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. IntroductionThe legacy of HERAI : What do we learn ?
II. Structure Function ResultsState of the art of Zeus and H1 inclusive measurements
III. Extraction of parton distributionsH1 and Zeus schemes
Motivation and necessity for a common fit
IV. Overview of present (and future) possibilities
Towards a H1+Zeus FitA brief look at Mw
2 22
2 4 2 3d 2d d
NCLY y Y
x Q xQF F xF
Deep Inelastic Scattering
At leading order in the EW interaction :
The QCD factorization theorem allows to express the structure functions as convolutions of universal
parton density functions (p.d.fs)and perturbatively computable kernels
22 222
2 2 2 2 3dd d 4
CC WF
W
CC CC CCL
MG Y y Yx Q x Q M
F F xF
dominanthigh y
high Q2
Through the measurement of high Q2 inclusiveCross 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
WM
low Q2 ( ) ( )e NC e NC
high Q2
( ) ( )e NC e NC
(F2)
(xF3)
The HERA EW plot
Charged Current ( ) ( )e CC e CC
parton distributionshelicity factor
2 2WQ M
2 2
4
216
F
W
GM
( ) ( )CC NC
The HERA QCD plot
beautifulScaling
Violations
HERA dataFar from fixed
target precision at high x
(stat. lim.)Important for QCD evolution
BCDMSF2/F2~7%
HERA
typicalF2/F2~2-3%
F2/F2~30%
Interesting Region for
exotic searches
24
2
d12 d d
NCNC
xQY x Q
2
2 3NC LYyF F x F
Y Y
xF3 contributionchanges sign between e+/e-(by definition)
Extraction doneby subtraction
23 3 32Z Z
e Z e e ZxF a xF a v xF
3 2 ( ) 2Zi i i i
ival valxF e a x q q x xu d
2 2 2( )Z ZQ Q M
suppressed (<3% contribution to xF3)
access to valence p.d.fs
evolved to the same Q2
~30% error, dominated by e- statistics
xF3Z
22 2 2
2 4 2
d2d d
W CCCC
F W
Q MxG M x Q
21CC x u c y d s
Direct constraint on d at high x
Typical systematic errors
are ~6%
21CC x u c y d s
Direct constraint on u at high x
Both e+ and e-
Cross sectionsAre necessary
For flavorseparation in QCD fits
2 32 ,CC CC CC
LCC CCF xF FY
2 2 2CC CC CCF F F
2CCF u d s c u d s c
extraction with
from fitmeasuredextend CCFR measurement
uncertainty from e-
statistics
H1 & Zeus QCD FitsZeus Fits : ZEUS-Standard
Use Zeus NC 96/97 e+
BCDMS, NMC, E665 proton dataNMC,E665 deuterium data, CCFR xF3 iron data
For high x constraint and better flavor separation
ZEUS-OnlyUse only Zeus data NC and CC e+ and e- up to 99
The number of d.o.f. is reduced by fixing parametersBoth use TR Variable Flavour Scheme
H1PDF2000 and H1+BCDMSUse only H1 data (all HERAI NC and CC
high Q2 +low Q2 96/97)Massless Flavour Scheme
, , , ,g U u c D d s U D , , , ,v vg u d u d d u Too much freedom to constrain all these
parton densities with H1 alone or Zeus aloneNeed for additional assumptions or data
Fixes parameters robust scheme Use internal constraints
Between parameters
c cfrac Us sfrac D
d u Not constrained by HERA dataAssumptions are needed (parameters
fixed/constrained)
Zeus H1
Error determination
Both fits handle (differently) correlated systematic errors in parameter
determinationand error estimate
H1 : Pascaud-Zomer methodZeus : 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
2 1
The Art of parameterization
At the (low) scale Q02 parton distributions are
Parameterized with 20( , ) (1 ) ( )B Cx f x Q Ax x P 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 MINUITas the fit is non-linear (dependency
upon the starting parameters …)Any choice is arbitrary (nature do not choose
a parametric form)
low x high x
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 possibilitiesUse all HERA data to gain in flexibility
Reasonableagreement
between the fitsgiven the different
Data and fitting schemes
HERA data and global fitsThe 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 correlatedsystematic 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 fitsNow (nearly) all Zeus and H1 data sets
are availableThe Zeus and H1 data are in very good agreement(in the sense of global parton distribution analysis)
Test of the Zeus data with H1PDF2000 :2Data set
NC e+ low Q2 104/75NC e+ highQ2 210/162CC e+ 19/29NC e- 53/92CC e- 23/26
/ndata
96/97
98/99
NB : Zeussystematics
fitted
Potential of an HERA fitFit 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
2 1
To confront the SM with experimental dataone needs to specify several parameters:
The On Mass Shell (OMS) scheme uses masses as an input: Whereas the Modified OMS uses:
Electroweak reminder
22
2
11 ( , , , , )
2 1F
W Z H topWW
Z
Gr M M M mM M
M
, , ,W Z HM M M, , ,F Z HG M M
The couplings of leptons to the Z0 and its propagator normalisation also depend on the scheme
Several strategies are possible :
It is possible to fit Mw to the CC cross sectionAs a ‘propagator mass’ with fixed
Structure Functions (used by Zeus and H1)
Or fit Mw together with the p.d.fsOMS scheme, Mw as propagator mass
and normalisation( error estimate, similar to s)
HERA fit (no Zeus 99/00, r fixed)H1PDF2000 scheme
Fitting strategies for WM
2 1
Results and expected sensitivity
0.2%W WM M experimental error only
(central value consistent with world average)
Significant improvement
Still far from world average(not so far from NuTeV alone
or D0 alone ~80 MeVuncertainty)
HERA fit
Results and expected sensitivity
Major improvements in sensitivityCould be better using Zeus 99/00
Unfortunately a significant theoretical error maybe 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
ConclusionMany 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, …)