ZEUS PDF fitsA M Cooper-Sarkar HERA/LHC w/shop March 26 2004

Published GLOBAL ZEUS-S fits to 30 pb-1 of ZEUS 96/97 NC e+ differential cross-section data and fixed target DIS structure function data

Phys. Rev. D67,012007(2003) (hep-ex/0208023)

Central PDFs and error analysis available on http://durpdg.dur.ac.uk/hepdata/zeus2002.html

as eigenvector PDF sets in LHAPDF compatible format

Preliminary ZEUS-Only fits to 109 pb-1 of HERA-I data: 94-97 NC/CC e+/e-inclusive differential cross-section data

Proton target data from a single experiment

Discussion of ways of treating correlated systematic errors

Use of jet data as well as inclusive xsecns

Terrific expansion in measured range across the x, Q2 plane due to HERA data

Pre HERA fixed target µp,µDNMC,BDCMS, E665 and ν,ν Fe CCFR

Not

e st

rong

rise

at s

mal

l x

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

100

101

102

103

104

105

106

107

108

109

fixedtarget

HERA

x1,2

= (M/14 TeV) exp(±y)Q = M

LHC parton kinematics

M = 10 GeV

M = 100 GeV

M = 1 TeV

M = 10 TeV

66y = 40 224

Q2

(GeV

2 )

x

• xuv(x) = Au xav (1-x)bu (1 + cu x)xdv(x) = Ad xav (1-x)bd (1 + cd x) xS(x) = As xas (1-x)bs (1 + cs x)xg(x) = Ag xag (1-x)bg (1 + cg x)x∆(x) = A∆ xav (1-x)bs+2

These parameters control the low-x shape

These parameters control the high-x shape

These parameters control the middling-x shape

Parametrize parton distributions at Q20

Evolve in Q2 using NLO DGLAP (QCDNUM)

Convolute with coefficient functions structure functions cross-sections

Treatment of Heavy Quarks by Thorne-Roberts Variable Flavour Number

Cuts, W2 > 20 (to remove higher twist), 30,000 > Q2 > 2.7, x > 6.3 10-5

χ2 fit to 1263 data points errors on params – errors on extracted PDF shapes, predicted structure functions and cross-sections

Accounting for correlated systematic errors by Offset method

Model choices ⇒Form of parametrization at Q2

0, value of Q20,,

flavour structure of sea, cuts applied, heavy flavour scheme

Au, Ad, Ag are fixed by the number and momentum sum-rules

Treatment of correlated systematic errors

χ2 = 3i [ FiQCD (p) – Fi

MEAS]2

(σiSTAT)2+(∆i

SYS)2

Errors on the fit parameters, p, evaluated from ∆χ2 = 1,

THIS IS NOT GOOD ENOUGH if experimental systematic errors are correlated between data points- e.g. Normalisations

BUT there are more subtle cases- e.g. Calorimeter energy scale/angular resolutions can move events between x,Q2 bins and thus change the shape of experimental distributions

χ2 = Σi Σj [ FiQCD(p) – Fi

MEAS] Vij-1 [ Fj

QCD(p) – FjMEAS]

Vij = δij(бiSTAT)2 + Σλ ∆iλ

SYS ∆jλSYS

Where )i8SYS is the correlated error on point i due to systematic error source λ

It can be established that this is equivalent to

χ2 = 3i [ FiQCD(p) – 38 sλ∆iλ

SYS – FiMEAS]2 + 3 sλ2

(σiSTAT) 2

Where s8 are systematic uncertainty fit parameters of zero mean and unit variance

This has modified the fit prediction by each source of systematic uncertainty

How do experimentalists usually proceed: OFFSET method

1. Perform fit without correlated errors (sλ = 0) for central fit

2. Shift measurement to upper limit of one of its systematic uncertainties (sλ = +1)

3. Redo fit, record differences of parameters from those of step 1

4. Go back to 2, shift measurement to lower limit (sλ = -1)

5. Go back to 2, repeat 2-4 for next source of systematic uncertainty

6. Add all deviations from central fit in quadrature (positive and negative deviations added in quadrature separately)

7. This method does not assume that correlated systematic uncertainties are Gaussian distributed

Fortunately, there are smart ways to do this (Pascaud and Zomer LAL-95-05, Botje hep-ph-0110123)

ZEUS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10-3

10-2

10-1

ZEUS NLO-QCD Fit

tot. error (αs-free Fit)

tot. error (αs-fixed Fit)

uncorr. error (αs-fixed Fit)

Q2=10 GeV2

xuv

xdv

xg(× 0.05)

xS(× 0.05)

X

xqi Value of "s and shape of gluon are correlated in

DGLAP evolution"s increases Y harder gluon

So fit αs and PDF parameters simultaneously Uncertainty on gluon increases

αs = 0.1166 ± 0.0008 ± 0.0032 ± 0.0036 ± 0.0018stat. sys. norms. model

Evolve in Q2 ⇒low-x uncertainties of sea/gluon decrease

It was a surprise to see F2 still steep at small x - even for Q2 ~ 1 GeV2 should perturbative QCD work? "s is becoming largeBUT below Q2 ~ 5 GeV2 the gluon is no

longer steep at small x – in fact its becoming valence-like, and then negative!

ZEUS

-2

0

2

4

6 Q2=1 GeV2

ZEUS NLO QCD fit

xg

xS

2.5 GeV2

xS

xg

0

10

207 GeV2

tot. error(αs free)

xS

xg

xf

20 GeV2

tot. error(αs fixed)

uncorr. error(αs fixed)

xS

xg

0

10

20

30

10-4

10-3

10-2

10-1

1

200 GeV2

xS

xg

10-4

10-3

10-2

10-1

1

2000 GeV2

x

xS

xg

Look more closely at small-x

0

10ZEUS NLO QCD fit

-0.5-0.25

00.250.5

10-4

10-3

10-2

10-1

1

tot. error (αs free)tot. error (αs fixed)uncorr. error (αs fixed)

10-4

10-3

10-2

10-1

1

0

10

20 7 GeV2

xg

-0.5-0.25

00.250.5

10-4

10-3

10-2

10-1

1

20 GeV2

10-4

10-3

10-2

10-1

1

0

10

20 200 GeV2

-0.5-0.25

00.250.5

10-4

10-3

10-2

10-1

1

2000 GeV2

10-4

10-3

10-2

10-1

1x

0

10

20

ZEUS NLO QCD fit

-0.5-0.25

00.250.5

10-4

10-3

10-2

10-1

1

tot. error (αs free)tot. error (αs fixed)uncorr. error (αs fixed)

10-4

10-3

10-2

10-1

1

0

10

20 7 GeV2

xS

-0.5-0.25

00.250.5

10-4

10-3

10-2

10-1

1

20 GeV2

10-4

10-3

10-2

10-1

1

0

10

20 200 GeV2

-0.5-0.25

00.250.5

10-4

10-3

10-2

10-1

1

2000 GeV2

10-4

10-3

10-2

10-1

1x

-0.5

-0.25

0

0.25

0.5

0 0.2 0.4 0.6 0.8 1

xdV

0 0.2 0.4 0.6 0.8 1

10-2

10-1

1

200 GeV2

tot. error (αs free)

-0.5

-0.25

0

0.25

0.5

0 0.2 0.4 0.6 0.8 1

2000 GeV2

tot. error (αs fixed)uncorr. error (αs fixed)

0 0.2 0.4 0.6 0.8 1

x

-0.5

-0.25

0

0.25

0.5

0 0.2 0.4 0.6 0.8 1

xuV

0 0.2 0.4 0.6 0.8 1

10-2

10-1

1

200 GeV2

tot. error (αs free)

-0.5

-0.25

0

0.25

0.5

0 0.2 0.4 0.6 0.8 1

2000 GeV2

tot. error (αs fixed)uncorr. error (αs fixed)

0 0.2 0.4 0.6 0.8 1

x

Look more closely at high-x

uv much better measured than dv

Valence much better measured than sea/gluon

Uncertainties at high-x do not decrease so much with Q2 evolution uv dv

Sea Gluon

Compare PDFs at high-x

High-x gluon ⇒High ET jet production at Tevatron/LHC

There are other ways to treat correlated systematic errors- HESSIAN method (covariance method)

Allow sλ parameters to vary for the central fit –there are smart ways to do this CTEQ hep-ph/0101032

If we believe the theory why not let it calibrate the detector(s)? The fit determines the optimal settings for correlated systematic shifts.

The resulting estimate of PDF errors is much smaller than for the Offset method for ∆χ2 = 1

We must be very confident of the theory – but more dubiously we must be very confident of the model choices we made in setting boundary conditions

In a global fit the best fit parameters can be far from those which would be acceptable for some of the individual experiments- data inconsistencies?

One could restrict the data sets to those which are sufficiently consistent that these problems do not arise – (e.g.Giele, Keller, Kosover,FNAL)

But one loses information since partons need constraints from many different data sets – no single experiment has sufficient kinematic range / flavour info.

CTEQ use an increased χ2 tolerance, ∆χ2 = T2, T = 10 to make an estimate of the PDF error which allows for this level of inconsistency in the data

MRST have also used increased tolerances in recent fits

Offset method Hessian method T=1

Compare gluon PDFs for Hessian and Offset methods for the ZEUS fit analysis

Hessian method T=7The Hessian method gives comparable size of error band as the Offset method, when the tolerance is raised to T ~ 7 – (similar ball park to CTEQ, T=10)

Note this makes the error band large enough to encompass reasonable variations of model choice since the criterion for acceptability of an alternative hypothesis, or model, is that χ2 lie in the range N ± √2N, where N is the number of degrees of freedom. For the ZEUS global fit √2N=50.

To do better investigate the possibility of using ZEUS data alone

Where does the information come from in a global PDF fit to DIS data?

Valence: from fixed target data – CCFR ν Fe xF3, NMC D/p ratio at high-x –HEAVY target corrections

Sea: Low-x from HERA F2 data

High-x from fixed target F2 data

Gluon: Low-x from HERA dF2/dlnQ2 data

High-x from mom-sum rule only- (UNLESS we put in JET DATA!)

Where does the information come from in a ZEUS-Only fit ?

Valence: HERA High-Q2 cross-sections CC/NC e+/-

Sea: Low-x from HERA F2 dataGluon: Low-x from HERA dF2/dlnQ2 data

High-x from mom-sum rule only- (UNLESS we put in JET DATA!)

Advantages:

Pure proton target- no heavy target correction or deuterium corrections

Single experiment - correlated systematic errors well understood

HERA at high Q2 ⇒ Z0 and W+/- exchanges become important

for NC processesF2 = 3i Ai(Q2) [xqi(x,Q2) + xqi(x,Q2)]

xF3= 3i Bi(Q2) [xqi(x,Q2) - xqi(x,Q2)]

Ai(Q2) = ei2 – 2 ei vi ve PZ + (ve

2+ae2)(vi

2+ai2) PZ

2

Bi(Q2) = – 2 ei ai ae PZ + 4ai ae vi ve PZ2

PZ2 = Q2/(Q2 + M2

Z) 1/sin22W

Y Z exchange gives a new valence structure function xF3 measurable from low to high x- on a pure proton target

Use ALL HERA-I data on NC/CC e+/e- high-Q2

differential cross-sections ~ 109pb-1, 509 data points

ZEUS

10-3

10-2

10-1

1

10

10 2

10 3

103

104

Q2 (GeV2)

σ∼ZEUS e−p 98−99 √s=318 GeV e−p ZEUS-S √s=318 GeV

ZEUS e+p 96−97 √s=300 GeV e+p ZEUS-S √s=300 GeV

CC processes give flavour information

d2σ(e-p) = GF2 M4

W [x (u+c) + (1-y)2x (d+s)] dxdy 2πx(Q2+M2

W)2

d2σ(e+p) = GF2 M4

W [x (u+c) + (1-y)2x (d+s)]dxdy 2πx(Q2+M2

W)2

MW informationuv at high x dv at high x

Measurement of high x, d-valence on a pure proton target. Most processes dominantly measure u- valence, only νFe xF3 and µD/p give d-valence info.

And these are heavy target - even Deuterium needs corrections, does dv/uv → 0, as x → 1?

ZEUS

0

0.5

1

1.5

2Q2 = 280 GeV2σ~

Q2 = 530 GeV2 Q2 = 950 GeV2

0

0.2

0.4

0.6Q2 = 1700 GeV2 Q2 = 3000 GeV2 Q2 = 5300 GeV2

0

0.05

0.1

0.15

10-2

10-1

Q2 = 9500 GeV2

10-2

10-1

Q2 = 17000 GeV2

x

ZEUS e+p 99-00

ZEUS-S

(1-y)2x(d+s)

x(u_+c

_)

0.5

1

1.5

2

0.5

1

0.2

0.4

0.6

0.8

10-1

10-1

10-1

ZEUSQ2 = 280 GeV 2

σ∼

Q2 = 530 GeV 2 Q2 = 950 GeV 2

Q2 = 1700 GeV 2 Q2 = 3000 GeV 2 Q2 = 5300 GeV 2

Q2 = 9500 GeV 2 Q2 = 17000 GeV 2 Q2 = 30000 GeV 2

x

ZEUS e-p 98-99ZEUS NLOQCD fitx (u + c)(1-y)2x (d

_+s

_)

ZEUS-O fit precision is becoming competitive – and is on a proton target-statistical precision will improve with HERA-II data. ZEUS-S global fit precision is already systematics dominated

Compare valence PDFs for ZEUS-Only and ZEUS-S global fits

ZEUS-S global

The precision on dv is much worse than for uv because most cross-sections measure uv,but HERA high Q2 CC e+ measures dv on a proton target

In HERA-II things can only get better! – more high Q2 CC plus NC xF3 data

ZEUS-O (prel) 94-00

2 = 1 GeV2

Q

vxu

vxd

uncorrelated errorcorrelated errormodel dependence error

2 = 20 GeV2

Q

vxu

vxd

2 = 200 GeV2

Q

vxu

vxd

2 = 2000 GeV2

Q

vxu

vxd10

-2

10-1

1

10

10-2

10-1

1

10

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 10 0.2 0.4 0.6 0.8 1

x

xf

ZEUSZEUS

10-2

10-1

1

0 0.2 0.4 0.6 0.8 1

xqV

Q2=1 GeV2

0 0.2 0.4 0.6 0.8 1

20 GeV2

ZEUS NLO QCD fit

10-2

10-1

1

0 0.2 0.4 0.6 0.8 1

200 GeV2

tot. error

xuV

xdV

0 0.2 0.4 0.6 0.8 1

x

2000 GeV2

uncorr. error

ZEUS-O proton target only

’STANDARD’ FITg5d; p2u=p2 + FREE p

13 free parameters

2 = 10 GeV2

Q

10-4

10-3

10-2

10-1

1-0.4-0.2

00.20.4

0

2

4

6

8

10

12

14

x

’STANDARD’ FITg5d; p2u=p2 + FREE p

12 free parameters

2 = 10 GeV2

Q

10-4

10-3

10-2

10-1

1-0.4-0.2

00.20.4

0

2

4

6

8

10

12

14

Sea

’STANDARD’ FITg5d; p2u=p2 + FREE p

13 free parameters

2 = 10 GeV2

Q

10-4

10-3

10-2

10-1

1-0.4-0.2

00.20.4

0

5

10

15

20

x

’STANDARD’ FITg5d; p2u=p2 + FREE p

12 free parameters

2 = 10 GeV2

Q

10-4

10-3

10-2

10-1

1-0.4-0.2

00.20.4

0

5

10

15

20

Glue

ZEUS-S ZEUS-O

ZEUS-O (prel) 94-00

2 = 1 GeV2

Q

xS

xg

2 = 2.5 GeV2

Q

xS

xg

uncorrelated errorcorrelated errormodel dependence error

2 = 7 GeV2

Q

xS

xg

2 = 20 GeV2

Q

xS

xg

2 = 200 GeV2

Q

xS

xg

2 = 2000 GeV2

Q

xS

xg

x

xf

ZEUS

10-4

10-3

10-2

10-1

1 10-4

10-3

10-2

10-1

1

0

10

20

30

0

10

20

-2

0

2

4

6

Compare sea and gluon PDFs for ZEUS-Only and ZEUS-S global fitsLow-x precision is comparable – info. In global fit came from ZEUS dataHigh-x precision is worse.

Interim solution: simplify sea/glue high-x param. Eigenvector procedure gives information on fit stability and parameter correlations- tells you which params are constrained best/which you need

Long term solution: HERA-II dataMedium term solution:use ZEUS jet data from HERA-I ⇒ impacts on gluon 0.01 < x < 0.1⇒ via momentum sum-rule on higher-x gluon

Interim solution: Compare HERA-I ZEUS-Only PDFs extracted from inclusive cross-section data to published ZEUS-S Global PDFs, and to MRST and H1 PDFS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10-3

10-2

10-1

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 ZEUS-O (prel) 94-00 uncorrelated error correlated error model dependence error

MRST 2001 ZEUS-S

ZEUS-O (prel) 94-00 uncorrelated error correlated error model dependence error

MRST 2001 ZEUS-S

x

xf

ZEUS2 = 10 GeV

2Q

vxu

vxd

0.05)×xS (

0.05)×xg (

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10-3

10-2

10-1

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 ZEUS-O (prel) 94-00 uncorrelated error correlated error model dependence error

MRST 2001 H1-O

x

ZEUS2 = 10 GeV

2Q

vxu

vxd

0.05)×xS (

0.05)×xg (

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

ZEUS

10-5

10-3

10-1

10

10 3

10 5

20 30 40 50 60 70

dσ/

dE

T

jet

1 (

pb

/GeV

)

ZEUS 96-97NLO (GRV) ⊗ HADNLO (GRV) ⊗ HADNLO (AFG) ⊗ HAD

xγ obs > 0.75

ET jet1 (GeV)

-1 < ηjet1,2< 0 (x 0.00001)

0 < ηjet1< 1 -1 < ηjet2< 0(x 0.0005)

0 < ηjet1,2< 1(x 0.01)

1 < ηjet1< 2.4-1 < ηjet2< 0(x 20)

1 < ηjet1< 2.40 < ηjet2< 1(x 100)

1 < ηjet1,2< 2.4(x 20000)

Jet energy scale uncertainty

(GeV)jet1TE

15 20 25 30 35 40 45 50

(p

b/G

eV)

jet1

T/d

Eze

us

σ -

dje

t1T

/dE

σd

-10

-8

-6

-4

-2

0

2

4

6 >11GeVjet2T>14GeV , Ejet1

TE

<1jet2η , jet1η>0.75 , 0<γx

All flavors up/down error ZEUS gluon up/down error Data+stat+syst errors Data+energy scale uncertainity

(GeV)jet1TE

15 20 25 30 35 40 45 50

(p

b/G

eV)

jet1

T/d

Eze

us

σ -

dje

t1T

/dE

σd

-10

-8

-6

-4

-2

0

2

4

6

(GeV)jet1TE20 30 40 50 60

(p

b/G

eV)

jet1

T/d

Eze

us

σ -

dje

t1T

/dE

σd

-8

-6

-4

-2

0

2

4

6 >11GeVjet2T>14GeV , Ejet1

TE

<1jet2η<2.4 , 0<jet1η>0.75 , 1<γx

All flavors up/down error ZEUS gluon up/down error Data+stat+syst errors Data+energy scale uncertainity

(GeV)jet1TE20 30 40 50 60

(p

b/G

eV)

jet1

T/d

Eze

us

σ -

dje

t1T

/dE

σd

-8

-6

-4

-2

0

2

4

6

Photproduction dijet cross-sections vs ET

Have significant impact on the uncertainties of the ZEUS-Only fit

Many jet cross-sections can be exploited to improve gluon measurement pre-LHC

Mid term solution