1. PDF fits with free electroweak parameters Overview of what has happened since March’06 Collaboration meeting Emphasis on the NC couplings au,vu,ad,vd and how to calculate their contours when all 4 parameters are free (together with the PDF parameters OFFSET method plus stretching for correlated errors QUADRATURE errors HESSIAN method Short section on CC M W fits Some comments on combining with H1 in context of EW fits

2. All contours have 4-EW params free what we thought we had got from polarised data at the time of the collaboration meeting (statistical) compared to: H1, ZEUS from HERA-I But by DIS06 the yellow above had become the purple below (the data changed slightly) au/vu contour is not so different and is much better than without polarised data The ad/vd contour is a somwehat different shape and more extended in ad, BUT still a substantial improvement in vd when compared to HERA-I data

3. Look more closely at the contours for a fit without polarised data Note so far all ZEUS contours are for uncorrelated errors only so the purple shapes are comparable to the blue in the slide above. The yellow show the effect of adding in correlated errors by the stretching method. Note the old data do not seem to have a double minimum problem Yes the yellow correlated contour is cocked up

4. Now let’s look at the same information with the polarised data added These purple contours have uncorrelated errors The vu,vd parameters are obviously better detrmined BUT au is only marginally better and ad is not better at all. In fact there is a double minimum in au/ad space – au~0.5, ad~-0.5 AND au~0.65, ad~0.1 But where are the uncorrelated errors?

5. Before doing the correlated errors I decided it would be best to have correlated errors on the new polarised data as well as the HERA-I data This was done in June And here are the results Yellow are uncorrelated errors and blue adds in the correlated errors by the stretching method ( OFFSET method with non- centred stretch) (If you are worrying about what correlated errors on the polarised data do to the 2 parameter contours we sent to DIS06 its OK - see extra slides)

6. These contours are ugly. So what methods might we use to calculate contours? MINUIT command MNCONT will do this for you from whatever you have defined as your χ2 χ2 = Σ i [ F i QCD (p) –Σ λ s λ Δ iλ SYS – F i MEAS ] 2 + Σs λ 2 (  i UNCORR ) 2 Now for the OFFSET method we set all the correlated systematic error parameters, s λ =0, for the central value of the fit and its uncorrelated errors, and we calculate the correlated errors later, letting each s λ parameter be ± 1 This means that the MINUIT contour will only include the uncorrelated errors. So to display the effect of correlated errors we have stretched the contours by  [ δp i 2 ( UNCORR ) + δp i 2 ( CORR ) ] / δp i 2 ( UNCORR ) where δp i ( UNCORR/CORR ) are the uncorrelated and correlated errors on parameter p i This stretch is illustrated wrt the value of p i as determined by the fit. However, since the fit has a tendency to find a double minimum, the value of p i as determined by the fit is NOT actually at the centre of the contour – hence the term OFFSET method with non-centred stretch. It is easy to stretch wrt the centre of the contour instead- you can imagine it yourself.

7. The OFFSET method 4-EW parameter contours are quite ugly- the double minimum makes the stretching large and asymmetric. What else might we do? Well the same as well do when we quote the χ2 of our fit to the outside world- Recalculate it with errors in QUADRATURE χ2 = Σ i [ F i QCD (p) – F i MEAS ] 2 (  i UNCORR ) 2 +( Δ i CORR ) 2 And then let MINUIT do the contours. I would be happy with them since this is a well defined procedure, and easy to explain outside ZEUS But since the OFFSET with stretch contours are sometimes larger we could ask if we are deceiving ourselves and correlations should be accounted somehow…..

8. Which brings us to the HESSIAN method -using the form of the χ2 with the sλ parameters in it, and letting these parameters be free in the fit. As used by H1. So here are the HESSIAN contours- where correlated errors on both new polarised and ZEUS HERA-I data have been included I’d be happy with these too. It is also a well defined procedure- but it does mean changing our method to the HESSIAN for the whole fit Or does it? After all for PDFs we want to be conservative, but this is not necessarily true for EW contours- we could quote the OFFSET errors in a Table but show these contours?

9. The central values for the parameters are compatible for all three methods auadvuvd SM value0.5-0.50.196-0.346 OFFSET0.51±0.10±0.22-0.46±0.36±0.400.15±0.16±0.07-0.34±0.35±0.35 QUADRATure0.53±0.19-0.33±0.660.09±0.10-0.56±0.20 HESSIAN0.53±0.11-0.41±0.380.14±0.13-0.32±0.30 Note although errors are quoted as symmetric in practice they are not, and this shows up when plotting contours. This effect is most severe for the OFFSET method and for 4 EW parameter contours rather than 2 EW parameter contours.

10. Will this be easier to solve our problems with more data? Is there more e- which didn’t go into the DIS06 analysis? – surely we should wait for that? Should we wait for the final e+ as well? Remember that even without these NC contours we have a nice result on improvement of the valence PDFs.. And on M W (Other possibilities to improve PDFs – new high-x analysis, more photoproduced jets from HERA-I, more DIS inclusive jets from HERA-1, have not yielded much.) Now let’s consider the M W fits Results change a little when the errors on the polarised data are separated into correlated and uncorrelated There is also the questions about ‘fancy’ ways of getting at M W

11. FIRST just M W as a free parameter of the fit, together with the PDF parameters How does M W enter the fit? In the factor G F 2 M W 4 /(Q 2 +M W 2 ) 2 79.1 ± 0.77 ± 0.99 79.0 ± 0.72 ± 1.47 77.6 ± 1.4 ± 2.5 78.9 ± 2.0(stat) ± 1.8 (sys) +2.2 -1.8 (PDF) 82.87 ± 1.82(exp) +0.32 -0.18 (model) Result for DIS06..but no correlated errors on new polarised data Result if polarised data errors are separated into correlated and uncorrelated – not so impressive, but still better than the HERA-I results below ZEUS HERA-I data done by this EW+PDF fit method ZEUS DESY-03-093 published HERA-I result H1 HERA-I data done by EW+PDF method, note H1 uses the HESSIAN method so their errors are always better than ours on comparable data samples Value of M W (=80.4 SM) Specifications of the fit

12. Can also fit BOTH G F and M W remember GF SM= 1.11639×10-5 Or we can fit a more general formalism: fit g and M W in g 2 / (Q 2 + M W 2 ) 2 such that g 2 =G F 2 M W 4 = 0.07542 for standard model, G F =1.127 ± 0.013 ± 0.014 ×10 -5 G F =1.128 ± 0.012 ± 0.025 ×10 -5 M W =82.8 ± 1.5 ± 1.3 M W =82.4 ± 1.4 ± 2.4 g= 0.0772 ± 0.0021 ± 0.0019 g= 0.0767 ± 0.0019 ± 0.0032 M W =82.8 ± 1.5 ± 1.3 M W =82.4 ± 1.4 ± 2.4 Result for DIS06..but no correlated errors on new polarised data Result if polarised data errors are separated into correlated and uncorrelated – not so impressive

13. Alternatively USE the standard model relationship G F 2 M W 4 = 0.5 (πά/ (1 – M W 2 /M Z 2 )) 2 So that M W is the only parameter entering into either shape or normalisation M W = 80.6 ± 0.08 ± 0.08 M W = 80.1 ± 0.09 ± 0.233 H1 result using this technique on HERA-I data M W = 80.8 ± 0.21 -we suffer from using the OFFSET method Strictly speaking there should be - a factor of (1-Δr) entering into both the G F M W 2 relationship when loops are included where Δr depends on m top and m Higgs – I have also applied this and found very little difference in the results. We did not pursue this because Shima had no Δr code, but also because the meaning of it is not very clear- it assumes so much of the SM already. However it has been suggested that one can interpret it better as a measurement of G F at high scale→ G F = (1.146 ± 0.006 ± 0.016 )×10 -5 Maybe we can also pursue this with the complete data set?

14. Now what about combining with H1- different meeting but the EW results are interesting. I have tried the EW fit on the HERA-I ZEUS/H1 combined data set as produced by Sasha Glazov for the 1st HERA/LHC workshop. Uncorrelated and correlated errors are combined in quadrature since after the H1/ZEUS combination the correlated systematic errors are always smaller than the statistical Then I’ve compared it to ZEUS and H1 HERA-I data considered separately Then I’ve added the ZEUS polarised data to the Glazov combined HERA data. Just to see what happens… This should be a fruitful area for combination, because correlations between the PDF and EW parameters are not strong, so our disagreements on PDF fit formalism should not affect the EW fits so much. The Glazov combination also removes most of the HESSIAN/OFFSET controversy because it makes the residual systematic errors small.

15. EW fit contours for Glazov combined HERA-I data

16. Reminder of what H1 and ZEUS HERA-I analyses look like when considered separately

17. H1/ZEUS Glazov combined HERA-I plus ZEUS HERA-II contours Quadrature because of Glazov fit style

18. Extras

19. 2-param contours OFFSET method NEW because correlations are included for the new polarised data i.e.NOT as for DIS06..ie not as the purple and yellow ones in the next slide..

20. 2 param contours as for DIS06, not quite the same as after correlations are put in the new polarised data, but not so different either, so not worth new preliminary. Hence the DIS06 was sent to ICHEP06