Hadron Structure from inclusive and exclusive cross-sections in ep scattering On behalf of ZEUS and H1 A M Cooper-Sarkar Oxford HS07 H1 and ZEUS published PDF fits on HERA-I data Including jet production data in fits to improve gluon PDF determination Including jet production data in fits to determine α s (M Z ) H1 and ZEUS combined α s (M Z ) Preliminary ZEUS-pol PDF fit to HERA-II polarized data - improves valence The future: combination of H1 and ZEUS inclusive cross-sections : F2c and F2b data : more jet data : high-y and FL data

Terrific expansion in measured range across the x, Q 2 plane from HERA data This plots show the HERA-I data using the new preliminary combination of H1 and ZEUS data (see later) The fits illustrated are the published H1 and ZEUS fits to their own HERA-I data d 2  (e±N) = [ Y + F 2 (x,Q 2 ) - y 2 F L (x,Q 2 ) ± Y_xF 3 (x,Q 2 )], Y± = 1 ± (1-y) 2 dxdy q = k – k´, Q 2 = -q 2, s= (p + k) 2 x = Q 2 / (2p.q), y = (p.q)/(p.k)

Limit on the quark radius from H1 data HERA I+II 435 pb -1 R q = m (95% CL) Before we begin.. Down to what scales are we probing? How does the data relate to the parton distribution functions PDFs of the proton?

HERA data have provided information at high Q 2 → Z 0 and W +/- become as important as γ exchange → NC and CC cross-sections comparable For NC processes at LO in QCD F 2 =  i A i (Q 2 ) [xq i (x,Q 2 ) + xq i (x,Q 2 )] xF 3 =  i B i (Q 2 ) [xq i (x,Q 2 ) - xq i (x,Q 2 )] A i (Q 2 ) = e i 2 – 2 e i v i v e P Z + (v e 2 +a e 2 )(v i 2 +a i 2 ) P Z 2 B i (Q 2 ) = – 2 e i a i a e P Z + 4a i a e v i v e P Z 2 P Z 2 = Q 2 /(Q 2 + M 2 Z ) 1/sin 2 θ W Structure function F 2 relates to the sum over quark flavours → information on sea quarks at low-x, valence at high-x Structure function xF 3 due to Z exchange relates to valence quarks from low to high x- on a pure proton target → no heavy target corrections- no assumptions about strong isospin e- running at HERA-II has improved this measurement and a combination of ZEUS and H1 data gives the most precise results

CC processes give flavour information d 2  (e - p) = G F 2 M 4 W [x (u+c) + (1-y) 2 x (d+s)] dxdy 2  x(Q 2 +M 2 W ) 2 d 2  (e + p) = G F 2 M 4 W [x (u+c) + (1-y) 2 x (d+s)] dxdy 2  x(Q 2 +M 2 W ) 2 M W information u v at high x d v at high x Measurement of high-x d v on a pure proton target is unique (even Deuterium needs corrections. Does d v /u v  0, as x  1? Does u in proton = d in neutron?)

ANALYSES FROM HERA ONLY … Systematics well understood - measurements from our own experiments !!! No complications from heavy target Fe or D corrections No assumptions on isospin (d in proton = u in neutron ?) GlobalHERA Only ValencePredominantly fixed target data ( -Fe and  D/  p) High Q 2 NC/CC e  cross sections SeaLow-x from HERA NC DIS High-x from fixed target Flavour from fixed target p/D Low-x from NC DIS High-x less precise Flavour ?(need assumptions) GluonLow-x from HERA dF 2 /dlnQ 2 High-x from momentum sum ZEUS and H1 published PDF analyses Both ZEUS and H1 make PDF fits to their own inclusive differential cross section data. Where does the information come from in a HERA only fit compared to a global fit ? Tevatron +HERA jet dataHERA jet data Mostly u-valence Can also access d-valence

The parametrisations are somewhat different for ZEUS and H1-- see next two slides Model choices : Form of parametrization at Q 2 0, value of Q 2 0,, flavour structure of sea, cuts applied, heavy flavour scheme Recap of the method Parametrize parton distribution functions PDFs at Q 2 0 Gev 2 Evolve in Q 2 using NLO DGLAP (QCDNUM 16.12). Data cuts are applied to avoid regions where NLO DGLAP may not be applicable Convolute PDFs with coefficient functions to give structure functions and hence cross-sections Coefficient functions can incorporate treatment of massive heavy quarks: for ZEUS-JETS fit this is done using Thorne-Roberts Variable Flavour Number Scheme, for H1 a massless scheme is used

xuv(x) = Au x av (1-x) bu (1 + c u x) xdv(x) = Ad x av (1-x) bd (1 + c d x) xS(x) = As x as (1-x) bs (1 + c s x) xg(x) = Ag x ag (1-x) bg (1 + c g x) xΔ(x) = x(d-u) = A Δ x av (1-x) bs+2 Consider the form of the parametrization at Q 2 0 No χ2 advantage in more terms in the polynomial No sensitivity to shape of Δ= d – u A Δ fixed consistent with Gottfried sum- rule - shape from E866 Assume s = (d+u)/4 consistent with ν dimuon data Au, Ad, Ag are fixed by the number and momentum sum-rules au=ad=av for low-x valence since there is little information to distinguish → 12 parameters for the PDF fit Now consider the high-x Sea and gluon High-x sea is constrained by simplifying form of parametrization - c s =0 → 11 param High-x gluon is constrained by adding ZEUS JET data ZEUS PDF 2005 Analysis Called the ZEUS-JETS fit Eur.Phys.J.C42(2005) 1 A total of 577 data points from 112pb -1 of HERA-I data on NC/CC cross-sections 2.7 < Q 2 < GeV 2, < x < 0.65 χ 2 /data-points470/577

This looks like 19 parameters BUT A U =A U, b U =b U, A D =A D, b D =b D → 15 so that U and U (and D and D) are equal as x → 0 →strong constraint on shape of low-x valence, where there’s little data and b U =b D → 14, since there’s no information on the difference of U and D Then the valence number sum rules and the momentum sum rule determine A g, A U, A D → 11 Finally A U =A D (1-f s )/(1-f c ) → 10 parameters constrains the amount of U and D in the sea, fs=0.33, fc=0.15 H PDF analysis Called H1 PDF 2000 Eur.Phys.J C30 (2003) 1 Consider the form of the parametrization at Q 2 0 No χ2 advantage in more terms in the polynomial χ 2 /data-points540/621 A total of 621 data points from HERA-I data on NC/CC cross-sections 3.5 < Q 2 < GeV 2, < x < 0.65

Experimental systematic errors are correlated between data points, so the correct form of the χ2 is χ 2 = Σ i Σ j [ F i QCD (p) – F i MEAS ] V ij - 1 [ F j QCD (p) – F j MEAS ] V ij = δ ij (б i STAT ) 2 + Σ λ Δ iλ SYS Δ jλ SYS Where Δ iλ SYS is the correlated error on point i due to systematic error source λ It can be established that this is equivalent to χ 2 = Σ i [ F i QCD (p) – Σ λ s λ Δ iλ SYS – F i MEAS ] 2 + Σ s λ 2 ( s i STAT ) 2 Where s λ are systematic uncertainty fit parameters of zero mean and unit variance This form modifies the fit prediction by each source of systematic uncertainty Uncertainty estimation in PDF fitting……

How ZEUS uses this: OFFSET method 1.Perform fit without correlated errors (s λ = 0) for central fit 2.Shift measurement to upper limit of one of its systematic uncertainties (s λ = +1) 3.Redo fit, record differences of parameters from those of step 1 4.Go back to 2, shift measurement to lower limit (s λ = -1) 5.Go back to 2, repeat 2-4 for next source of systematic uncertainty 6.Add all deviations from central fit in quadrature (positive and negative deviations added in quadrature separately) 7.This method does not assume that correlated systematic uncertainties are Gaussian distributed

How H1 uses this: HESSIAN method Allow s λ parameters to vary for the central fit 1.If we believe the theory why not let it calibrate the detector(s)? Effectively the theoretical prediction is not fitted to the central values of published experimental data, but allows these data points to move collectively according to their correlated systematic uncertainties 2.The fit determines the optimal settings for correlated systematic shifts s λ such that the most consistent fit to all data sets is obtained. In a global fit the systematic uncertainties of one experiment would correlate to those of another through the fit 3.We must be very confident of the theory to trust it for calibration– but more significantly we must be very confident of the model choices we made in setting boundary conditions to the theory - increased model dependence. 4.CTEQ use this method but then raise the χ2 tolerance to Δχ2=100 to account for inconsistencies between data sets and model uncertainties. H1 use it on their own data only with Δχ2=1

Comparison off Hessian and Offset methods for ZEUS-JETS FIT The Hessian method does give a smaller estimated of the PDF errors if you stick to Δχ2=1 However it gives larger model errors, because each change of model assumption can give a different set of systematic uncertainty parameters, sλ, and thus a different estimate of the shifted positions of the data points. For the gluon and sea distributions the Hessian method gives a much narrower error band. Equivalent to raising the Δχ2 in the Offset method to 50.

Compare in terms of U = u + c =u v + u sea + c, D = d + s (+b) = d v + d sea +s (+b) and the corresponding Ubar Dbar distributions Model uncertainty is also included in the comparison Model uncertainties are large compared to the HESSIAN exp. uncertainties of H1, and small compared to the OFFSET exp. uncertainties of ZEUS. Comparison including model uncertainties gives a similar size of total uncertainty ZEUS/H1 published fits comparison

ZEUS-JETS PDFs compatible with the previous ZEUS-S global fit and with MRST and CTEQ PDFs Size of uncertainties is comparable for low-x sea and gluon, where information is dominated by HERA data, somewhat poorer for high-x valence.. But see 2007 update (later)

Inclusion of Jet cross sections in PDF fits High-E T jet production in the Breit Frame: LO contributions: - boson-gluon fusion: - QCD-Compton: ÞBGF is directly sensitive to gluon density in the proton, both processes are sensitive to α s pioneering paper H1 Eur.Phys.J.C19(2001)289 made a simultaneous fit to the gluon PDF and α s (M Z ), ZEUS-JETS fit takes this further..

Computation of NLO jet cross sections extremely CPU intensive (~  (10) hours ) => original programs cannot be used directly in the fit… …so we used these programs to compute α s - and PDF-independent LO/NLO weights, σ, obtained by integrating the partonic cross sections over the 3(2)-dimensional bins of the (ξ,μ R,μ F ) space. The NLO cross sections were then obtained by folding these weights with the PDFs and α s according to The method This procedure reproduces the “exact” NLO predictions to better than 0.5% ~

The data used: Inclusive Jet Cross Sections in e + p NC DIS Phase space: Q 2 > 125 GeV 2 E B T,jet > 8 GeV and -2 < η B jet < 1.8 Jets identified with the k T cluster algorithm in the Breit frame Small Experimental uncertainties: → jet energy scale (~1% for E T,jet >10 GeV) => ± 5% on the cross sections Small theoretical uncertainties: - higher order terms ± 5% - Hadronic corrections (C had <10 % and ΔC had ~ 1%) ZEUS coll., PL B (2002) HERA-I data from 96/97 The calorimeter energy scale is treated as a correlated systematic uncertainty The factorization scale, μ F = Q, renormalization scale μ R =Q, (ET as a cross-check)

The data used: Dijet photoproduction Direct processResolved process Measure dijet production in γ p collisions via ep scattering for Q 2 ~0 At LO two processes contribute => Direct sensitivity to α s and proton gluon PDFs But for the resolved process there will be some sensitivity to the photon PDFs. So the PDF fit analysis was restricted to the direct-process-enriched region, x γ obs > 0.75, where is the fraction of the photon’s momentum taking part in the hard process. X γ obs = Σ i E T jet i exp(-η jet i ) / (2yE e ) At NLO one cannot make this distinctions precisely, there will be some sensitivity to photon PDFs even in the direct enriched sample- The AFG photon PDF is used, and the CJK and GRV photon PDFs are used as checks

Dijet γ p cross sections for x γ obs > 0.75 Phase space: E T jet1,(2), > 14 (11) GeV and and Q 2 <1 GeV 2 and 134 <W γp 2 < 277 GeV 2 Jets identified with the k T cluster algorithm in the Lab frame Small Experimental uncertainties: → jet energy scale (~1% for E T,jet >10 GeV) => ± 5% on the cross sections Small theoretical uncertainties: - higher order terms ± 10% - Hadronic corrections (C had <10 % and ΔC had ~ 2-3%) ZEUS Coll., EPJ C (2002) HERA-I data from 96/97 The calorimeter energy scale is treated as a correlated systematic uncertainty The factorization and renormalization scales, μ F = μ R =ET/2 (summed ET of final state particles)

The results: Jet data & gluons Comparing the gluon distribution obtained from fits with and without jet data: - no significant change of shape: no tension between incl. and jet data - jet cross sections help in constraining the gluon density in the region: 0.01 < x < Sizeable reduction of the gluon unc: e.g. from 17% to 10% at x=0.06 and Q 2 =7 GeV 2 →similar reduction by a factor two in the mid-x region over the full Q 2 region

The sea distribution rises at low-x for all Q 2 The gluon density becomes valence-like at low Q 2 is this credible? We only measure F 2 ~ xq dF 2 /dlnQ 2 ~ Pqg xg We assume Pqg is known to get xg but unusual behaviour of dF 2 /dlnQ 2 may come from unusual gluon or from unusual Pqg Is there a need for alternative evolution? BFKL, CCFM or even Non-linear effects? We need other gluon sensitive measurements at low x- like FL. We await the analysis of the low energy HERA-II running for a fully model independent measurement. Gluon and sea

Jet data also allow determination of α s (M Z ) -In the DGLAP equations the gluon density and the value of α s are correlated -A simultaneous determination of PDFs and α s from inclusive cross-section data alone suffers from this correlation - Inclusion of jet data greatly improves the determination of α s and reduces this correlation - Extracted value: α s (M Z ) = ± (uncor.) ± (corr.) ± (model) The theoretical uncertainty due to terms beyond NLO is : Δα s (th)= ± (limited by theory => need NNLO jet calculations, NNLO is ready for the rest of the fit)

PDFs with α s free The extracted α s (M Z ) value is very close to the fixed value, 0.118, used in the ZEUS-JETS fit => there are no significant changes in the central values of the PDFs parameters Uncertainties: - The valence and sea uncertainty are unaffected - The gluon uncertainty increases somewhat in the low-Q 2 region Before jets ZEUS-S-α s global fit to inclusive data alone After jets ZEUS-JETS-α s fit Since the correlation between gluon PDF and α s is reduced the contribution of the uncertainty on α s to the uncertainty on the gluon PDF is much reduced

HERA Jet data have also been used independently from PDF fits to determine alphas: HERA 2007 combined result (C. Glasman EPS 2007) makes a simultaneous fit to H1 normalised inclusive jet cross-sections (150 < Q 2 < GeV 2 ) and ZEUS inclusive jet cross-sections (125 < Q 2 < 105 GeV 2 ) from ~ 150 pb-1 HERA-I data α s (M Z ) = ± (exp.) ± (th.)

HERA jet data also provide a beautiful demonstration of the running of alphas from a determination with a consistent approach to all the systematic errors of the input experiments ZEUS and H1

Valence distributions from the ZEUS-JETS fit At high-x HERA only PDFs are not as well constrained as global fits including fixed-target data - but they are becoming competitive and they are free from heavy-target corrections and isospin-symmetry assumptions To further improve here we need precision high-Q2 e ± p CC/NC data from HERA II…see next slide

New NC e- data with –ve polarisation P= Lumi=105 pb -1 ± 3.5% New NC e- data with +ve polarisation P= Lumi=71.8 pb -1 ± 3.5% ZEUS-pol 2007 updated fit: Including HERA-II data: NC (2004/06) and CC (2004/05) e- cross sections

PDFs from the new ZEUS-pol 2007 fit compared to published ZEUS-JETS 2005 fit – central values of the PDFs hardly change at all….. ZEUS-pol 2007 PDFs

ZEUS-pol 2007 updated Fit: Fractional uncertainties PDF uncertainties are reduced at high-x, particularly for xu v …..as expected since NC and CC e- cross-sections are both u dominated Uncertainties on u- valence now comparable to those of global fits

Combining the data sets could bring real advantages in decreasing the systematic errors as well as the statistical errors. A PDF fit to the combined data set would then be a HERA legacy To make this combination we make a fit with the only theoretical input being that each experiment is measuring the same ‘truth’ at the same x, Q 2 the theoretical parameters are the true values of the cross-sections at each x,Q 2 and they are fitted to the H1 and ZEUS measurements The combination is a Hessian fit which floats the systematic uncertainty parameters of each data set to obtain the best fit to this assumption Once the fit is done the systematic uncertainties of the combined data points are considerably smaller than those of each experiment separately- each experiment calibrates the other. Cross Calibration → Reduction of syst. unc. as a result of averaging Cross Check → also as a result of the studies in this WG, the H1 low-Q2 data had to be scaled up by 3.4% (official) The future: Combining ZEUS and H1 HERA-I inclusive cross- section data

Data sets and treatment - All HERA I cross sections: NC and CC e ± p < Q 2 <30000 GeV 2 → ~230 pb -1 - average cross sections determined in a simultaneous fit of these data. - prior to combination the H1 and ZEUS measurements are transformed to a common grid of x-Q 2 points - treatment of the 820 GeV and 920 GeV data sets: in this analysis all data points are moved to 920 GeV In the future will not correct points at high-y (y>0.35) in order to reduce model dependence (FL):

CC e - p CC e + p Results

NC e+p

The future: Including heavy quark structure functions Charm and beauty are generated by boson-gluon fusion Thus measurements could give information on the gluon PDF There are a lot of new measurements: ZEUS HERA-I data DESY from 82pb -1 of 1998/2000 running. Analysis of D 0,D +, D + s and D + * ZEUS HERA-II data 2003/5 running EPS07 abstract106 from 162pb -1 analysis of D* AND EPS07 abstract107 from 135pb - 1 analysis of D using MVD H1 HERA-II data 2006 running H1-prelim from 54pb -1 analysis of c and b using VD impact parameter. HERA-II data are shown averaged together with HERA-I VD data

ZEUS beauty data from 39pb -1 HERA-II 2003/4 running EPS07 abstract108 H1 HERA I+II beauty data also from VD analysis H1-prelim In practice NLO calculations are done in differing heavy quark schemes Fixed Flavour Number : HQVDIS, MRST2004FF3, CTEQ5F4 General-Mass Variable Flavour Number: MRST04, MRST NNLO, CTEQ6.5, ZEUS- JETS, ZEUS-S Zero Mass Variable Flavour Number: CTEQ6.1, H1 PDF 2000 Measurements may tell us more about the applicability of schemes than about gluon PDF

H normalised inclusive jet cross-sections DESY And add new HERA-II 320pb -1 preliminary H1 prelim The future: Including more jet data

ZEUS Photoproduction optimised dijet cross-sections from HERA-I ZEUS Inclusive jet cross sections from 82pb -1 HERA-I Nucl Phys B765 (2007)1 And HERA-II data have been added to dijet data Data from and make 209pb -1 EPS07 abstract 75

High-y data from 30 pb -1 running 2006 EPS07 abstract-78 The future: high-y data and preparing for FL High-y and high-Q 2 from HERA-I+II complete data set H1 prelim High-y and low Q 2 from HERA-I+II H1 prelim (all HERA-II) and HERA-I prelim low Q2 data The structure function FL is only significant at high-y. Determining it by using data from different beam energies (different y values for the same x, Q 2 ) requires measurements at high-y

Compared H1 and ZEUS published PDF fits on HERA-I data Discussed including jet production data in fits to improve gluon PDF determination and to determine α s (M Z ) Presented H1 and ZEUS combined α s (M Z ) Presented preliminary ZEUS-pol PDF fit to HERA-II polarized data - improved u-valence PDF determination Looking forward to using more accurate data and more types of data combination of H1 and ZEUS inclusive cross-sections F2c and F2b data more jet data high-y and FL data Summary

Extras

ZEUS-JETS QCD fit results: Inclusive NC Very good description of the low- medium-Q 2 e + p NC reduced cross sections

ZEUS-JETS QCD fit results: high-Q 2 NC and CC NC: CC: Good description - still limited by statistics => HERAII

Compare the uncertainties for uv, dv, Sea and glue in a global fit to DIS data High-x Sea and Gluon are considerably less well determined than high-x valence (note log scales) even in a global fit - this gets worse when fitting HERA data alone uvdvSeaGluon uv and dv are now determined by the HERA highQ2 data not by fixed target data and precision is comparable- particularly for dv Sea and gluon at low-x are determined by HERA data with comparable precision for both fits – but at mid/high-x precision is much worse Compare the uncertainties for uv, dv, Sea and glue in a fit to ZEUS data alone

Or in more familiar format Both collaborations include model errors – These are large compared to the HESSIAN exp. errors of H1, and small compared to the OFFSET exp. errors of ZEUS. Comparison with model errors included gives similar size of errors – but some difference in central values ZEUS/H1 published fits comparison

ZEUS analysis/ZEUS data ZEUS analysis/H1 data ZEUS analysis/H1 data compared to H1 analysis/H1 data Here we see the effect of differences in the data, recall that the gluon is not directly measured (no jets) The data differences are most notable in the large 96/97 NC samples at low-Q2 The data are NOT incompatible, but seem to ‘pull against each other’ IF a fit is done to ZEUS and H1 together the χ2 for both these data sets rise compared to when they are fitted separately……….. Here we see the effect of differences of analysis choice - form of parametrization at Q2_0 etc

CC e- data with –ve polarisation P= Lumi= 78.8 pb -1 ± 3.5% CC e- data with +ve polarisation P= 0.33 Lumi=42.7pb -1 ± 3.5% CC vs Updated ZEUS-Pol Fit

H1 prelim-0-171

More H1 data from HERA-I in the low Q2 transition region