Low-x meeting 2003
Zeus structure function results
What’s new this year?
A.M. Cooper-Sarkar
Oxford
• Data NC and CC data from 99/00 runs: e+p data
63pb-1
• NLO-QCD fits including this data
• Hope for FL and F2charm
A and B distinct for U and D type quarks
σ e-p = x [ u + c + (1-y)2 (d + s) ]
y
CC
data
x
Q2
Single differential cross-sections vs x, y, Q2
For CC e+p 99/00 61pb-1
Agreement with SM evaluated using ZEUS-S
NLOQCD fit
Q2
Sensitivity to dv at high-x
Use new CC e+ 99/00 data and
published CC e- 98/99 data
together to construct
F2CC = F2CC e+ + F2CC e= x (d + s + u + c) +
x (u + c + d + s)
Directly comparable to F2 from
neutrino data –CCFR
Extracted from cross-sections
(NOT preliminary any more!)
Limit on uncertainty from estatistics
Compare helicity structure of
e+ and eб e-p = x [ u + c + (1-y)2 (d + s)]
б e+p = x [ u + c + (1-y)2 (d + s)]
Hence subtracting
б e-p – б e+p =
x uv – (1-y)2 xdv
Sensitivity to valence
distributions
63pb-1 of new NC e+p data allows us
to update this
NC data
with this
Still PRELIMINARY for about 10
days!
And this
with this
16pb-1 e- and 30 pb-1 e+
(H1 not prelim anymore)
16pb-1 e- and 96 pb-1 e+
But we cannot
improve the
precision of the
xF3 extraction
from combining
e+ and e- NC
data since it is
limited by the
statistics of the
e- sample
Similarly we cannot
improve the xG3 extraction
xG3 is xF3 with the Q2 dependence
from the Z propagator removed- can
be compared to BCDMS
xG3 = x (2uv – dv)/3
Still preliminary
Double differential cross-sections for NC e+ 63pb-1 and NC e- 16pb-1
F2 em from combining the
new e+p NC 99/00 ZEUS
data with previous NC
96/97 e+p ZEUS data
giving 93 pb-1 of total data
Compared to ZEUS-S
MRST01 and CTEQ6
PDFS
Still preliminary
So now we have about
100 pb-1 per experiment
of NC and CC data
not
(only 16pb-1 of it e-)
What can we do with it?
A new round of NLO QCD
fits now to ZEUS data
alone
ZEUS-S published fits
Phys.Rev. D67,012007(2003)
http://durpdg.dur.ac.uk/hepdata
/zeus2002.html
used fixed target data and
only 30 pb-1 ZEUS 96/97 of
NC e+ data
Can now use ZEUS high-Q2 data to
constrain valence distributions
independent of nuclear corrections
needed by fixed target data
96/97 e+p NC 30 pb-1 2.7 < Q2 < 30000 GeV2 242 d.p. 10 corr..err. 2 norms
94/97 e+p CC 33 pb-1 280. < Q2 < 30000 GeV2 29 d.p.
3 corr. err.
98/99 e-p NC 16 pb-1 200 < Q2 < 30000 GeV2
92 d.p. 6 corr err. 1 norm
98/99 e-p CC 16 pb-1 200 < Q2 < 30000 GeV2
26 d.p. 3 corr. err.
99/00 e+p NC 63 pb-1 200 < Q2 < 30000 GeV2
90 d.p. 9 corr. err. 1 norm
99/00 e-p CC 61 pb-1 200 < Q2 < 30000 GeV2
29 d.p. 3 corr. err.
χ2 = Σi [ FiNLOQCD(p) + Σλ sλ Δiλ sys – Fi(meas)]2
(σ2
i stat +
+ Σλ sλ2
σi2unc)
χ2 must account for correlated systematic errors AND normalizations
Total of 37 sources of point to point correlated errors and 4 normalizations
Applied conservatively by OFFSET method see J.Phys.G 28(2002) 2717
Model errors are small by comparison
Eigenvector PDF sets- a better way to store the results of the fits
see http://durpdg.dur.ac.uk/hepdata/zeus2002.html
• 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
• ΔF2=∑ij ∂F/∂pi Vij
∂F/∂pj
• This would clearly be
easier if V were
diagonalised
• 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
• 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
i=1,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
• ΔF2= ½∑I ( F(Si+) – F(Si-) )2
• It has been the experience of CTEQ and MRST- that along some
eigenvector directions the χ2 increases very slowly-leading to asymmetries
and the breakdown of the quadratic approximation for χ2 . 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. Avoid this by not assuming that we can determine more
parameters than we actually can!
Where does the information come from in a global PDF fit?
Valence: xF3 ~ x(uv +dv) from neutrino-Fe heavy target data
F2n/F2p ~ xdv/xuv at high-x from μ D/p data
Sea: Low-x from HERA F2 e p data
High-x dominantly from fixed target F2 μ p data
Flavour structure from μ D and p, (plus Drell-Yan)
Gluon: Low-x from HERA dF2/dlnQ2 e p data
High-x from mom-sum rule or other input (Tevatron jets)
What can HERA high Q2 data add?- TODAY HERA-I
High-x valence information- particularly on xdv from e+p CCOn a pure proton target- no heavy target correction or deuterium corrections
-TOMORROW HERA-II
xF3/xG3 measurement : valence information from low to high-x
More accurate xdv, xuv flavour separated from CC interactions
More accurate high-x sea distributions too
xuv(x) =Auxau (1-x)bu (1+ γu x)
xdv(x) =Adxad (1-x)bd (1 + γd x)
2
2
at Q 0=7 GeV
xS(x) =Asx-λs (1-x)bs (1 + γs x)
Fix Au, Ad, Ag by xg(x) =Agx -λg (1-x)bg (1 + γg x)
number and momentum
d – u fixed
sum rules, set au=ad
Parametrize by
Evolve in Q2 using NLO
DGLAP equations convolute
with coefficient functions in
Thorne-Roberts Variable
Flavour Number Scheme
Comparing the eigenvectors and eigenvalues of the total error matrix of the
ZEUS global fit and the new fit to ZEUS data alone shows that for both fits:
the best determined parameters are λs and As for the Sea –i.e the low –x
behaviour of the Sea as determined by the ZEUS data -.
the next best determined parameter is λg for the glue – the low-x behaviour of
the glue also from the ZEUS data
After that: bu for the high-x u valence- is best determined from the fixed target data-
but high Q2 ZEUS data is nearly as good
The high-x parameters bs,bd for the Sea and d-valence, and γu for the u valence are
moderately well determined from the fixed target data high Q2 ZEUS e+p CC data
determines bd just as well but not bs or γu.
The high-x parameters bg for the glue and γs,yd γg for the Sea d-valence and gluon are
the least well determined parameters for both fits- but are better determined from the
fixed target data
Global
Zeus-Only –prel. AMCS
Low-x Sea and Gluon in ZEUS-S fits were strongly constrained by
ZEUS 96/7 e+p data – so are well constrained using ZEUS data alone
Sea and glue distributions from
ZEUS only with 94-99 data
16pb-1 e- and 30pb-1 e+
published
Sea and glue distributions from ZEUS
only with 94-00 data 16pb-1 e- and
93 pb-1 e+ preliminary AMCS
Global
ZEUS-Only prel.
ZEUS-S fit constrained valence distributions by using fixed target data
now the new 99/00 e+p data allows high-x valence distributions to be
well constrained from a fit to ZEUS data alone
Valence distributions from ZEUS
data alone 16pb-1 e- data and
37pb^-1 e+ data
ZEUS ONLY -published
Valence distributions from ZEUS
data alone 16pb-1 e- data and
100pb-1 e+ data
ZEUS-ONLY new/prel. AMCS
Anything could be going on at high-x
Look at high-x more closely
Global-ZEUS-S published
ZEUS-only prel. AMCS
Gluon from ZEUS alone is almost as well determined as in the global fit for all x
Medium to high x sea is not as well determined as in the global fit
Errors on high-x xuv not quite as good as global fit but HERA-II will
improve
Errors on High-x xdv now as good as global fit- and mostly statisticalHERA-II will improve!
Summary
• New High Q2 data NC and CC e+p
• New NLOQCD PDF fits  better
understanding of where the gaps in our
knowledge lie
Can construct xU, xD, xU xD for direct comparison to H1 - AMCS
But note that low-x valence distributions are not really well determined-small
errors are an artefact of the parametrization- need xF3 from NC e+/e- at HERA-II
xU xD xU xD xg at Q2=10 and 1000 Gev2 compared to MRST2001