Inclusive Dijet Cross Sections in Neutral Current Deep Inelastic Scattering and Photoproduction at HERA
aa r X i v : . [ h e p - e x ] A ug Inclusive Dijet Cross Sections in Neutral CurrentDeep Inelastic Scattering and Photoproductionat HERA
Oleg Kuprash (for the ZEUS Collaboration)Deutsches Elektronen-Synchrotron, Notkestraße 85, 22607 Hamburg, GermanyTaras Shevchenko National University of Kyiv
Abstract.
Recent results from the ep collier HERA are presented. Inclusive dijet cross sections havebeen measured in neutral current deep inelastic scattering, for virtualities of the exchanged boson inthe range 125 < Q <
20 000 GeV and in photoproduction, Q ∼ . The measurements arecompared to perturbative QCD calculations at next-to-leading order. Keywords: dijet production, deep inelastic scattering, photoproduction
PACS:
INTRODUCTION
At HERA, two kinematic regions can be distinguished: in deep inelastic scattering (DIS)the electron interacts with a parton from the proton via the exchange of a virtual bosonwith large virtuality, Q . In contrast, in photoproduction the exchanged photon is quasi-real and the electron escapes the detector through the beam pipe. The virtuality of theexchanged boson in DIS is Q & , whereas in photoproduction the exchangedboson is almost on its mass shell, and Q . holds.The measurements of jet production are a well established tool for stringent tests ofquantum chromodynamics (QCD) and have been performed at HERA for many jet ob-servables. The production of jets allows a direct measurement of the strong coupling con-stant, a s , and photon (in photoproduction) and proton parton density functions (PDFs)can be extracted.In DIS, two processes contribute to the production of two jets in leading-order (LO) a s : boson-gluon fusion (Fig. 1, left) and QCD Compton scattering (Fig. 1, middle). Forthe dijet measurement in DIS, the Breit reference frame was used, since it providesa maximal separation between the hard jets and the beam fragmentation products. Inthis frame the exchanged boson collides head-on with the parton. Therefore, transverseenergies are an indicator for the occurrence of strong processes. Dijet measurementsin DIS have been performed at large virtualities Q , where both the theoretical andexperimental uncertainties are relatively small. Jet data have been included in the ZEUS-JETS [1] fit of the proton PDFs, which significantly reduced the uncertainty on the gluondensity in the regions of medium and high x .In the photoproduction regime two types of processes contribute to dijet productionin LO a s : in direct photon processes the photon interacts with a parton as a point-like ( p )¯ q ( p ) e ( l ) e ( l ′ ) p ( P ) X jet jet α S γ/Z ( q ) α S q ( p ) g ( p ) e ( l ) e ( l ′ ) p ( P ) Xγ/Z ( q ) jet j e t α S q ( p )¯ q ( p ) e ( l ) e ( l ′ ) p ( P ) X p jet jet α S X γ FIGURE 1.
Boson-Gluon Fusion (left); QCD Compton scattering (middle); LO diagram for resolvedphotoproduction (right). object whereas in resolved photon processes (Fig. 1, right) the photon acts as a sourceof partons, one of which interacts with the parton from the proton. Thereby, in addition,in photoproduction the measurement is sensitive to the photon PDFs.In both DIS and photoproduction, jets were reconstructed with the k T cluster algo-rithm [2] in the longitudinally invariant inclusive mode [3] using the smallest calorime-ter units called cells. The jet search in DIS was performed in the Breit reference frame,whereas in photoproduction it was performed in the laboratory frame. In order to takeinto account detector effects, LO Monte Carlo (MC) samples were used, which utilisedifferent approaches for the parton cascade. The next-to-leading order (NLO) QCD pre-dictions were corrected using these MCs to take into account hadronisation and electro-weak effects.In this report, recent measurements of inclusive dijet production in neutral current(NC) DIS [4] and photoproduction [5] performed with the ZEUS detector are presented.The measurements presented here correspond to integrated luminosities of 189 pb − for the photoproduction and of 374 pb − for the NC DIS analysis, respectively. INCLUSIVE DIJETS IN NEUTRAL CURRENT DIS
The phase space of the measurement was defined by 125 < Q <
20 000 GeV and0 . < y < .
6, where y is the inelasticity determined using the relation y = Q / x Bj s .In this formula, x Bj is the Bjorken scaling variable and s is the square of the centre-of-mass energy. The selected events were required to have a well reconstructed and isolatedscattered electron. The pseudorapidities of the jets in the laboratory frame, h jetLAB , wererequired to satisfy − < h jetLAB < .
5. For the measurement of the jet cross sectionsevents with at least two jets with transverse energies in the Breit frame, E jet T , B , greaterthan 8 GeV were selected. Additionally, the invariant mass of the dijet system had to begreater than 20 GeV. The latter cut was introduced to suppress infrared sensitive regionsin the fixed-order calculations.Cross sections were compared to NLO QCD calculations as implemented in the N LO - JET ++ program [6]. The calculations were obtained using the CTEQ6.6 parameterisa-tions for the proton PDFs with the factorisation and renormalisation scales set to m F = Q and m R = Q + E jet T , B2 , respectively. Here, E jet T , B is the mean jet transverse energy of thedijet system in the Breit frame. The uncertainty on the NLO predictions due to missinghigher orders was estimated by varying m R by a factor 2 up and down and was foundto be below ±
6% at low Q and low E jet T , B and below ±
3% in the highest Q region. ( pb / G e V / d Q s d −4 −3 −2 −1 ) −1 ZEUS (374 pb Z C ˜ hadr C ˜ NLO E+ =Q R2 m =Q m E= m ) (GeV Q re l . d i ff . t o N L O −0.200.2 jet energy scale uncertaintyNLO uncertainty ( pb / G e V ) j e t T , B E / d s d −1 ) −1 ZEUS (374 pb Z C ˜ hadr C ˜ NLO E+ =Q R2 m =Q m E= m (GeV) jetT,B E
10 20 30 40 50 60 re l . d i ff . t o N L O −0.200.2 jet energy scale uncertaintyNLO uncertainty FIGURE 2.
The differential cross sections as functions of the exchanged boson virtuality, Q (left), andthe mean energy of the jets of the dijet system in the Breit frame, E jetT , B (right). The calculations provide a good description of the measured cross sections, as demon-strated in Fig. 2, where the differential cross sections as functions of Q and E jet T , B arecompared with the NLO QCD predictions. The data and the theory agree very wellin shape and normalisation. The theoretical uncertainty in the lower Q region, whichamounts to about ± ≈ ± < Q <
250 GeV to about 5% in the highest Q region investigated. The PDFuncertainty in the medium Q region is larger than the theoretical uncertainty due tothe choice of m R . Therefore precise input for the determination of the gluon distributionfunction is expected. INCLUSIVE DIJETS IN PHOTOPRODUCTION
In photoproduction the electron escapes undetected through the beam pipe. Thus, the jetsof the dijet system are approximately balancing each other in the transverse plane. Thephase space of the measurement was defined by Q < with the centre-of-massenergy of the photon-proton system, W g p , in the range 142 < W g p <
293 GeV. Selectedevents were required to lack an identified scattered electron. For the cross sectionspresented here, only events with at least two jets with transverse energies E jet1 T >
21 GeVand E jet2 T >
17 GeV were considered. The latter cuts, which are asymmetric, wereapplied to make the theory infrared insensitive. The pseudorapidities of the jets had tosatisfy − < h jet < . x g was used, which is the fraction of the photon momentum participating in the productionof the two most energetic jets. This variable can be determined according to x obs g = E jet1 T e − h jet1 + E jet2 T e − h jet2 ) / yE e , where E e = . x g is close to one, whereas for events with resolvedphotons characteristic x g values are smaller.Cross sections were compared to NLO QCD calculations obtained using the programfrom Klasen, Kleinwort and Kramer [7]. The ZEUS-S proton PDFs and the GRV-HOphoton PDFs were used. The scales m R and m F were set to m R = m F = ( E jet T ) max . Therenormalisation scale uncertainty was evaluated by scaling m R by a factor 2 up and downand amounts to 20%. As shown in Fig. 3, where the cross sections as functions of x obs g and E jet T are compared with NLO QCD predictions, the NLO calculations provide a gooddescription of the data. The cross section measured as a function of x obs g is sensitive to thephoton PDFs, due to the large spread observed between the predictions using differentparameterisations of the photon PDFs. This sensitivity is especially pronounced in thelow- x obs g region, in which resolved photon events are dominating. In all investigated crosssection bins, the theoretical uncertainties are larger than the experimental uncertainties. ZEUS -1 NLO hadr: p/ g PDFs ˜ (Klasen et al.)ZEUS-S/GRV-HO MSTW08/GRV-HOZEUS-S/AFG04ZEUS-S/CJK E jet1T >
21 GeV, E jet2T >
17 GeV -1 < h jet < < < y < d s / d x g o b s ( pb ) -0.500.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x g obs re l . d i ff . t o N L O ZEUS -1 -2 -3 ZEUS (prel.) 189 pb -1 NLO hadr: p/ g PDFs ˜ (Klasen et al.)ZEUS-S/GRV-HO MSTW08/GRV-HOZEUS-S/AFG04ZEUS-S/CJK E jet1T >
21 GeV, E jet2T >
17 GeV -1 < h jet < < < y < d s / d E –– j e t T ( pb / G e V ) -0.500.5 20 30 40 50 60 70 80 E –– jetT (GeV) re l . d i ff . t o N L O FIGURE 3.
The differential cross sections as functions of x obs g (left) E jet T (right). The measured differential cross sections of inclusive dijet production in both neutralcurrent DIS and photoproduction have small statistical and systematic uncertainties.The description of the data by NLO QCD is good. These jet data have the potentialto significantly reduce PDF uncertainties and provide information for the determinationof the strong coupling constant.
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