1. Paul Laycock University of Liverpool BLOIS 2007 Diffractive PDFs

2. Paul Laycock Diffractive PDFs BLOIS 2007 Page 2 Overview ● Diffractive DIS at Hera – Kinematics and Observables ● Comparison of Experimental Techniques – Rapidity gap, M X and leading proton techniques ● Factorisation, NLO QCD Fits and Diffractive PDFs – M Y, t and x IP dependences factorise from Q 2 and β dependences – QCD and the unconstrained high z gluon ● Diffractive dijets – Factorisation holds in diffractive DIS ● Combined fit and Diffractive PDFs – Diffractive PDFs with more constraints on the gluon

3. Paul Laycock Diffractive PDFs BLOIS 2007 Page 3 Diffractive DIS Kinematics and Observables Large Gap in Rapidity ` Cross section:

4. Paul Laycock Diffractive PDFs BLOIS 2007 Page 4 Experimentally selecting Require Large Rapidity Gap (LRG) spanning at least 3.3 < η < ~7.5 Kinematics measured from X system, integrate |t| < 1.0 GeV 2, M Y < 1.6 GeV High detector acceptance → precision Forward Proton Spectrometer Large Rapidity Gap Measure Leading Proton (FPS) No proton dissociation Measure the t dependence Low detector acceptance X e p Large Rapidity Gap in H1

5. Paul Laycock Diffractive PDFs BLOIS 2007 Page 5 Latest Zeus results – M X and LRG Zeus and H1 both comparing LRG and M X methods Shown here – Zeus LRG (blue) and Zeus M X (red) Reasonable agreement but ongoing work to understand the differences A wealth of precision data to add to future diffractive PDFs

6. Paul Laycock Diffractive PDFs BLOIS 2007 Page 6 QCD hard scattering collinear factorisation (Collins) at fixed x IP and t `Proton vertex’ factorisation of β and Q 2 from x IP, t, and M Y dependences Two Levels of Factorisation Applied after integration over measured M Y and t ranges

7. Paul Laycock Diffractive PDFs BLOIS 2007 Page 7 H1 Inclusive Data Overview FPS: Y=p LRG: M Y < 1.6 GeV

8. Paul Laycock Diffractive PDFs BLOIS 2007 Page 8 Detailed Comparison LRG v FPS M Y dependence factorises from x IP, β and Q 2 within 10% (non-normalisation) errors LRG measurement also done with FPS bins Form ratio of measurements as a function of x IP, β and Q 2

9. Paul Laycock Diffractive PDFs BLOIS 2007 Page 9 Effective Pomeron Intercept Independent of β and Q 2 From fits to LRG and M X data, with current experimental precision: Data compatible with no dependence of  IP (0) on Q 2 (Zeus and H1) or β (H1) The x IP dependence also factorises from Q 2 and  x IP, t and M Y dependences factorise from the Q 2 and β dependences within errors → Data support Proton Vertex Factorisation

10. Paul Laycock Diffractive PDFs BLOIS 2007 Page 10 Study β and Q 2 dependences at fixed x IP Analogous to making an inclusive F 2 measurement at each value of x IP

11. Paul Laycock Diffractive PDFs BLOIS 2007 Page 11 Q 2 Dependence in More Detail Derivatives large and positive… suggests large gluon such that Fit data at fixed x, x IP to Divide results by to compare different x IP values Different x IP measurements agree

12. Paul Laycock Diffractive PDFs BLOIS 2007 Page 12 H1 2006 DPDF Fit - Overview IP component: Fit  IP (0) (x IP dependence). Simultaneously, fit 5 parameters of DPDFs (β and Q 2 dependences) using NLO QCD. a IP (0) DPDF IR component: Fit n IR one parameter for normalisation. All flux parameters taken from previous H1 data. PDFs taken from Owens-p.

13. Paul Laycock Diffractive PDFs BLOIS 2007 Page 13 IP component: Fit  IP (0) (x IP dependence). Simultaneously, fit 5 parameters of DPDFs (β and Q 2 dependences) using NLO QCD. Fit is stable with variations of, e.g.  max – the maximum value of β allowed in the fit. Fit stable for Q 2 min > 8.5 GeV 2. Fit all data with: Parameterise quark singlet z  z,Q 0 2 ) and gluon zg  z,Q 0 2 ) densities, where z is parton momentum fraction (=  for QPM). Parameterisation used is and (gluon insensitive to B g ) Results reproducible with Chebyshev polynomials. H1 2006 DPDF Fit - Details a IP (0) DPDF

14. Paul Laycock Diffractive PDFs BLOIS 2007 Page 14 DPDFs from inclusive data Fit A Fit B Drop C g - gluon is parameterised as a constant at the starting scale!  2 ~164 / 184 d.o.f. Q 0 2 = 2.5 GeV 2 Quarks very stable Gluon similar at low z No sensitivity to gluon at high z Q 0 2 = 1.75 GeV 2  2 ~158 / 183 d.o.f.

15. Paul Laycock Diffractive PDFs BLOIS 2007 Page 15 A Closer Look at the High z Region We have only singlet quarks, so DGLAP evolution equation for F 2 D …. At high , relative error on derivative grows, contribution to evolution becomes important … sensitivity to gluon is lost +

16. Paul Laycock Diffractive PDFs BLOIS 2007 Page 16 Compare to diffractive dijets in DIS We can compare the predictions of Fit A and Fit B with the experimental measurement of diffractive dijets in DIS This process is particularly sensitive to the gluon

17. Paul Laycock Diffractive PDFs BLOIS 2007 Page 17 Compare to diffractive dijets in DIS At low z IP (< 0.3) Fit A and Fit B are similar The data are in good agreement with the predictions, consistent with factorisation (more on factorisation in A. Bonato’s talk) At high z IP the diffractive dijet data clearly prefer Fit B

18. Paul Laycock Diffractive PDFs BLOIS 2007 Page 18 Combined fit of dijet and inclusive data The diffractive dijet data can be used as an additional constraint in a NLO QCD fit procedure Details similar to the inclusive case but can now consrtain 3 parameters for the gluon Very good simultaneous fit of both inclusive and dijet data achieved

19. Paul Laycock Diffractive PDFs BLOIS 2007 Page 19 Combined fit DPDFs from H1 The singlet and gluon are constrained with similar precision across the kinematic range To be published very soon!

20. Paul Laycock Diffractive PDFs BLOIS 2007 Page 20 Summary ● A wealth of inclusive data from H1 and Zeus using LPS, M X and LRG methods (I didn’t have time to show it all!) ● Proton vertex factorisation holds: M Y, t and x IP dependences factorise from β and Q 2 ● DPDFs from NLO QCD fits to , Q 2 dependences (H1 2006 DPDF Fits A+B) – Quark singlet very well constrained (~5%) – Gluon constrained to ~15%, but poorly known at high z ● Combined fit to inclusive and dijet data finally constrains both the quark and the gluon to similar precision H1 2007 Jets DPDF to appear soon – use it!

21. Paul Laycock Diffractive PDFs BLOIS 2007 Page 21 BACK-UP SLIDES FOLLOW

22. Paul Laycock Diffractive PDFs BLOIS 2007 Page 22 Effective Pomeron Intercept Independent of β and Q 2 From fit to LRG data: No dependence of  IP (0) on Q 2 or β The x IP dependence also factorises from Q 2 and  x IP, t and M Y dependences factorise from the Q 2 and β dependences within errors → Data support Proton Vertex Factorisation

23. Paul Laycock Diffractive PDFs BLOIS 2007 Page 23 t Slope Dependence on β or Q 2 ? t dependence does not change with  or Q 2 at fixed x IP B measured double differentially in (  or Q 2 ) at fixed x IP

24. Paul Laycock Diffractive PDFs BLOIS 2007 Page 24 B(x IP ) data constrain IP, IR flux factors in proton vertex factorisation model t dependence from FPS measurements B(x IP ) from fit to Fitting low x IP data to yields:

25. Paul Laycock Diffractive PDFs BLOIS 2007 Page 25 Comparison of H1 LRG, H1 FPS, ZEUS LPS Data ZEUS (LPS) and H1 (FPS) Leading Proton Data agree very well (they agree to 8% cf. 10% normalisation uncertainities) ZEUS LPS and H1 FPS scaled by global factor of 1.23 to compare with LRG M Y < 1.6 GeV Very good agreement between Leading Proton and LRG methods after accounting for proton diss’n Both experimental techniques measure the same cross section

26. Paul Laycock Diffractive PDFs BLOIS 2007 Page 26

27. Paul Laycock Diffractive PDFs BLOIS 2007 Page 27 Q 2 derivative and gluon/quark ratios If then At low x, gluon:quark ratio ~ 70%/30%, common to diffractive and inclusive Diffractive Inclusive 0.7 0.3