Proton Structure Functions at High Q 2 and High x at HERA
aa r X i v : . [ h e p - e x ] J u l PROTON STRUCTURE FUNCTIONS AT HIGH Q AND HIGH x AT HERA
S. U. NOOR(On behalf of the ZEUS and H1 collaborations)
York University,Petrie Science and Engineering Building,4700 Keele St., Toronto, Ontario, M3J 1P3, Canada
Proton structure measurements at high Q and high x , performed by the H1 and ZEUScollaborations at the HERA collider, are reviewed. Neutral and charged current deep inelasticscattering cross sections and structure functions are presented. The review also discussesimprovements to the parton density measurements using jet cross section data and recenthigh Q inclusive cross section measurements. The projected parton density uncertaintiesusing the entire HERA data set are also presented. Precise measurements of the proton parton density functions (PDFs) are crucial for understand-ing the structure of the proton. This is of particular importance with the imminent start of theLHC proton-proton collider. Unpolarised lepton beams were used before the luminosity upgradein 2000 (HERA-I), whereas the post-upgrade collider (HERA-II) has delivered polarised leptonsbeams. This paper reviews the latest measurements at high Q and high x performed by theZEUS and H1 collaborations at HERA.The PDFs are determined in global fits at next-to-leading order (NLO) in QCD using datafrom deep inelastic scattering (DIS) experiments. The kinematic range covered by HERA hasallowed the determination of PDFs across a wide range of phase space spanned by the fractionalproton momentum of the struck quark, Bjorken- x , and the negative squared four-momentumtransfer, Q , of approximately 10 − < x < < Q < GeV . The Born-level reduced cross section for the e ± p neutral current (NC) interaction with polarisedlepton beams can be written as 1,˜ σ e ± p = xQ πα Y + d σ ( e ± p ) dxdQ = F ± ( x, Q ) ∓ Y − Y + xF ± ( x, Q ) − y Y + F ± L ( x, Q ) , (1)where α is the fine-structure constant, Y ± ≡ ± (1 − y ) and y is related to the centre-of-massenergy, √ s , via Q = sxy . The longitudinal structure function, F L , is small in the kinematicregion considered and can be ignored. The structure functions, F and xF , contain the sumand difference of the quark and anti-quark PDFs and can be separated into contributions frompure γ exchange, the interference of γ and Z boson exchange and from pure Z exchange. These a ) ( b ) Figure 1: Graph (a) shows the combined measurement of the structure function xF γZ versus x at Q = 1500 GeV from the H1 and ZEUS collaborations using e ± p NC DIS data. The curves represent the SM prediction from theH1 2000 and ZEUS-JETS PDFs. The plots shown in (b) present the CC e − p reduced cross section as a functionof x in fixed bins of Q . The SM prediction using the ZEUS-JETS PDF is shown in red and dashed lines indicatethe contributions from terms involving up type quarks and down type anti-quarks. terms depend on the lepton beam charge, the longitudinal polarisation of the lepton beam, P e ,the mass of the Z and W bosons, M Z and M W , and the weak-mixing angle, θ , to give thefollowing 2, F ± = F γ + k ( − v e ∓ P e a e ) F γZ + k ( v e + a e ± P e v e a e ) F Z , (2) xF ± = k ( − a e ∓ P e v e ) xF γZ + k (2 v e a e ± P e ( v e + a e )) xF Z , (3)where k =
14 sin θ cos θ Q Q + M Z and the vector and axial-vector coupling of the electron to the Z boson are v e = − / θ and a e = − / σ e − p − ˜ σ e + p one can extract xF using unpolarised HERA-I data and net unpolarised data from HERA-II.As the polarisation dependence is removed, xF can be written as, xF = − a e kxF γZ + 2 v e a e k xF Z . (4)Since the coupling v e is small and k <
1, the interference term dominates xF . In leading order(LO) perturbative QCD the interference structure function can be explicitly written in terms ofthe valence quark distributions, u v and d v , xF γZ = x u v + d v + ∆) , (5)where ∆ = 2( u sea − ¯ u + c − ¯ c ) + ( d sea − ¯ d + s − ¯ s ). Therefore xF γZ is determined by the valencequark distribution if the ∆ term is ignored, and is only weakly dependent on Q . To minimisestatistical errors, the xF γZ measurements can be extrapolated in Q and averaged in x . Resultsfrom the ZEUS and H1 collaborations are shown in Fig. 1(a). -4 -3 -2 -1
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ZEUS-JETS fit-0.4-0.3-0.2-0.1-00.10.20.30.4 -0.4-0.3-0.2-0.1-00.10.20.30.4 xg -4 -3 -2 -1
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HERA-II projection-0.4-0.3-0.2-0.1-00.10.20.30.4 x f r a c t i o n a l un cer t a i n t y ( a ) ( b ) Figure 2: The ZEUS-pol PDFs for the valence ( u v , d v ), sea ( S ), and gluons ( g ) are shown in figure (a) comparedwith the ZEUS-JETS PDFs central values. Figure (b) shows the uncertainties for the ZEUS-JETS PDFs in redand the HERA-II projected uncertainties in yellow. The Born level charged current (CC) e ± p cross section with polarised leptons can be ex-pressed at LO in QCD as 1, d σ CC ( e − p ) dxdQ = (1 − P e ) G F π (cid:18) M W M W + Q (cid:19) [ u + c + (1 − y ) ( ¯ d + ¯ s )] , (6) d σ CC ( e + p ) dxdQ = (1 + P e ) G F π (cid:18) M W M W + Q (cid:19) [¯ u + ¯ c + (1 − y ) ( d + s )] , (7)where G F is the Fermi coupling constant and u, c, d, s are the respective quark densities. Theflavour selecting nature of the CC interaction is apparent as u quark content is revealed through e − p DIS, whereas d quark constraints are possible through e + p scattering. This can be illustratedin the e − p CC DIS reduced cross section measurements 4 shown in Fig. 1(b), where the SMprediction describes the data well and is dominated by the u quark density. The PDFs are usually determined in global fits using data from many different experiments.However, the high precision and wide kinematic coverage of existing HERA data allow preciseextractions of the proton PDFs using only HERA data. The use of HERA data alone eliminatesthe uncertainty from heavy-target corrections and also avoids difficulties that can sometimesarise from combining data sets from several different experiments.The high statistics HERA NC data is used to determine the low x sea and gluon distributionswhile information on the valence quarks is provided by the higher- Q NC and CC data. Thegluon density contributes indirectly to the inclusive DIS cross sections, however it makes a directcontribution to the jet cross sections through boson-gluon fusion. The ZEUS collaboration hasperformed a combined NLO QCD fit (ZEUS-JETS PDF 5) to inclusive NC and CC DIS dataas well as high precision jet data in DIS and γp scattering.The ZEUS-JETS PDFs agree well with the previous ZEUS-S PDF global fits and are alsocompatible with the MRST 6 and CTEQ 7 PDFs. The shapes of the PDFs are not changedignificantly by including jet data but the decrease in the uncertainty on the gluon distributionis significant, approximately halved, in the mid- x region over the full Q range. The PDF uncertainties from current global fits are, in general, limited by irreducible experimen-tal systematics. In contrast, the fits to HERA data alone are largely limited by the statisticalprecision of existing measurements. Since 2003, HERA has delivered a substantial amount ofluminosity with polarised lepton beams. Figure 2(a) shows a new PDF fit named ZEUS-pol 8which includes HERA-II e − p NC and CC inclusive cross section data with a total integrated lu-minosity of 121 . − . This leads to an improvement in PDF uncertainties at high x , especiallyfor the u valence quark.As new HERA data is analysed, a significant impact on the gluon uncertainties could be madeby future jet cross section measurements in kinematic regions optimised for PDF sensitivity.The effect on the PDF uncertainties using the entire HERA data set has been estimated in theHERA-II projection fit 9. A total integrated luminosity of 700 pb − was assumed for the high Q inclusive data, and 500 pb − was assumed for the jet measurements with central values andsystematic uncertainties taken from the published data in each case. A set of optimised jet crosssections were included for forward γp collisions assuming a luminosity of 500 pb − .The increased statistical precision of the assumed amount of high Q data gives a signifi-cant improvement in the valence quark uncertainties over the whole range of x . A significantimprovement at high x is seen for the sea quarks, however the low x sea and low x gluons arenot significantly impacted as the data constraining this region tends to be at lower Q and soalready systematically limited. Much improvement is seen in the mid-to-high x gluon which isconstrained by jet data. Approximately half of the projected reduction in the gluon uncertaintiesis due to the inclusion of optimised jet cross sections.Accurate proton PDFs are of great importance, especially for the LHC proton-proton colliderwhich is planning to deliver high energy collisions in 2008. With HERA shutting down in July2007, the projected improvements to the PDF uncertainties using solely HERA data will beparticularly relevant to future physics at the LHC. References
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