Structure function measurements and what they tell us

Structure function measurements and what they tell us about PDFs and the strong coupling constant Tomáš Laštovička (H 1 collaboration) DESY Zeuthen, Charles University Prague at LLWI 2003, Lake Louise, Canada H 1 and ZEUS Structure functions at HERA αs and PDFs Summary/Outlook Tomas Lastovicka, LLWI 2003

H 1 and ZEUS at HERA at DESY, Hamburg ep accelerator ring, 27. 5 x 920 Ge. V circumference: 6. 3 km ZEUS 4 experiment halls H 1 Tomas Lastovicka, LLWI 2003 2

H 1 and ZEUS experiments nearly aparatus delivering data since early 90 ies 2 recently both experiments upgraded Tomas Lastovicka, LLWI 2003 3

Deep Inelastic Scattering Four-momentum transfer squared: Bjorken scaling variable: Inelasticity scaling variable: Centre of mass energy squared: Tomas Lastovicka, LLWI 2003 4

Cross-sections and Structure Functions NC Cross Section: NC Reduced cross section: Dominant contribution Sizeable only at high y (y>~0. 6) CC Cross Section: Contribution only important at high Q 2 CC Reduced cross section: Tomas Lastovicka, LLWI 2003 5

DIS slang reminder low Q 2 - transition domain from non-perturbative domain to deep inelastic domain strong coupling is large, limits of p. QCD high Q 2 - strong coupling is relatively small p. QCD calculations reliable x. F 3 and CC enter the game at large Q 2 low x (high y) - driven by gluons sea (confinement) region longitudinal str. function FL unique acceptance by H 1 high x (low y) - driven by quarks valence quark region fixed target experiments Tomas Lastovicka, LLWI 2003 6

Kinematic plane coverage § covered almost to the limits of phase space § compared to fixed target experiments, measurements extend to high Q 2 and high y by more than 2 orders of magnitude Tomas Lastovicka, LLWI 2003 7

The Structure Function F 2 § F 2 is not calculable from the first principles § Various theoretical predictions a decade ago § during its running HERA made an impressive progress - directly related to quark densities § Tomas Lastovicka, LLWI 2003 1993 2000 8

The Structure Function F 2 Tomas Lastovicka, LLWI 2003 9

Scaling violations of F 2 at low x driven by gluons described by QCD: DGLAP evolution equations § many open questions: § does F 2 saturate? when gluon density is large -> gluon fusion § low Q 2 region § § § QCD analysis digests quarks and gluon densities from fits to F 2 (parametrised at an initial scale, then DGLAP evolution takes over) e. g. Tomas Lastovicka, LLWI 2003 10

CC and NC measurements Tomas Lastovicka, LLWI 2003 § Standard model describes both NC and CC very well over a large range of Q 2 § Electroweak unification at about MZ 2 scale § e+ and e- cross sections different due to different quark contribution and helicity structure of EW interactions 11

x. F 3 and FL measurements x. F 3 errors dominated by stat. errors, higher luminosity needed FL not measured directly, runs at different beam energies needed Tomas Lastovicka, LLWI 2003 12

PDF fits and the strong coupling QCD analyses require many choices to be made Should be reflected in PDF uncertainty: § § § § § Choice of data sets used Treatment of experimental systematic uncertainties Q 02 starting scale Q 2 min of data included in fit Renormalisation / factorisation scales Choice of densities to parameterise Allowed functional form of PDF parameterisation Cuts to limit analysis to perturbative phase space Treatment of heavy quarks etc. . . Tomas Lastovicka, LLWI 2003 13

Results on the strong coupling constant • H 1 • ZEUS 0. 1150 +-0. 0017(exp) +0. 0009 -0. 0007(model) H 1 + BCDMS precise data if: systematíc errors are not fitted: +0. 0005 NMC replaces BCDMS 0. 116+-0. 003 (exp) 4 light flavours: +0. 0003 BCDMS deuteron data added: 0. 1158 +- 0. 0016 (exp) EPJ C 21(01)33 0. 1166 +-0. 0008(unc) +-0. 0032(corr) +-0. 0036(norm) +-0. 0018(model) p: BCDMS, NMC, E 665 d: NMC, E 665 d/p: NMC x. F 3: CCFR systematíc errors are not allowed to vary in chi 2 minimisation Q 2>2. 5 Ge. V 2, W 2>20 Ge. V 2, RT-VFNS, b(uv)=1/2, b(dv)=1/2 fit alphas, xg, uv, dv, sea, dbar-ubar (MRST) Phys. Rev. D 67(03) if fixed flavour scheme is used: +0. 0010 large chi 2 variations if Q 2 (¼. . 4) Q 2 renormalisation scale: +-0. 005 (H 1) (½. . 2) : +- 0. 004 (ZEUS) not included in error Tomas Lastovicka, LLWI 2003 14

Parton distribution functions from NLO QCD fits (ZEUS) dv uv Sea, g § xg and Sea distributions determined by low x / Q 2 HERA F 2 data § xuv determined from high x NC data § xdv determined from high x CC e+ data Tomas Lastovicka, LLWI 2003 15

Parton distribution functions from NLO QCD fits (H 1) CC and NC cross sections are sensitive only to U, anti. U, D, anti. D (F 2 N has c-s admixture) H 1+BCDMS H 1 only uv, dv, sea are replaced by the observables ! possible to determine PDFs with H 1 data alone (with assumption on sea symmetry) Tomas Lastovicka, LLWI 2003 H 1 ICHEP 02 16

Parton distribution functions from NLO QCD fits H 1 vs ZEUS ~3% comparison of PDFs independent fits, different approaches ~10% Tomas Lastovicka, LLWI 2003 only experimental errors! (matter of choice) 17

NLO gluon momentum density fixed flavour number scheme Laenen, Riemersma, Smith, van. Neerven needs precision data at low Q 2, all x! needs precision FL measurement! H 1 EPJ C 21(01)33 Tomas Lastovicka, LLWI 2003 18

New low Q 2 measurements low Q 2 1999 dedicated run low Q 2 x-section and F 2 determination at low x shifted vertex 2000 run Transition region between perturbative and non-perturbative kinematic range Tomas Lastovicka, LLWI 2003 19

New measurements at low Q 2, small x Extended phase space: Data fill the gap in precision measurements around Q 2~1 Ge. V 2 and extend phase space to higher y at all Q 2 (till 12 Ge. V 2) sr changes behavior at high y (small x) g FL signature (even at very low Q 2) Data with Q 2 g 0: Valuable for studying underlying dynamics of DIS → γp Tomas Lastovicka, LLWI 2003 20

Rise of F 2 towards low x § H 1 / ZEUS / NMC data used to fit Q 2 dependencies for x<0. 01 : § Behaviour is changing at around 1 Ge. V 2 § Theory expects λ to reach value of ~0. 08 for Q 2 → 0 § No sign of saturation at small x observed (yet) Tomas Lastovicka, LLWI 2003 21

Summary (concluding remarks) First phase of HERA running delivered many interesting results Precision of ~2− 3 % achieved for F 2 The inclusive DIS data at HERA are confronted with NLO QCD analyses QCD (the DGLAP equations) is able to describe all the cross section data: e+p, e-p, NC, CC in a wide kinematical range: both Q 2 & x covering 5 orders of magnitude extracted from DIS data is competetive with the world average Fits allow HERA data to constrain PDFs HERA 2 (after luminosity upgrade): high precision x. F 3 direct measurement of FL The next important step: e-d runs (dv/uv at high x), HERA 3 Tomas Lastovicka, LLWI 2003 ? ! 22