Further investigations on the fits to new data Jan 12 th 2009 A M Cooper-Sarkar Considering ONLY fits with Q 2 0 =1.9 or 2.0 –mostly comparing RTVFN to ZMVFN 1.Compare fit to New data combination (1.9) to older data combination (2.0 variant) - fits otherwise as for HERAPDF0.1 2.Compare New ZMVFN to New RTVFN using 100 quadratic errors 3.(Compare OLD ZMVFN to OLD RTVFN using 43 quadratic errors(+4 procedural)) 4.Compare New ZMVFN to New RTVFN using 102 fully correlated errors 5. As for 2. but using QCDNUM17-02 with linear spline interpolation 6. As for 4. but using QCDNUM17-02 with linear spline interpolation. 7.Comparisons to MRST01/MSTW08 and CTEQ61/CTEQ65 at low-x and high-x 8.Comparison to E. Perez

First note that our problem in November was that in the fit to the new data the extra NC e+ data pulls the fit to a somewhat different minimum than we had for HERAPDF0.1 (when considering fits at Q20=2.0) This has some unpleasant features (d-bar > d-valence for x> 0.6) - and is at the expense of the fit to CCe+ data (though that is still acceptable). Some suggestions were made on Nov 20th 1.Weighting the CCe+ data up by 2 (or 4 in chisq contribution) recovers the older fit PDF shapes Cutting out Q2 < 10 GeV2 data does not change the new fit- it is NOT new data at lower Q2 which is making the difference it is the bulk data. 3.Check if there are enough grid points at high x – a comparison of QCDNUM 16 to 17 addresses this – 17 has more high-x grid points- I find that fits with 16 and 17 are similar- see below. 4.Check effect of correlations by comparing fits with correlations on/ with all errors added in quadrature- see below 5. It is still very interesting to see zooms of our PDFs vs MSTW and CTEQ at high –x - see below 6. I have concentrated on the comparison on ZMVFN and RTVFN heavy quark schemes

First just comparing NEW (black) and OLD (red) with a focus on high-x (on the right). (Both of these fits are ZMVFN) Valence are softer at high-x whereas sea is harder, such that dbar> dvalence for x> 0.65 – but note (as Joel said) d-valence is also different at smaller x from x> 0.01 Gluon is almost the same (ie NOT harder as Sasha speculated). To illustrate the problem

Now comparing two NEW fits BLACK is ZMVFN RED is RTVFN The RTVFN is more like the old fit -see previous page..(dbar still becomes bigger than d-valence but it doesn’t do it until x > 0.83) RTVFN is also more like the old fit for x>0.01 But the use of RTVFN changes the picture

Now comparing two OLD fits BLACK is ZMVFN RED is RTVFN The differences between ZMVFN and RTVFN are still there and they go in the same direction for OLD or NEW fits -BUT they are not so large for the older data-I don’t see d-valence looking very different either for and there is no crossing of dbar over d-valence at high-x for either fit Note that the use of RTVFN did not make such a pronounced difference for the OLD fit- so if we had compared NEW and OLD sing RTVFN we would not have been so alarmed.

Now comparing two NEW fits BUT both done with fully correlated errors BLACK is ZMVFN RED is RTVFN These are BOTh more similar to the OLD fits! OR to the NEW with RTVFN (This means that the New fit with quadratic errors is like the New fit with correlated errors if you use RTVFN -but not for ZMVFN) Now make these ZMVFN/RTVFN comparisons using fully correlated errors

Now comparing two NEW fits both using QCDNUM17-02 (linear spline interpolation) BLACK is ZMVFN RED is RTVFN Similar to QCDQNUM16 (see page 3) but with experimental error bands- the shift ZM to RT is outside these bands (note- model error is not accounted here) Now make these ZMVFN/RTVFN comparisons using QCDNUM17-02

Now comparing two NEW fits both using QCDNUM17-02 BUT with fully correlated errors BLACK is ZMVFN RED is RTVFN These are BOTh quite similar to the OLD fits! Just as we found on page 4 for QCDNUM16. And they are similar to the NEW with RTVFN Now make these ZMVFN/RTVFN comparisons using QCDNUM17-02 and fully correlated errors

Interim Conclusions We had wanted to move to a more correct Variable Flavour Number Scheme than the zer0-mass (ZMVFN), and the use of the Thorne RTVFN scheme (2008 version) also seems to solve some of our problems. Using RTVFN for both the fit to the NEW data and to the older data gives more compatible results than using ZMVFN (and it has the added advantage of looking more like HERAPDF0.1) It is also the case that using fully correlated errors (all 102 of them) gives a result which resembles HERAPDF0.1 when using either ZMVFN or RTVFN. But what is more important is that the use of quadratic errors or correlated errors give compatible results only when using RTVFN. The use of QCDNUM17-02 gives similar results to using QCDNUM16.12 no matter what type of job- ZMVFN/RTVFN quadratic/correlated Now to compare our results with MRST/MSTW/CTEQ… For this I will just show fits to NEW data QCDNUM16.12, quadratic errors, ZMVFN or RTVFN

Comparison of NEW fits to MRST01 ZMVFN fit left RTVFN fit right Comparison of NEW fits to MSTW08 ZMVFN fit left RTVFN fit right Agreement is clearly better for the RTVFN fit at high-x, which is where they have data and we don’t!

Comparison of NEW fits to CTEQ61 ZMVFN fit left RTVFN fit right Comparison of NEW fits to CTEQ65 ZMVFN fit left RTVFN fit right Agreement is clearly better for the RTVFN fit at high-x, which is where they have data and we don’t!

Comparison of NEW fits to MRST01 ZMVFN fit left RTVFN fit right Comparison of NEW fits to MSTW08 ZMVFN fit left RTVFN fit right Zoom in on high-x Agreement is clearly better for the RTVFN fit at high-x, which is where they have data and we don’t! NOTe the cross-over of gluon and sea for us- we already decided not to worry about this-(its inside model error bands) BUT notice that MRSTW Sea is nowhere near crossing with its valence

Comparison of NEW fits to CTEQ61 ZMVFN fit left RTVFN fit right Comparison of NEW fits to CTEQ65 ZMVFN fit left RTVFN fit right Zoom in on high-x Agreement is clearly better for the RTVFN fit at high-x, which is where they have data and we don’t! NOTe the cross-over of gluon and sea for us- we already decided not to worry about this-(its inside model error bands) BUT notice that CTEQ Sea is nowhere near crossing with its valence

These comparisons with MRST/MSTW/CTEQ were all done to the fits to the NEW HERA data with QCDNUM16.12 and quadratic errors. It seems clear that the RTVFN version of our fit is much more comparable with the MRST/MSTW/CTEQ PDFs (whatever the version number) than the ZMVFN version of our fit. These comparisons are particularly important at high-x where they have data and we do not. So I recommend. 1.Use of RTVFN 2.I am agnostic about correlated errors/quadratic errors- but quadratic maybe easiest for comparisons- see next slide. 3.I am happy to move to QCDNUM17-02 firstly because we will need it for NNLO and secondly because I can use it to make direct comparisons with Emmanuelle Perez- see next slide 4.To make progress now we have to be able to compare analyses- which of our analyses are strictly comparable- we need to define this and then define what is our CENTRAL fit and what model variations we will do.

PARAMETERS for RTVFN fit /with fully correlated errors/ QCDNUM17 E.Perez AMCS 1'Bg ' E E 'Cg ' E E 'Buv ' E E 'Cuv ' E E 'Cdv ' E E 'Adbar ' E E 'Bdbar ' E E 'CDbar ' E E 'CUbar ' E E 'Euv ' E E 'Duv ' E E Good agreement of parameters- Only CUbar significantly different. Have tried starting with E. Perez parameters- fit still moves to my minimum. Have tried making my x- grid and Q2-grid for QCDNUM EXACTLY the same as E.Perez – fit still moves to my minimum. One more thing – our Chisq are not easy to compare beacuse they are formulated differently: I use Equation 6:15 of Devenish and Cooper-Sarkar and Emmanuelle uses equation 6:13. I get a much lower Chisq=498, Emmanuelle gets 606- but for quadratic surely we must agree.