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 parametrisationxf(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 s

imila

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