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A.Rostovtsev DIS Structure Functions at HERA Institute f. Theor. and Exp. Physics in Moscow, DESY at Hamburg May 2004 DIS kinematics Q 2 x 1 d 2 r 2 2 Y dxdQ2 Schematic view of the H1 detector Kinematic plane coverage Coverage 5 decades in x and Q2 Sensitivity to Z0 exchange FL Saturation Q2 s y 1 x0 QCD evolution – over the bulk of the data x F2 measurements Proton structure function data accurate to 2 to 3% over bulk of phase space Extraction of NLO PDFs Direct constraint on d at high x n CC e+ p W+ d Typical systematic errors are ~6% Direct constraint on u at high x ~ CC n CC ep W- u Both e-p and e+p are important x F2cc and F2 bb at high Q2 • Studies of beauty and charm production using H1 central silicon tracker (CST). • Flavour identification using distance of closest approach of track to vertex d. d1 B d2 B • Determine significance S = d/(d) for all CST tracks. • Use 2 tracks with largest significance, S1 and S2 • Example, S2 distribution: • Determine ratios f cc F2cc F2 and f bb F2bb F2 • fb ~ 2%, fc ~ 25% • Resulting F2cc (large acceptance, extrapolations small). • First F2 measurement, in good agreement with expectations from NLO calc. using H1 PDFs. bb New cross-section measurements • • Some regions of kinematic plane remain to be studied, particularly intermediate x at low Q2. Radiative events, effective reduction in Ee. coll. g e+ g q p • 2 Access larger x = Q ys for given Q2. Cross-section at low Q2 • Identify ISR events without tagging g via: E pz eh • 2E e 2E g Mean “Eeff” ~ 15 GeV, c.f. nominal value Ee = 27.6 GeV. • Use shifted vertex data (low Q2). • BST and SpaCal necessary for measurement of scattered electron and rejection of photoproduction background. • Cross-section from H1 ISR and QED Compton data (final results) in good agreement. • Measurements consistent with other data in regions of overlap. Behaviour of F2 at low x • Can parameterise structure function as F2 x, Q • • • • 2 c Q x 2 l Q2 . Extract l(Q2) by fitting F2 as function of x at constant Q2. Behaviour of l(Q2) in “transition region” (Q2 ~ 1 GeV2) intriguing. Probing limits of perturbative QCD. Further investigation not possible at HERA II because of acceptance limitations introduced by new focussing magnets. • Measurements of l(Q2): FL determination (H1) r F2 y 2 FL / Y Sensitivity to FL at high y (low x) Assumptions: F2 C x l FL const ..at small x Very good description r shape is defined by a kinematical factor y2/Y+ FL results The new ( ) data allow H1 to distinguish between various models Still need to improve accuracy of the data Possible future FL measurements at HERA Measure cross section at fixed x and Q2 varying y by changing Ep in a range from 400 GeV upwards. From 3 to 10 pb-1 is necessary at lower Ep Systematic errors included PDF extraction PDF analysis of the data coming from a single experiment reduces the uncertainty involved in the combination of correlated systematic errors from many different experiments with possible incompatibilities. The uncertainties from the Global (ZEUS + Fix target data) fit: This gets worse when using ZEUS data alone: …mid and high x gluons especially problematic “One experiment” PDF extraction is dominated by stat. errors. Include Jet measurements in PDF analysis T E Jet [GeV ] Jets in DIS (Breit frame) T EJet [GeV ] Di-jets in photoproduction (xg >0.75) Jets constrain medium x gluon distribution Improved precision on the gluon at higher x x Good agreement with the Global ZEUS fit Agreement with H1 PDFs except for a small difference in gluon shape MRST2001 underestimates gluon density at low x Fractal structure of the protons Scaling, self-similarity and power-law behavior are F2 properties, which also characterize fractal objects Serpinsky carpet z = 10 20 50 D = 1.5849 1 10 . x = . .. 100 1000 Proton: 2 scales 1/x , (Q 2o + Q2 )/Q2o Generalized expression for unintegrated structure function: Limited applicability of perturbative QCD ZEUS hep-ex/0208023 For x < 0.01 и 0.35 < Q < 120 GeV2 : c2 /ndf = 0.82 !!! With only 4 free parameters Summary HERA provides • rich inclusive data with a 5 decades coverage in x and Q2 with a precision reaching up to 2%. • PDFs can be extracted from the data collected by a single experiment • FL measurement made down to Q2 of 1 GeV2 • information about heavy quark content of DIS • much more which was not covered in this report