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ZEUS PDF analysis A.M Cooper-Sarkar_ Oxford DIS2004

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ZEUS PDF analysis A.M Cooper-Sarkar_  Oxford DIS2004 Powered By Docstoc
					                       Combining ZEUS and H1 data sets?
                                   A M Cooper-Sarkar Oct 06
               Let’s refresh our memories- all HERA-I in this talk, and NO jets.



•  In the context of the HERA-LHC workshop the idea of combining the H1 and
   ZEUS data arose. Not just putting both data sets into a common PDF fit but
   actually averaging the data first.
• Why? Well, because combining ZEUS and H1 data in fits has not been very
   successful, e.g. MRST say ‘ZEUS and H1 data sets pull against each other’
→ let’s not rely on MRST, so I tried looking at H1 data myself, with the ZEUS PDF
   analysis
• I also collaborated with Sasha Glazov to ensure that the averaging of ZEUS and
   H1 was done with the correct ZEUS data sets and correlations (and this enabled me
    to understand the H1 correlations!)
•    I then made a PDF fit to the resulting combined HERA data and compared it to
    fitting the data sets separately
•   And I made a brief model dependence analysis of this fit
ZEUS analysis/ZEUS data     ZEUS analysis/H1 data    ZEUS analysis/H1 data
     Here we see the effect of differences in the   compared to
     data, recall that the gluon is not directly    H1 analysis/H1 data
     measured (no jets)
     The data differences are most notable in        Here we see the effect
     the large 96/97 NC samples at low-Q2 The        of differences of
     data are NOT incompatible, but seem to          analysis choice - form
     ‘pull against each other’                       of parametrization at
                                                     Q2_0 etc
     IF a fit is done to ZEUS and H1 together
     the χ2 for both these data sets rise
     compared to when they are fitted
     separately………..
See if you can spot
the data differences
between ZEUS/H1 at
low Q2..It is mostly in
slope.
Look at the effect of ADDING H1 data to the ZEUS data in the ZEUS PDF analysis-
  the OFFSET method is used for the correlated systematic errors




       ZEUS ONLY                     ZEUS+H1
 Adding H1 data does NOT significantly improve errors on the gluon -
 statistical uncertainty improves - but systematic uncertainty does not -χ2
 for each data set increases- and OFFSET errors reflect this
ZEUS ONLY                  ZEUS+H1
Whereas adding H1 to ZEUS data brings no big improvement for the sea and
gluon determination, it does bring improvement to the high-x valence
distributions, where statistical errors dominate




 The ZEUS and H1 high-Q2 data are also seem more compatible – there must
 be an advantage in having a joint H1/ZEUS data set?
So it is hoped that combining the data sets could bring real advantages in
   decreasing the PDF errors, if the low-Q2 discrepancies in the data sets can be
   resolved.

How could this be done?

Any combination of the data points would have to be done accounting for the
   correlated systematic errors

One could use the HESSIAN method
Essentially the Hessian method of combination can swim each experiment towards
   the other within the tolerance of the systematic errors of each data set.


Let’s remind ourselves what the Hessian method and Offset methods are in PDF
   fitting……
Experimental systematic errors are correlated between data points, so the correct
form of the χ2 is

               χ 2 = Σi   Σj [ FiQCD(p) – Fi MEAS] Vij-1 [ FjQCD(p) – FjMEAS]
                            Vij = δij(бiSTAT)2 + Σλ ΔiλSYS ΔjλSYS
    Where )i8SYS is the correlated error on point i due to systematic error source λ
                    It can be established that this is equivalent to
                  χ2 = 3i [ FiQCD(p) – 38 slDilSYS – Fi MEAS]2 + 3 sl2

                                      (siSTAT) 2

 Where s8 are systematic uncertainty fit parameters of zero mean and unit variance
 This form modifies the fit prediction by each source of systematic uncertainty
                        How ZEUS uses this: OFFSET method


•   Perform fit without correlated errors (sλ = 0) for central fit
•   Shift measurement to upper limit of one of its systematic uncertainties (sλ = +1)
•   Redo fit, record differences of parameters from those of step 1
•   Go back to 2, shift measurement to lower limit (sλ = -1)
•   Go back to 2, repeat 2-4 for next source of systematic uncertainty
•   Add all deviations from central fit in quadrature (positive and negative deviations
    added in quadrature separately)
•   This method does not assume that correlated systematic uncertainties are
    Gaussian distributed


Of course it is actually done in a very smart quick way using matrices, follwing
    Botje
                                  HESSIAN method
•   Allow sλ parameters to vary for the central fit
•   The total covariance matrix is then the inverse of a single Hessian matrix
    expressing the variation of χ2 wrt both theoretical and systematic uncertainty
    parameters.
•   If we believe the theory why not let it calibrate the detector(s)? Effectively the
    theoretical prediction is not fitted to the central values of published experimental
    data, but allows these data points to move collectively according to their
    correlated systematic uncertainties
•   The fit determines the optimal settings for correlated systematic shifts sλ such
    that the most consistent fit to all data sets is obtained. In a global fit the
    systematic uncertainties of one experiment will correlate to those of another
    through the fit
•   We must be very confident of the theory to trust it for calibration– but more
    dubiously we must be very confident of the model choices we made in setting
    boundary conditions to the theory
•   CTEQ use this method but then raise the χ2 tolerance to Δχ2=100 to account for
    inconsistencies between data sets and model uncertainties. H1 use it on their
    own data only with Δχ2=1
The HESSIAN method does give a
smaller estimated of the PDF errors than
the OFFSET method if you stick to
Δχ2=1
Comparison off HESSIAN and OFFSET
methods for ZEUS-JETS fit
However it gives larger model errors,
because each change of model
assumption can give a different set of
systematic error parameters, and thus a
different estimate of the shifted positions
of the data points.
Compare the latest H1 and ZEUS PDFs
–SEE next slide—in the end there is no
great advantage in the Hessian method..
                                              For the gluon and sea distributions
                                              the Hessian method gives a much
                                              narrower error band. Equivalent to
                                              raising the Δχ2 in the Offset
                                              method to 50.
Compare the latest H1 and ZEUS PDFs
–in the end there is no great advantage
in the Hessian method for the ZEUS-
ONLy or H1-ONLY PDF fits, because
the model dependence ‘cancels it out’.


But the current proposal is not to do a
Hessian PDF fit of both data sets BUT
to do a Hessian fit to combine the data
points without model assumptions..
ASIDE: I Have always distrusted the Hessian method – WHY?
Because the fitted values of the systematic error parameters change A LOT according
   to model assumptions and according to the different data sets used in the fit.
e.g. one is using the fit to calibrate the data, and one PDF analysis tells us that the
   correct setting for our RCAL energy scale is up by 2.4%, whereas another PDF
   analysis tells us that it is down by 1.8% - they can’t both be true- compare CTEQ
   and ZEUS-S global fit analyses (both done by Hessian method) for ZEUS
   systematic error parameters for the NC 96/97 data set
                         Zeus sλ         CTEQ6             ZEUS-S
                         1               1.67              -0.36
                         2               -0.67             1.17
                         3               -1.25             1.20
                         4               -0.44             0.40
                         5               0.00              0.32
                         6               -1.07             0.39
                         7               1.28              -1.40
                         8               0.62              0.20
                         9               -0.40             0.04
                         10              0.21              -0.06
So to return to the idea of combining or averaging the ZEUS/H1 data
accounting for the correlated systematic errors ….
         Using the Hessian method………. without any theoretical model.
                                What does this mean? Briefly
•For each cross-section measurement (NC e+/e- CCe+/e-), each x,Q2 point must
have a true value of the cross-section
•Let this true value be a parameter of a new ZEUS+H1 averaging fit, ie there is one
parameter for each x,Q2 point
•We now have at least two measurements –one from ZEUS one from H1 to
determine this parameter (sometimes, eg for e+ p, there maybe more than one data set
per experiment –e+ p 96/97 and e+ p 99/00)

•The systematic error parameters, sλ, for each experiment, must also be
parameters of this fit and all of the x,Q2 points for all of the data sets are fitted at
once so that correlated systematic errors between data points, and between data
sets, are included.
•E.G For NC e+p 96/97 there are ~250 x,Q2 points per expt. So there will be 250
parameters for the true values of the cross section and ~20 systematic
parameters (~10 per expt.). These are fitted to the ~500 total data points.
Essentially the Hessian method of combination swims each experiment towards the
   other within the tolerance of the systematic errors of each data set.
Technical matters:
•   Have agreed the exact ZEUS and H1 data sets to be used with S. Glazov of H1
•   Have agreed treatment of correlations within each experiment
•   H1/ ZEUS measurements are not in fact at the same x,Q2 values so need to
    agree x,Q2 grid: so used an H1 optimized grid and checked with a ZEUS
    optimized grid
•   Points which are Not on this grid must be swum to it, used H1’s fractal fit to do
    the swimming. However results are not sensitive to the grid choice and hence not
    sensitive to the swimming procedure
                              SO what does it look like?
It has 1153 data points: ZEUS+H1
548 free parameters for all the x,Q2 points of the grid for the 4 xsecns (NC/CC e+/e-)
Plus 18 (H1) + 26 (ZEUS) independent systematic parameters, sλ
Χ2=579 for (1153-548-44)=561 degrees of freedom
                                                  CC e-
                                                  Red is H1
                                                  Green is ZEUS
                                                  Black is the HERA average
                                                  – slightly displaced so you
                                                  can see the size of its error
                                                  compared to the input
                                                  ZEUS/H1 points
Q2=500                     Q2=1000


                                                  CC e+
                                                  Red is H1 94/97
                                                  Green is H1 99/00
                                                  Blue is ZEUS 94/97
                                                  Yellow is ZEUS 99/00
                                                  Black is the HERA average
Averaging does not favour one expt or the other
                                                NC e-
                                                Red is H1
                                                Green is H1 Fl
                                                Blue is ZEUS
                                                Black is the HERAaverage–
                                                slightly displaced so you
Q2=250                    Q2=2000               can see the size of its error
                                                compared to the input
                                                ZEUS/H1 points
                                                NC e+
                                                Red is H1 bulk 96/97
                                                Green is H1 mb 96/97
                                                Blue is H1 highq2 96/97
                                                Yellow is H1 99/00
Q2=90                     Q2=650
                                                Diamonds are ZEUS 96/97
                                                Squares are ZEUS 96/97
 Averaging does not favour one expt or the other Triangles are ZEUS 99/00
                                                Full Black is the HERA average
                                               NC e+ at lower Q2
                                               Red is H1 bulk 96/97
                                               Green is H1 mb 96/97
                                               Blue is H1 highq2 96/97
                                               Yellow is H1 99/00
Q2=3.5                    Q2=6.5               Diamonds are ZEUS 96/97
                                               Squares are ZEUS 96/97
                                               Triangles are ZEUS 99/00
                                               Full Black is the HERA
                                               average
                                               – slightly displaced so you
                                               can see the size of its error
                                               compared to the input
Q2=15                     Q2=25                ZEUS/H1 points



 Averaging does favour H1 to some extent at Q2~ 15 - 65
                                Technical checks
  Here are the NC 96/97 ZEUS systematic error parameters as determined by
  the averaging fit, using the two different x,Q2 grids

                      NC96/97 systematic
                       Sλ, λ=1,10        ZEUSgrid        H1grid
                      1 zd1_e_eff           0.3           0.15
                      2 zd2_e_theta_a      -0.07          0.4
                      3 zd3_e_theta_b      -0.45         -0.21
                      4 zd4_e_escale        0.97          1.04
                      5 zd5_had1            0.36          0.31
                      6 zd6_had2            0.4           0.39
                      7 zd7_had3          -1.1           -0.62
                      8 zd8_had_flow       0.05           0.84
                      9 zd9_bg            -0.07          -0.38
                      10 zd10_had_flow_b -0.06           -0.26

Reasonable consistency between choices of grid-  see EXTRAS for comparison of
H1, ZEUS and combined points using the ZEUS grid
sλ shifts are not so big (see also next slide) – remember sλ = ±1`represents a one б shift
CC e+   CC e-
                No of standard devns the
                original data points are
                pulled by the fit
                Vs Q2 for each data set




NC e+   NC e-
                 This means sλ


            This means the
            uncertainty on sλ, Δsλ




i.e Δsλ, becoming smaller
Systematic               sλ       Δsλ
                                            Let’s look at ZEUS instead
1 zlumi1_zncepl       -1.2841     0.5836
20 zd1_e_eff           0.0372     0.7500    Large reductions in uncertainty Δsλ
21 zd2_e_theta_a        0.4317     0.6674   are highlighted
22 zd3_e_theta_b       -0.1718     0.7836   What we NEED is a large reduction
23 zd4_e_escale         1.0641    0.4874
24 zd5_had1             0.3632     0.5873
                                            in any systematic uncertainty which
25 zd6_had2            0.3600     0.6440    is a big contributor to the total
26 zd7_had3           -0.6905     0.7383    uncertainty
27 zd8_had_flow         0.8052    0.6519
                                            For example, there is an impressive
28 zd9_bg              -0.2694    0.4054
29 zd10_had_flow_b     -0.2623    0.1686    reduction in uncertainty in the photo-
30 zd11               -0.6408     0.5995    production background for the 96-97
31 z1nce-_e_scale       0.1555    0.9384    NC data
32 z2nce-_bg          -0.3000     0.9215
33 z3nce-_eff1         0.0076     0.9310
                                            How does this come about….see
34 z4nce-_eff2         0.3770     0.5543    next slide
35 z5nce-_vtx         -0.6828     0.9274    Large shifts i.e. large values of sλ are
36 z6nce-              0.2241     0.4158
                                            also highlighted- these are mostly in
37 z1cce-              0.1846     0.8409
38 z2cce-              0.1920     0.8687    normalisations
39 zlumi2_zccem       -0.7516     0.7739    And most of the normalisation shift is
40 zd5nc00             0.0835     0.9842    obtained by averaging ZEUS to itself
41 zd7nc00             0.1174     0.2068
                                            (e.g. 96/97 to 99/00) rather than to H1!
42 zd8nc00             0.3087     0.9258
43 zluminc           -1.8738     0.3755     - See EXTRAS
                       H1                 ZEUS




The fit calibrates one experiment against the other
Let’s see some results –HERA averaged data points for low Q2 NC e+
  Q2        x        б      Δб(stat) Δб(sys) Δб(tot)
 2.5000   0.0001   0.7426    0.0102   0.0073   0.0126
 2.5000   0.0002   0.7015    0.0195   0.0075   0.0209
 2.5000   0.0003   0.6427    0.0145   0.0068   0.0160
 2.5000   0.0005   0.6075    0.0137   0.0070   0.0154   Now that all data points have
 2.5000   0.0008   0.5616    0.0162   0.0061   0.0173   been averaged the systematic
 2.5000   0.0016   0.5214    0.0140   0.0059   0.0152
 2.5000   0.0050   0.4104    0.0161   0.0057   0.0171   errors are smaller than the
 3.5000   0.0001   0.8875    0.0130   0.0091   0.0158   statistical for all data points-
 3.5000   0.0002   0.8330    0.0122   0.0086   0.0149
 3.5000   0.0003   0.7835    0.0122   0.0082   0.0147    including those at low-Q2,
 3.5000   0.0005   0.7290    0.0117   0.0083   0.0143   where systematic error was up
 3.5000   0.0008   0.6544    0.0126   0.0070   0.0144   to 3 times statistical in the
 3.5000   0.0013   0.6136    0.0119   0.0073   0.0140
 3.5000   0.0025   0.5266    0.0062   0.0054   0.0083   separate data sets
 3.5000   0.0080   0.4409    0.0076   0.0054   0.0093
 5.0000   0.0001   1.0376    0.0151   0.0109   0.0186
 5.0000   0.0002   0.9803    0.0143   0.0106   0.0178
 5.0000   0.0003   0.9138    0.0145   0.0091   0.0171
 5.0000   0.0005   0.8222    0.0125   0.0084   0.0151
 5.0000   0.0008   0.7193    0.0135   0.0080   0.0157
 5.0000   0.0013   0.6760    0.0130   0.0091   0.0158
 5.0000   0.0020   0.6277    0.0123   0.0069   0.0140
 5.0000   0.0040   0.5492    0.0092   0.0061   0.0111
 5.0000   0.0130   0.4220    0.0137   0.0046   0.0145

Hence a new PDF fit can be done which should be much less sensitive to treatment
of systematics… I’ve simply added errors in quadrature
                              New PDF fit to the HERA
                              averaged inclusive xsecn
                              data using the ZEUS fit
                              analysis
                              Compare to the published
                              PDF shapes for H1 PDF 2000
                              and ZEUS-JETS
The gluon of the HERA                                           The d-valence of the
averaged data set is more     The sea and the u-valence         HERA averaged data set
like the ZEUS published       are very similar                  is not really like either
gluon                                                           ZEUS or H1 published d-
                                                                valence
 The χ2 of this 11 parameter quadrature fit are
 1.23 for 34 e+ CC data points - errors underestimated? Hence small d valence PDF error
 0.59 for 31 e- CC data points – errors overestimated?
 1.02 for 318 e+ NC data points
 0.81 for 145 e- NC data points
Compare this new PDF fit to
the HERA averaged
inclusive xsecn data
To a PDF fit to H1 and
ZEUS inclusive xsecn data
NOT averaged –where we
get more of a compromise
between ZEUS and H1
published PDF shapes
The PDF fit to H1 and ZEUS
not averaged was done by
the ZEUS analysis using the
OFFSET method ..
We could consider doing it
by the HESSIAN method-
allowing the systematic
errors parameters to be
detemined by the fit
Compare the PDF fit to the
HERA averaged inclusive
xsecn data
To the PDF fit to H1 and
ZEUS inclusive xsecn data
NOT averaged –done by the
ZEUS PDF analysis but
using the HESSIAN method
As expected the errors are
much more comparable
But the central values are
rather different
This is because the
systematic shifts determined
by these fits are different
systematic shift sλ     QCDfit Hessian ZEUS+H1         GLAZOV theory free ZEUS+H1

 zd1_e_eff                      1.65                   0.31
 zd2_e_theta_a                 -0.56                    0.38
 zd3_e_theta_b                  -1.26                 -0.11
 zd4_e_escale                   -1.04                    0.97
 zd5_had1                       -0.40                   0.33
 zd6_had2                       -0.85                   0.39
 zd7_had3                        1.05                  -0.58
 zd8_had_flow                   -0.28                   0.83
 zd9_bg                         -0.23                  -0.42
 zd10_had_flow_b                0.27                   -0.26
h2_Ee_Spacal                   -0.51                     0.61
h4_ThetaE_sp                  -0.19                   -0.28
h5_ThetaE_94                    0.39                  -0.18
h7_H_Scale_S                   0.13                    0.35
h8_H_Scale_L                   -0.26                   -0.98
h9_Noise_Hca                   1.00                   -0.63
h10_GP_BG_Sp                    0.16                   -0.38
h11_GP_BG_LA                  -0.36                     0.97

A very boring slide- but the point is that it may be dangerous to let a QCDfit determine
   the optimal values for the systematic shift parameters.
And using Δχ2=1 on such a fit gives beautiful small PDF uncertainties but a central
   value which is far from that of the theory free combination!!..
       Now consider model dependence of PDF fit to HERA
       averaged data
       First a reminder of what goes into the standard fit



                                                 No sensitivity to shape of Δ= dbar-ubar
   •    xuv(x) = Au  xav    (1-x)bu
                                (1 + cu x)       so AΔ fixed consistent with Gottfried
        xdv(x) = Ad  xav    (1-x)bd
                                (1 + cd x)
                       as
        xS(x) = As x (1-x)       bs              sum-rule
   •    xg(x) = Ag xag (1-x)bg (1 + cg x)        Assume sbar = (dbar+ubar)/4
        xΔ(x) = AΔ x0.5 (1-x)bs+2                consistent with neutrino dimuon data

Au, Ad, Ag are fixed by the number and momentum sum-rules
au=ad=av for low-x valence -11 params


Call this the STANDARD fit
                               Model variations – see EXTRAS for dbar-ubar variationn
•   (1+cs x) term in the sea param.
•   (1+cg x + eg√x) in the gluon param.
•   xdv(x) = Ad xav (1-x)bd (1 + cd x) + B xuv(x) . x(1+x) extra term in d-valence
•   au￿ for low-x valence
      ad
•   (1+cu x +eu √x) and (1+cd x +ed√x) for both uv and dv param.
       These variations are displayed in the next few plots in the order
       0. standard                  1. sea x term         2. glue √x term
       3. dv/uv term                4. low-x valence     5. valence √x terms
       There is no dramatic change in central values of the PDFs

     Note the addition of extra freedom does not improve χ2 much
     Standard χ2 is 504.7 for 529 data points, 11 params
            0. Δχ2=0                   1. Δχ2= -0.8            2. Δχ2= -10 (but nonsense-
                                                            high x gluon becomes negative!)
           3. Δχ2=-0.5                4. Δχ2=-0.6           5. Δχ2= -7 (all from u valence)
                                Conclusions


•The averaging idea looks promising
•It is better to combine at the level of the data, than within the PDf fit itself
•The resultant PDFs look promising
•Model dependence does not seem severe
                              EXtras
•   Glazov’s own plots of how the HERA average data compares to H1 and
    ZEUS data points
•   Some plots which show that choice of grid, and hence swimming
    approximations, do not count for much
•   Slides on averaging ZEUS within itself (i.e. e+ 96/97 and 99/00) as
    compared to averaging ZEUS and H1
•   Further model dependence variations of the PDF fit to the HERA averaged
    data
                                                      CC e-
                                                      Red is H1
                                                      Green is ZEUS
                                                      Black is the average



Q2=530                       Q2=950
                                                       CC e+
                                                       Red is H1 94/97
                                                       Green is H1 99/00
                                                       Blue is ZEUS 94/97
                                                       Yellow is ZEUS 99/00
                                                       Black is the average

Alternative results using ZEUS grid points - Choice of grid is not so crucial
                                                      NC e-
                                                      Red is H1
                                                      Green is H1 Fl
                                                      Blue is ZEUS
Q2=250                       Q2=2000
                                                      NC e+
                                                      Red is H1 bulk 96/97
                                                      Green is H1 mb 96/97
                                                      Blue is H1 highq2 96/97
                                                      Yellow is H1 99/00
                                                      Diamonds are ZEUS 96/97

                             Q2=650                   Squares are ZEUS 96/97
Q2=90
                                                      Triangles are ZEUS 99/00

  Alternative results using ZEUS grid points - Choice of grid is not so crucial
                                                       NC e+ at lower Q2
                                                       Red is H1 bulk 96/97
                             Q2=6.5                    Green is H1 mb 96/97
Q2=3.5
                                                       Blue is H1 highq2 96/97
                                                       Yellow is H1 99/00
                                                       Diamonds are ZEUS 96/97
                                                       Squares are ZEUS 96/97
                                                       Triangles are ZEUS 99/00


Q2=15                        Q2=25




    Alternative results using ZEUS grid points - Choice of grid is not so crucial
1 zlumi1_zncepl       -1.2841     0.5836    1 zlumi1_zncepl           -0.6889 0.8305
20 zd1_e_eff           0.0372     0.7500    20 zd1_e_eff             -0.0320 0.8939
21 zd2_e_theta_a        0.4317     0.6674   21 zd2_e_theta_a          -0.0104 0.9904
22 zd3_e_theta_b       -0.1718     0.7836   22 zd3_e_theta_b           -0.5166 0.8447
23 zd4_e_escale         1.0641    0.4874    23 zd4_e_escale            1.3358 0.6843
24 zd5_had1             0.3632     0.5873   24 zd5_had1                0.1296 0.7275
25 zd6_had2            0.3600     0.6440    25 zd6_had2                0.3411 0.7531
26 zd7_had3           -0.6905     0.7383    26 zd7_had3               -0.5524 0.9721
27 zd8_had_flow         0.8052    0.6519    27 zd8_had_flow            0.3981 0.9790
28 zd9_bg              -0.2694    0.4054    28 zd9_bg                0.0904 0.9970
29 zd10_had_flow_b     -0.2623    0.1686    29 zd10_had_flow_b      0.2050 0.3440
30 zd11               -0.6408     0.5995    30 zd11                0.0000 1.0000
31 z1nce-_e_scale       0.1555    0.9384    31 z1nce-_e_scale        0.1372 0.9806
32 z2nce-_bg          -0.3000     0.9215    32 z2nce-_bg              -0.1003 0.9639
33 z3nce-_eff1         0.0076     0.9310    33 z3nce-_eff1             0.0460 0.9739
34 z4nce-_eff2         0.3770     0.5543    34 z4nce-_eff2             0.1471 0.6959
35 z5nce-_vtx         -0.6828     0.9274    35 z5nce-_vtx             0.0000 1.0000
36 z6nce-              0.2241     0.4158    36 z6nce-               0.5106 0.5940
37 z1cce-              0.1846     0.8409    37 z1cce-              0.3715 0.9254
38 z2cce-              0.1920     0.8687    38 z2cce-              0.0837 0.9408
39 zlumi2_zccem       -0.7516     0.7739    39 zlumi2_zccem           0.0000 1.0000
40 zd5nc00             0.0835     0.9842    40 zd5nc00                0.1649 0.9907
41 zd7nc00             0.1174     0.2068    41 zd7nc00                0.2065 0.2629
42 zd8nc00             0.3087     0.9258    42 zd8nc00                0.0650 0.9547
43 zluminc           -1.8738     0.3755     43 zluminc00             -1.6620 0.6677

  ZEUS against H1                            ZEUS against itself
Q2           x      б     Δб(stat) Δб(sys) Δб(tot)   Q2           x      б      Δб(stat)   Δб(sys)   Δб(tot)
 3.5000   0.0001   0.9818 0.0384 0.0320 0.0500       3.5000   0.0001   1.0764   0.0509     0.1286     0.1383
 3.5000   0.0001   0.9385 0.0158 0.0129 0.0204       3.5000   0.0001   0.9660   0.0275     0.0311     0.0415
 3.5000   0.0001   0.8874 0.0130 0.0091 0.0158       3.5000   0.0001   0.9014   0.0250     0.0197     0.0318
 3.5000   0.0002   0.8333 0.0122 0.0087 0.0149       3.5000   0.0002   0.8483   0.0221     0.0188     0.0290
 3.5000   0.0003   0.7840 0.0122 0.0082 0.0147       3.5000   0.0003   0.8094   0.0231     0.0182     0.0295
 3.5000   0.0005   0.7296 0.0117 0.0083 0.0143       3.5000   0.0005   0.7291   0.0227     0.0166     0.0281
 3.5000   0.0025   0.5269 0.0062 0.0054 0.0083       3.5000   0.0025   0.5247   0.0086     0.0119     0.0146
 3.5000   0.0080   0.4413 0.0076 0.0054 0.0093       3.5000   0.0080   0.4680   0.0090     0.0138     0.0165


    ZEUS averaged to H1                                  ZEUS averaged to itself




     Averaging with H1 is much better than just averaging ZEUS to itself
     Not only is there a stronger reduction in statistical error when H1 is added
     there is a much more significant reduction in systematic error
                                                    Extra model dependence:
                                                    (1+cd x +ed√x) in d-valence
                                                    alone




Extra model dependence: dbar – ubar not forced to
zero as x → 0

				
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