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Stefan Schlenstedt DESY Zeuthen

Structure Functions at HERA. Stefan Schlenstedt DESY Zeuthen. Introduction The “transition region” of low Q 2 and x F 2 at medium Q 2 : F 2 slopes, QCD fits F L F 2 charm Large Q 2 NC/CC cross sections Summary and perspectives. Workshop on

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Stefan Schlenstedt DESY Zeuthen

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  1. Structure Functions at HERA Stefan Schlenstedt DESY Zeuthen • Introduction • The “transition region” of low Q2 and x • F2 at medium Q2: F2 slopes, QCD fits • FL • F2charm • Large Q2 NC/CC cross sections • Summary and perspectives Workshop on Exclusive and Semiexclusive Processes, JLab, 20/5/99

  2. 1994-97 e+ (27.5 GeV) p (820 GeV) e- (27.5 GeV) p (920 GeV) 1998-99 e(k) e'(k') 2 Q g *(q) 2 W xP p(P) Introduction (equivalent to 47-50 TeV fixed target energy) S = (k+P)2, = energy in the ep c.m.s. Q2 = -(k-k')2 = -q2 =virtuality of the exchanged  X = Q2/(2P•Q)=fraction of proton momentum carried by the struck quark y = (P•q)/(P•k) =fraction of beam lepton energy transferred to the photon W2 = ys = energy in the *p c.m.s. Q2 = xys SemiExclusive Workshop

  3. HERA Kinematic Range • HERA has unique “depth of field” on the proton structure: • Q2 from ~ 0.04 GeV2 to ~ 105 GeV2 • x down to 10-6 • extension by two orders of magnitude both in x and Q2 SemiExclusive Workshop

  4. F2 Measurement at HERA Explore new kinematic regions: where does the Standard Model break down? High Q2 F2: Higher and higher precision measurement over a wide kinematic range Low Q2 Study the transition from Photoproduction (Q2 0) to DIS (Q2 > few GeV2): where does pQCD begin to dominate? • We have to precisely measure F2 to • get handle on QCD evolution and • constrain PDF’s SemiExclusive Workshop

  5. Lumi good for physics 1994-99 HERA Luminosity Luminosity available for physics (ZEUS): 1994-97  48 pb-1 e+p s = 300 GeV 1998-99  16 pb-1 e–p s = 320 GeV + running July 99-April 00 EW physics at HERA just starting... SemiExclusive Workshop

  6. for not too large y The ep Neutral Current Cross Section (QED radiative corrections have been neglected) where: quark densities relevant for Q2  MZ02 At low Q2, Ai are the quark electric charges SemiExclusive Workshop

  7. High precision p structure at low x-Q2 • In 1997 ZEUS installed a silicon tracker (BPT) • in front of a calorimeter (BPC) to improve the • detection of positrons at small scattered angles • The BPC/T allows F2 (or ) to be measured • with high precision in the range: • 0.045 < Q2 < 0.65 GeV2 • 6 ·10-7 < x < 1·10-3 • 3.9 pb-1 collected in 6 weeks during 1997 • geometrical acceptance 4-14% depending on the (x,Q2) bin • Typical error: 2.6% (stat) 3.3% (syst) SemiExclusive Workshop

  8. High precision p structure at low x-Q2 F2 values at lowest ever x-Q2: w.r.t. previous measurements: - extension of kinematic range - higher precision SemiExclusive Workshop

  9. High precision p structure at low x-Q2  Regge models provide a good description of the transition region SemiExclusive Workshop

  10. 2 m g g s = s * p 2 2 p 2 0 ( W , Q ) ( W ) tot tot + 2 2 m Q 0 Extrapolation to Photoproduction stotg*p = 42a/Q2  F2 By assuming Q2 dependence of of GVDM: can extrapolate data to compare with real photoproduction cross-section stotgp (Q2 = 0): SemiExclusive Workshop

  11. Extrapolation to Photoproduction • W2 dependence of stotgp à la Regge: • stotgp(W2) = ARW 2(aR-1) + APW 2(aP-1) • Results (aR = 0.5, free parameters: AR, AP, aP ) • Fit 1: aP = 1.087  0.004(stat)  0.008(syst) • Fit 2: aP = 1.105  0.001(stat)  0.007(syst) SemiExclusive Workshop

  12. F2 at Medium Q2: Precision Data • Recent data made measurement of F2 possible with • improved precision due to higher event statistics and • the new backward silicon tracker in H1: • typical errors  1% (stat) and  3-4% (syst) •  approaching fixed target experiments! • Syst. error dominant up to Q2 1000 GeV2 Q2 = 15 GeV2 • Strong rise of F2 at HERA regime • (q(x)  F2/x  quark density is zooming up) • Good agreement between H1 and ZEUS SemiExclusive Workshop

  13. Overview of F2 Measurements Scaling violation by gluons Bjorken scaling • NLO DGLAP gives good description of the • HERA, NMC and BCDMS data • Scaling violations well interpreted by QCD SemiExclusive Workshop

  14. Slopes of F2 x-slope small at small Q2, then increases Fit F2= const · x-leff at small x SemiExclusive Workshop

  15. Fit to F2 x-leff vs. Q2 at small x This is in relation with the W2e dependence of cross sections, since 1/x ~ W2 at small x, leff e = apom(0) - 1 Soft pomeron: leff 0.08 LO BKFL: leff 0.5 NLO BFKL: leff ??? • Smooth rise of the slope parameter leff - • larger than Regge models even at low Q2 • F2 is rising  sea is rising. • What about gluons? SemiExclusive Workshop

  16. dF2(x,Q2)/dlnQ2 At small x, quark pair creation from gluons dominates scaling violations  dF2(x,Q2)/dlnQ2 const · xg(x,Q2) Logarithmic slope dF2/dlnQ2 derived from data fitting: F2 = a + b ·ln Q2 in bins of fixed x Different behaviour at similar Q2 but smaller x - turning over of gluon distribution at small x? SemiExclusive Workshop

  17. ZEUS 1995 QCD Fit to F2 • ZEUS DGLAP NLO fit: • Gluon (xg), Sea quark (xS) and u - d difference (xDud) • parameterised as: A·xd ·(1-x)h · polynomial in x • Input u,d valence distributions from MRS(R2) • Apply momentum sum rule • Inner error bands: • exp. Errors on as, mc and • strange quark content DKs • Outer error bands: • variation of Q02 and • xg(x) parameterised with • Chebycheff polinomials. Strong rise of gluon density at large Q2 but consistent with zero at Q2 = 1 GeV2 SemiExclusive Workshop

  18. ZEUS 1995 QCD Fit to F2 : Gluon and Singlet • At Q2 = 1 GeV2, Sea is still rising but Gluon at • small x is compatible with zero • Uncertainty for gluon at lowest x,Q2 is large • Although error band goes negative (possible in NLO backward evolution): • FL and F2charm stay positive • the fit can be extended down to Q2 = 0.4 GeV2 without deteriorating its quality •  NLO DGLAP does not break down before the formalism becomes suspect SemiExclusive Workshop

  19. ZEUS bpt (red square) F2(x,Q2) vs.  = log(x0/x)·log(1+Q2/Q02) Phenomenological investigation by D. Haidt: in the HERA domain with x < 0.001 (Sea region) F2 has a simple form in the empirical variable  = log(x0/x) ·log(1+Q2/Q02) where x0 = 0.04 and Q02 = 0.5 GeV2 • F2(x,Q2)  F2() • Linearity: F2() = const · • Representation valid in perturbative and • non-perturbative regions of Q2 • consistent with MRST for Q2 > 1.25 GeV2 SemiExclusive Workshop

  20. Extraction of FL DIS cross section: (for Q2 << MZ2 and neglecting radiative corrections) Reduced cross section: H1 uses the “Subtraction method”: access to FL from high y cross sections using assumption on F2 by extrapolation of DGLAP fit from low y SemiExclusive Workshop

  21. Extraction of FL • F2QCD is the H1 QCD NLO preliminary fit for y < 0.35 • extrapolate the fit results to high y • FL =[1+(1-y)2]/y2 ·(F2QCD - sr) SemiExclusive Workshop

  22. Extraction of FL FL = FLQCD Extracted FL consistent with pQCD (yellow band) - at highest y systematically higher Cross check and extension towards low Q2 done by another method (indicated by star in the figure). SemiExclusive Workshop

  23. F2charm from D*, D0 in DIS Charm cross section in DIS is expected to be dominated by Boson-Gluon-Fusion • Measurement of visible D*, D0 cross section, • extrapolation outside kinematic region in pT, h • extract F2charm: Very effective test of QCD: F2charm calculable from pQCD knowing xg(x) Direct measurement of F2charm SemiExclusive Workshop

  24. pQCD DGLAP fit F2charm from D*, D0 in DIS • Steep rise of F2charm as we go to lower x • Indication that BGF is the dominant • mechanism for charm production at HERA SemiExclusive Workshop

  25. F2charm/F2 vs. x in Q2 bins • F2charm rises more rapidly than F2 •  dominated by gluon contribution, • while F2 has also quarks • F2charm is 25% of F2 at low x and high Q2 SemiExclusive Workshop

  26. e e' g*,Z0 q p p remnant High Q2 Neutral Currents Handle on xF3 is given by the  sign due to the different charge of the lepton beam. Need luminosity with e– beams to access xF3 SemiExclusive Workshop

  27. High Q2 Neutral Currents : dse+p/dQ2 • dse+p/dQ2 falls over 7 orders of magnitude • NLO QCD fit to low Q2 data (Q2 < 120 GeV2) • works well for high Q2 triumph of QCD! • Larger luminosity needed to constrain PDFs • Slight excess at Q2 > 15000 GeV2 remains SemiExclusive Workshop

  28. ( 5pb-1 taken in 98/99) High Q2 Neutral Currents: e+ vs. e- For Q2 > 3000 GeV2 all e–p measurements are above e+p, in agreement with SM gZ interference SemiExclusive Workshop

  29. e n W q’ q p p remnant High Q2 Charged Currents • probe valence u,d quarks at large x and Q2 • dsCC/dQ2 shape is sensitive to propagator mass SemiExclusive Workshop

  30. High Q2 Charged Currents: dse+p/dx • Reasonable agreement between SM and data • At high x data systematically above SM (CTEQ4) • Need for Bodek & Yang like treatment of d/u ratio • (d/u = 0.2 for x  1) SemiExclusive Workshop

  31. MW from dsCC/dQ2 • Unconstrained fitto dCC/dQ2: • measurement of the mass of spacelike W •  complementary to e+e- and pp timelike measurements. • Preliminary results: •  no evidence for anomalous space-like EW sector. • Use Standard Model relation: Exploiting correlation between shape and normalization in a model dependent fit. • A sensitive electroweak consistency check! • (PDG: MW = 80.41 ± 0.10 GeV) ZEUS H1 Extract MWat MH= 100 GeV, MT= 175 GeV: Preliminary Note: the above is not a measurement, but indicates the sensitivity of the CC cross section to MW assuming the Standard Model. SemiExclusive Workshop

  32. MW from dsCC/dQ2 GF[GeV-2] 1 s contour of 2 distrib. ZEUS model dependent fit MW[GeV] GF depends very strongly on MW  sensitivity to MW within the Standard Model SemiExclusive Workshop

  33. High Q2 Charged Currents: e+ vs. e- (1998-99 data) (1994-97 data) e-p data an order of magnitude above e+p, since se-p (u+c) while se+p (1-y)2 ·(d+s)  probing different quark flavours SemiExclusive Workshop

  34. NC and CC e–p Cross Sections 1998+99 data! Unification of charged and neutral currents! SemiExclusive Workshop

  35. Summary and Perspectives • Small Q2: • F2 data at lowest ever x-Q2 can be described • by Regge parameterisations • Medium Q2: • precision approaching fixed target data • NLO DGLAP pQCD fit ok down to Q2 1 GeV2 • F2 rise at small x,Q2 seems driven by Sea quarks • F2charm grows up to  25% of F2 • Large Q2: • NC - triumph of QCD: NLO fit extrapolation ok • - need more lumi to constrain PDFs • CC - need for Bodek &Yang d/u ratio for x  1 • - spacelike-W mass consistent with timelike • Unification of Neutral & Charged currents measured • Perspectives: • FL: direct measurement needs dedicated runs • xF3: needs more e- data • High Q2: HERA high luminosity programme: • deliver  1 fb-1 2001 2005 SemiExclusive Workshop

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