1. Marta Ruspa, "Inclusive diffraction", DIS 20041 Inclusive diffractive DIS Diffractive cross section and diffractive structure function Comparison with colour dipole models NLO QCD fit Marta Ruspa Univ. of Eastern Piedmont-Novara and INFN-Torino (Italy) XII International Workshop on Deep Inelastic Scattering Strbske Pleso, High Tatras, Slovakia April 14-18, 2004 on behalf of

2. Marta Ruspa, "Inclusive diffraction", DIS 20042 IP Q2Q2 W MXMX e’ p’ ** e p Q 2 = virtuality of photon = = (4-momentum exchanged at e vertex) 2 t = (4-momentum exchanged at p vertex) 2 typically: |t|<1 GeV 2 W = invariant mass of photon-proton system M X = invariant mass of photon-Pomeron system x IP = fraction of proton’s momentum taken by Pomeron ß = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/x IP x IP t Inclusive diffraction γ * p  Xp  Exchange of an object with the vacuum q. n.  Proton almost intact after the collision

3. Marta Ruspa, "Inclusive diffraction", DIS 20043 (Breit frame) Diffractive DIS in the Breit frame Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton relevant when the vacuum quantum numbers are exchanged f i/p D (z,Q 2,x IP,t): probability to find in a proton, with a probe of resolution Q 2, parton i with momentum fraction z, under the condition that the proton remains intact and emerges with small energy loss, x IP, and momentum transfer,t HARD SCATTERING FACTORISATION  DIS of a pointlike virtual photon off the exchanged object  PDFs

4. Marta Ruspa, "Inclusive diffraction", DIS 20044 Diffractive DIS in the colour dipole picture We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton (γ* much faster than p) Lifetime of dipoles very long due to large γ boost (E γ ~ W 2 ~ 1/x  50TeV ! )  it is the dipole that interacts with the proton ! Transverse size of dipoles proportional to  can be so small that the strong interaction with proton can be treated perturbatively ! 2 gluon exchange: LO QCD realisation of vacuum q.n.

5. Marta Ruspa, "Inclusive diffraction", DIS 20045 Diffractive DIS in the colour dipole picture BEKW model : at medium β; at small β saturation model : : as Q 2  0, growth tamed by requiring saturation We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton (γ* much faster than p) 2 gluon exchange: LO QCD realisation of vacuum q.n.

6. Marta Ruspa, "Inclusive diffraction", DIS 20046 e p Exchange of color singlet producing a GAP in the particle flow Inclusive diffraction γ * p  Xp  No activity in the forward direction  Proton suffers only a small energy loss M X method

7. Marta Ruspa, "Inclusive diffraction", DIS 20047 Diffr. Non-diffr. c, b from fit  n.d. events subtracted contamination from reaction ep  eXN Selection of events γ * p  Xp with M x method Properties of M x distribution: - exponentially falling for decreasing M x for non- diffractive events - flat vs ln M x 2 for diffractive events Forward Plug Calorimeter (FPC): CAL acceptance extended by 1 unit in pseudorapidity from η=4 to η=5  higher M x and lower W  if M N > 2.3 GeV deposits E FPC > 1 GeV recognized and rejected! Diffr. Non-diffr.

8. Marta Ruspa, "Inclusive diffraction", DIS 20048 e p Exchange of color singlet producing a GAP in the particle flow Inclusive diffraction γ * p  Xp  No activity in the forward direction  Proton suffers only a small energy loss LPS method M X method

9. Marta Ruspa, "Inclusive diffraction", DIS 20049 Free of p-diss background Low acceptance  low statistics Selection of events γ * p  Xp with LPS Diffractive peak

10. Marta Ruspa, "Inclusive diffraction", DIS 200410 97 LPS sample 0.03 < Q 2 < 100 GeV 2 25 < W < 280 GeV 1.5 < M x < 70 GeV x IP < 0.1 Higher x IP region 99-00 FPC sample (M x method) 22 < Q 2 < 80 GeV 2 37 < W < 245 GeV M x < 35 GeV M N < 2.3 GeV Higher β region Data samples

11. Marta Ruspa, "Inclusive diffraction", DIS 200411 diffractive γ * p cross section diffractive structure function (assumes ) Cross section and structure function

12. Marta Ruspa, "Inclusive diffraction", DIS 200412 x IP dep. of F 2 D(3) equivalent to W dep. of dσ/dM x (1/x IP ~ W 2 ) F 2 D(3) x IP dependence Data agree with Regge factorisation assumption in the region of the fit (LPS) Regge fit (x IP <0.01) : with

13. Marta Ruspa, "Inclusive diffraction", DIS 200413 p-dissociation events with M N <2.3 GeV included M X < 2 GeV: weak W dep. M X > 2 GeV: d  /dM X rises with W Cross section W dependence (M x method) power-like fit

14. Marta Ruspa, "Inclusive diffraction", DIS 200414 fit to total cross section data: fit to diffractive cross section data: Evidence of a rise of  IP diff with Q 2  mild Regge factorisation violation. α IP from diffractive and total γ * p scattering  IP diff higher than soft Pomeron Similar W dep. of diffractive and total cross section (M x method)

15. Marta Ruspa, "Inclusive diffraction", DIS 200415 low M X : strong decrease of  diff /  tot with increasing Q 2 high M X : no Q 2 dependence ! Regge expectation: σ diff / σ tot W and Q 2 dependence (M x method) [hep-ph 0203258] Explained by saturation model BUT ratio ~ flat in W

16. Marta Ruspa, "Inclusive diffraction", DIS 200416 Main features of the data described by BEKW parametrization (x IP <0.01) Cross section Q 2 dependence Transition to a constant cross section as Q 2  0 (similar to total cross section ) qqg fluctuations dominant at low Q 2 (Bartels, Ellis, Kowalski and Wüsthoff) medium β small β (LPS)

17. Marta Ruspa, "Inclusive diffraction", DIS 200417 F 2 D(3) Q 2 dependence (LPS) Data well described by BGK saturation model (x IP <0.01) Positive scaling violation at all values of β QCD fit (prel.)

18. Marta Ruspa, "Inclusive diffraction", DIS 200418 QCD fit describes data fractional gluon momentum is at initial scale NLO QCD fit on LPS+charm data [F 2 D(3)cc from DESY-03-094, see N. Vlasov talk] x IP <0.01 QCDNUM Regge factorisation assumption possible for this small data set DL flux initial scale Q 2 =2 GeV 2 zf(z)=(a 1 +a 2 z+a 3 z 2) (1-x) a4 other PDFs parametrisation tried Thorne-Robert variable-flavour- number-scheme (LPS)

19. Marta Ruspa, "Inclusive diffraction", DIS 200419 LPS QCD fit compared to M x data Main discrepancies at high β, where no LPS data available NB: fits scaled by 0.69 to account for p-diss background in M x data M x method data described by the fit in the region of overlap LPS-M x method ZEUS (M X method)

20. Marta Ruspa, "Inclusive diffraction", DIS 200420 x IP.F 2 D(3) /F 2 Q 2 and x BJ dependences (LPS) Compare the proton structure function for events with a leading proton and without Nearly the same Q 2 dep. (except high β and low x IP ) Different behaviour vs x at low x IP

21. Marta Ruspa, "Inclusive diffraction", DIS 200421 Recent data from ZEUS with improved precision and extended kinematic range Data described by colour dipole models (BEKW, saturation) Data described by a NLO QCD fit  lots of gluons Possible indication that α IP increases with Q 2 in diffraction W dep. of diffractive and total cross section similar at high Q 2 Summary

22. Marta Ruspa, "Inclusive diffraction", DIS 200422 RESERVE

23. Marta Ruspa, "Inclusive diffraction", DIS 200423 Diffractive DIS in the proton rest frame We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton (γ* much faster than p) Lifetime of dipoles very long due to large γ boost (E γ ~ W 2 ~ 1/x  50TeV ! )  it is the dipole that interacts with the proton ! Transverse size of dipoles proportional to  can be so small that the strong interaction with proton can be treated perturbatively ! 2 gluon exchange: LO QCD realisation of vacuum q.n. saturation model : (colour transparency) as Q 2  0, growth tamed by saturating BEKW model : at medium β; at small β

24. Marta Ruspa, "Inclusive diffraction", DIS 200424 IP Q2Q2 W MXMX e’ p’ ** e p Q 2 = virtuality of photon = = (4-momentum exchanged at e vertex) 2 t = (4-momentum exchanged at p vertex) 2 typically: |t|<1 GeV 2 W = invariant mass of photon-proton system M X = invariant mass of photon-Pomeron system x IP = fraction of proton’s momentum taken by Pomeron ß = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/x IP x IP t Inclusive diffraction γ * p  Xp  Exchange of an object with the vacuum q. n.  Proton almost intact after the collision

25. Marta Ruspa, "Inclusive diffraction", DIS 200425 (Breit frame) Diffractive DIS in the Breit frame Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton relevant when the vacuum quantum numbers are exchanged f i/p D (z,Q 2,x IP,t): probability to find in a proton, with a probe of resolution Q 2 parton i with momentum fraction z, under the condition that proton remains intact and emerges with small energy loss, x IP, and momentum transfer, t  diffractive PDFs are a feature of the proton HARD SCATTERING FACTORISATION

26. Marta Ruspa, "Inclusive diffraction", DIS 200426 e p Exchange of color singlet producing a GAP in the particle flow Inclusive diffraction γ * p  Xp diffractive γ * p cross section diffractive structure function (assumes )  No activity in the forward direction  Proton almost intact after the collision

27. Marta Ruspa, "Inclusive diffraction", DIS 200427 diffractive γ * p cross section diffractive structure function (assumes ) Cross section and structure function  x IP dependence of F 2 D(3) and W dependence of dσ/dM X - extraction of α IP - Regge factorisation  Q 2 dependence of F 2 D(3) and dσ/dM X -sensitivity to diffractive PDFs  comparison to BEKW model and to saturation model

28. Marta Ruspa, "Inclusive diffraction", DIS 200428 F 2 D(3) β dependence Different β dep. at low and high x IP Data well described by BGK saturation model (x IP <0.01) (LPS)

29. Marta Ruspa, "Inclusive diffraction", DIS 200429 For high β F 2 D(2) decrease with rising Q 2 F 2 D(3) at fixed x IP As β  0 F 2 D(2) rises. The rise becomes stronger as Q 2 increases Maximum near β=0.5 consistent with a β(1- β) behaviour suggesting main contribution from a quark-antiquark state (M x method) Evidence for pQCD evolution

30. Marta Ruspa, "Inclusive diffraction", DIS 200430 MICHELE

31. Marta Ruspa, "Inclusive diffraction", DIS 200431 pQCD :  qq  r   1/Q 2 (colour transparency) As Q 2  0,  qq   violation of unitarity Growth tamed by  qq saturating at  qq   (  p) Part III: saturation (how dense is the proton at low x ???) Saturation occurs at “saturation scale” Q s 2 (x)  xg(x)]  x   x) with x 0  10 -4, 0.3 (proton denser at small x)  qq r Saturation npQCD pQCD ** r cf talks by S. Munier, D. Kharzeev, C. Marquet Connection to high-density QCD, saturation of parton densities, Colour Glass Condensate, geometric scaling, physics of RHIC ~1/Q s large x small x

32. Marta Ruspa, "Inclusive diffraction", DIS 200432 Saturation vs data Q2Q2 x IP F 2 D(3) F2F2 Inclusive diffraction: Inclusive DIS: Golec-Biernat,Wuesthoff, Bartels, Golec-Biernat, Kowalski Diffraction more sensitive to saturation than inclusive: mainly probe intermediate dipole sizes, close to saturation Also good description of VM, DVCS...

33. Marta Ruspa, "Inclusive diffraction", DIS 200433 Standard Deep Inelastic Scattering For Q 2 << M Z 2 : In a frame in which the proton is very fast (Breit frame): x = Bjorken’s variable= = fraction of proton’s momentum carried by struck quark  Q 2 /W 2 W = photon-proton centre of mass energy y = W 2 /s F 2 =  i [e i 2 x f i (x,Q 2 )] R=  L  T DIS probes the partonic structure of the proton Q2Q2 W proton PDF

34. Marta Ruspa, "Inclusive diffraction", DIS 200434 Diffractive Deep Inelastic Scattering x IP = fraction of proton’s momentum taken by Pomeron =   in  Fermilab jargon  = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/x IP Flux of Pomerons “Pomeron structure function” Naively, if IP were particle: [Ingelman, Schlein] x IP IP Q2Q2 t ** e e’ pp’ F 2 D(4)  f IP (x IP,t) F 2 IP ( ,Q 2 )

35. Marta Ruspa, "Inclusive diffraction", DIS 200435 IP Q2Q2 W MXMX e’ p’ ** e p Q 2 = virtuality of photon = = (4-momentum exchanged at e vertex) 2 t = (4-momentum exchanged at p vertex) 2 typically: |t|<1 GeV 2 W = invariant mass of photon-proton system M X = invariant mass of photon-Pomeron system x IP = fraction of proton’s momentum taken by Pomeron =  in Fermilab jargon  = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/x IP x IP Previous talk: Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton, relevant when the vacuum quantum numbers are exchanged Diffractive DIS t N.B. will drop e, e’ from the diagrams in the rest of the talk

36. Marta Ruspa, "Inclusive diffraction", DIS 200436 (Diffractive) hard scattering factorisation universal partonic cross section f i/p D (z,Q 2,x IP,t): probability to find, with probe of resolution Q 2, in a proton, parton i with momentum fraction z, under the condition that proton remains intact, and emerges with small energy loss, x IP, and momentum transfer t – diffractive PDFs are a feature of the proton A new type of PDFs, with same dignity as standard PDFs. Applies when vacuum quantum numbers are exchanged Diffractive DIS, like inclusive DIS, is factorisable [Collins (1998); Trentadue, Veneziano (1994); Berera, Soper (1996)…] : diffractive parton distribution functions: evolve according to DGLAP Rather than IP exchange: probe diffractive PDFs of proton

37. Marta Ruspa, "Inclusive diffraction", DIS 200437 Diffractive DIS in the proton rest frame 2-gluon exchange: LO realisation of vacuum quantum numbers in QCD Cross section proportional to probability of finding 2 gluons in the proton Gluon density in the proton ! X p p X p + p X p ** IP

38. Marta Ruspa, "Inclusive diffraction", DIS 200438 Part I: The colour dipole approach The picture discussed in the previous talk emerges in a frame in which the proton is fast (the Breit frame) Can learn more about the structure of the proton by studying diffraction in a frame in which the virtual photon is faster than the proton. Find out that in exclusive processes  diffr  [gluon density in proton] 2 Example: exclusive vector meson production Calculable in QCD ! Correlations in the proton: Generalised Parton Distributions (GPDs)

39. Marta Ruspa, "Inclusive diffraction", DIS 200439 Lifetime of dipoles very long because of large  boost (E   50TeV!)  it is the dipole that interacts with the proton Transverse size proportional to 1/  (Q 2 + M qq 2 ) (for longitudinally polarised photons) This is why can do diffraction in ep collisions ! Virtual photon fluctuates to qq, qqg states (colour dipoles) Transverse size of incoming hadron beam can be reduced at will. Can be so small that strong interaction with proton becomes perturbative (colour transparency) ! The colour dipole picture ** **

40. Marta Ruspa, "Inclusive diffraction", DIS 200440 Factorization  Regge factorization - “resolved IP model” ( IP with partonic structure): (Breit frame)  QCD Hard Scattering factorization ( by Collins; Trentadue, Veneziano; Berera, Soper…:) Regge motivated pomeron flux At fixed x IP and t diffractive Parton Densities evolve according to DGLAP Shape of diffractive pdfs independent of x IP and t