HERA I - Preliminary H1 and ZEUS QCD Fit

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HERA I - Preliminary H1 and ZEUS QCD
Fit 28/03/08
A.Cooper-Sarkar, R.Devenish, C.Gwenlan,
K.Nagano, J.Ferrando, Y.Ri, E.Tassi, J.Feltesse,
A.Glazov, M.Klein, G.Li, B. Olivier, V.Radescu,
E.Rizvi, V.Shekelian, Z.Zhang

• Choice of data set
• Central fit choice of parametrization
• Central fit choice of error treatment
• Central fit choice of model assumptions
• Quality of fit to data
• PDFs plus experimental errors
• PDFs plus model uncertainties
• Comparison to older H1/ZEUS fits, comparison to
  CTEQ, MRST
• Model uncertainty investigations
• Model Variations

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Preliminary QCD Fit to Combined H1-ZEUS HERA-I
data

• A.Cooper-Sarkar, R.Devenish, C.Gwenlan, K.Nagano,
  J.Ferrando, Y.Ri, E.Tassi,
• J.Feltesse, A.Glazov, M.Klein, G.Li, B. Olivier,
  V.Radescu,
• E.Rizvi, V.Shekelian, Z.Zhang

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QCD Fits of the preliminary combined data set
presented at LP07
Input data sets Published HERA I cross sections
NC and CC e, e- 1.5 lt Q2 lt 30000 GeV2 ? 240
pb-1
1.5
With H1 NC MB (Q2 lt 12 GeV2) moved up by 3.4
after reanalysis of luminosity
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Possible forms of PDF parametrization H1 style
Published H1 PDF2000
New H1-style parametrization optimised for
combined data set
Optimization means starting without D,E,F
parameters and adding parameters until there is
no further ?2 advantage
PDFs gluon, Uuc, Ubarubarcbar, Ddsb,
Dbardbarsbarbbar Sea flavour break-up at Q0 s
fsD, cfcU AU(1-fs)/(1-fc)AD
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Possible forms of PDF parametrization ZEUS style
ZEUS-JETS published
New ZEUS-JETS optimized for combined data set
PDFs gluon, uv, dv, Sea useaubardseadbarssb
arccbar Sea flavour break-up at Q0 sbar
(dbarubar)/4, charm dynamically generated,
dbar-ubar fixed to fit E866 data
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Possible forms of PDF parametrization inbetween
Original inbetween parametrization
Lim x?0 u/d ?1
inbetween parametrization optimized to combined
data set
Lim x?0 u/d ?1
PDFs gluon, uv, dv, Ubarubarcbar,
Dbardbarsbarbbar Sea flavour break-up at Q0 s
fsD, cfcU AUbar(1-fs)/(1-fc)ADbar Can
also dynamically generate charm, but need to keep
AUbar to ADbar relationship as here
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For each of the old parametrizations, which have
non-zero D parameter for the gluon, there are two
minima straight gluon and humpy gluon
solution.
Which look rather like the published ZEUS and H1
gluons respectively! For the H1/ZEUS combined
data set the ?2 of the straight solution is
always lower by about 10 ?2 points. For the H1
data set alone the humpy gluon had the lower
?2, whereas for the ZEUS data set alone the
straight gluon had the lower ?2
This ?2 table compares humpy and straight gluon
solutions for the old parametrizations and the
straight solution for the new parametrizations
using a ?2 definition where all 47 systematic
errors of the combined data set are added in
quadrature.
Table from J.Feltesse excellent agreement on all
results in this talk
433.6
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Choice of parameterization

• All parametrizations give an excellent ?2 /degree
  of freedom
• Inbetween 431.9/563(573-10)
• H1 param 434.7/563(573-10)
• ZEUS_Jet 433.6/562(573-11)
• Chosen central parameterization optimized
  Inbetween
• Motivations
• Less model dependence on B parameters than in H1
  param.
• No need for an additional input (ubar-dbar) x
  distribution as in ZEUS-Jet param
• Most conservative errors.
• It is inspired by both H1 and ZEUS
  parameterizations.
• The two other parameterizations AND humpy
  solution for inbetween the are considered in the
  model variations

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Choice of treatment of systematic errors
Reminder combining H1 ZEUS cross-sections Ful
l account taken of systematic uncertainties of H1
and ZEUS measurements, including correlations
43 separate sources plus 4 procedural
uncertainties 44   photoproduction assumed
correlated in H1-ZEUS 45  FL is set to 0 for
Centre-of-Mass Energy shift 46  Difference
between "all relative" -- "global normalisations
relative" treatement 47  Extra 1 for ylt0.02
NC data to take into account correlated HFS
simulation   (based on hadronic energy scale
correlations study)
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47 systematic errors added to statistical
quadratically ?2 428.0
47 systematic errors treated by Hessian method
?2553.1
43 original sources of systematic errors added to
statistical quadratically and 4 procedural errors
Offset ?2476.7
Central values very similar, uncertainties
largest for OFFSET method, we chose this because
it is most conservative. Note there is not much
difference between these different error
treatments since systematic errors not so
big Proposal that these ?2 values be made
preliminary, all are for 563 degrees of freedom
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Theoretical framework
NLO DGLAP evolution Facttorisation and
renormalisation scales Q2 Zero-mass variable
flavour number heavy quark scheme
Model assumptions Which will be varied to assess
model uncertainty
Q02 4 GeV2 input scale Q2min 3.5 GeV2
minimum Q2 of input data fs 0.33D strange sea
fraction, means s0.5d fc 0.15U charm sea
fraction, means c0.176u mc1.4 mass of charm
quark mb4.75 mass of beauty quark as(Mz)
0.1176 PDG2006 value Form of the parametrization
in between/ H1/ ZEUS-JETS/ humpy
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PDF fit RESULTSlets call it the HERA-I
PDFComparison to HERA combined data
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HERA I - Preliminary H1 and ZEUS QCD Fit
Preliminary status requested
Blow up just three x values to see older
ZEUS-JETS PDF and H12000 PDF plus new HERA-I PDF
New HERA-I PDF fit predictions vs. H1/ZEUS
combined data for NC ep. Experimental
uncertainties on the PDF fit predictions are
included but can barely be be resolved.
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HERA I - Preliminary H1 and ZEUS QCD Fit
Preliminary status requested
New H1/ZEUS combined PDF fit predictions vs.
H1/ZEUS combined data for NC ep and e-p at low
Q2. Experimental and model uncertainties on the
PDF fit predictions are included but barely be
resolved
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HERA I - Preliminary H1 and ZEUS QCD Fit
Preliminary status requested
New H1/ZEUS combined PDF fit predictions vs.
H1/ZEUS combined data for NC ep and e-p at high
Q2. Experimental and model uncertainties on the
PDF fit predictions are included but cannot be
resolved
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HERA I - Preliminary H1 and ZEUS QCD Fit
Preliminary status requested
New H1/ZEUS combined PDF fit predictions vs.
H1/ZEUS combined data for NC ep and e-p at high
Q2. Experimental and model uncertainties on the
PDF fit predictions are included
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HERA I - Preliminary H1 and ZEUS QCD Fit
CC ep (left) e-p (right) compared to older
ZEUS-JETS PDF and H12000 PDF plus new HERA-I PDF.
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PDF fit RESULTSPDFs experimental and model
errorsComparison to other PDFs
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First consider experimental uncertainties
HERA I PDFs
New H1/ZEUS combined PDFs with experimental
uncertainty bands from statistical errors plus 43
sources of systematics in quadrature plus 4
procedural systematics OFFSET
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Now add 6 sources of model dependence

• mc 1.3 ? 1.55 GeV variation of mass of c quark
• mb 4.3 ? 5.0 GeV variation of mass of b quark
• fs 0.25? 0.40 variation of strange sea
  fraction at Q0
• fc 0.10? 0.20 variation of charm sea
  fraction at Q0
• Q02 2.0 ?6.0 GeV2 variation of starting scale
• Qmin2 2.5?5.0 GeV2 variation of cuts on the data
  included

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Now add 6 sources of model dependence
HERA I PDFs
HERA I PDFs
New H1/ZEUS combined PDFs with total experimental
uncertainty plus model uncertainty
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Compare to previous ZEUS/H1 results
Preliminary status requested
HERA I PDFs
Resolution of previous discrepancies, improvement
in level of uncertainty
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Compare to CTEQ and MRST analyses
Do we want preliminary status for these?
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Compare to CTEQ and MRST analyses 2008
Note MSTW08 is as yet unpublished- I have a
pre-release
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Look at our results in more detail vs Q2
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HERA I PDFs
HERA I PDFs
Preliminary status requested
New H1/ZEUS combined PDFs with total experimental
uncertainty bands plus model uncertainty bands AT
THE STARTING SCALE Q20 4 GeV2
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HERA I PDFs
HERA I PDFs
Preliminary status requested
New H1/ZEUS combined PDFs with total experimental
uncertainty bands plus model uncertainty bands
At Q2 10 GeV2
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HERA I PDFs
HERA I PDFs
Preliminary status requested
New H1/ZEUS combined PDFs with total experimental
uncertainty bands plus model uncertainty bands
from 6 sources of model variation AT Q20 100
GeV2 . Note how uncertainties are decreasing
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HERA I PDFs
HERA I PDFs
Preliminary status requested
New H1/ZEUS combined PDFs with total experimental
uncertainty bands plus model uncertainty bands
from 6 sources of model variation AT Q20
10000 GeV2 . At scales relevant to LHC physics
uncertainties are impressively small.
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Checks between ZEUS and H1
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Check analysis
H1 Package
ZEUS Package
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Investigate model uncertainties
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Include only variation of charm mass and beauty
mass mc1.35?1.5 GeV and mb 4.3 ?5.0 GeV This
model dependence is invisible
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Include only variation of strange fraction fs
0.25 ?0.40 Makes very little difference in the
total Sea, but affects sea flavour break-up
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Include only variation of charm fraction fc 0.10
?0.20 A smaller effect than fs makes very little
difference in the total Sea, but affects sea
flavour break-up
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Include only variation of starting scale Q02 2 ?
6 GeV2 Has a small asymmetric effect on PDF
ucertainties
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Include only variation of minimum Q2 of fitted
data Qmin2 2.5 ? 5 GeV2 Has an even smaller
asymmetric effect on PDF ucertainties
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We illustrate some of the other choices as
variations compared to our central value

• aS(Mz) 0.1156 ? 0.1196
• New H1 optimized parametrization
• New ZEUS-JETS optimized parametrization
• Old in-between parametrization with humpy
  gluon solution
• Use of massive variable flavour number scheme-
  cannot be checked by both ZEUS and H1 yet, so no
  preliminary request

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HERA I PDFs
HERA I PDFs
Preliminary status requested
Comparison of central fit plus total
uncertainties to variations with as(Mz)0.1156
(left) and 0.1196 (right) Confirms what weve
already seen-variation is outside the gluon error
bands even when other model dependence is
accounted.
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HERA I PDFs
HERA I PDFs
Preliminary status requested
Comparison of central fit plus total
uncertainties to parametrization variation using
New H1 optimised parametrization Marginally
outside normal error bands for valence even when
other model dependence is accounted (but note
this is at low x where valence isnt very
significant)
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HERA I PDFs
HERA I PDFs
Preliminary status requested
Comparison of central fit plus total
uncertainties to parametrization variation using
New ZEUS-JETS optimised parametrization Inside
error bands if other model dependence is
accounted
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HERA I PDFs
HERA I PDFs
Preliminary status requested
Comparison of central fit plus total
uncertainties to parametrization variation using
the humpysolution for the h1/zeus
parametrization. At Q210 (left) and Q24
(right)GeV2 where the humpy structure is more
visible. Marginally outside normal error bands
for valence more than for gluon! even when other
model dependence is accounted (but note this is
at low x where valence isnt very significant)
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Finally we may be criticized for the use of a
zero-mass scheme. Comparison of central fit plus
total uncertainties to variation of heavy quark
scheme using massive variable flavour number
scheme of Thorne. This cannot yet be checked by
both H1 and ZEUS
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Summary

• An immense amount of work has been done to
  resolve differences between ZEUS and H1 PDF
  fitting analyses
• Agreement has been reached on procedure AND
• Agreement has been reached on fit results
• We wish to make preliminary
• Plots of the new HERA-I PDF fit compared to the
  new HERA-I combined data
• Plots of the PDFs u-valence, d-valence, gluon
  and total Sea
• U, D, Ubar, Dbar
• with experimental uncertainty bands and model
  uncertainty bands
• and additional plots showing variations NOT
  added into model uncertainty
• Plots of the PDFs in comparison to previous ZEUS
  and H1 analyses
• Plots of the PDFs in comparison to CTEQ6 and
  MRST04 analyses

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EXTRAS Questions asked by ZEUS and H1 already
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Compare to previous ZEUS-JETS fit with errors
on both
The extra data and reduction of systematics
constrains gluon better at low-x, which by the
momentum sum-rule constrains it better at high-x.
Hence it is precise even without jets.
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What would it look like with the parametrization
uncertainty added in
Illustration of the difference between using 6 or
7 sources of model uncertainty On the right the
7th uncertainty from form of parametrization h1
vs zeus-jet is added in.
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How much of the change is data and how much is
the parametrization the plots below are ALL with
the new combined data- parametrization make a
large difference to the error estimate
ZEUS-Jets Parametrization in between
H1 parametrization
Central values are really very similar- quite
remarkable since ZEUS and H1 parametrizations are
not- however the size of errors differs, with in
between being the most conservative
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Other extras
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Now in terms of ubar, dbar, sbar, cbar
xubar
xcbar
xdbar
xsbar
ZEUS-Jets Parametrization in between
H1 parametrization
The similarity of these is perhaps even more
remarkable given the different treatment of
charm- clearly the fixed fraction fc0.15 is
about right compared to dynamical turn on at
Q2mc2
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Compare to previous ZEUS and H1 analyses in a
different style
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And we could have added in Include only variation
of as (Mz) 0.1156 ? 0.1196 (PDG2006) Looking at
this uncertainty alone it affects only the gluon
PDF
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And if we add in the variation of as (Mz) to the
other 6 model uncertainties. I chose not to add
this in since MRST(MSTW) and CTEQ both use fixed
alphas and I want the public to compare like
with like.
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Comparison of central fit plus total
uncertainties to variations with alphas0.1156
(left) and 0.1196 (right) U D plots
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There is another model uncertainty that we could
add in- the variation if one uses different forms
of parametrization H1 style newly optimized
paremetrization and ZEUS-JETs style newly
optimized parametrization. Looking at this
uncertainty alone there is a small asymmetric
effect, most visible in valence distributions.
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Illustration of the difference between using 6 or
7 sources of model uncertainty On the right the
7th uncertainty from form of parametrization h1
vs zeus-jet is added in. There is excellent
agreement with J Feltesse. I chose not to add
this in because its not the same kind of
variation as the others- varying our new
parametrization to two others is not an up and
down variation!
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Comparison of central fit plus total
uncertainties to parametrization variation using
the humpysolution for the h1/zeus
parametrization
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NC ep low and high Q2 from Enrico, only
experimental errors
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NC e-p high Q2 from Enrico, only experimental
errors
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CC e-p and ep from Enrico, only experimental
errors
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Check analysis
H1 Package
ZEUS Package
Gluon PDF
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Check analysis
H1 Package
ZEUS Package
u-valence
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Check analysis
H1 Package
ZEUS Package
d-valence