Update on QCD Fits, error estimates

25/03/2008 H1Z Meeting Joël Feltesse 1

Update on QCD Fits,error estimates


Outlook

• Parameterizations• Assumptions for central fit• Systematics from model dependence• Variations• Options to be decided


Parameterizations

• All based on the same PDF functional form :

x f(x) = A xB (1 - x)C (1 + D x + E x2 +F x3 )

• The optimal number of parameters depend on the data set.

• The former ‘H1 parameterization’ (H1PDF2K), ‘ZEUS-Jet’, ‘Inbetween’ (EP) have been optimised to the H1-ZEUS combined data set (see previous meetings)


Comparison between parameterizations


Comparison between parameterizations


Additional assumptions for heavy quark

• H1 param : s = 0.33 Dbar• ZEUS param : (s + sbar) = 0.2 sea• Wthin the Zero Mass Variable Flavour Number (ZMVFN)

– H1 : charmed quark = 0.15 Ubar above threshold.– ZEUS : charmed quark, dynamically introduced by

evolution • H1 parameterization: dbar/ubar → 1 as x → 0. • ZEUS param’s : dbar – ubar = fixed function of x• In between : same assumptions as H1 parameterization.


Choice of parameterization

• All parametrizations give an excellent Chi2 / 573 :– Inbetween : 476.3– H1 param : 479.1– ZEUS_Jet : 475.6

• Chosen central parameterization : ‘optimized Inbetween’ • Motivations :

– Less model dependence on B parameters than in H1 param.– No need for an additional input (ubar-dbar) x distribution as in

ZEUS-Jet param– Most conservative errors.– It is inspired by both H1 and ZEUS parameterizations.

• The two other parameterizations are considered in the model dependence or in the variations ?


Central fit uses :

• The data sets which we have already been using for our comparisons- not any new MB99 or ZVTX 2000 (low Q2 from H1).

• Parameterization : ‘optimized in_between‘• DGLAP NLO fit based on QCDNUM package• alpha_s = PDG 2006 = 0.1176• Cuts Q2 = 3.5 GeV2

• Q02 = 4. GeV2

• mc = 1.4 GeV2

• mb = 4.75 GeV2

• fs = 0.33• fc = 0.15• ZMVFNS • Chi2 definition : uncorrelated for the 43 errors of the two

experiments, but correlated for the 4-procedural errors (here Hessian method, but ZEUS uses offset method)


Model dependence

Each source to be considered as a variation from the central job.1) Q0

2 = 2.0 GeV2 - 6.0 GeV2

2) Q2 min = 2.5 GeV2 - 5.0 GeV2

3) mc = 1.3 GeV2 - 1.55 GeV2

4) mb = 4.3 GeV2 - 5. GeV2

5) fs = 0.25 – 0.406) fc = 0.10 – 0.207) Optimized H1 and New ZEUS_JETS parameterization

(debatable)

Each systematic effect has been compared between H1 and ZEUS package → Excellent agreement.(one minor issue : Q2 min = 2 (H1) or 2.5 (ZEUS))

Excellent agreement also with QCDFIT (Li et al.) tested on a few key issues.


Variation of Q02 of

the input parameterization


Variation of the Q2 cut applied to the

data


Variation of the Q2 cut applied to the

data


Variation of fs,the fraction of Dbar strange = fs * dbar


Variation of fc,the fraction of cbar charm = fc * Ubar


Variation of mb, the mass of b quark


Blue : experimental errorsRed : (exp + model) errors.

Q2 = 4 GeV2

uv

dv

gluon

All model dependence with uncertainty on input parametrisation(i.e. 7 sources)


All model dependence without uncertainty on input parametrisation(i.e. 6 sources)


Blue : experimental errorsRed : (exp + model) errors.

Q2 = 4 GeV2

Ubar

Dbar

Sea

All model dependence with uncertainty on input parametrisation(i.e. 7 sources)


All model dependence without uncertainty on input parametrisation(i.e. 6 sources)


Variation with Q2


Blue : experimental errorsRed : (exp + model) errors

Q2 = 10000 GeV2

uv

dv

gluon Impressive shrinkage oferrors at low x


Blue : experimental errorsRed : (exp + model) errors

Q2 = 10000 GeV2

Ubar

Dbar

Sea


Variations - not model dependences.

Not to be added together in quadrature but shown separately.– use of general mass VFN -like Robert Thorne's or

(and) ACOT (not yet ready but not mandatory for preliminary results)

– use of alpha_s = 0.1176 +/- 0.002 – use of humpy not straight solution.


Alpha_s variation +- 0.002


Comparison between straight and humpy minima


Comparison with humpy solution

Reminder : two minima havebeen observed:Chi2 straight = 476.3 / 573Chi2 humpy = 494.6 / 573(With original inbetween parameterization)

All model dependence with uncertainty on input parametrisation without double minima

uv

dv

gluon


All model dependence with uncertainty on input parametrisationand on double minima(i.e.8 sources)


Comparison with published H1 and ZEUS PDFs (2002-2003)

Without double minima uncertainty

Much narrowerError band !



With double minima uncertainty






New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands from 6 sources of model variation:

AT THE STARTING SCALE Q20 = 4 GeV2

Last result from ZEUS Package Last result from H1 Package








Final options to decide today

• Q2 min = 2.5 or 2 GeV2 ?• Offset or Hessian for the 4 correlated errors ?

• Add parameterizatios uncertainty in model dependence or show it as a variation ?

• Add double minima uncertainty in model dependence or show it as a variation ?

• Which plots do we want to be stamped by H1 and ZEUS ?


EXTRA SLIDES


The sources of procedural errors related to the averaging procedure :

– Center of Mass Energy correction

– Multiplicative vs additive systematic errors

– Uncertainty on correlations between experiments

They are at the few permille level across most of

kinematic plane (with few exceptions)




Results of ZEUS-Jet

Old ZEUS-JET parametrisation (11 parameters) A B C D E!

gluon From Sum Rule

0.

uv From Sum Rule

0.

dv From Sum Rule

= Buv 0.

ubar - dbar from Z_S_11 fit

from Z_S_11 fit

from Z_S_11 fit

0. 0.

Sea

0. 0.

New ZEUS-JET parametrisation (11 parameters) A B C D E!

gluon From Sum Rule

0.

uv From Sum Rule

0.

dv From Sum Rule

= Buv 0.

ubar - dbar from Z_S_11 fit

from Z_S_11 fit

from Z_S_11 fit

0. 0.

Sea

0. 0.

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Update on QCD Fits, error estimates