process DVCS described in terms of generalized parton distributions (GPD) which contain information on transverse distributions of partons in the proton. Recently high statistics measurements of DVCS by H1 became available for electron-proton and positron-proton scattering. It is, however, still along way before one can extract GPDs. Apologies to HERMES ! The HERMES experiment have measured DVCS to a larger extent, also beam-spin asymmetries. These data are typically at Q 2 of 1-2 GeV 2. It is not really clear whether pQCD is already applicable at these low Q 2. Summary of Deeply Virtual Compton Scattering Bernd Löhr, DESYPage 32

33. Definition of Inclusive Diffraction e e’ p e P’ p no colour exchange, vacuum quantum numbers no colour exchange, vacuum quantum numbers Model of a resolved pomeronColour dipole model Definition of inclusive diffractive scattering: The quantum numbers of the vacuum are exchanged between the proton and the virtual photon. (The proton stays intact.) Attention: different definitions of diffractive cross-sections, proton dissociative events are (partially) included or not. Bernd Löhr, DESYPage 33

34. Inclusive Diffraction I e e’ p Diffractive/proton dissociative scattering in the parton picture : MXMX MYMY Large rapidity gap t W x IP ß Momentum fraction of the proton carried by the Pomeron Momentum fraction of the Pomeron carried by the struck quark Two additional variables Experimentally there are three different methods used to select diffractive events : 1. Detection of outgoing proton : includes reggeon exchange 2. Large rapidity gap : includes reggeon exchange and proton dissociation into small mass 3. M X – method : includes proton dissociation into small mass Bernd Löhr, DESYPage 34 There is no method available to measure directly inclusive diffractive cross-sections

35. The Proton Detection Method Bernd Löhr, DESYPage 35 1.) Detection of outgoing proton ( H1,ZEUS) x L = 1-x IP Detection of the diffractive proton is the only method to measure the t-distribution Proton-beam direction Z=96 m Z=26 m S1+S2+S3 : horizontal spectrometer S4+S5+S6 : vertical spectrometer Fraction of initial proton momentum carried by the diffractive proton Silicon strip detectors The ZEUS Leading Proton Spectrometer LPS diffractive peak Advantage: no proton dissociaton Disadvantage: small acceptance possible Reggeon contributions

36. No tracks or energy deposits in calorimeter for rapidities greater than  max or at angles less than  min.  min. H1 LEPTO : nondiffractice MC-simulation Requiring a rapidity gap Dh (e.g. h max <2) in the events removes most of the nondiffractive contribution. mostly diffractive This is equivalent to restrict measurements to low x IP. h max Bernd Löhr, DESYPage 36 Advantage: large acceptance -> high statistics Disadvantage: contains contributions from nondiffractive and proton dissociative reactions and Reggeon contributions The Rapidity Gap Method

37. Rapidity Uncorrelated particle emission between incoming p-direction and scattered quark. Poisson distr. for  y in nondiffractive events The M X -Method (I) Non diffractive events Property of a produced particle Idealised rapidity distribution Length of rapidity distribution is given by cms-energy Rapidity gap as a statistical fluctuation Bernd Löhr, DESYPage 37

38. Bernd Löhr, DESYPage 38 The M X -Method (II)  < 0.1 Experimentally at high energies and not too low M X Cortousy of K.Goulianos with This follows also from a triple Regge model t-averaged

39. Nondiffractive + diffractive contributions for Fit slope b, c and D D is the diffractive contribution Two approaches for fit to the data 1.) take D=const. for a limited range in ln M 2 X 2.) take D from a BEKW-model (see later) parametrization which describes the measured data. This is an iterative procedure. Determine diffractive events by subtracting nondiffractive events from measured data bin by bin as calculated from fitted values b and c. Both approaches give the same results Bernd Löhr, DESY Page 39 The M X -Method (III) Advantage: no nondiffractive contribution large acceptance -> high statistics Disadvantage: contains contribution from proton dissociation

40. Diffractive Cross-Section and Diffractive Structure Functions Bernd Löhr, DESYPage 40 sizeable only at high y, can safely be neglected in the range of HERA measurements. If t is not measured, i.e. integrated over and anlogously H1 uses, ZEUS neglects the longitudinal part and uses

41. Diffractive DIS Factorization In the same way as for DIS, diffractive deep inelastic cross sections can be expressed as a convolution of diffractive parton densities with a deep inelastic cross section. diffractive parton distribution function (dpdf) number density of a parton i in the proton under the condition that it undergoes a diffractive reaction dpdfs at fixed t and x IP evolve with Q 2 according to DGLAP hard universal DIS cross section DDIS factorization rigorously proven: Collins ; Berera, Soper ; Trentadue, Veneziano dpdfs are universal for all hard diffractive processes Bernd Löhr, DESYPage 41

42. Regge-Factorization Bernd Löhr, DESYPage 42 Regge theory originally developed for eleastich 2-body scattering Extension to inclusive diffraction: Triple-Regge formalism This expression allows the decomposition into a flux factor and a cross section: Based on the triple-Regge formalism the diffractive parton distribution functions are factorized accordingly: with This Regge- or vertex-factorization cannot be proven in pQCD

43. Separation of Pomeron from Reggeon Contributions Bernd Löhr, DESYPage 43 Results obtained with LPS/FPS method and the LRG method may contain nondiffractive contributions from Reggeon exchanges. They are fitted by a sum of Pomeron and Reggeon contributions. From the fit the Pomeron contribution can be extracted. is taken from a parametrization of the pion structure function The fluxes are normalized according to: Fitted values areand, the normalization of the Reggeon contribution Other parameters, like, are also fitted or taken from other measurements. with

44. Bernd Löhr, DESYPage 44 Parametrization at a starting value Q 0 2 as : z is the longitudinal momentum fraction of the parton entering the hard sub-process. z =  for lowest order quark-parton modell process, 0 <  < z for higher order processes. QCD DGLAP Fits In a picture where the Pomeron has a partonic structure (Ingelmann-Schlein Model) can be interpreted as the Pomeron structure function Pomeron structure function expressed as a sum of universal Pomeron parton distribution functions : Pomeron pdfs obey DGLAP evolution A DGLAP fit and the Regge fit are usually carried out simultaneously

45. Results from Proton Detection Method Bernd Löhr, DESYPage 45 H1: Forward Proton Spectrometer (FPS)ZEUS: Leading Proton Spectrometer (LPS) combined Regge and DGLAP fit --- extrapolation to nonmeasured Q 2..... Pomeron contribution only Regge fit at two t-values

46. Bernd Löhr, DESYPage 46 Comparison FPS with LPS data Both datasets have systematic uncertainties from the beam divergence H1: +/- 10% ZEUS: +12%/-10% They are not shown in the figures. Fair agreement in shape between the FPS and LPS results

47. Bernd Löhr, DESYPage 47 H1 LRG Results DGLAP fit to H1 data Regge fit to ZEUS data Both data show qualitatively the same features Data contain contributions from proton dissociation

48. Bernd Löhr, DESYPage 48 Comparison between H1 and ZEUS LRG Results The ZEUS data are normalized to the H1 data Reason : The H1 dataset and the ZEUS dataset contain different amounts of proton dissociation. The data are not corrected for that. Good agreement in shape

49. Bernd Löhr, DESYPage 49 Comparison between H1 FPS and LRG Results The LRG data contain contributions from proton dissociation up to masses of 1.6 GeV. The FPS data are multiplied by a factor 1.23 such that they correspond to the LRG data

50. Singlet Structure function Bernd Löhr, DESYPage 50 H1 DPDF Fits Differences between fit A and fit B Gluon structure function Fit A: For both fits only data with Q 2 >8.5 GeV 2 have been used. B g is set to zero Q o 2 = 1.75 GeV 2 Fit B: Q o 2 = 2.5 GeV 2 A q, B q, C q are always fitted B g, C g is set to zero The gluon density is only weakly constraint by the data For fit A the fraction of exchanged momentum carried by gluons in the range 0.0043<z<0.8 is around 70% throughout the studied Q 2 range. For fit B it is a little less but compatible with fit A.

51. Bernd Löhr, DESYPage 51 Results from the M X -Method : d s diff /dM X ZEUS results: FPC I published 2005, FPC II preliminary 2007 1.2 GeV < M X < 30 GeVFPC I: 2.7 GeV 2 < Q 2 < 55 GeV 2 FPC II: 2.7 GeV 2 < Q 2 < 320 GeV 2 Data contain contributions from proton dissociation with M N <2.3 GeV

52. Fit of W-dependence of inclusive DIS and inclusive diffractive DIS cross sections Inclusive DIS: Bernd Löhr, DESY Page 52 For small x, F 2 rises rapidly as x-> 0 Inclusive diffractive DIS: e.g.measured by ZEUS LPS Inclusive DIS and inclusive diffractive DIS are not described by the same ‘Pomeron’. < < < From W dependence, averaged over t : ; With

53. Ratio of total diffractive cross-section to total DIS cross-section Ratio plotted at W=220 GeV because only there the full M X range is covered by measurments Mx 98-99 Mx 99-00 (prel.) Within the errors of the measurements r is independent of W. At W=220 GeV, r can be fitted by r =  diff (0.28<M X <35 GeV)/  tot r = 0.22 – 0.034. ln(1+Q 2 ) This logarithmic dependence of the ratio of total diffractive cross-section to the total DIS cross section indicates that diffraction is a leading twist process for not too low Q 2. Bernd Löhr, DESY Page 53

54. The ZEUS data support taking n T (Q 2 )=n g (Q 2 )=n L (Q 2 )= n 1` ln(1+Q 2 /Q 2 0 ) Taking x 0 = 0.01 and Q 2 0 = 0.4 GeV 2 results in the modified BEKW model with the 5 free papameters : c T, c L, c g, n 1 T,L,g,  Bernd Löhr, DESYPage 54 ZEUS BEKW(mod) Fit Dipole Model

55. BEKW-fit : transverse qq contribution longitudinal qq contribution transverse qqg contribution sum of all contributions FPC IFPC II Page 55 Bernd Löhr, > 400 points 5 parameters   /n D = 0.71 ZEUS-M X Diffractive Structure Functions with BEKW(mod.) Fit

56. Page 56 Bernd Löhr, ZEUS-M X Diffractive Structure Functions Relation between differential diffractive cross section and diffractive structure function F 2 D(3) specifies the probability to find a in diffractive reaction a quark in a proton carrying a fraction x=  x IP of the proton momentum. rises approximately proportional to. This rise reflects the increase of the diffractive cross section with W. At small x IP the development of the diffractive cross section is governed by the increase of the gluon density as W increases or x IP decreases.

57. Bernd Löhr, DESYPage 57 ZEUS-M X Diffractive Structure Function and the BEKW(mod) Fit - - Towards low  values the qqg contribution rises strongly due to the increase in gluon density. The longitudinal qq L contribution is sizeable only at very high  and is responsible for a finite value of the diffractive structure function at  For fixed Q 2 and fixed x IP the data show a broad maximun around b =0.5 which originates from the  dependence of the tansverse qq T contribution.

58. Bernd Löhr, DESYPage 58 ZEUS M X : QCD Scaling Violations ZEUS BEKW(mod) fit x IP F 2 D(3) in fixed (x IP,  )-bins x IP F 2 D(3) shows considerable scaling violations: from positive scaling violations over near constancy to negative scaling violations. Scaling violations well described by BEKW model -> effective DGLAP evolution present in this model.

59. Bernd Löhr, DESYPage 59 H1 and ZEUS: QCD Scaling Violations H1: DPDF fit ZEUS: BEKW(mod) fit

60. Bernd Löhr, DESYPage 60 Summary of Inclusive Diffraction 1.) Three experimental methods to measure inclusive diffraction at HERA : PS/LPS, LRG, and M X. All include contributions of different magnitude from proton dissociation or from Reggeon exchange or from both. 2.) Inclusive diffraction is a leading twist reaction. 2.) The diffractive cross-section can be expressed in terms of diffractive structure functions. 3.) Assuming Regge factorization H1 separated Pomeron and Reggeon contributions and extracted DPDFs from the LRG data. 4.) QCD inspired dipole models can describe inclusive diffraction as well. The ZEUS M X data are described rather precisely over the whole kinematic range by the BEKW(mod) parametrization. 5.) The BEKW modell explains the diffractive structure function F 2 D(3) in terms of transverse and longitudinal quark-antiquark and quark-antiquark-gluon contributions. 6.) The diffractive structure function F 2 D(3) shows large scaling violations. This points to a large gluon fraction in the colourless exchange.

61. Inclusive diffraction Exclusive diffractive processes Bernd Löhr, DESYPage 61 Semi-Inclusive Diffraction And Tests of QCD Factodization exclusive vector meson production transition from soft to hard diffractive reactions diffractive structure functions description by quark-dipole models universal diffractive parton densities Semi-inclusive diffractive processes diffractive final states with special properties: jets, heavy quarks,.... Semi-inclusive diffractive processes are a testing ground for the universality of the diffractive parton distributions derived from inclusive reactions. P’ p VM ** p ** z 1-z P’ e e’ p P’ e e’ p P’

62. Bernd Löhr, DESYPage 62 Semi-Inclusive Diffractive DIS D * (2010) Production Kinematical selection:  max <3, x IP < 0.035,  < 0.8 ACTW fit (Alvero et al.): Combined fit of DPDFs to H1 and ZEUS inclusive diffractive data and to ZEUS diffractive di-jet photoproduction data, all data up to 1998. The pQCD fit using the DPDFs from inclusive diffraction gives acceptable descriptions of diffractive D * (2010) Production. Confirmation of the universality of DPDFs from inclusive diffraction. c c  - D*D* c

63. Bernd Löhr, DESYPage 63 Semi-Inclusive Diffractive DIS Di-Jet Production jet z IP : part of the Pomeron momentum that goes into the hard interaction Diffractive di-jet production is sensitive to the gluon DPDF Diffractive photon-gluon fusion H1 fits A and B used in NLO calculation (Z.Nagy) Fit B gives an acceptable description of the data diffractive System X Fit A Fit B Confirmation of the universality of DPDFs from inclusive diffraction.

64. Bernd Löhr, DESYPage 64 Combined Fit to DIS Inclusive Diffractive and Diffractive Di-Jet Production Experimental validation of universality of DPDFs make combined fit The information from diffractive di-jet production improves the fit of the gluon density in particular at high z IP.

65. Bernd Löhr, DESYPage 65 HERA DPDFs and Predictions for the Tevatron Do the DIS-DPDFs from HERA also describe diffraction in hadron-hadron interactions ? Note: QCD factorization has not been proven for hadron-hadron interactions Diffracitve di-jet production at CDF jet  hard scattering IP LRG jet Convolution of 2 structure functions Predictions from DIS diffractive structure functions fail by factor 5-7. Final state interaction between proton remnent and antiproton possible : gap survival probability is not one.

66. Bernd Löhr, DESYPage 66 Semi-Inclusive Diffractive Photoproduction at HERA What is special about photoproduction (Q 2 > 0 GeV 2 ) ? Direct photoproduction Photon takes part directly in hard interaction X   Resolved photoproduction Photon fluctuates into a hadronic state of which only a part enters the hard interaction X  < 1 operational definition: X  > 0.7 direct X  < 0.7 resolved Resolved photoproduction is similar to hadron-hadron interactions Is diffractive resolved photoproduction also suppressed ? Do final state interactions play a role also in photoproduction ?

67. Bernd Löhr, DESYPage 67 Diffractive D*(2010) Photoproduction at HERA NLO calculations: Frixione et al. FMNR-code and H1 DPDFs Qualitative good agreement with NLO QCD calculations using inclusive DPDFs

68. Bernd Löhr, DESY Diffractive Di-Jet Photoproduction at HERA H1: Q 2 d 1 GeV 2 ; 165 < W < 242 GeV  max = 3.2 ; x IP < 0.03 E T *,jet1 > 5 GeV ; E T *,jet2 > 4 GeV -1 <  jet lab < 2 ZEUS: Q 2 < 1 GeV 2 ;  max = 2.8 ; x IP < 0.028 E T jet1 > 7.5 GeV ; E T jet2 > 6.5 GeV -1.5 <  jet lab < 1.5 Note : NLO predictions scaled by 0.5 Note : H1 and ZEUS are quoting results for different kinematical regions Page 68

69. Bernd Löhr, DESYPage 69 Diffractive Di-Jet Photoproduction at HERA : cont. Results from H1 and ZEUS separately for direct and resolved photoproduction H1: data for all x    in NLO calculation  x  PL > 0.9 no scaling factor  x  PL < 0.9 scale factor 0.44  -> unacceptable fit Fit with 2 free normalizations for x ,PL 0.9 yielded 0.47 +/-0.16 and 0.53+/-0.14 ZEUS diffractive di-jet photoproduction direct enrichedX  obs < 0.75resolved enrichedX  obs > 0.75 Agreement within errors between data and NLO calculations with inclusive DPDFs Note, however, that kinematic regions for H1 and ZEUS data are different -> may not be a contradiction

70. Bernd Löhr, DESYPage 70 Summary of Semi-Inclusive Diffraction and Tests of QCD Factorization 1.) QCD inspired models using the DPDFs determined from inclusive diffractive DIS describe at least qualitatively semi-inclusive diffractive production of heavy quarks and di-jets. 2.) The QCD factorization scheme in DIS is experimentally verified in diffractive DIS. 3.) Although theoretically not expected, Regge factorization seems to hold in practice. 4.) These are experimental indications that DPDFs might be universal in DIS. 5.) QCD factorization does not hold for diffractive hadron-hadron interactions. Using HERA DPDFs leads to a gross overestimation of dijet production at the Tevatron. The survival probability of diffractive gaps is smaller than one. 6.) The situation in semi-inclusive diffractive photoproduction needs further clarification. For heavy quark production the QCD factorization seems to hold also for the resolved photon contribution. For di-jet production there are indications from H1 that QCD factorization might not be valid whereas ZEUS results confirm QCD factorization although in a slightly different kinematical regime.