ZEUS PDF analysis A.M Cooper-Sarkar, Oxford DIS2004

1

• PDF fits with free electroweak parameters
• Overview of what has happened since March06
  Collaboration meeting
• Emphasis on the NC couplings au,vu,ad,vd and how
  to calculate their contours
• when all 4 parameters are free (together with the
  PDF parameters
• OFFSET method plus stretching for correlated
  errors
• QUADRATURE errors
• HESSIAN method
• Short section on CC MW fits
• Some comments on combining with H1 in context of
  EW fits

2
All contours have 4-EW params free what we
thought we had got from polarised data at the
time of the collaboration meeting (statistical)
compared to H1, ZEUS from HERA-I But by DIS06
the yellow above had become the purple below (the
data changed slightly) au/vu contour is not so
different and is much better than without
polarised data The ad/vd contour is a somwehat
different shape and more extended in ad, BUT
still a substantial improvement in vd when
compared to HERA-I data
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Look more closely at the contours for a fit
without polarised data Note so far all ZEUS
contours are for uncorrelated errors only so the
purple shapes are comparable to the blue in the
slide above. The yellow show the effect of
adding in correlated errors by the stretching
method. Note the old data do not seem to have a
double minimum problem
Yes the yellow correlated contour is cocked up
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Now lets look at the same information with the
polarised data added These purple contours have
uncorrelated errors The vu,vd parameters are
obviously better detrmined BUT au is only
marginally better and ad is not better at all.
In fact there is a double minimum in au/ad space
au0.5, ad-0.5 AND au0.65, ad0.1 But where
are the uncorrelated errors?
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Before doing the correlated errors I decided it
would be best to have correlated errors on the
new polarised data as well as the HERA-I
data This was done in June And here are the
results Yellow are uncorrelated errors and blue
adds in the correlated errors by the stretching
method (OFFSET method with non-centred
stretch) (If you are worrying about what
correlated errors on the polarised data do to the
2 parameter contours we sent to DIS06 its OK -
see extra slides)
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These contours are ugly. So what methods might we
use to calculate contours? MINUIT command MNCONT
will do this for you from whatever you have
defined as your ?2 ?2 Si FiQCD(p)
S?s??i?SYS Fi MEAS2 Ss?2
(siUNCORR) 2
Now for the OFFSET method we set all the
correlated systematic error parameters, s?0, for
the central value of the fit and its uncorrelated
errors, and we calculate the correlated errors
later, letting each s? parameter be 1 This
means that the MINUIT contour will only include
the uncorrelated errors. So to display the effect
of correlated errors we have stretched the
contours by ?
dpi2(UNCORR) dpi2(CORR) / dpi2(UNCORR) where
dpi(UNCORR/CORR) are the uncorrelated and
correlated errors on parameter pi This stretch is
illustrated wrt the value of pi as determined by
the fit. However, since the fit has a tendency
to find a double minimum, the value of pi as
determined by the fit is NOT actually at the
centre of the contour hence the term OFFSET
method with non-centred stretch. It is easy to
stretch wrt the centre of the contour instead-
you can imagine it yourself.
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The OFFSET method 4-EW parameter contours are
quite ugly- the double minimum makes the
stretching large and asymmetric . What else might
we do? Well the same as well do when we quote the
?2 of our fit to the outside world- Recalculate
it with errors in QUADRATURE ?2 Si FiQCD (p)
Fi MEAS2
(siUNCORR)2(?iCORR)2
And then let MINUIT do the contours. I would be
happy with them since this is a well defined
procedure, and easy to explain outside ZEUS But
since the OFFSET with stretch contours are
sometimes larger we could ask if we are deceiving
ourselves and correlations should be accounted
somehow..
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Which brings us to the HESSIAN method -using the
form of the ?2 with the s? parameters in it, and
letting these parameters be free in the fit. As
used by H1. So here are the HESSIAN contours-
where correlated errors on both new polarised and
ZEUS HERA-I data have been included Id be happy
with these too. It is also a well defined
procedure- but it does mean changing our method
to the HESSIAN for the whole fit Or does it?
After all for PDFs we want to be conservative,
but this is not necessarily true for EW contours-
we could quote the OFFSET errors in a Table but
show these contours?
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The central values for the parameters are
compatible for all three methods
au ad vu vd
SM value 0.5 -0.5 0.196 -0.346
OFFSET 0.510.100.22 -0.460.360.40 0.150.160.07 -0.340.350.35
QUADRATure 0.530.19 -0.330.66 0.090.10 -0.560.20
HESSIAN 0.530.11 -0.410.38 0.140.13 -0.320.30
Note although errors are quoted as symmetric in
practice they are not, and this shows up when
plotting contours. This effect is most severe for
the OFFSET method and for 4 EW parameter contours
rather than 2 EW parameter contours.
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Will this be easier to solve our problems with
more data? Is there more e- which didnt go into
the DIS06 analysis? surely we should wait for
that? Should we wait for the final e as
well? Remember that even without these NC
contours we have a nice result on improvement of
the valence PDFs.. And on MW (Other possibilities
to improve PDFs new high-x analysis, more
photoproduced jets from HERA-I, more DIS
inclusive jets from HERA-1, have not yielded
much.)

• Now lets consider the MW fits
• Results change a little when the errors on the
  polarised data are separated into correlated and
  uncorrelated
• There is also the questions about fancy ways of
  getting at MW

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FIRST just MW as a free parameter of the fit,
together with the PDF parameters How does MW
enter the fit? In the factor GF2 MW4/(Q2MW2)2
Value of MW (80.4 SM) Specifications of
the fit
79.1 0.77 0.99 79.0 0.72 1.47 77.6 1.4 2.5 78.9 2.0(stat) 1.8 (sys) 2.2 -1.8 (PDF) 82.87 1.82(exp) 0.32-0.18 (model) Result for DIS06..but no correlated errors on new polarised data Result if polarised data errors are separated into correlated and uncorrelated not so impressive, but still better than the HERA-I results below ZEUS HERA-I data done by this EWPDF fit method ZEUS DESY-03-093 published HERA-I result H1 HERA-I data done by EWPDF method, note H1 uses the HESSIAN method so their errors are always better than ours on comparable data samples

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Can also fit BOTH GF and MW remember GF SM
1.1163910-5 Or we can fit a more general
formalism fit g and MW in g2 / (Q2 MW2)2 such
that g2GF2 MW4 0.07542 for standard model,
GF1.127 0.013 0.014 10-5 GF1.128 0.012 0.025 10-5 MW82.8 1.5 1.3 MW82.4 1.4 2.4
g 0.0772 0.0021 0.0019 g 0.0767 0.0019 0.0032 MW82.8 1.5 1.3 MW82.4 1.4 2.4
Result for DIS06..but no correlated errors on new
polarised data Result if polarised data errors
are separated into correlated and uncorrelated
not so impressive
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Alternatively USE the standard model
relationship GF2 MW4 0.5 (p?/ (1
MW2/MZ2))2 So that MW is the only parameter
entering into either shape or normalisation
MW 80.6 0.08 0.08 MW 80.1 0.09 0.233
H1 result using this technique on HERA-I data MW
80.8 0.21 -we suffer from using the OFFSET
method Strictly speaking there should be - a
factor of (1-?r) entering into both the GF MW2
relationship when loops are included where ?r
depends on mtop and mHiggs I have also applied
this and found very little difference in the
results. We did not pursue this because Shima had
no ?r code, but also because the meaning of it is
not very clear- it assumes so much of the SM
already. However it has been suggested that one
can interpret it better as a measurement of GF at
high scale? GF (1.146 0.006 0.016
)10-5 Maybe we can also pursue this with the
complete data set?
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Now what about combining with H1- different
meeting but the EW results are interesting. I
have tried the EW fit on the HERA-I ZEUS/H1
combined data set as produced by Sasha Glazov for
the 1st HERA/LHC workshop. Uncorrelated and
correlated errors are combined in quadrature
since after the H1/ZEUS combination the
correlated systematic errors are always smaller
than the statistical Then Ive compared it to
ZEUS and H1 HERA-I data considered
separately Then Ive added the ZEUS polarised
data to the Glazov combined HERA data. Just to
see what happens This should be a fruitful area
for combination, because correlations between the
PDF and EW parameters are not strong, so our
disagreements on PDF fit formalism should not
affect the EW fits so much. The Glazov
combination also removes most of the
HESSIAN/OFFSET controversy because it makes the
residual systematic errors small.
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EW fit contours for Glazov combined HERA-I data
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Reminder of what H1 and ZEUS HERA-I analyses look
like when considered separately
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H1/ZEUS Glazov combined HERA-I plus ZEUS HERA-II
contours Quadrature because of Glazov fit style
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Extras
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2-param contours OFFSET method NEW because
correlations are included for the new polarised
data i.e.NOT as for DIS06..ie not as the purple
and yellow ones in the next slide..
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2 param contours as for DIS06, not quite the same
as after correlations are put in the new
polarised data, but not so different either, so
not worth new preliminary. Hence the DIS06 was
sent to ICHEP06
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