NLO QCD fitsHow far can we get without jet data/HERA-II data?A . M . Cooper-Sarkar March-04 Collaboration Meeting ZEUSNOTE-04-001

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 94-98 compared to 94-00ZEUS-Only fits parametrization dependenceZEUS-Only fits plus BCDMSHERA-Only fitsSuggestion for DIS2004Suggestions for the future

Extend ZEUS-S (ZEUS+fixed target data) fits11 to 13 parameters!xuv(x) =p1u xp2u (1-x)p3u (1 + p5u x) xdv(x) =p1d xp2d (1-x)p3d (1 + p5d x) xS(x) =p1s xp2s (1-x)p3s (1 + p5s x) xg(x) =p1g xp2g (1-x)p3g (1 + p5g x)

These parameters control the low-x shapeThese parameters control the high-x shapeThese parameters control the middling-x shapeIn 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 x=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-parameters13 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 fitsCC 94-97, NC+CC 98/99 and NC+CC 99/00 data

96/97 e+p NC 30 pb-1 2.7 < Q2 < 30000 GeV2 242 d.p. 10 corr..err. 2 norms94/97 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 norm98/99 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. 8 corr. err. 1 norm99/00 e-p CC 61 pb-1 200 < Q2 < 30000 GeV2 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 94-98 data were included in the old fit paper. ZEUS-Only fits have now been done to data sets from 1994-2000 with full correlated systematic errorsThe standard fit to 1994-1998 ZEUS-Only data (as published) had 10 free parameters. The same as the ZEUS-S fit, but the normalisation of x fixed

First compare ZEUS-Only fits with 94-98 data and with 94-00 dataClear 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=p2dExtend the standard 10 parameters to 12 parameters by freeing p2u=p2d and p5g. SeaxuvxdvFreeing 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 SeaGlue

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 D/p data Sea: Low-x from HERA F2 e p data High-x dominantly from fixed target F2 p data Flavour structure from 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 ruleSea: 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 uncertaintiesCompare ZEUS-Only 94-00 fit PDFs with ZEUS-S fit PDFsZEUS-S ZEUS-O xuvZEUS-S ZEUS-O xdvThe 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 94-00 fit PDFs with ZEUS-S fit PDFsSeaZEUS-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 dataGlueZEUS-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 DONT 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 seeingWe 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 error10 param fitGluon shape looks much as it did before

ZEUS-O 12 parameter fitZEUS-O 10 parameter fit p3s and p3g fixed by ZEUS-S2 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 setsZEUS-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 dvWhat 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 muchmore humpy!

Lets compare ZEUSOnly to ZEUS +H1 distributionsxuvZEUS+H1 ZEUS-OxdvZEUS+H1 ZEUS-OClear improvement for uv, less clear for dv but acceptableZEUS+H1 ZEUS-OSeaImprovement in precision of high-x glue and Sea BUT gluon shape has become pronouncedly humpy

GlueZEUS+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 gluons 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 aloneGluon from ZEUS data plus Tevatron jet pseudo-gluon dataGluon from ZEUS+H1 data Solution to the problem of not knowing enough about the high-x gluon?Add H1 data doesnt really helpAdd jet data- Tevatron jet data NO - ZEUS jet data - YES -comingRight 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 error10 param fit

10 param. fit12 param. fitDespite the differences in gluon shape it is hard to see the difference in fit to data

Chris Collins Tooths 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 2 for the NC 96/7 data sets for both of us. This can be ameliorated by freeing normalisations (ZEUS 0.986: H1 1.013) 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 distributionsValence distributions for various Q2

Sea and gluon distributions in various Q2 bins

Sea and gluon u and d valence summary plots

Compare 94-98 published ZEUS-O to new 94-00 ZEUS-OImprovement, and lots of scope for more improvement

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

And for the record lets 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 2nd analysis by Chris Collins Tooth

PDFp1p2p3p5xuv(2.8 0.6 1.0)(2.7 0.6 1.0)0.61 0.05 0.070.60 0.05 0.073.97 0.17 0.243.97 0.16 0.252.4 1.0 0.92.6 1.1 1.0xdv(1.6 0.3 0.5)(1.5 0.3 0.5)0.61 0.05 0.070.60 0.05 0.074.3 0.8 0.84.4 0.7 0.81.6 2.0 1.42.2 2.0 1.6xS0.75 0.02 0.080.75 0.02 0.08-0.209 0.004 0.015-0.210 0.004 0.0157.50.8 0.8 2.20.9 0.9 2.3xg(1.4 0.1 0.5)(1.5 0.1 0.5)-0.23 0.01 0.05-0.22 0.01 0.055.91.1 0.5 2.20.8 0.5 2.2

Data SetNo of points 2 per point96/97 e+ NC2420.70 0.7294/97 e+ CC290.60 0.5698/99 e- NC920.72 0.7098/99 e- CC260.85 0.8899/00 e+ NC900.88 0.8599/00 e+ CC301.09 1.11

The fit prediction is only shown for proton beam energy 920ZEUS-O 94-00 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 enough2. Our own jet data? - ongoing

3. HERA-II

GlueSea

SummaryI 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 2002Time scale DIS 2004If 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 hydrogenAt 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 shapesI 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 studiesLets 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