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Parton Density Function Fitting Update

Parton Density Function Fitting Update. ZEUS Collaboration Meeting 19-June-2003 Chris Collins-Tooth Amanda Cooper-Sarkar, Claire Gwenlan. Introduction. How we parameterise the PDFs Method for fitting data to obtain the PDFs Where does the information come from for the fits?

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Parton Density Function Fitting Update

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  1. Parton Density Function Fitting Update ZEUS Collaboration Meeting 19-June-2003 Chris Collins-Tooth Amanda Cooper-Sarkar, Claire Gwenlan

  2. Introduction • How we parameterise the PDFs • Method for fitting data to obtain the PDFs • Where does the information come from for the fits? • What can we add/What data do we have to study? • Which parameters are best/worst determined? • Comparing new ZEUS ‘O’ fit with old ‘O’ fit and ZEUS-S • To Do: Ideas for the future

  3. How we parameterise the PDFs • At some particular value of Q02 (=7 GeV2) we parameterise the parton momentum distribution with the parameters pi xf(x) = p1.xp2(1-x)p3(1+p5x) • Gives flexibility at low (p2),high (p3) and mid (p5)x. • Distributions we parameterise are: • xuv(x) u-valence: p1u,p2u,p3u,p5u • xdv(x) d-valence: p1d,p2d,p3d,p5d • xS(x) total sea: p1S,p2S,p3S,p5S • xg(x) gluon: p1g,p2g,p3g,p5g • x =x(d-u) : p1,p2,p3,p5

  4. 5 distributions  4 parameters = 20 possible free params. • Luckily, some we can fix (eg ZEUS-S fit; 11 free params): • p1u, p1d fixed through number sum rules • p1g fixed through momentum sum rule • p2u, p2d =0.5 little information exists for low-x valence after data cuts • p2 =0.5 , p3(=p3S+2), p5=0 as per MRST eg EPJ C4, 463(1998);EPJ C14 133(2000) • p5g =0 since this choice constrains high-x gluon to be positive (leaves 11 free) • Additionally, for the ZEUS-O fit (ZEUS data only): • p1 fixed to value determined by ZEUS-S (10 free params) • The values are evolved in Q2 using NLO DGLAP equations, convoluted with coefficient functions in Roberts-Thorne Variable Flavour Number scheme • This list of parameters is fed to an evaluation function which calculates Chi-squared based on the data and theory PDFs

  5. Chi-squared definition 2 = i(Fi(p,s)-Fi(meas))2 + s2 (2i,stat+ 2i,unc) • Fi(p,s) = FiNLOQCD(p) + s i • Fi(meas) represents a measured data point • 2i,stat and 2i,unc represent stat. and uncorr. syst errors. •  are systematic error sources. 1 s.d. uncertainty on a data point i, due to source  , is i  • s are independent Gaussians, with zero mean and unit variance. • Accounts for systematic errors AND normalisations. • Applied conservatively by OFFSET method see J.Phys.G 28(2002) 2717

  6. Fitting method • Parameters s =0 for central values of fit • Obtain usual Hessian matrix Mjk = 1 22 2 pjpk • s allowed to vary for error analysis • Obtain 2nd Hessian matrix Cj = 1 22 2 pjs • Systematic covariance matrix = Vsy = M-1CCTM-1 • Stat. and uncorr. syst. covariance matrix =Vst= M-1 • Uncertainty on any distribution (eg PDF) calculated using Vsy,Vst

  7. Errors on the PDF parameters are given by the error matrices Vij . These are propagated to quantities of interest like structure functions, parton densities and reduced cross sections via: < F2>= ij F VijF pi pj Clearly, this is easier if V is diagonalised Diagonalisation has various other benefits: It tells you if you have a stable fit - are the eigenvalues all positive? It tells you if you actually NEED all the parameters you are using It tells you which parameters are constrained best

  8. Where does the information come from in the fits? • ZEUS-S, short for ‘ZEUS-Standard’ is a fit using GLOBAL data. Some ZEUS data (96-97) is included in this. • Valence: xF3 ~ x(uv+dv) from neutrino-Fe heavy target data F2n/F2p ~ xdv/xuv at high-x from muon+D/p data (NMC) • Sea: Low-x from HERA F2 e p data High-x predominantly from fixed target F2 muon+p data Flavour structure from muon+D and p • Gluon: Low-x from HERA dF2/dlnQ2 e p data High-x from mom-sum rule only (unless we add JET DATA) • ZEUS-O, short for ‘ZEUS-Only’ is a fit using ZEUS data only. • Still makes some assumptions from ZEUS-S fit, eg p1. • The old ZEUS-O fit (94-99 ZEUS data) is available - see http://www-pnp.physics.ox.ac.uk/~cooper/zeus2002.html for PDF sets. • Now, using 99/00 CC/NC e+p data with correlated systematic error sources this fit is being improved.

  9. What can HERA high Q2 data add? • TODAY HERA-I • High-x valence info-particularly on xdv from e+p CC. No deuterium or heavy target corrections. • TOMORROW HERA-II • xF3/xG3 measurement: valence info from low to high-x • More accurate xdv, xuv flavour separated from CC interactions • More accurate high-x sea distributions too (and better jet data for high-x glue)

  10. What data do we have to study? • We have about ~100pb-1 per experiment of NC and CC data (only 16pb-1 of it e-) • A new round of NLO QCD fits now to ZEUS data alone • Can use ZEUS high-Q2 data to constrain valence distributions independent of nuclear corrections needed by fixed target data. • ZEUS-S published fits used fixed target data and only 30pb-1 of NC e+ data. Phys Rev D67, 012007 (2003) • http://durpdg.dur.ac.uk/hepdata/zeus2002.html

  11. Which parameters are best/worst determined? • For both ZEUS-S and ZEUS-O fits, p1S and p2S are the best determined - ie the low-x behaviour of the sea. • Next best is the p2g - the low-x gluon • After that, p3u (high-x, u valence) is best determined from fixed target data, but high Q2 ZEUS data is nearly as good. • p3d, p3S (high-x d valence and sea) and p5u (mid-x u valence) are moderately well determined by fixed target data, but in new ZEUS-O fit, high Q2 ZEUS e+p CC data now determines p3d (high-x d valence) just as well • p3g (high-x glue) and p5S,p5g,p5d (mid-x sea,glue,d valence) are the least well determined in both fits, but are better determined from fixed target data.

  12. ZEUS-S New ZEUS-O 94-00 -amcs • At one stage, the ZEUS-S fit was used to determine as, by allowing it to vary as a fit parameter, and this error (blue) is only shown for reference. • Low-x Sea and Gluon in ZEUS-S fits were strongly constrained by ZEUS 96/7 e+p data – so are well constrained using ZEUS data alone

  13. PUBLISHED ZEUS-O Sea and glue distributions from ZEUS only with 94-99 data 16pb-1 e- and 30pb-1 e+ NEW ZEUS-O 94-00 Sea and glue distributions from ZEUS only with 94-00 data 16pb-1 e- and 93pb-1 e+

  14. ZEUS-S NEW ZEUS-O 94-00. • ZEUS-S constrained valence distributions by using fixed target data • Now the new 99/00 e+p data allows high-x valence distributions to be well constrained from a fit to ZEUS data alone

  15. NEW ZEUS-O 94-00 PUBLISHED ZEUS-O Valence distributions from ZEUS data alone 16pb-1 e- data and 37pb-1 e+ data Valence distributions from ZEUS data alone 16pb-1 e- data and 100pb-1 e+ data

  16. ZEUS-S NEW ZEUS-O 94-00 NEW ZEUS-O Gluon is almost as well determined as ZEUS-S gluon for all x

  17. ZEUS-S NEW ZEUS-O 94-00 Medium to high x sea is not as well determined for ZEUS-O as for ZEUS-S

  18. NEW ZEUS-O 94-00 ZEUS-S Errors on high-x xuv for ZEUS-O not quite as good as for ZEUS-S but HERA-II will improve

  19. NEW ZEUS-O 94-00 ZEUS-S Errors on High-x xdv from ZEUS-O as good as ZEUS-S and mostly statistical so that HERA-II will improve more!

  20. NEW ZEUS-O amcs 2nd Analysis A second analysis is underway (by me!) . Results so far look very promising.

  21. To do... • Investigate model dependence further - effect of fixing/freeing various parameters e.g. • valence shapes of ZEUS-O and ZEUS-S do differ significantly (and hence differ from MRST/CTEQ) • Look back and try to understand comparison of ZEUS-S fit with latest high Q2 data sets (seems higher at x~0.2, so this diff could be genuine) • Aside- you will NOT see any difference between ZEUS-O and MRST if you parameterise like H1 have done in DESY-03-38 (their H1-only fit). In such a plot, a comparison ZEUS/H1 or ZEUS/MRST looks quite sensible! • Ideas: • free low-x valence parameters • investigate effect of freeing/fixing sea parameters on valence shapes- the high-x sea also differs significantly from ZEUS-S fit and is not well determined in ZEUS-O since we have very little data for x>0.4 • vary assumptions on flavour structure of sea • Other model dependences not yet thought of!

  22. ZEUS-O vs MRST

  23. xU xD xU xD xg at Q2=10 and 1000 Gev2 compared to MRST2001 (can compare to H1’s plots) But this can hide a multitude of sins!

  24. For the new ZEUS-O fit, the following data is used : 96/97 e+p NC 30 pb-1 2.7 < Q2 < 30000 GeV2 242 d.p. 10 corr..err. 2 norms 94/97 e+p CC 33 pb-1 280. < Q2 < 30000 GeV2 29 d.p. 3 corr. err. 98/99 e-p NC 16 pb-1 200 < Q2 < 30000 GeV2 92 d.p. 6 corr err. 1 norm 98/99 e-p CC 16 pb-1 200 < Q2 < 30000 GeV2 26 d.p. 3 corr. err. 99/00 e+p NC 63 pb-1 200 < Q2 < 30000 GeV2 90 d.p. 9 corr. err. 1 norm 99/00 e+p CC 61 pb-1 200 < Q2 < 30000 GeV2 29 d.p. 3 corr. err.

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