Inclusive Cross Sections at HERA and Determinations of F L

Transcription

1 Inclusive Cross Sections at HERA and Determinations of F L Vladimir Chekelian (MPI for Physics, Munich) on behalf of the H and ZEUS Collaborations HERA The World s Only ep Collider HERA / DIS / NC / CC Combination of H & ZEUS - HERA I - HERA I+II Longitudinal sf F L (x,q 2 ) Summary

2 HERA: 5 years of operation (992 27) low E p running Ep = 92 (82,575,46) GeV located at DESY, Hamburg peak luminosity 5 3 cm -2 sec - Q 2 max = 5 GeV 2 λ min ~ / r proton longitudinal e-beam polarisation HERA I ~2 pb- HERA II ~38 pb- H+ZEUS in total ~ fb - about equally shared between - experiments (H, ZEUS) - e + and e -, - positive and negative P e low proton energy running for F L 2

3 Deep Inelastic Scattering (DIS) Neutral Current (NC) : e ± p e ± X P H q k Charged Current (CC) : e ± p ν X k ZEUS Q 2 = -q 2 = -(k-k ) 2 virtuality of γ*, Z, W x = Q 2 /2(Pq) Bjorken x y = (Pq)/(Pk) inelasticity Q 2 = sxy s=(k+p) 2 Factorisation: ^ V. Chekelian, Incl. σ Cross Sections perturbative QCD cross section 3 HERA and Determinations pdf universal of FL parton distribution functions

4 Inclusive NC and CC at HERA HERA: span 6 orders of magnitude in x and Q 2 (QPM) Large number of individual data sets from H and ZEUS, covering different parts of the phase space, obtained in different periods, using different detector components, different beam energies, combine 4

5 Combination of H and ZEUS The goal is to have the unique HERA data set which includes expert knowledge in the treatment of the correlations between many individual data sets from H and ZEUS most precise, complete and easy in use Combine inclusive unpolarised NC & CC cross sections from H and ZEUS at HERA I (994-2) all HERA I analyses are completed and published. Exploit differences between H and ZEUS in detectors, methods and systematics to cross-calibrate and hence to reduce the systematic uncertainties. - for each channel move measured points to a common x-q 2 grid - correct E pbeam =82 GeV data to E pbeam =92 GeV - average H and ZEUS points at given x,q 2 at y <.35 - keep all data points at y >.35, modifying them to account for the determined shifts in the correlated systematic sources. The averaging exploits a concept of correlated syst. errors, assuming that systematic uncertainties are proportional to expected values and statistical uncertainties are defined by of expected number of events: 5

6 Combination of H and ZEUS data from HERA I 42 points are combined to 74 unique cross section measurements χ 2 /ndf = 636.5/656 the original H and ZEUS data are fully consistent JHEP(2)9 combined data set: corr. syst. sources from individual data sets 3 correlated errors from averaging procedure: - difference between multiplicative treatment of errors and additive - photoproduction background - hadronic energy scale more than just double statistics: significant reduction of systematics and little difference then how to treat corr. syst. sources in QCD fits - the simplest approach is to added them in quadrature to the uncorrelated errors 6

7 Combination of H and ZEUS data from HERA I 42 points are combined to 74 unique cross section measurements χ 2 /ndf = 636.5/656 the original H and ZEUS data are fully consistent JHEP(2)9 combined data set: corr. syst. sources from individual data sets 3 correlated errors from averaging procedure: - difference between multiplicative treatment of errors and additive - photoproduction background - hadronic energy scale more than just double statistics: significant reduction of systematics and little difference then how to treat corr. syst. sources in QCD fits - the simplest approach is to added them in quadrature to the uncorrelated errors 7

8 Combination of HERA I and HERA II The combination is extended to include unpolarised NC, CC high Q 2 data from HERA II : HERA I+II, e ± p NC, CC χ 2 /ndf = 967/32 for polarised effects in NC, CC and xf 3 see talks of S. Habib, T. Stewart for EW&QCD fit of polarised data see talk of E. Rizvi H and ZEUS H and ZEUS r,nc (x,q 2 ) x 2 i x =.5, i=2 x =.8, i=2 x =.3, i=9 x =.2, i=8 x =.32, i=7 x =.5, i=6 x =.8, i=5 x =.3, i=4 x =.2, i=3 x =.32, i=2 x =.5, i= x =.8, i= HERA I+II NC e + p (prel.) Fixed Target HERAPDF.5 x =.3, i=9 x =.2, i=8 x =.32, i=7 x =.5, i=6 e + p NC HERA I+II x =.8, i=5 x =.3, i=4 x =.8, i=3 x =.25, i=2 x =.4, i= x =.65, i= Q 2 / GeV 2 HERA Inclusive Working Group August 2 r,cc (x,q 2 ) Q 2 = 3 GeV 2 Q 2 = 2 GeV 2 Q 2 = 3 GeV 2 Q 2 = 5 GeV Q 2 = 5 GeV 2 Q 2 = GeV 2 Q 2 = 5 GeV 2 Q 2 = 3 GeV NLO QCD fits of the combined HERA data: HERA I HERA I+II x Q 2 = 5 GeV 2 e + p CC HERA I+II -2 - Q 2 = 8 GeV x HERA Inclusive Working Group August 2 HERA I+II CC e + p (prel.) HERAPDF.5 HERAPDF. HERAPDF.5 8

9 HERA I vs HERA I+II HERA I H vs. and HERAPDF. ZEUS HERA I+II H and vs. ZEUS HERAPDF.5 r,nc (x,q 2 )! HERA I NC e + p HERA I NC e - p x =.2 (x3.) x =.32 (x7.) HERAPDF. e + p HERAPDF. e - p x =.5 (x9.) x =.8 (x5.) x =.3 (x2.) x =.8 (x8.) x =.25 (x2.4) e - p e + p x =.4 (x.7) x =.65 r,nc (x,q 2 )! HERA I+II NC e + p (prel.) HERA I+II NC e - p (prel.) x =.2 (x3.) x =.32 (x7.) HERAPDF.5 e + p HERAPDF.5 e - p x =.5 (x9.) x =.8 (x5.) x =.3 (x2.) x =.8 (x8.) x =.25 (x2.4) e - p e + p x =.4 (x.7) x =.65 HERA Inclusive Working Group August Q 2 / GeV Q 2 / GeV 2 - inclusion of the HERA II high Q 2 data improves precision at high Q 2 and high x 9

10 HERAPDF: QCD Fits using HERA data only PDFs : xg, xuv, xdv, xs (xs=xubar+xdbar) at the scale Q 2 = GeV2 xf xs (!.5) xg (!.5) H and ZEUS HERAPDF. HERAPDF. exp. uncert. model uncert. parametrization uncert. 2 2 Q = GeV xu v xd v xf H and ZEUS HERA I+II Combined PDF Fit HERAPDF.5 xg (!.5) xs (!.5) HERAPDF.5 (prel.) exp. uncert. model uncert. parametrization uncert. 2 2 Q = GeV xu v xd v HERA Structure Functions Working Group July x x - inclusion of the HERA II high Q 2 data improves uncertainties of PDFs in the high x region especially visible for the valence quark distributions for HERAPDF NLO/NNLO inclusive, with jets, and with F 2 cc see talk of A. M. Cooper-Sarkar

11 The longitudinal structure function F L (x,q 2 ) - F L is a pure QCD effect which allows to make critical tests of the perturbative QCD framework used for pdf determinations - F L is directly sensitive to gluon density in QPM due to helicity and angular momentum conservation for spin ½ quarks F L = F 2-2xF = Callan-Gross relation in QCD:.8 F L and F 2 can be determined from linear fits at each x and Q 2 Q 2 =6.5 GeV 2 r x=.2 x=.4 x= x=.7 F 2 x=.2 H Collaboration Ep = GeV x=.26 E p =92 GeV E p =575 GeV E p =46 GeV Linear fit F L y 2 /(+(-y) 2 ) improved determination procedure takes into account correlation of systematic errors

12 Combination of the H and ZEUS F L data F L H and ZEUS HERA prelim. ZEUS H prelim. HERAPDF Q 2 / GeV 2 Good agreement between H and ZEUS The combined HERA F L is measured in the region 2.5 Q 2 8 GeV 2 HERA Inclusive Workging Group March 2 F L To obtain combined F L from H and ZEUS, the NC cross section data at different proton beam energies (E p = 46, 575, 92 GeV) were combined x HERA preliminary HERAPDF. H and ZEUS Q 2 / GeV HERA Inclusive Workging Group March 2 2

13 F L measurements at HERA and QCD predictions Using backward silicon tracker (BST) H extended F L measurements down to Q 2.5 GeV 2 F L.4 H Collaboration x EPJ C7(2) ZEUS HERAPDF. NLO CT NLO NNPDF2. NLO H MSTW8 NNLO JR9 NNLO ABKM9 NNLO 2 5 Q 2 / GeV 2 - perfect description of the F L data by QCD at Q 2 GeV 2 - large spread/uncertainty of the QCD predictions at low Q 2 F L data are a valuable input to the QCD fits 3

14 The Ratio R = F L / (F 2 - F L ) H Collaboration R Q 2 = 2 GeV 2 Q 2 = 2.5 GeV 2 Q 2 = 3.5 GeV 2.5 R=.25 R= Q 2 = 5 GeV 2 Q 2 = 6.5 GeV 2 Q 2 = 8.5 GeV Q 2 = 2 GeV 2 Q 2 = 5 GeV 2 Q 2 = 2 GeV 2.5 Q 2 = 25 GeV 2 SLAC EMC BCDMS Q 2 = 35 GeV 2 NMC ZEUS Q 2 = 45 GeV 2 H ACOT x HERA F L data are consistent with constant value of R =.26 ±.5 4

15 Summary - Combination of the H and ZEUS inclusive NC and CC e ± p data - HERA I: all inclusive results are published and combined using a model independent approach leading to significant reduction of systematic uncertainties - HERA I+II: extension of the combination to include HERA II data leads to improved precision at high Q 2 and high x the combined data sets have small errors (down to ~%) and used to make HERAPDF fits (HERAPDF., HERAPDF.5, ) with inclusive HERA data alone and including jets and charm data - The low proton beam energy data are used to measure the longitudinal structure function F L - combination of the H and ZEUS F L data for 2.5 Q 2 8 GeV 2 - H extended the F L measurement down to Q 2.5 GeV 2 HERA data are consistent with R = F L /(F 2 -F L ) =

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