Combined electroweak and PDF fits
 Mandy Cooper-Sarkar, Claire Gwenlan, Kunihiro Nagano, Shima Shimizu

On this page, the final preliminary plots and values (as decided in PCOOR) for the electroweak fits are shown. Please see Mandy's page for much more detail on the various investigations and fits that have been carried out, as well as the second analysis checks.

The PDF fit analysis formalism is exactly as described in the paper hep-ph/0503274(DESY-05-050) the ZEUS-JETS fit.
We then input the new NC and CC polarised e- data to this fit. These data have only statistical and overall systematic errors at present, hence the Chi2 for these data simply adds these errors in quadrature. In addition. an overall normalisation error for these data of 3.5% is input as a correlated systematic error, using the usual ZEUS OFFSET method.

1. First we vary only the PDF parameters, keeping all electroweak parameters fixed.

THE FOLLOWING PLOTS HAVE BEEN MADE PRELIMINARY:

CC+error.eps CC P=+0.33 polarised data and new ZEUS-PDF fit prediction

CC-error.eps CC P=-0.27 polarised data and new ZEUS-PDF fit prediction

NC+error.eps NC P=+0.33 polarised data and new ZEUS-PDF fit prediction

NC-error.eps NC P=-0.27 polarised data and new ZEUS-PDF fit prediction

The values of the PDF parameters are hardly changed from those of the ZEUS-JETS fit and this is illustrated below, where a plot of the new PDFs is compared to the ZEUS-JETS PDFs

PDF-SUMMARY.eps PDFs from the new ZEUS-PDF analysis including polarised data compared to those from the ZEUS-JETS fit analysis

However, although the central values have not altered significantly, the uncertainties on these PDFs are significantly reduced at high-x particularly for the u-valence quark, as expected when inputting e- data:  this is illustrated below in these plots of the fractional PDF uncertainties, displayed at Q2=10 GeV2.

PDF_Uncertainties_10GeV2.eps PDF uncertainties from the new ZEUS-PDF analysis including polarised data compared to those from the ZEUS-JETS fit analysis at Q2=10GeV2

This improvement is still visible at LHC scales Q2=10,000 GeV2.

PDF_Uncertainties_10000GeV2.eps PDF uncertainties from the new ZEUS-PDF analysis including polarised data compared to those from the ZEUS-JETS fit analysis at Q2=10,000GeV2

2. Next we began to allow electroweak parameters to be free in the fit, in addition to the PDF parameters.

We begin with the CC parameters, M_W and G_F, which enter into the CC cross-section in the propagator term G_F^2 M_W^4/(Q^2+M_W^2)^2
and we also define a more general coupling, g, by using the form g^2/(Q^2+M_W^2)^2

THE FOLLOWING VALUES HAVE BEEN MADE PRELIMINARY:

 MW
 GF
 g
79.1 \pm 0.77 \pm 0.99
 1.16637 fixed
 NA
82.8 \pm 1.5 \pm 1.3
 1.127 \pm 0.013  \pm 0.014
NA
82.8 \pm 1.5 \pm 1.3
 NA
 0.0772 \pm 0.0021 \pm 0.0019

3. Next we vary NC electroweak parameters as well as the PDF parameters: .

 THE FOLLOWING VALUES AND PLOTS HAVE BEEN MADE PRELIMINARY:

a_u
 a_d
 v_u
 v_d
0.50 \pm 0.04 \pm 0.09
 -0.5
 0.19 \pm 0.06 \pm 0.06
 -0.346
0.5
 -0.49 \pm 0.14 \pm 0.28
 0.196
 -0.37 \pm 0.14 \pm 0.16
0.48 \pm 0.06 \pm 0.10 -0.55 \pm 0.10 \pm 0.21 0.196
 -0.346
0.5
 -0.5
 0.12 \pm 0.10 \pm 0.05 -0.47 \pm 0.15 \pm 0.19

The 68% 2-parameter contours corresponding to these fits are here

au/vu 2-parameter contours compared to H1 and CDF and LEP: CONTOURauvuALL.eps

ad/vd 2-parameter contour compared to H1 and CDF and LEP: CONTOURadvdALL.eps

au/vu 2-parameter contour for 2 -parameter EW fit compared to equivalent ZEUS-JETS contour: CONTOURauvuOLD.eps

ad/vd 2-parameter contour for 2 -parameter EW fit compared to equivalent ZEUS-JETS contour: CONTOURadvdOLD.eps

au/ad 2-parameter contour for 2 -parameter EW fit compared to equivalent ZEUS-JETS contour: CONTOURauadOLD.eps

vu/vd 2-parameter contour for 2 -parameter EW fit compared to equivalent ZEUS-JETS contour: CONTOURvuvdOLD.eps


4. Next we consider varying the standard model formalism as follows: .

a_u = T3_uL- T3_uR , v_u = T3_uL+T3_uR -2 e_u sin^2\theta_W
a_d = T3_dL - T3_dR , v_d = T3_d +T3_dR -2 e_d sin^2\theta_W
and fitting, T3_uR, T3_dR, while keeping T3_uL,T3_dL an sin^\2theta_W at their SM values
and fitting, T3_uR, T3_dR, sin^2\thetaw_W, while keeping T3_uL,T3_dL at their SM values , the latter fit allows for the idea that if there are right-handed couplings they most likely involve heavier mass Z's and so the effective value of sin^2\theta_W can change.

THE FOLLOWING VALUES AND PLOTS HAVE BEEN MADE PRELIMINARY:

T3_uL
 T3_uR
 T3_dL
 T3_dR
 sin^2\theta_W
0.47\pm0.05\pm0.13
 0
 -0.55\pm0.18\pm0.35
 0
 0.231\pm0.024\pm0.070
0.5
 -0.04\pm0.06\pm0.13
-0.5
 -0.14\pm0.18\pm0.33
0.2315
0.5
 -0.07\pm0.07\pm0.07
-0.5
 -0.26\pm0.19\pm0.19
0.238\pm0.011\pm0.023

T3uR/T3dR 2-parameter contours for 2 -parameter T3_uR, T3_dR EW fit: CONTOURT3uRT3dR.eps