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 schemesMotivation 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 2

d dNC

LY y Yx Q xQ

F 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 3d

d d 4CC WF

W

CC CC CCL

MGY y Y

x Q x Q MF 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 distributions

helicity factor

2 2WQ M

2 2

4

2

16F

W

G

M

( ) ( )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

d1

2 d dNC

NC

xQ

Y x Q

2

2 3NC L

YyF 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

xF3

Z

22 2 2

2 4 2

d2

d dW CC

CCF W

Q Mx

G 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 3

2,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 fitmeasured

extend CCFR measurement

uncertainty from e-

statistics

H1 & Zeus QCD Fits

Zeus Fits : ZEUS-StandardUse 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 constraintsBetween parameters

c cfrac U

s 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 fits

The HERA data are highly valuable for global analysisof Parton distributions :

Crucial low x constraint on quarks and antiquarks, gluonHigh 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 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 :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 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

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

1

1 ( , , , , )2 1

FW Z H topW

WZ

Gr M M M mM

MM

, , ,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

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, …)