Low-x meeting 2003

Zeus structure function resultsWhat’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 F2

charm

σ e-p = x [ u + c + (1-y)2 (d + s) ]A and B distinct for U and D type quarks

y 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

CC data

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 = F2

CC 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 e- statistics

Compare helicity structure of e+ and e-

б 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 with this NC data

Still PRELIMINARY for about 10 days!

And this with this (H1 not prelim anymore)16pb-1 e- and 30 pb-1 e+ 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

Double differential cross-sections for NC e+ 63pb-1 and NC e- 16pb-1

Still preliminary

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

(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

not

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 + Σλ sλ

2

( σi2

stat + σi2

unc)

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

• 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 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

• 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 CC-

On 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

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

Parametrize by

at Q20=7 GeV2

Fix Au, Ad, Ag by number and momentum sum rules, set au=ad

xuv(x) =Auxau (1-x)bu (1+ γu x)xdv(x) =Adxad (1-x)bd (1 + γd x) xS(x) =Asx-λs (1-x)bs (1 + γs x)xg(x) =Agx -λg (1-x)bg (1 + γg x)

Evolve in Q2 using NLO DGLAP equations convolute with coefficient functions in Thorne-Roberts Variable Flavour Number Schemed – u fixed

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

Global Zeus-Only –prel. AMCS

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

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

Global ZEUS-Only prel.

Valence distributions from ZEUS data alone 16pb-1 e- data and 37pb^-1 e+ data

Valence distributions from ZEUS data alone 16pb-1 e- data and 100pb-1 e+ data

ZEUS ONLY -published ZEUS-ONLY new/prel. AMCS

Anything could be going on at high-x

Look at high-x more closely

Gluon from ZEUS alone is almost as well determined as in the global fit for all x

Global-ZEUS-S published ZEUS-only prel. AMCS

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 statistical- HERA-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