25/03/2008 H1Z Meeting Joël Felt esse 1 Update on QCD Fits, error estimates
Jan 01, 2016
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Outlook
• Parameterizations• Assumptions for central fit• Systematics from model dependence• Variations• Options to be decided
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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)
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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.
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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 ?
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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)
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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.
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Blue : experimental errorsRed : (exp + model) errors.
Q2 = 4 GeV2
uv
dv
gluon
All model dependence with uncertainty on input parametrisation(i.e. 7 sources)
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All model dependence without uncertainty on input parametrisation(i.e. 6 sources)
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Blue : experimental errorsRed : (exp + model) errors.
Q2 = 4 GeV2
Ubar
Dbar
Sea
All model dependence with uncertainty on input parametrisation(i.e. 7 sources)
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All model dependence without uncertainty on input parametrisation(i.e. 6 sources)
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Blue : experimental errorsRed : (exp + model) errors
Q2 = 10000 GeV2
uv
dv
gluon Impressive shrinkage oferrors at low x
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Blue : experimental errorsRed : (exp + model) errors
Q2 = 10000 GeV2
Ubar
Dbar
Sea
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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.
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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
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All model dependence with uncertainty on input parametrisationand on double minima(i.e.8 sources)
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Comparison with published H1 and ZEUS PDFs (2002-2003)
Without double minima uncertainty
Much narrowerError band !
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Comparison with published H1 and ZEUS PDFs (2002-2003)
With double minima uncertainty
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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
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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
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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
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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 ?
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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)
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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.