Recap of PDF fitting to the HERA average data
Oct 12th 2007
AMCS
•Model dependence from assumptions about averaging procedure
•Model dependence from PDF parametrisation
•Model dependence from fitting programme!
•Free alphas
•Compare ZEUS and H1-style parametrisation
Version of the combination agreed as standard in July was: all sources of error relative; y>0.35 for NC 820,920 not combined
Had considered variations on this see talk of 04june07
Illustrated here: only normalisations relative and NC 820,920 combined to 920
Conclusion model dependence from averaging procedure not large
To test model dependence from parametrisation – change Q0
2 from 7 GeV2 to 4 GeV2 to 2 GeV2
Changes are as expected – gluon gets a bit humpier, reflects instability at Q0
2=2
d valence is also affected
Sea and u valence stable
Conclusion: Model dependence not too bad- but certainly as large as changes due to the choices in our procedure – see talk of 22 june07
Q02=7 GeV2 Q0
2=4 GeV2
Q02=2 GeV2
Model dependence – why chose Q02 as low as 2
GeV2? Because for QCDNUM17 you have to! It HAS to start below the charm threshold whether you chose NLO or NNLO.
These fits show only NLO.
There is a choice of linear spline interpolation (as for QCDNUM16) or Quadratic spline interpolation which is more accurate at high-x… and it makes a difference! See talk of 22June07
QCDNUM16 QCDNUM17linear
QCDNUM17 quadratic
compatible
Free αS(MZ)
αS(MZ) =0.121 ± 0.003 χ2=500
Investigate scale dependence
Renormalisation scale usually the biggest so start with that
Scale= 2 Q2 αS(MZ) =0.123 χ2=502
Scale= 4Q2 αS(MZ) =0.124 χ2=507
Scale= Q2/2 αS(MZ) =0.118 χ2=526
Scale= Q2/4 job blows up!
Scale dependence 0.002-0.003?
Not as bad as I thought!
Q02=4 GeV2 Q0
2=4 GeV2
ZEUS parametrization H1-style parametrization
Nature of the parametrization forces the errors on the low-x valence distributions to be very small- better to compare U,D
Central values of the fits are very close- good news I
haven’t added the charm into the sea for H1 in the plot, so it’s a bit low
Very similar χ2 ~ 500 for 584 points
ZEUS parametrisation
xf(x) = A xa (1-x)b (1+ c x)
For u,d valence, sea and glue
Au,Ad,Ag from sum rules, ad=au, cs=0
au=0.72 ± 0.04
bu=3.99 ± 0.13
cu=1.5 ±0.71
bd=5.18 ± 0.72
cd=2.54 ± 2.02
As=0.63 ± 0.02
as= -0.197 ± 0.004
bs=6.85 ± 0.71
ag= -0.128 ± 0.02
bg= 11 ± 1
cg= 16 ± 5
H1 parametrisation
xf(x) = A xa (1-x)b (1+ c x) (no x3 term)
For U=u+c, D=d+s, Ubar, Dbar and glue AU,AD,Ag from sum-rules,
aU=aD=aUbar=aDbar,cUbar=cDbar=0
aU= -0.195±0.004
bU=3.5± 0.05
cU=31 ± 2
bD=4.5 ± 0.22
cD=34 ± 8
AUbar=AU, ADbar=AD
bUbar = 10.8 ± 0.5
bDbar = 2.7 ± 0.9
ag= -0.115 ± 0.03
bg= 11 ± 5
cg= 12 ± 5
Gluon similar
Low-x
sea
simila
r
Looking back at old slides cg was sometimes written negative, sorry it is always positive!
Then we had the final decision to combine all data at 920, with all input errors relative AND the output had extra uncertainties from our procedures
Here I combined all output errors in quadrature for the PDF fit
Here I treat the 4 procedural errors by the OFFSET method for the PDF fit
Here I compare fits with Q2_min > 2.5 and Q2min > 1.5- since the fits to the lowets Q2 point didn’t look so goof
Q2_min=2.5 Q2_min=1.5
No of data points 584
NC e+ data points 371 χ2/dp = 0.93
No of data points 596
NC e+ data points 383 χ2/dp = 1.14
The shape of the low-x gluon is significantly affected
BUT the chisq for these low Q2 points is not good
What else ?
1. Investigate other model dependence changes…
2. Investigate NNLO
3. Implement Hessian+Offset as well as quadratic chisq