43 rd Rencontres de Moriond : QCD and High Energy Interactions 8-15 March 2008, La Thuile, Italy

1. Diffraction at HERA 43rd Rencontres de Moriond : QCD and High Energy Interactions 8-15 March 2008, La Thuile, Italy Heuijin Lim (ANL) on behalf of H1 and ZEUS collaborations • Measurements of inclusive diffraction • Diffractive Parton Densities • Test of factorization in diffractive Final States Moriond QCD, 8-15 March 2008

2. Inclusive Diffraction in Deep Inelastic Scattering • DIS : Probe structure of proton • Diffractive DIS : Probe structure of colorless system, Pomeron, exchange Inclusive DISprocess Kinematics of ep  eXp Diffractive DIS process N (MN) In pQCD, Pomeron exchange can be described by two-gluon exchange. Moriond QCD, 8-15 March 2008

3. Event selection MX method LPS method Diffractive DIS process Mass of X  MX xL=1-xIP=p⁄Z/pZ Leading Proton Spectrometer Outgoing proton Scattered electrons Large Rapidity Gap LRG method Inclusive DISprocess ηmax η=-ln(tan(θ/2)) Moriond QCD, 8-15 March 2008

4. Measurements of inclusive diffractive DIS • Diffractive cross-section : dσ(MX,W,Q2)/dMX Comparison of diffractive and total γ*p scattering  Q2 dependence of αIP(0) and rdiff(=σdiff/σtot) • Diffractive structure function : xIPF2D(3)(β,xIP,Q2), xIPF2D(4)(β,xIP,Q2, t) Q2 dependence and β dependence Comparison with MX, LRG and LPS measurements • Diffractive Parton Densities • Extract DPDFs from QCD fit to inclusive diffractive DIS • Combined QCD fit to inclusive diffractive and Dijets • Test of factorization in diffractive Final States • Dijets in DIS and Photoproduction Moriond QCD, 8-15 March 2008

5. Diffractive Cross Section with MX method FPCI (98-99) : 4.2 pb-1 2.2 < Q2 < 80 GeV2 Nucl. Phys. B713, 3(2005) FPCII (99-00) : 52.4 pb-1 20 < Q2 < 450 GeV2 Submitted to Nucl. Phys. B. (arXiv:0802.3017) • Within systematic errors, good agreement between FPCI and FPCII. Moriond QCD, 8-15 March 2008

6. Comparison of diffractive and total γ*p scattering • For Q2 < 20 GeV 2, αIPdiff(0)is consistent with soft Pomeron. • For Q2 > 30 GeV2, data suggest increase with Q2.  Regge factorisation breaking. • αIPdiff(0) is lower than αIPtot(0) : • Different Pomeron trajectory! • r = σdiff(0.28 < MX < 35 GeV)/σtot • Within the errors of the measurements, r is independent on W. • At W=220 GeV, r ~ 15.8 % at Q2= 4 GeV2 r ~ 5.0 % at Q2= 190 GeV2 r shows a logarithmic dependence on Q2. Moriond QCD, 8-15 March 2008

7. Q2 dependence of xIPF2D(3)  Probability to find a quark carrying x=βxIP in a proton undergoing a diffractive process. x = β xIP < 0.001 • For β≥ 0.9 • (dominated by events with MX<2 GeV), • Constant or slowly decreasing with Q2 • Expect higher twist effect from • For x=β xIP < 0.001, • xIPF2D(3) increases with increasing Q2. •  Positive scaling violations. • Suggest perturbative effects such as gluon emission • For fixed β, • Q2 dependence of xIPF2D(3) changes with xIP.  Inconsistent with the Regge • factorisation hypothesis Moriond QCD, 8-15 March 2008

8. Diffractive structure function with LPS method • The parameterization of xIP dependence gives the intercept of αIP. Moriond QCD, 8-15 March 2008

9. Comparison of LRG with LPS measurements ZEUS LRG 00 (prel.), ZEUS LPS 00 (prel.) (LPS/LRG) (LPS/LRG) H1 LRG with MN<1.6 GeV ZEUS LRG with MN < 2.3 GeV • Ratio between LRG and LPS is independent of Q2, β and xIP within errors. •  It shows 23~25 % of proton dissociation contribution in LRG data. • For xIP > 0.01, their constant ratio tells that the LRG data also contain the reggeon contribution. Moriond QCD, 8-15 March 2008

10. Factorization in Diffractive DIS • Diffractive DIS, like inclusive DIS, is factorizable : Diffractive parton distribution function Universal partonic cross section • fi/pD(z,Q2,xIP,t) : Probability to find in a proton, with a probe of resolution Q2, parton i with momentum fraction z, under the condition that the proton remains intact and emerges with small energy loss,xIP, and momentum transfer, t. • Obey DGLAP • universal for diffractive ep DIS (inclusive, Dijet, Cham) • Assumption : Proton vertex factorization  Shape of diffractive PDFs independent of xIP and t. Regge motivated IP flux At large xIP, a separately factorizable sub-leading exchange (IR), with different xIP dependence and partonic composition. Moriond QCD, 8-15 March 2008

11. H1 2006 DPDF Fits • Fit H1 LRG data • with Q2≥8.5 GeV2, MX>2 GeV, β≤0.8) • Parameterize the parton density • χ2 ~ 158/183 d.o.f., Q02=1.75 GeV2 • Effective Pomeron trajectory (Fit A) : • ~70 % gluons in diffractive exchange • Due to lack of sensitivity for the gluon density at high z. •  Fit B : using zg(z,Q02)=Ag • χ2 ~ 164/184 d.o.f. , Q02=2.5 GeV2 Moriond QCD, 8-15 March 2008

12. Diffractive dijets in DIS H1 2007 Jets DPDF Fit 2006 - B Rapidity Gap H1 2007 Jets DPDF zIP= longitudinal momentum fraction of color singlet carried by parton entering hard sub-process  zIP distribution is sensitive to gluon DPDF. • H1 Dijet data are in better agreement with H1 Fit B. • ZEUS Dijet data consistent with H1 Fit B and MRW 2006 fit. • Combined Fit to inclusive and Dijet data  better constraint to quark and gluon densities, close to H1 Fit B. Fit 2006 – A Fit 2006 -- B Moriond QCD, 8-15 March 2008

13. Diffractive dijets in Photoproduction (Q2 ~ 0 GeV2) Interactions destroy gap for resolved PHP. xγ = 1 xγ < 1 xγ = fraction of photon momentum in hard scattering. • Dijets are suppressed by a factor~0.5 for direct and resolved γ. • (big difference: ETjet1 (ETjet2) > 5 (4) GeV) • Dijets are weakly suppressed by a factor ~ 0.87 for direct and resolved γ. • (ETjet1 (ETjet2) > 7.5 (6.5) GeV) Moriond QCD, 8-15 March 2008  ET distribution may not be well reproduced by NLO. Still work in progress.

14. Conclusion • Inclusive diffraction was measured with high statistics for a wide kinematic range from low to high Q2. • Good agreement with the results measured by MX, LPS and LRG methods. • Diffractive DIS and total γ*p process cannot be described by an unique pomeron and r=σdiff(0.28 < MX < 35 GeV)/σtot decreases ~ ln(1+Q2). • Indication for Regge factorisation breaking was seen in • Q2 dependence of αIPdiff(0) • Q2 dependence of xIPF2D(3) for fixed β and fixed xIP • Evidence for pQCD evolution with Q2 as xIP0 or β 0. • Combined QCD fit to inclusive diffractive DIS and Dijets • It improved the gluon structure at high z.  Gluon dominated: ~ 70 %. • Diffractive charm and Dijets DIS data are consistent with NLO predictions based on DPDFs from inclusive data. • Diffractive Dijets in photoproduction ZEUS : agreement with NLO prediction and no large suppression(~0.87). H1 : suppression(~0.5) • ETjet dependence is investigated. Moriond QCD, 8-15 March 2008