High Q2 Structure Functions
and
Parton Distributions
Ringberg Workshop 2003 : New Trends in HERA physics
Benjamin Portheault
LAL Orsay
On behalf of the Zeus and H1 Collaborations
I. Introduction
The legacy of HERAI : What do we learn ?
II. Structure Function Results
State of the art of Zeus and H1 inclusive measurements
III. Extraction of parton distributions
H1 and Zeus schemes
Motivation and necessity for a common fit
IV. Overview of present (and future)
possibilities
Towards a H1+Zeus Fit
A brief look at Mw
Deep Inelastic Scattering
At leading order in the EW interaction :
dominant
high y
high Q2
2
The QCD factorization theorem allows to express
the structure functions as convolutions of universal
parton density functions (p.d.fs)
and perturbatively computable kernels
Through the measurement of high Q2 inclusive
Cross Section :
We can measure/extract structure functions
Test the structure of the EW interaction
(and look for new physics)
Use fits to test the pQCD evolution and
Measure the universal p.d.fs
An HERA QCD analysis can also be used to
Extract p.d.fs and the EW parameters (
,…)
For s and the gluon measurements and
prospects see talk by V. Shekelian
low Q2
(F2)
Charged Current
parton distributions
helicity factor
high Q2
(xF3)
The HERA EW plot
The HERA QCD plot
beautiful
Scaling
Violations
HERA data
Far from fixed
target precision
at high x
(stat. lim.)
Important for
QCD evolution
BCDMS
dF2/F2~7%
HERA
typical
dF2/F2
~2-3%
dF2/F2~30%
Interesting
Region for
exotic
searches
xF3 contribution
changes sign
between e+/e(by definition)
Extraction done
by subtraction
suppressed (<3% contribution to xF3)
access to valence p.d.fs
~30% error, dominated by e- statistics
xF3Z
evolved to the same Q2
Typical
systematic errors
are ~6%
Direct constraint
on d at high x
Direct constraint
on u at high x
Both e+ and eCross sections
Are necessary
For flavor
separation
in QCD fits
extraction with
measured
from fit
extend CCFR
measurement
uncertainty from estatistics
H1 & Zeus QCD Fits
Zeus Fits : ZEUS-Standard
Use Zeus NC 96/97 e+
BCDMS, NMC, E665 proton data
NMC,E665 deuterium data, CCFR xF3 iron data
For high x constraint and better flavor separation
ZEUS-Only
Use only Zeus data NC and CC e+ and e- up to 99
The number of d.o.f. is reduced by fixing parameters
Both use TR Variable Flavour Scheme
H1PDF2000 and H1+BCDMS
Use only H1 data (all HERAI NC and CC
high Q2 +low Q2 96/97)
Massless Flavour Scheme
H1
Zeus
Too much freedom to constrain all these parton
densities with H1 alone or Zeus alone
Need for additional assumptions or data
Fixes parameters
robust scheme
Use internal constraints
Between parameters
Not constrained by HERA data
Assumptions are needed (parameters
fixed/constrained)
Error determination
Both fits handle (differently) correlated
systematic errors in parameter determination
and error estimate
H1 : Pascaud-Zomer method
Zeus : offset method
(uses external data sets)
Only a proper treatment of the these correlated
Systematic error allow the application
Of a
error estimate
See talk by J. Pumplin
The Art of parameterization
At the (low) scale Q02 parton distributions are
Parameterized with
low x high x
It is not trivial to have P(x) such that the fit is
flexible enough and stable
Errors (and distributions) depend on the
parametric form chosen
One also has to be kind enough with MINUIT
as the fit is non-linear (dependency
upon the starting parameters …)
Any choice is arbitrary (nature do not choose a
parametric form)
Results on parton
distributions
u type quark distribution precision is 1% for
x=0.001 and 7% for x=0.65 (H1PDF2000)
d type quark distribution precision is 2% for
x=0.001 and 30% for x=0.65 (H1PDF2000)
Sea distribution precision is 5%
between x=10-4 and 10-1 (ZEUS-S)
Good achievement but the fits are at the edge
of the fitting possibilities
Use all HERA data to gain in flexibility
Reasonable
agreement
between the fits
given the different
Data and
fitting schemes
HERA data and global fits
The HERA data are highly valuable for global analysis
of Parton distributions :
Crucial low x constraint on quarks and antiquarks, gluon
High y data also constraining gluons
The knowledge and understanding of the correlated
systematic errors of HERA data made then
central in any of parton distributions analysis
Reliable error determination
The CTEQ and MRST will benefit from including
the 99/00 Zeus and H1 data in their fits
Towards HERA fits
Now (nearly) all Zeus and H1 data sets
are available
The Zeus and H1 data are in very good agreement
(in the sense of global parton distribution analysis)
Test of the Zeus data with H1PDF2000 :
Data set
96/97
98/99
/ndata
NC e+ low Q2 104/75
NC e+ highQ2 210/162
CC e+
19/29
NC e53/92
CC e23/26
NB : Zeus
systematics
fitted
Potential of an HERA fit
Fit procedure using less technical assumptions
Combination could help a lot on technical fit aspects
(we can also run into new problems)
And a meaningful
for error determination
Extensive studies must be made e.g. for the choice of
parametric forms (and settle if the
HERA gluon is ‘H1 like’ or ‘Zeus like’, see talk by V.
Shekelian)
As a proof of principle :
Prospects using a case study fit of Zeus+H1 data
(except Zeus 99/00 data)
The Mw mass measurement
Electroweak reminder
To confront the SM with experimental data
one needs to specify several parameters:
The On Mass Shell (OMS) scheme uses masses
as an input:
Whereas the Modified OMS uses:
The couplings of leptons to the Z0 and its
propagator normalisation also depend on the scheme
Fitting strategies for
Several strategies are possible :
It is possible to fit Mw to the CC cross section
As a ‘propagator mass’ with fixed
Structure Functions (used by Zeus and H1)
Or fit Mw together with the p.d.fs
OMS scheme, Mw as propagator mass
and normalisation
(
error estimate, similar to s)
HERA fit (no Zeus 99/00, r fixed)
H1PDF2000 scheme
Results and expected sensitivity
Significant improvement
HERA
fit
Still far from world average
experimental error only
(not so far from NuTeV alone
(central value consistent with
or D0 alone ~80 MeV
world average)
uncertainty)
Results and expected sensitivity
Major improvements in sensitivity
Could be better using Zeus 99/00
Unfortunately a significant theoretical error may
be present even with better data
But still far from world average :
HERA is not an electroweak facility
QCD (EW) common fits should start now
to prepare the strong physics message of
HERAI+II on p.d.fs and SM parameters
Conclusion
Many cornerstone results in DIS have been achieved
by HERAI.
DIS NC and CC differential cross sections are
measured with reasonable precision. High statistics
(and polarization) would bring more accuracy
Has already been turned into many
physics results through QCD Fits
The potential for the results still unexploited:
Zeus-H1 common fit is absent and needed to settle
important physics issues (pdfs, s , gluon, …)