More on NLOQCD fits ZEUS Collab Meeting March 2003 Eigenvector PDF sets- ZEUS-S 2002 PDFS accessible on HEPDATA High x valence distributions from ZEUS-Only fits- including 99/00 NC and CC data with correlations Extension of above to determine M W, sin 2  W ZEUS H1 comparison A.M.Cooper-Sarkar Oxford

Eigenvector PDF sets- a better way to store the results of the fits see soon to go public on Durham HEPDATA and LHAPDF siteshttp://www-pnp.physics.ox.ac.uk/~cooper/zeus2002.html Diagonalising the error matrix of the fit has various further benefits It tells you if you have a stable fit- are the eigenvalues all positive? It tells you if you NEED all the parameters you are using It tells you which parameters are constrained best See pnp.phyiscs.ox.ac.uk/~cooper/v alence.html for full write-uphttp://www- pnp.phyiscs.ox.ac.uk/~cooper/v alence.html The errors on the PDF parameters are given by the error matrices V ij and are propagated to quantities of interest like parton distributions, structure functions and reduced cross- sections via ΔF 2 =∑ ij ∂F/∂p i V ij ∂F/∂p j This would clearly be easier if V were diagonalised

The results of the fit are then summarised in one central PDF set and 2 * N pdf parameter sets for the errors. N pdf is the number of PDF parameters (11 for ZEUS-S). These parameter sets are obtained by moving up(+) or down(-) along the i=1,N pdf eigenvector directions by the corresponding error (square-root of the corresponding eigenvalue). These moves are propagated back to the original PDF parameters to create new PDF sets- (Si+) (Si-). ( Movement along an eigenvector direction can change all of the original PDF parameters at the same time). The error on a derived quantity is then obtained from ΔF 2 = ½∑ I ( F(Si+) – F(Si-) ) 2 The ZEUS-S fit with its 11 parameters is well-behaved. It has been the experience of CTEQ and MRST- (who both use more parameters)- that along some eigenvector directions the χ2 increases very slowly-leading to asymmetries and the breakdown of the quadratic approximation for χ2. Such directions (or equivalently such combinations of parameters) are not well constrained by their fits and they have had to fix some parameters in order to produce meaningful errors. ZEUS has avoided this by not assuming that we can determine more parameters than we actually can!

The form of our parametrisation is xq(x) = p1 x p2 (1-x) p3 (1+p5x) Examining the eigenvectors and eigenvalues of the total error matrix of the ZEUS-S fit shows that The best determined parameters are p2 and p1 for the Sea –i.e the low –x behaviour of the Sea as determined by the ZEUS data - and that a combination of parameters which is 90% p2 Sea and 6% p1 Sea with negligible amounts of the other PDF parameters is BETTER determined than either of these parameters separately. The next best determined parameter is p2 for the glue – the low-x behaviour of the glue also from the ZEUS data Then p3 for the u-valence –high-x u valence- from the fixed target data The high-x parameters p3 for the Sea and d-valence, and p5 for the u valence are moderately well determined from the fixed target data, and so is the parameter which allows for d ≠ u in the Sea. The high-x parameters p3 for the glue and p5 for the Sea and d-valence are the worst determined in this fit (which uses only DIS data). In future gain more information on the glue from jets in photo production?- meeting tonight Meanwhile- Beware of adding more parameters (like p5 for glue or p2 for valence)

So what is available? On – soon to be linked to the ZEUS public pages or from Durham HEPDATA PDF grids: u_v, d_v, Sea, Glue, plus Sea flavour break up into u, d, s, c, b and also (new) d/u Structure function grids: F2 (em), FL (em) F2 charm, F2(NC), FL(NC) and xF3(NC) Reduced cross-section grids: б(NC e+), б(NC e-), б(CC e+), б(NC e-) Central PDF set for ZMVFN/ FFN/ RTVFN heavy flavour schgemes -plus corresponding eigenvector PDF sets so that you could make all these calculations (and more) yourself straight from the PDF parameters WITH ERRORS. These eigenvector sets are available separately for 1.statistical plus uncorrelated systematic errors, 2.correlated systematic errors 3.and total errors. A programme qcd_results.f to show you how use eigenvector PDF sets Central PDF set plus covariance matrices if you want to do it the hard way. These are also available for ZMVFN/ FFN/ RTVFN and uncorrelated plus correlated errors as well as total errors

Compare Valence distributions from the ZEUS-S fit with fixed target data to the ZEUS-O fit using only ZEUS data- plots below are from the paper - but this was before the 99/00 data Updates of ZEUS NLOQCD fits with new data

The 99/00 data could NOT be included in the paper BUT the right hand plot was shown as preliminary last year- NOW let’s make it FINAL!

Here are the ZEUS-Only valence distributions updated- Now including the latest 99/00 NC and CC data – with full correlations. The distributions are VERY similar to the preliminary results u- valence d-valence

But should one extend the simple ZEUS parametrizations? xq(x) = p1 x p2 (1-x) p3 (1+p5x) For the valence distributions p2=0.5 fixed- Why? Because the only information came from CCFR  Fe data- with significant heavy target corrections- ZEUS does not contribute here (until we have good xF3 determinations of our own!) But freeing p2 – which affects small–x valence- may affect large x valence via the number sum-rules- this was NOT a problem for the standard fit-the CCFR data tied down the high x valence—BUT is it a problem for ZEUS ONLY fits-? Are we underestimating the large-x error by fixing p2? NO!- see d-valence plot with p2 free

Of course one can see a difference between fixed and free p2 valence if one looks at the low-x valence shapes- But we are not yet claiming to measure these d valence distributions with p2 fixed. Low-x scale expanded Note this fit is still diagonalisable- a fit with p5 glue free as well is not! d valence distributions with p2 free. Low-x scale expanded

In case you think there’s no more to do post upgrade - we COULD consider more radical changes to the high x valence distributions – dv  dv +uv * B x (1+x) Then for B=0.1 dv/uv  0.2 as x  1 B=0 fixed forces dv/uv  0 as x  1 B = ±0.38 ± 1.76 –ZEUS-ONLY B = 0.2 ± 0.02 ± 0.09 – ZEUS-S The ZEUS-S fit (not illustrated) is still much better on high-x valence distributions

Investigation of electroweak parameters- make M W one of the fit parameters in the ZEUS-Only fit (including latest ZEUS NC/CC data 99/00 as well as NC/CC 98/99 NC96/7 and CC94-97) and the PDF errors are taken into account automatically – does this reduce the overall error? Obtain M W = 82.6 ± 1.7(stat) ± 1.9(sys) Compare 80.2 ± 1.3(stat) ± 1.4 (sys) ± ~2.3(PDF) SO YES the overall error does decrease even using most conservative possible ZEUS OFFSET errors

Can do various further investigations Free more PDF parameters- e.g if p2 valence is free obtain MW = 81.9 ± 1.6(stat) ± 2.1(sys)-similar Free more electroweak parameters e.g let sin 2  W be one of the fit parameters sin 2  W = ± 0.011(stat) ± (sys) and M W = 81.9 ± 1.5(stat) ± 2.3 (sys) Investigate different error treatments without going as far as fitting all systematic error parameters one could free the relative normalisations of the ZEUS data sets  then the systematic error on M W decreases from ~ 2.0 to 1.3

H1 and ZEUS comparisons Remember the fuss about this plot? - But the analyses were very different So we defined a benchmark fit- VERY similar to ZEUS-S fit conditions for published HERA data alone See pnp.phyics.ox.ac.uk/~cooper/valen ce.html for full specificationshttp://www- pnp.phyics.ox.ac.uk/~cooper/valen ce.html Main point- gluon parameterization xg(x) = p1.x p2 (1-x) p3 (1 + p5 x) p5 non zero for both ZEUS and H1 (subsidiary point -p2 for the valence distributions is also free)

statistical errors only HERA data: NC 96/7 CC94-97 NC 98/9 CC 98/9 ZEUS only gluon: p3 = 5.8 ±4.2 p5 = ± 15. (p2 valence = 0.61 ± 0.14) H1 only gluon: p3 = 14.5 ± 0.6 p5 = 48.2 ± 3.6 (p2 valence = 0.89 ± 0.03) The gluons really are very different even when exactly the same analysis is performed

Combine ZEUS and H1- allow free relative normalisations ZEUS 96/7 norm H1 96/7norm With just statistical errors With statistical plus Offset method correlated errors p3 = 11.0 ± 1.5 ± 3.8 p5 = 11.8 ± 5.8 ± 15.9 With Offset errors we achieve a reasonable compromise – but because of data differences/incompatibility(?) the combination does not have much smaller errors than ZEUS alone

Summary Eigenvector PDF sets (and plenty more) on pnp.physics.ox.ac.uk/~cooper/zeus2002.html on and soon from ZEUS web pageshttp://www- pnp.physics.ox.ac.uk/~cooper/zeus2002.html 1.Let’s update the ZEUS-ONLY valence distributions with 99/00 data 2.Let’s look at fitting electro weak parameters with the fit 3.Need a second analysis for points 1. and 2. 4.Interesting differences with H1 seem to be at the data, rather than at the analysis level