NLO QCD fits How far can we get without jet data/HERA-II data? A. M. Cooper-Sarkar March-04 Collaboration Meeting ZEUSNOTE Extended ZEUS-S fits (ZEUS NC 96/7 data plus fixed target data) Updated ZEUS-S fits (ZEUS-S plus ZEUS high-Q2 cross-sections) ZEUS-Only fits compared to ZEUS-Only fits parametrization dependence ZEUS-Only fits plus BCDMS HERA-Only fits Suggestion for DIS2004 Suggestions for the future

Extend ZEUS-S (ZEUS+fixed target data) fits 11 to 13 parameters ! xuv(x) =p1u x p2u (1-x) p3u (1 + p5u x) xdv(x) =p1d x p2d (1-x) p3d (1 + p5d x) xS(x) =p1s x p2s (1-x) p3s (1 + p5s x) xg(x) =p1g x p2g (1-x) p3g (1 + p5g x) These parameters control the low-x shape These parameters control the high-x shape These parameters control the middling-x shape In the published ZEUS-S fit p1u,p1d,p1g are fixed by sum rules, p2u=p2d=0.5 is fixed, and p5g is fixed. We also free the normalisation of xΔ=x(d-u), but its shape is taken from the Sea shape. This makes 11 parameters.

Freeing p2u =p2d and freeing p5g makes NO significant change to ZEUS-S PDFs 11-parameters 13 parameters

The Obvious thing to do next is to update these extended ZEUS-S fits to include the high-Q2 cross-section data, which was not included in the published ZEUS-S fits CC 94-97, NC+CC 98/99 and NC+CC 99/00 data

96/97 e+p NC 30 pb < Q2 < GeV d.p. 10 corr..err. 2 norms 94/97 e+p CC 33 pb < Q2 < GeV 2 29 d.p. 3 corr. err. 98/99 e-p NC 16 pb < Q2 < GeV 2 92 d.p. 6 corr err. 1 norm 98/99 e-p CC 16 pb < Q2 < GeV 2 26 d.p. 3 corr. err. 99/00 e+p NC 63 pb < Q2 < GeV 2 90 d.p. 8 corr. err. 1 norm 99/00 e-p CC 61 pb < Q2 < GeV 2 29 d.p. 6 corr. err. The point is to try to see how far we can get with ZEUS data alone. ZEUS-Only fits to data were included in the old fit paper. ZEUS-Only fits have now been done to data sets from with full correlated systematic errors The standard fit to ZEUS-Only data (as published) had 10 free parameters. The same as the ZEUS-S fit, but the normalisation of xΔ fixed

First compare ZEUS-Only fits with data and with data Clear improvements in both u-valence and d-valence with errors still mostly statistical –scope for further improvement (HERA-II) Sea and glue are not significantly affected since the precision on the low- x Sea and glue come from the NC 96/97 sample which is in both fits

Main effect on the valence parametrizations is increase in uncertainty due to the freeing of the low-x valence parameter p2u=p2d Extend the standard 10 parameters to 12 parameters by freeing p2u=p2d and p5g. Sea xu v xd v Freeing the middling-x gluon parameter p5g has significant effects on the shape and uncertainty of the high-x gluon and on the uncertainty of the high-x Sea Glue

Where does the information come from in a global PDF fit like ZEUS-S? Valence: xF3 ~ x(uv +dv) from neutrino-Fe heavy target data F2n/F2p ~ xdv/xuv at high-x from μ D/p data Sea: Low-x from HERA F2 e p data High-x dominantly from fixed target F2 μ p data Flavour structure from μ D and p Gluon: Low-x from HERA dF2/dlnQ2 e p data High-x from mom-sum rule only- (UNLESS we put in JET DATA!) Where does the information come from in a ZEUS-Only fit Valence: High-Q2 cross-sections CC/NC e+/- particularly xdv from e+p CC. This only constrains high-x. For low-x there is only the number sum rule Sea: Low-x from the ZEUS NC 96/7 `all’ Q2 sample. High-x missing! Gluon: Low-x from ZEUS NC96/7 ‘all’ Q2, dF2/dlnQ2 data. High-x from mom-sum rule only- largely missing! On a pure proton target- no heavy target correction or deuterium corrections -

ZEUS-S fit precision cannot improve significantly since it is already systematics dominated. ZEUS-O fit precision can improve AND its all done on a pure hydrogen target- no heavy target uncertainties Compare ZEUS-Only fit PDFs with ZEUS-S fit PDFs ZEUS-S ZEUS-O xuv ZEUS-S ZEUS-O xdv The ZEUS-S fit precision on d-valence is much worse than for u-valence because most cross-sections measure u-valence. The information comes only from CCFR xF3 Fe target data and NMC F2D/F2p data. The ZEUS-O fit uses CC e+ p data, and already approaches the same precision, with much more room for improvement, since its error is statistics dominated

High-x Sea precision is a lot worse for ZEUS-O, whereas the low-x Sea precision is comparable - the low-x information was coming from ZEUS data anyway. Compare ZEUS-Only fit PDFs with ZEUS-S fit PDFs Sea ZEUS-S ZEUS-O Middling to high-x gluon precision is a lot worse for ZEUS-O. Again the low-x precision is comparable- coming from ZEUS data anyway. We hope to gain further information from the ZEUS-jet data Glue ZEUS-S ZEUS-O

Now I show the ZEUS-O fit on scales which exaggerate low-x valence and high-x Sea and gluon- where we DON’T measure! 12 param fit

Clearly some interplay between the shape of the sea and that of the d valence is possible for 0.02 < x < 0.2, and that is what we are seeing We need more high-x CC e+ data, or we need to tie down the high-x Sea better – fix the high-x Sea p3s parameter to the value as determined in the ZEUS-S fit (13 param.) using the uncertainties on these parameters from the ZEUS-S fit to determine the model error – Such plots were already shown in Oct 2003 Collab meeting

ZEUS-O fits with p3s fixed to ZEUS-S values, plus model error 10 param fit Gluon shape looks much as it did before

ZEUS-O 12 parameter fit ZEUS-O 10 parameter fit p3s and p3g fixed by ZEUS-S Χ 2 difference « √ 2 N

The ZEUS-O fit has produced rather unconventional shapes for the Sea and the d-valence. Is this the truth for fits with hydrogen only data? Put differently are the shapes obtained by the global fits (ZEUS-S, MRST or CTEQ) a feature of the use of heavy target data, or simply of the use of more data at high-x? We must use some high-x data taken on a hydrogen target to find out BCDMS data has the highest x of all the possible data sets ZEUS-O plus BCDMS H2 data has a much more conventional sea shape

So, we conclude that the Sea shape probably should be closer to the conventional global fit extractions – fixing p3s is a good idea There is a good reason NOT to do fits with BCDMS and ZEUS-Only data sets. The BCDMS data seems only marginally compatible to our data and the systematic uncertainties thus give a large contribution to the overall error-particularly for dv What we are gaining in statistics we are losing on systematics – not worth it! xdv ZEUS-O ZEUS+BCDMS

Secondly one can try to add in H1 data, to see the effect of more statistics in the HERA kinematic regime. Again with pure hydrogen data. The interplay between the sea and the d-valence is much as for the ZEUS-Only fit. The gluon is very much more humpy!

Let’s compare ZEUS–Only to ZEUS +H1 distributions xuv ZEUS+H1 ZEUS-O xdv ZEUS+H1 ZEUS-O Clear improvement for uv, less clear for dv – but acceptable ZEUS+H1 ZEUS-O Sea Improvement in precision of high-x glue and Sea BUT gluon shape has become pronouncedly humpy Glue ZEUS+H1 ZEUS-O

Consider the gluon shape The fact is that all DIS only fits lack information on the high-x gluon, but fits to restricted data sets are more vulnerable. The problem with the humpy gluon shape is not the hump itself, but the fact that it absorbs quite a lot of the gluon’s momentum in the hump and none is left for high-x. Again one can ask if the more conventional shape for the gluon derived in the ZEUS-S fit (and MRST/CTEQ) is a consequence of the use of heavy target data. BCDMS data are no use now since they also give a large error on the gluon. But hydrogen data sets are precisely what is conventionally used to determine the gluon in the professional global fits of MRST and CTEQ: Namely the Tevatron high-ET jet data. To produce high-ET jets one needs quite a hard high-x gluon. MRST have produced a pseudo gluon data set, which is compatible with the high-ET jet data. If we fit ZEUS data alone plus this gluon pseudo data, we get a very much harder gluon shape with no hump.

Gluon from ZEUS data alone Gluon from ZEUS data plus Tevatron jet pseudo-gluon data Gluon from ZEUS+H1 data Solution to the problem of not knowing enough about the high-x gluon? Add H1 data – doesn’t really help Add jet data- Tevatron jet data – NO - ZEUS jet data - YES -coming Right now - set p3g equal to the ZEUS-S value and use the uncertainties on ZEUS-S to calculate the model errors.

ZEUS-O fits with p3s and p3g fixed to ZEUS-S values, plus model error 10 param fit

10 param. fit 12 param. fit Despite the differences in gluon shape it is hard to see the difference in fit to data

Chris Collins Tooth’s plot for the low-Q2 part of the NC cross-sections, showing both ZEUS and H1 data. Fits done to both data sets have poor χ2 for the NC 96/7 data sets for both of us. This can be ameliorated by freeing normalisations (ZEUS 0.986: H ) but there is a remaining shape difference which leads to the differences in the tendencies of our gluon shapes

So the current solution is to admit that with ZEUS data alone we cannot measure high-x Sea and gluon and set the high-x parameters p3s and p3g equal to the ZEUS-S values (using ZEUS-S uncertainties to get the model error). This gives a 10 parameter fit. (Same number of parameters as the H1 Only PDF fit). Our focus is the valence distributions Valence distributions for various Q2

Sea and gluon distributions in various Q2 bins

Sea and gluon u and d valence summary plots

Compare published ZEUS-O to new ZEUS-O Improvement, and lots of scope for more improvement

Compare our final solution ZEUS-Only PDFs to published ZEUS-S PDFs

And for the record let’s compare them to H1

Comparison of AMCS analysis to Chris Collins Tooth analysis- includes further model errors (Q2, x, W2 cuts, p4 params., Q2_0)

Agreement with 2 nd analysis by Chris Collins Tooth PDF p1p2p3p5 xuv (2.8 ± 0.6 ± 1.0) (2.7 ± 0.6 ± 1.0) 0.61 ±0.05 ± ±0.05 ± ± 0.17 ± ± 0.16 ± ± 1.0 ± ± 1.1 ± 1.0 xdv (1.6 ± 0.3 ± 0.5) (1.5 ± 0.3 ± 0.5) 0.61 ±0.05 ± ±0.05 ± ± 0.8 ± ± 0.7 ± ± 2.0 ± ± 2.0 ± 1.6 xS 0.75 ± 0.02 ± ±0.004 ± ±0.004 ± ± 0.8 ± ± 0.9 ± 2.3 xg (1.4 ± 0.1 ± 0.5) (1.5 ± 0.1 ± 0.5) ±0.01 ± ±0.01 ± ± 0.5 ± ± 0.5 ± 2.2 Data SetNo of pointsΧ2 per point 96/97 e+ NC /97 e+ CC /99 e- NC /99 e- CC /00 e+ NC /00 e+ CC

The fit prediction is only shown for proton beam energy 920 ZEUS-O fit predictions for the high-Q2 cross-sections

The final fit compared to low-Q2 data

Solutions for the future We need more information on the low-x Sea and gluon. Where are we going to get it from? 1.CHARM –it does help, but not enough 2. Our own jet data? - ongoing 3. HERA-II Glue Sea

Summary I think its time we said something about our ZEUS-Only PDF fits with the full HERA-I data set – that old preliminary valence plot with the 99/00 data in it has been hanging around since 2002 Time scale DIS 2004 If work from the jets is available great!- but meanwhile we have as good a fit as the H1-Only PDFs (with the same number of free parameters). We are honest and admit that it is NOT as good as a global PDF fit like ZEUS-S but it is ALL hydrogen At the current state of knowledge it does lack information on high-x glue and Sea and this means parameter fixing BUT our main focus is on the valence shapes I want ZEUS-preliminary status on the plots of u and d valence glue and Sea at various Q2. The plots of the fit on the NC/CC cross-sections data and the comparisons to ZEUS-S/H1/MRST

On the other hand it is not as great as we at first thought it was before we did model dependence studies Let’s not emphasize that too much!

This is new ZEUS-O compared to published ZEUS-S. Not yet as good But on a hydrogen target AND with plenty of room for statistical improvement