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Experimental uncertainties in the parton distributions on Higgs production

Experimental uncertainties in the parton distributions on Higgs production. Stan Bentvelsen Michiel Botje Job Thijssen This is somewhat ‘older’ work of last year Have not been able to update since…. Uncertainty on the PDF’s:

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Experimental uncertainties in the parton distributions on Higgs production

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  1. Experimental uncertainties in the parton distributions on Higgs production Stan Bentvelsen Michiel Botje Job Thijssen This is somewhat ‘older’ work of last year Have not been able to update since…

  2. Uncertainty on the PDF’s: Propagation of uncertainties on experimental data to the fitted PDF’s Statistical uncertainties and (correlated) systematic effects Uncertainties in the theoretical description of the fit procedure Flavour thresholds, s Scales uncertainties Nuclear effects Higher twist, … A number of groups have published the PDF fits with propagated experimental uncertainties: Botje (Eur Phys J C14 (dec 1999)) CTEQ (J. Pumplin et al, hep-ph/0201195) MRST (A. Martin et al, hep-ph/0211080) Alekhin (S. Alekhin, hep-ph/0011002) Fermi2001 (Giele et al, hep-ph/0104052) Theoretical uncertainties not treated here PDF’s obtained from QCD DGLAP evolution fits to data. DIS data from fixed target and HERA Jet cross sections pp colliders Drell-Yan processes Parton parameterizations

  3. Botje (Dec 1999) Q02 = 4 GeV2, 28 free parameters X>10-3 Q2> 3 GeV2 W2>7 GeV2 Total 1578 data points, 2min=1537 Structure function data only (no pp jet data, no W± asymmetry) Not including ‘latest’ HERA structure functions CTEQ (Dec 2002) Q02 = 1.3 GeV2 20 (effectively independent) free parameters Q2> 4 GeV2 Total 1757 data points, 2min =1980 MRST (Nov 2002) Q02 = 1 GeV2 15 (effectively independent) free parameters, Q2> 2 GeV2 Total 2097 data points, 2min ~2267 Considered pdf data sets All parameterizations use NLO DGLAP evolution inMS-scheme. CTEQ and MRST also providepdf’s in DIS scheme, as well asleading order (event generators) Botje Needs update with latest data ‘CTEQ6’ series Gluon distribution somewhat harder wrt CTEQ5 ‘MRST02’ series Gluon distribution slightly harder wrt MRST2001

  4. Correlations between the mutual pdf’s important. The largest origin of the correlations are the momentum sum rules Uncertainty on gluon- and quark integrals separately much larger than on the sum of the two (Q2=4 GeV2): Also large correlation of gluon distribution and value of s. The value of s is kept fixed in the QCD evolution, at values obtained from precision e+e- collisions. As consistency checks the fits are repeated for varying s Quoted obtained errors on s from these checks range between 1 – 6 % In this study uncertainties on s are ignored Correlations

  5. Input parameters pi from least squares 2 minimalization Covariance matrix of input parameters pi obtained from expansion around minimim 2 Two methods to propagate the experimental systematic uncertainties: (Botje: hep-ph/0110123) Covariance matrix method (Hessian method) CTEQ, MRS, H1, … Rigorous statistical technique Assume errors are gaussian distributed, use linear approximation Exact in 1st order approximation Offset method Botje, ZEUS. Offset data by systematic error, redo fit, add deviations in quadrature Gives a conservative error of uncertainties Error estimates on PDF’s

  6. Covariance of any F and G: Botje: Store covariance matrix Vijp, parton densities, and all derivatives q/piin tables Error propagation done by EPDFLIB library User supplies FORTRAN function with definition F and G in terms of pdf’sas well as derivatives F/q and G/q. EPDFLIB calculates <FG> CTEQ, MRS: Diagonalize the covariance matrix Vijp using ‘rotated’ parameters zi Uncertainty on F and G simplifies to In order to sample quadratic behavior 2 accurately, pdf sets are determined for both zi+z, zi-z : (F+I,F-I) Store set of 2Np pdf’s for systematic uncertainties. Uncertainty on F corresponds to: Using uncertainties pi: free fit parameters CTEQ: sum over 40 sets MRST: sum over 30 sets

  7. Uncertainty on quantity F given by Deviation from 2=1 by CTEQ and MRS groups, by the factor: CTEQ: produce pdf sets with tolerance T2=100 MRST: produce pdf sets with tolerance T2=50 Rather arbitrary definition to get the standard deviations of a quantity Motivated by investigation probabilities of individual data sets Botje: produce sets for statistical and systematic errors separately Tolerance T2=1 for statistical uncertainty Added in quadrature to systematic uncertainty Error definition with tolerance Tolerance T2= 2

  8. Up-valence distribution As function of log10(x) at Q2=10 GeV2 Relative uncertainties large at very small and very large values of x Region around x=10-2 where the three sets are not compatible at 1 Botje CTEQ MRST Example: valence distributions Distributions normalized to MRST MRST Relative uncertainty CTEQ Botje

  9. At larger Q2 values the uncertainties tend to get smaller Up-valence distribution at Q2=106 GeV2 Up-valence at high Q2 value Distributions normalized to MRST MRST Relative uncertainty CTEQ Botje

  10. Gluon distribution at two scales Botje Cteq MRS Uncertainty on gluon distribution Gluon distribution at Q2=10 GeV2 Larger uncertainties (note the scale) Botje deviates from MRST/CTEQ at low x(cf data cut at x>10-3) Very typical small uncertainty around x~0.2, rapid increase for larger x MRST smallest uncertainties Distributions normalized to MRST MRST Relative uncertainty CTEQ Botje

  11. Gluon at large Q Gluon distribution at Q2=106 GeV2 Uncertainties at small values of xare getting very small Distributions normalized to MRST MRST Relative uncertainty CTEQ Botje

  12. Higgs production cross section • ‘gluon-gluon’ luminosity • Uncertainties remarkable small • At Mh=100: • Botje: 5.6%, CTEQ: 4.6%, MRST: 2.2% • At Mh=1000: • Botje: ~10%, CTEQ: ~10%, MRST: 5% Distributions normalized to MRST MRST CTEQ Relative uncertainty Botje Log10(Mh)

  13. Higgs production uncertainty • Full check by interfacing to HiGlu package with pdf sets • NLO ggHiggs production in MS-scheme • Matches the PDF sets scheme evolution • Cross section ratio NLO to LO given by K-factor (1.5-1.7) • Pdf uncertainty very similar for LO and NLO Born At TevaTron the uncertainties forthis process are larger NLO Cm energy=2 TeV Log10(Mh) Log10(Mh)

  14. WW production • Other luminosity functions readily be obtained • Example of W+ and W- production at LHC • Uncertainty fairly constant over range s • MRS smallest uncertainty, -1-2% • Botje and CTEQ in range 4-5% qqW- qqW+ Correlation between Higgs and W production, ~0.6

  15. Conclusions • Propagation of experimental uncertainties to pdf available • Correlations and systematic experimental uncertainties are important and are taken into account • Definition of the uncertainty on pdf’s not straightforward • cf ‘tolerances’ MRST/CTEQ • Cleary theoretical uncertainties –not treated here, are important • And probably more important • Most interesting distributions not looked at so far. • I’m afraid I don’t have the ‘manpower’ to pursue very far…

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