ZEUS PDF analysis 2004 A'M CooperSarkar, Oxford Lowx 2004

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ZEUS PDF analysis 2004 A.M Cooper-Sarkar,
OxfordLow-x 2004

• New Analysis of ZEUS data alone using inclusive
  cross-sections from all of ZEUS data from HERA-I
  112pb-1
• Proton target data no heavy target or deuterium
  corrections
• Information on d-valence at high-x
• Analysis within one experiment well understood
  systematic errors
• New analysis of ZEUS data alone including jet
  data from inclusive jet production in DIS and
  dijet production from photoproduction
• Extraction of as and PDFs simultaneously
• ICHEP04 Paper 5-0294, hep-ph/0407309 (DIS2004)

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Deep Inelastic Scattering
Q2 -(k-k)2
xp
x momentum fraction of proton carried by
quark (HERA 10-6 1) Q2 resolving power of
probe
Now, after the HERA I phase (1994-2000) of
data-taking, the full set of e and e- inclusive
Neutral Current (NC) and Charged Current (CC)
cross sections are available for QCD analysis
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• HERA data covers a large region in (x,Q2)
  
• ? Also in relevant x-region for LHC physics

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The HERA contribution- at low-x

• F2 dominates cross section
• ? direct information on quarks
• Information on gluon and sea through QCD
  radiation (scaling violations)
  at low-x
• But higher-Q2 data have been accumulating?high-x
• And this matters for PDF fits?
• Consequences for low-x

BCDMS ?F2/F27
HERA ?F2/F230
Typically 2-3 precision
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• HERA at high Q2 ? Z0 and W/- exchanges become
  important
• for NC processes
• F2 3i Ai(Q2) xqi(x,Q2) xqi(x,Q2)
• xF3 3i Bi(Q2) xqi(x,Q2) - xqi(x,Q2)
• Ai(Q2) ei2 2 ei vi ve PZ (ve2ae2)(vi2ai2)
  PZ2
• Bi(Q2) 2 ei ai ae PZ 4ai ae vi ve
  PZ2
• PZ2 Q2/(Q2 M2Z) 1/sin2?W
• Z exchange gives a new valence structure
  function xF3 measurable from low to high x- on a
  pure proton target

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At High Q2 there are also significant
cross-sections for CC processes which give
flavour information
d2s(ep) GF2 M4W x (uc) (1-y)2x (ds)
d2s(e-p) GF2 M4W x (uc) (1-y)2x (ds)
dxdy
2px(Q2M2W)2
dxdy
2px(Q2M2W)2
uv at high x
dv at high x
Typical systematic uncertainties are 6
Measurement of high x, d-valence on a pure proton
target. NC processes dominantly measure u-
valence. Fixed target measurement of d-valence is
from Fe/Deuterium target needs corrections even
for Deuterium
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Both ZEUS (2004) and H1 (2003) now make PDF fits
to their own data MRST, CTEQ (and ZEUS 2002) make
global fits to HERA data, fixed target DIS data
etc. Where does the information come from in a
global fit compared to a HERA only fit ?
Mostly uv
some dv
Tevatron jet data?
ZEUS jet data?
ANALYSES FROM HERA ONLY ? Systematics well
understood ? measurements from our own
experiments !!! ? No complications from
heavy target Fe or D corrections
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Now use ALL inclusive cross-section data from
HERA-I 112 pb-1
96/97 ep NC 30 pb-1 2.7 lt Q2 lt 30000 GeV2
Eur.Phys.J. C21(2001)443 94-97 ep CC 33 pb-1
280. lt Q2 lt 30000 GeV2 Eur Phys J
C12(2000)411 98/99 e-p NC 16 pb-1 200 lt Q2 lt
30000 GeV2 Eur Phys J C28
(2003)175 98/99 e-p CC 16 pb-1 200 lt Q2 lt 30000
GeV2 Phys Lett B539(2002)197 99/00 ep NC
63 pb-1 200 lt Q2 lt 30000 GeV2
hep-ex/0401003- Phys.Rev.D 99/00 ep CC 61 pb-1
200 lt Q2 lt 30000 GeV2 Eur Phys J
C32(2003)16 ?2 Si FiNLOQCD(p) S? s? ?i?
sys Fi(meas)2 S? s?2
( si2stat si2unc) ?2 must
account for correlated systematic errors AND
normalizations Total of 33 sources of point to
point correlated errors and 4 normalizations Appli
ed conservatively by OFFSET method see J.Phys.G
28(2002) 2717
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• xuv(x) Au xav (1-x)bu (1 cu x)xdv(x) Ad
  xav (1-x)bd (1 cd x) xS(x) As xas
  (1-x)bs (1 cs x)xg(x) Ag xag (1-x)bg (1
  cg x)
• x?(x) x(d-u) A? xav (1-x)bs2

Recap of the method Parametrize parton
distribution functions PDFs at Q20 ( 7
Gev2) Evolve in Q2 using NLO DGLAP (QCDNUM
16.12) Convolute PDFs with coefficient
functions to give structure functions and hence
cross-sections Coefficient functions incorporate
treatment of Heavy Quarks by Thorne-Roberts
Variable Flavour Number Fit to data under the
cuts, W2 gt 20 GeV2 (to remove higher twist),
30,000 gt Q2 gt 2.7 GeV2 x gt 6.3 10-5
Model choices ? Form of parametrization at Q20,
value of Q20,, flavour structure of sea, cuts
applied, heavy flavour scheme
?Use of NLO DGLAP?
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Major source of model dependence is the form of
the parametrization at Q20
No ?2 advantage in more terms in the
polynomial No sensitivity to shape of ? d u A?
fixed consistent with Gottfried sum-rule - shape
from E866 Assume s (du)/4 consistent with ?
dimuon data

• xuv(x) Au xav (1-x)bu (1 cu x)xdv(x) Ad
  xav (1-x)bd (1 cd x) xS(x) As xas
  (1-x)bs (1 cs x)xg(x) Ag xag (1-x)bg (1
  cg x)
• x?(x) A? xav (1-x)bs2

These parameters control the low-x shape
These parameters control the high-x shape
These parameters control the middling-x shape
Au, Ad, Ag are fixed by the number and momentum
sum-rules auadav for low-x valence since there
is little information to distinguish ? 12
parameters for the PDF fit Now consider the
high-x Sea and gluon
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Consider the uncertainties for uv, dv, Sea and
glue in the ZEUS-S 2002 global fit
uv
dv
Sea
Gluon
High-x Sea and Gluon are considerably less well
determined than high-x valence (note log scales)
even in a global fit - this gets worse when
fitting ZEUS data alone
Compare the uncertainties for uv, dv, Sea and
glue in a fit to ZEUS data alone
uv and dv are now determined by the ZEUS highQ2
data not by fixed target data and precision is
comparable- particularly for dv Sea and gluon at
low-x are determined by ZEUS data with comparable
precision for both fits but at mid/high-x
precision is much worse
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• STRATEGY A Constrain high-x Sea and gluon
  parameters
• xf(x) A xa (1-x)b (1 c x)
• The fit is not able to reliably determine both b
  and c parameters for the Sea and the gluon
  these parameters are highly correlated
• We could either
• Choose a simpler parametrization xf(x) A xa
  (1-x)b (e.g H1, Alekhin)
• Fix parameter b to the value from the ZEUS-S
  global fit, and vary this value between the one s
  errors determined in that fit
• xf(x) A xa
  (1-x)b?b (1cx)
• Choice 1. would not allow structure in the mid x
  Sea/gluon distributions even in principle (recall
  the difference in H1 and ZEUS published gluons)
• Thus choice 2 is made for the central 10
  parameter ZEUS Only fit
• In practice choice 1. and 2. give very similar
  results

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Zeus-Only
Zeus and H1 gluons are rather different even when
these data are used in the same analysis - AMCS
H1-Only
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ZEUS-S Global 2002
ZEUS-Only 2004

• Compare valence partons for ZEUS-S global fit and
  ZEUS ONLY 2004 fit
• Global fit uncertainty is systematics dominated
  whereas ZEUS-Only fit is statistics dominated-
  much improvement expected from HERA-II,
  particularly if there is lower energy running to
  access higher-x
• ZEUS-Only fit uses proton target data only-
  particularly important for dv

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Gluon and Sea from ZEUS-Only 2004 fit

• Blue hatched band represents model uncertainties
  with contributions from varying
• Starting scale Q02
• Form of parameterisation
• Values of cg and cS
• ? Compatible with ZEUS-S global fit
• low-x information comes from
• HERA data anyway
• high-x compatibility by construction
• Valence-like gluon at low-x

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And compare ZEUS-Only 2004 PDFs to published
ZEUS-S 2002 PDFs including error analyses
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• STRATEGY B Use more data to tie down the high-x
  gluon
• What data? Jet cross sections are directly
  sensitive to gluon
  through Boson-Gluon-Fusion process
  ?
• Use published ZEUS Jet production data from 96/97
  40 pb-1

Di-jet photproduction cross-sections vs ET(lab)
in bins of rapidity for direct photons (x? gt
0.75) Eur Phys J C23(20020615
Inclusive jet cross-sections vs ET(Breit) for DIS
in bins of Q2 Phys Lett B547(2002)164
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How? NLO QCD predictions for jet production
DISENT for DIS jets, FRIXIONE and RIDOLFI for
photoproduced di-jets are too slow to be used
every iteration of a fit. Use NLO QCD program
initially, to produce grid of weights in
(x,?F2), giving perturbatively calculable
part of cross section Then convolute with PDFs to
produce fast prediction for cross section
Where ca,n weight fa PDF of parton a The
DIS predictions must also be multiplied by
hadronization corrections and ZO corrections The
calorimeter energy scale and the luminosity are
treated as correlated systematic errors µF Q for
the DIS jets, µRQ or ET as a cross-check µR µF
ET/2 for the ? di-jets (ET is summed ET of
final state partons), the AFG photon PDF is used
but only direct photon events are used to
minimize sensitivity
This is how well the grids reproduce the
predictions to 0.05
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• Retain a, b, c all free in gluon param.
• xg(x) Ag xag (1-x)bg (1 cg x)
• ?11 parameter fit
• The reduction in the uncertainty of the gluon
  distribution at moderate to high-x is quite
  striking- but the gluon shape is not changed
• Although the jet data mostly affect 0.01ltxlt0.1
  the momentum sum-rule transfers some of this
  improvement to higher-x
• The Sea distribution is not significantly
  improved and we maintain our previous strategy of
  constraining a high-x sea parameter (choices 1 or
  2 are very similar)
• For a better high-x Sea determination we await
  HERA-II (and low energy running?)

Improvement in gluon determination without jets
? with jets 11 parameter fits
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The ZEUS-Only fit including jet data compared to
the inclusive cross-section data
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The ZEUS-Only fit with Jets compared to DIS
inclusive jet data
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The ZEUS-Only fit with jets compared to di-jet
photoproduction data Less good NLOQCD
description of data at the lowest ET ? hence a
cross-check removing the lowest ET bin from both
DIS and Photoproduction Jet data was made
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Now compare ZEUS-JETS 2004 to other
PDFs ZEUS-Only 2004 ZEUS-S Global 2002 (Phys ReV
D67(2003)012007) MRST2001 CTEQ6M

• ZEUS-JETS ?2/ndf 0.83
• Compatible with other fits given different data
  and fitting schemes

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Now compare to H1 with error bands agreement
has improved-but gluon shapes still somewhat
different
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• Extra information on gluon allows a competitive
  determination of ?s ? treat ?s as free parameter
  in fit
• Then the PDF errors in the as extraction are
  qutomatically accounted

as(MZ) 0.11830.0007(uncorr)0.0027(corr)0.0008(
model)
Compare this to as(MZ)0.11660.0008(uncorr)
0.0048(corr.)0.0018(model) Fr
om the previous ZEUS-S 2002 global fit
NLO scale uncertainties of 0.005 remain
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Of course when as is free there is a
corresponding increase in the gluon uncertainty
but this has decreased in comparison to the
global fit ZEUS-S
ZEUS-JETS 2004 gluon
ZEUS-S 2002 gluon
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SUMMARY AND CONCLUSION

• PDF Analysis of ZEUS data alone reduces the
  uncertainty involved in the combination of
  correlated systematic errors from many different
  experiments with possible incompatibilities
• Using ZEUS data alone also avoids uncertainty due
  to heavy target corrections for Fe and Deuterium
  particularly important for d valence
• ZEUS data now cover a large range in the x,Q2
  kinematic plane
• ? Valence is well measured ? low-x Sea/gluon
  are well measured
• Adding jet data gives a significant constraint
  on the mid/higher x gluon
• ?and a competitive as measurement
• Future prospects
• Add charm differential cross-sections in ET and
  rapidity
• Add resolved photon xsecns (if can control the
  photon PDF uncertainty)
• Add jet data from 1998/2000
• Add HERA-II data for more accurate valence (
  xF3 from NC/ flavours from CC)
  
  more accurate high-x Sea
• Low energy running at HERA-II ? for higher x
  and for FL ? Gluon

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Extras after here
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Model errors Percentage difference in choice 1
and choice 2 vs uncertainties on central fit
Percentage difference Sea choice 1
gluon choice 2. to Sea choice 2 gluon
choice 2
Percentage difference Sea choice 1
gluon choice 1. to Sea choice 2 gluon
choice 2
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Gluon with and without jets STRATEGY-B summary
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The ?2 includes the contribution of correlated
systematic errors ?2 3i FiQCD(p) 38
slDilSYS Fi MEAS2 3 sl2
(siSTAT) 2
Where ?i?SYS is the correlated error on point i
due to systematic error source ? and s8 are
systematic uncertainty fit parameters of zero
mean and unit variance This has modified the fit
prediction by each source of systematic
uncertainty The statistical errors on the fit
parameters, p, are evaluated from ??2 1,
s?0 The correlated systematic errors are
evaluated by the Offset method conservative
method - s?1 for each source of systematic
error For the global fit the Offset method gives
total errors which are significantly larger than
the Hessian method, in which s? varies for the
central fit. This reflects tensions between many
different data sets (no raise of ?2 tolerance is
needed) It yields an error band which is large
enough to encompass the usual variations of model
choice (variation of Q20, form of
parametrization, kinematic cuts applied) Now use
ZEUS data alone - minimizes data inconsistency
(but must consider model dependence carefully)
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