June 1st 2008 averaging meeting A M Cooper-Sarkar Model dependence fs Model dependence fc Model dependence need to be consistent when varying Q2_0 Model dependence need to be consistent when varying mc Low-x gluon High-x gluon LHAPDF

Model dependence fs We use fs=0.33±0.07, where s = fs.D = fs(d+s), so that s=0.5d This comes from importing knowledge from outside our fit that s quark is about ½ light quark at low scale But knowledge from outside out fit is now more precise i.e s quark is 0.33± 0.07 of light quark (0.5*(ubar+dbar)) at Q2=1.0 from Thorne’s fit to NuTeV dimuons, CTEQ are in agreement. Convert this into our fs (assuming dbar~ubar) and you get fs=0.25±0.04 at Q2=1.0 Then let it evolve up to Q2=4.0 and you get fs=0.30±0.05 Should we consider using these values?- it’s a minor change.

Model dependence fc We use fc=0.15±0.05, where c = fc.U = fc(u+c), so that c=0.176u This is used in two ways: to normalise Aubar=(1-fs)/(1-fc)Adbar and to actually set the amount of charm in the sea But when you have dynamic charm generation the amount of charm in the sea is set automatically- we should simply be consistent in the choice of fc Until now we stuck with fc=0.15 because it appeared reasonable ‘by eye’ with charm fractions generated by dynamic jobs like ZEUS-JETS, but I have now worked harder actually calculating the charm fractions in the dynamic job by integrating ubar,cbar (and dbar,sbar to check) Dynamic generation from mc=1.4 gives fc=0.09, with negligible error from model dependence (ie it varies only by 0.002, when using zeus-jets or inbetween dynamic jobs) We should use fc=0.09 and no model error on it- after all if we used Q2_0=2 we would have fc=0.0 and no argument. This won’t make so much difference, fc was not a big model error, unless you look at flavour break up- which we haven’t shown to the world so far

Model dependence need to be consistent when varying Q2_0 and mc Clearly the values fs=0.33 (or 0.30) and fc=0.15 (or 0.09) which hold at Q2=4, do not remain the same at Q2=2 or Q2=6 However when we varied Q2_0 we assumed they did. Looking at how these quantities evolve (by calculating the fractions of sbar,cbar etc by integration at various Q2) we can pick the right values. This mostly affects our predictions for flavour break-up, not the total Sea which we have already shown The value of fc also varies with the choice of mc and we should be consistent with this (small effect) Q2fsfc (mc=1.4)fc(mc=1.35)fc(mc=1.5) (0.28) (0.30)0.09 (0.15) (0.31)0.13 (0.18)

OLDNEW Here’s an illustration of the model dependence from just varying Q2_0 OLD: means keeping fs and fc the same as at Q2_0=4 NEW: means using fs=0.36, fc=0.22 at Q2_0=6 and fs=0.23, fc=0.0 at Q2_0=2 Yes, these are Not the values I just quoted they were earlier guesses- the illustration just shows that its barely visible except in the Sea

But when we look at flavour break-up into ubar, dbar, sbar, cbar, it does make quite a difference. Of course now I need to do this with all the right values Luckily we have not shown our flavour break-up to the world yet, so no-one will notice. NEWOLD

Low-x gluon What Thorne says about our parametrization limiting how big our uncertainty can be at low-x is quite true. But it is also a criticism of CTEQ Thorne’s parametrization HAS to be freer to accommodate the –ve gluon at Q2=1.0 If you evolve backwards pretty well everyone’s gluon goes –ve at low Q2, but we don’t have to put this into our parametrization because we start at higher Q2_0. CTEQ have also taken this attitude I am not sure that we NEED to address this

High-x gluon Last time I expressed a worry that our high-x gluon was not uncertain enough I am also not sure that we NEED to address this But I’ve been doing some more messing about Ultimately I need to see if we could describe Tevatron jet data- Thorne tends to say that it’s obvious we can’t, but I found that ZEUS-JETS could to a reasonable degree

Here’s the comparison to ZEUS-JETS Our HERAPDF Sea is harder, but gluon is softer. ZJ2005 can almost fit Tevatron jet data- χ2/d.p = 122/82 (for Run-I D0) HERA PDF will be somewhat worse

I already tried multilpying more terms (1+Dx) into the gluon PDF, in both humpy and non humpy solutions. This did not increase the uncertainty of our gluon…

So I’ve been ADDING completely ridiculous forms like +Gx or +Gx(1+x) Illustrated is just +Gx: G=-0.2±0.25 The (1-x) power on the gluon is harder C=5.7 rather than 8.4 Uncertainties are larger - But still this seems stupid

LHAPDF The optimal way to supply information to LHAPDF is to just supply the parameters at Q2_0 AND the eigenvector error sets. This is the LHpdf style rather than the LHgrid style. This can be done by diagonalising the outputs error matrices of MINUIT I have done this before for ZEUS PDFs and I’ve already done it for the April 2008 version of the HERA PDF fit- that’s how I got my LHC W/Z predictions. You can also provide the central parameters of the model variations so that can be used as users wish- added in quadrature for the 6 variations that we chose. The advantage of this is that full error correlations are taken into account The disadvantage is that the we also have to supply to Mike Whalley the Evolution routine for QCDNUM so that parameters like, fc,fs, are used correctly – thus we are exposing more of what exactly we do. The grid method does not do this, but it also cannot be used for calculating error correlations.