810 Brazilian Journal of Physics, vol. 37, no. 2C, June, 2007 Inclusive Measurements on Diffractive Processes in ep Collisions Xavier Janssen1, on behalf of the H1 and ZEUS Collaborations 1 Universite´ Libre de Bruxelles, IIHE - CP 230, Boulevard du Triomphe, B-1050 Bruxelles, Belgium Received on 25 November, 2006 Measurements from the H1 and ZEUS collaborations of the diffractive deep-inelastic scattering process, ep ! eXY, where Y is a proton or a low mass proton excitation, are presented for photon virtualities in the range 2:2 < Q2 < 1600 GeV2 and squared four-momentum transfer at the proton vertex satisfying jtj < 1 GeV2. Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis. Combining measurements of the inclusive diffractive deep-inelastic scattering process with an analysis of diffractive dijet production allows a very sensitive determination of both quark and gluon distributions. Keywords: Diffraction; Deep inelastic scattering I. INTRODUCTION in rapidity. Such processes are often discussed in terms of an exchange with net vacuum quantum numbers, the pomeron This proceeding summaries recent results [1–4] obtained (IP), and a fraction xIP of the proton longitudinal momentum with the H1 and ZEUS detectors at the HERA ep collider is transferred to the system X. Understanding the nature of on measurements of the diffractive deep-inelastic scattering the pomeron in terms of quarks and gluons is a challenge for (DIS) process, ep ! eXY, where Y is a proton or a low mass Quantum Chromodynamics (QCD). proton excitation, which represents at low Bjorken x approx- imatively 10% of the total cross section. In diffractive inter- actions, a photon of virtuality Q2 is emitted by the incom- II. CROSS SECTION MEASUREMENTS ing lepton and interacts strongly with the proton to form two hadronic final state systems X and Y separated by a large gap High statistic samples of diffractive DIS events are selected either by requesting a large rapidity gap (LRG) in the outgo- H1 Data H1 2006 DPDF Fit A 2 ing proton direction (H1 case [1]) or by a subtraction method (extrapol. fit) Q [ 2] β β β β β β β GeV differentially in the mass of the X system (MX Method, ZEUS 0.05 =0.01 =0.04 =0.1 =0.2 =0.4 =0.65 =0.9 D(3) 3.5 r case [3]). In such case, the measured process by H1 (ZEUS) 0 σ 0.05 5 is ep ! eXY, where Y corresponds to any baryonic system IP x 0 with mass MY < 1:6 GeV (MY < 2:3 GeV). Both experiments 0.05 6.5 0 have also collected smaller samples for the ep ! eX p process 0.05 8.5 by directly detecting the outgoing proton with Roman Pot de- 0 tectors [2, 4]. This last selection method allows to measure 0.05 12 0 the outgoing proton four-momentum and to reconstruct the 0.05 15 squared four-momentum transfer at the proton vertex t. In ad- 0 2 0.05 20 dition to t, xIP and the usual DIS variables x and Q , measure- 0 ments are made as a function of b = x=xIP, which corresponds 0.05 25 0 to the fraction of the exchanged longitudinal momentum car- 0.05 35 ried by the quark coupling to the virtual photon. Alltogether, 0 0.05 the collected data are covering photon virtualities in the range 45 2 2 2 0 2:2 < Q < 1600 GeV , xIP < 0:05 and jtj < 1 GeV . 0.05 60 0 D(3) 0.05 90 A. Reduced cross section sr 0 0.05 200 0 As the t dependence can not be measured in the case of the 0.05 400 LRG and MX Methods, the data are presented in the form of a 0 0.05 D(3) 800 “diffractive reduced cross section” sr , integrated over t and 0 0.05 1600 MY in the ranges specified above and related to the differential 0 -4 -2 -4 -2 -4 -2 -4 -2 -4 -2 -4 -2 -4 -2 cross section measured experimentally by 10 10 10 10 10 10 10 10 10 10 10 10 10 10 x IP 3 ep!eXY 2 d s 2pa D(3) 2 2 = 2 Y+ sr (xIP;x;Q ) FIG. 1: The xIP dependence of the diffractive reduced cross section, dxIPdxdQ xQ 2 multiplied by xIP, at fixed values of b and Q as measured by H1 [1]. The data are compared with the results of the “H1 2006 DPDF Fit 2 where Y+ = 1 + (1 ¡ y) . Similarly to inclusive DIS, the re- A” resulting from a NLO DGLAP analysis. duce cross section is related to the diffractive structure func- Xavier Janssen 811 D(3) D(3) tions F2 and FL in the one-photon exchange approxima- tion according to 2 D(3) D(3) y D(3) sr = F2 ¡ FL : Y+ The diffractive reduced cross section as measured via the LRG Method by the H1 experiment [1] is presented in Fig. 1 2 as function of xIP at fixed values of b and Q , together with results of the “H1 2006 DPDF Fit A” presented below. These data presents unprecedented precision of 5% statistical, 5% FIG. 3: Measurements of the slope parameter B by H1 and ZEUS. systematic and 6% normalization in the best-measured region. Fig. 2 present a comparaison of the results on the diffrac- tive reduced cross section obtained via the MX Method by the III. QCD ANALYSIS OF H1 DATA AND DIFFRACTIVE ZEUS experiment [3] with the H1 results. The two datasets PARTON DISTRIBUTIONS are globally consistent with however some differences at low Q2 and high b being observed. As proved in [5], QCD hard scattering collinear factorisa- tion is applicable to hard diffractive processes in ep interac- tions such that cross sections can be written in terms of con- B. t dependence volutions of partonic cross sections sˆ ei(x;Q2) with Diffractive D Parton Distribution Functions (DPDF) fi : The datasets collected by the Roman Pot detectors allow ep!eXY 2 D 2 ei 2 ds (x;Q ;xIP;t) = ∑ fi (x;Q ;xIP;t) ­ dsˆ (x;Q ): to measure the t dependence of the diffractive cross sec- i tions which is commonly parameterised with an exponential, ds=dt » eBt . The values of B resulting from such fits to the The partonic cross sections are the same as those for non- H1 [2] and ZEUS [4] data are shown as a function of x in diffractive interactions. The DPDFs represent probability dis- IP tributions for partons i in the proton under the constraint that Fig. 3. At low xIP, the H1 data are compatible with a con- ¡2 the proton is scattered to a specified system Y with a speci- stant slope parameter, B ' 6 GeV wheather the high xIP D region is thought to be dominated by the exchange of sub- fied four-momentum. If such a theorem holds, the DPDFs fi leading trajectory. In a Regge approach with a single lin- should be universal for all hard diffractive processes, e.g. in- ear exchanged pomeron trajectory, a (t) = a (0) + a0 t, the clusive diffraction, jet or heavy-quark production. They are IP IP IP not known from first principles, but can be determined from slope parameter decreases with increasing xIP according to 0 fits to the data using the DGLAP evolution equations. B = B0 ¡ 2aIP lnxIP. The low xIP H1 data favour a small value 2 0 ¡2 0 ¡2 The kinematic range in x and Q accessible being limited of aIP ' 0:06 GeV , though aIP ' 0:25 GeV , as obtained from soft hadronic interactions, cannot be excluded. for a given value of xIP, a parameterisation of the xIP depen- dence of the DPDFs is necessary. The proton vertex factori- sation framework, in which the DPDFs are factorised into a H1 Data 2 ZEUS (Mx) Q term depending only on x and t and a term depending only [GeV2] IP β=0.01 β=0.04 β=0.1 β=0.2 β=0.4 β=0.65 β=0.9 2 D(3) 0.05 on x (or b) and Q , is often assumed: r 3.5 σ D 2 2 IP 0 fi (x;Q ;xIP;t) = fIP=p(xIP;t) fi(b = x=xIP;Q ): x 0.05 6.5 This is equivalent to treating the diffractive exchange as a 0 “pomeron” with a partonic structure given by the parton dis- 0.05 8.5 2 tributions fi(b;Q ), the “pomeron flux factor” fIP=p(xIP;t) 0 representing the probability that a pomeron with particu- 0.05 15 lar values of xIP and t couples to the proton. The IP flux 0 can be parametrised using a Regge inspired form fIP=p = 0.05 2a (t)¡1 25 Bt IP AIPe =xIP . The H1 data [1, 2] are consistent with the 0 vertex factorisation assumption and it is then used in their 0.05 60 QCD fit. 0 The H1 collaboration performs next-to-leading order -4 -2 -4 -2 -4 -2 -4 -2 -4 -2 -4 -2 -4 -2 10 10 10 10 10 10 10 10 10 10 10 10 10 10 (NLO) QCD DGLAP fits to the reduced diffractive cross sec- x IP tion in order to extract DPDFs. To avoid regions which are most likely to be influenced by higher twist contributions or FIG. 2: Comparison of the xIP dependence of the diffractive reduced other problems with the chosen theoretical framework, only cross section, multiplied by x , at fixed values of b and Q2 as mea- 2 2 IP data with Mx > 2 GeV, b < 0:8 and Q > 8:5 GeV are in- sured by ZEUS [3] and H1 [1].