More on NLOQCD fits ZEUS Collab Meeting March 2003

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More on NLOQCD fitsZEUS Collab Meeting March 2003
A.M.Cooper-Sarkar Oxford

• 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 MW, sin2?W
• ZEUS H1 comparison

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Eigenvector PDF sets- a better way to store the
results of the fitssee http//www-pnp.physics.ox.
ac.uk/cooper/zeus2002.htmlsoon to go public on
Durham HEPDATA and LHAPDF sites

• 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 http//www-pnp.phyiscs.ox.ac.uk/cooper/valenc
  e.html for full write-up

• The errors on the PDF parameters are given by the
  error matrices Vij and are propagated to
  quantities of interest like parton distributions,
  structure functions and reduced cross-sections
  via
• ?F2?ij ?F/?pi Vij ?F/?pj
• This would clearly be easier if V were
  diagonalised

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• The results of the fit are then summarised in one
  central PDF set and 2 Npdf parameter sets for
  the errors. Npdf is the number of PDF parameters
  (11 for ZEUS-S).
• These parameter sets are obtained by moving up()
  or down(-) along the i1,Npdf 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
• ?F2 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 ?2
  increases very slowly-leading to asymmetries and
  the breakdown of the quadratic approximation for
  ?2 . 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!

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• The form of our parametrisation is
• xq(x) p1 x p2 (1-x) p3 (1p5x)
• 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 18.30
• Meanwhile- Beware of adding more parameters
  (like p5 for glue or p2 for valence)

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So what is available?On http//www-pnp.physics.o
x.ac.uk/cooper/zeus2002.html soon to be linked
to the ZEUS public pagesor from Durham HEPDATA
http//durpdg.dur.ac.uk/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 ?(NC e), ?(NC e-),
  ?(CC e), ?(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
• statistical plus uncorrelated systematic errors,
• correlated systematic errors
• 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

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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
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The 99/00 data could NOT be included in the
paper BUT the right hand plot was shown as
preliminary last year- NOW lets make it FINAL!
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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
d-valence
u- valence
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But should one extend the simple ZEUS
parametrizations? xq(x) p1 x p2 (1-x) p3
(1p5x) For the valence distributions p20.5
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 smallx
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
valenceBUT 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
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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
d valence distributions with p2 free. Low-x scale
expanded
Note this fit is still diagonalisable- a fit with
p5 glue free as well is not!
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In case you think theres no more to do post
upgrade - we COULD consider more radical changes
to the high x valence distributions dv ? dv
uv B x (1x) Then for B0.1 dv/uv ? 0.2 as x
? 1
B -0.04 0.38 1.76 ZEUS-ONLY B 0.2
0.02 0.09 ZEUS-S
B0 fixed forces dv/uv ? 0 as x ? 1
The ZEUS-S fit (not illustrated) is still much
better on high-x valence distributions
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Investigation of electroweak parameters-

• make MW 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 MW 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

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• 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 sin2?W
  be one of the fit parameters
• sin2?W 0.223 0.011(stat) 0.029 (sys)
• and MW 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 MW decreases from
  2.0 to 1.3

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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 http//www-pnp.phyics.ox.ac.uk/cooper/valence
  .html for full specifications
• 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)

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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 -0.56
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
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Combine ZEUS and H1- allow free relative
normalisations ZEUS 96/7 norm 0.986 H1
96/7norm 1.013
With statistical plus Offset method correlated
errors
With just statistical 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
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Summary

• Eigenvector PDF sets (and plenty more) on
  http//www-pnp.physics.ox.ac.uk/cooper/zeus2002.h
  tml on http//durpdg.dur.ac.uk/HEPDATA and soon
  from ZEUS web pages
• Lets update the ZEUS-ONLY valence distributions
  with 99/00 data
• Lets look at fitting electro weak parameters
  with the fit
• Need a second analysis for points 1. and 2.
• Interesting differences with H1 seem to be at the
  data, rather than at the analysis level