-
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