Paul Laycock University of Liverpool BLOIS 2007

1. Diffractive PDFs Paul Laycock University of Liverpool BLOIS 2007

2. Diffractive PDFs BLOIS 2007 Overview • Diffractive DIS at Hera • Kinematics and Observables • Comparison of Experimental Techniques • Rapidity gap, MX and leading proton techniques • Factorisation, NLO QCD Fits and Diffractive PDFs • MY, t and xIP dependences factorise from Q2and βdependences • 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. Diffractive PDFs BLOIS 2007 Diffractive DIS Kinematics and Observables ` Large Gap in Rapidity Cross section:

4. Experimentally selecting Forward Proton Spectrometer Large Rapidity Gap in H1 X Large Rapidity Gap e p Measure Leading Proton (FPS) No proton dissociation Measure the t dependence Low detector acceptance Require Large Rapidity Gap (LRG) spanning at least 3.3 < η< ~7.5 Kinematics measured from X system, integrate |t| < 1.0 GeV2, MY < 1.6 GeV High detector acceptance → precision Diffractive PDFs BLOIS 2007

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

6. Diffractive PDFs BLOIS 2007 Two Levels of Factorisation QCD hard scattering collinear factorisation (Collins) at fixed xIPand t Applied after integration over measured MY and t ranges `Proton vertex’ factorisation of βand Q2 from xIP, t, and MY dependences

7. Diffractive PDFs BLOIS 2007 H1 Inclusive Data Overview LRG: MY< 1.6 GeV FPS: Y=p

8. Detailed Comparison LRG v FPS • LRG measurement • also done with FPS bins • Form ratio of measurements as a function of xIP, β and Q2 MY dependence factorises from xIP, β and Q2 within 10% (non-normalisation) errors Diffractive PDFs BLOIS 2007

9. Diffractive PDFs BLOIS 2007 Effective Pomeron Intercept Independent of β and Q2 From fits to LRG and MX data, with current experimental precision: • Data compatible with no dependence of aIP(0) • on Q2 (Zeus and H1) or β(H1) • The xIP dependence also • factorises from Q2 and b • xIP, t and MY dependences factorise from the Q2 and β dependences within errors → Data support Proton Vertex Factorisation

10. Diffractive PDFs BLOIS 2007 Study β and Q2 dependences at fixed xIPAnalogous to making an inclusive F2 measurement at each value of xIP

11. Diffractive PDFs BLOIS 2007 Q2 Dependence in More Detail Fit data at fixed x, xIP to such that Divide results by to compare different xIP values Different xIP measurements agree Derivatives large and positive… suggestslarge gluon

12. Diffractive PDFs BLOIS 2007 H1 2006 DPDF Fit - Overview DPDF aIP(0) • IP component: • Fit aIP(0) (xIP dependence). • Simultaneously, fit 5 parameters of DPDFs (β and Q2 dependences) using NLO QCD. • IR component: • Fit nIRone parameter for normalisation. • All flux parameters taken from previous H1 data. PDFs taken from Owens-p.

13. H1 2006 DPDF Fit - Details • Fit is stable with variations of, e.g. bmax – the maximum value of β allowed in the fit. • Fit stable for Q2min > 8.5 GeV2. • Fit all data with: • Parameterise quark singlet zS(z,Q02) and gluon zg(z,Q02) densities, where z is parton momentum fraction (= b for QPM). • Parameterisation used is • and (gluon insensitive to Bg) • Results reproducible with Chebyshev polynomials. DPDF aIP(0) • IP component: • Fit aIP(0) (xIP dependence). • Simultaneously, fit 5 parameters of DPDFs (β and Q2 dependences) using NLO QCD. Diffractive PDFs BLOIS 2007

14. Diffractive PDFs BLOIS 2007 DPDFs from inclusive data • Fit A • Fit B • Drop Cg - gluon is parameterised as a constant at the starting scale! • c2 ~164 / 184 d.o.f. • Q02= 2.5 GeV2 • Quarks very stable • Gluon similar at low z • No sensitivity to gluon at high z Q02= 1.75 GeV2 c2 ~158 / 183 d.o.f.

15. Diffractive PDFs BLOIS 2007 A Closer Look at the High z Region We have only singlet quarks, so DGLAP evolution equation for F2D…. + At highb, relative error on derivative grows, contribution to evolution becomes important … sensitivity to gluon is lost

16. Diffractive PDFs BLOIS 2007 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. Diffractive PDFs BLOIS 2007 Compare to diffractive dijets in DIS At low zIP (< 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 zIP the diffractive dijet data clearly prefer Fit B

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

20. Diffractive PDFs BLOIS 2007 Summary • A wealth of inclusive data from H1 and Zeus using LPS, MX and LRG methods (I didn’t have time to show it all!) • Proton vertex factorisation holds: MY, t and xIP dependences factorise from β and Q2 • DPDFs from NLO QCD fits to , Q2 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. Diffractive PDFs BLOIS 2007 BACK-UP SLIDES FOLLOW

22. Diffractive PDFs BLOIS 2007 Effective Pomeron Intercept Independent of β and Q2 From fit to LRG data: • No dependence of aIP(0) • on Q2 or β • The xIP dependence also • factorises from Q2 and b • xIP, t and MY dependences factorise from the Q2 and β dependences within errors → Data support Proton Vertex Factorisation

23. Diffractive PDFs BLOIS 2007 t Slope Dependence on β or Q2? B measured double differentially in (b or Q2) at fixed xIP • t dependence does not change with b or Q2at fixed xIP

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

25. Diffractive PDFs BLOIS 2007 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 LPSandH1 FPS • scaled by global factor of 1.23 to compare with LRGMY < 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. Diffractive PDFs BLOIS 2007

27. Q2derivative and gluon/quark ratios Ifthen Inclusive Diffractive 0.7 0.3 At low x, gluon:quark ratio ~ 70%/30%, common to diffractive and inclusive Diffractive PDFs BLOIS 2007