arXiv:hep-ex/0509002v1 2 Sep 2005 Uncertainties on W and Z production at the LHC HERA - LHC Workshop Proceedings Alessandro Tricoli, Amanda Cooper-Sarkar, Claire Gwenlan Oxford University Abstract Uncertainties on low-x PDFs are crucial for the standard model benchmark processes of W and Z production at the LHC. The current level of PDF un- certainty is critically reviewed and the possibility of reducing this uncertainty using early LHC data is investigated taking into account realistic expectations for measurement accuracy, kinematic cuts and backgrounds. 1 Introduction At leading order (LO), W and Z production occur by the process, q ¯ q → W/Z , and the momentum fractions of the partons participating in this subprocess are given by, x 1,2 = M √ s exp(±y), where M is the centre of mass energy of the subprocess, M = M W or M Z , √ s is the centre of mass energy of the reaction ( √ s = 14 TeV at the LHC) and y = 1 2 ln (E+pl) (E-pl) gives the parton rapidity. The kinematic plane for LHC parton kinematics is shown in Fig. 1. Thus, at central rapidity, the participating partons have small momentum fractions, x ∼ 0.005. Moving away from central rapidity sends one parton to lower x and one to higher x, but over the measurable rapidity range, |y| < 2.5, x values remain in the range, 10 -4 <x< 0.1. Thus, in contrast to the situation at the Tevatron, valence quarks are not involved, the scattering is happening between sea quarks. Furthermore, the high scale of the process Q 2 = M 2 ∼ 10, 000 GeV 2 ensures that the gluon is the dominant parton, see Fig. 1, so that these sea quarks have mostly been generated by the flavour blind g → q ¯ q splitting process. Thus the precision of our knowledge of W and Z cross-sections at the LHC is crucially dependent on the uncertainty on the momentum distribution of the gluon. HERA data have dramatically improved our knowledge of the gluon, as illustrated in Fig. 2, which shows W and Z rapidity spectra predicted from a global PDF fit which does not include the HERA data, compared to a fit including HERA data. The latter fit is the ZEUS-S global fit [1], whereas the former is a fit using the same fitting analysis but leaving out the ZEUS data. The full PDF uncertainties for both fits are calculated from the error PDF sets of the ZEUS-S analysis using LHAPDF [2] (see the contribution of M.Whalley to these proceedings). The predictions for the W/Z cross-sections, decaying to the lepton decay mode, are summarised in Table 1. The uncertainties in the predictions for these cross-sections have decreased from ∼ 16% pre-HERA to ∼ 3.5% post-HERA. The reason for this can be seen clearly in Fig. 3, where the sea and gluon distributions for the pre- and post-HERA fits are shown for several different Q 2 bins, together with their uncertainty bands. It is the dramatically increased precision in the low-x gluon PDF, feeding into increased precision in the low-x sea quarks, which has led to the increased precision on the predictions for W/Z production at the LHC. Further evidence for the conclusion that the uncertainties on the gluon PDF at the input scale (Q 2 0 =7 GeV 2 , for ZEUS-S) are the major contributors to the uncertainty on the W/Z cross-sections at Q 2 = M W (M Z ), comes from decomposing the predictions down into their contributing eigenvectors. Fig 4 shows the dominant contributions to the total uncertainty from eigenvectors 3, 7, and 11 which are eigenvectors which are dominated by the parameters which control the low-x, mid-x and high-x, gluon respectively. The post-HERA level of precision illustrated in Fig. 2 is taken for granted in modern analyses, such that W/Z production have been suggested as ‘standard-candle’ processes for luminosity measurement. However, when considering the PDF uncertainties on the Standard Model (SM) predictions it is necessary