Luminosity monitors at the LHC

TL;DR

This work assesses the theoretical precision of three main luminosity-monitoring strategies for the LHC: forward elastic scattering via the optical theorem, exclusive lepton-pair production through photon-photon fusion, and W/Z production with leptonic decays. It demonstrates that elastic-channel extrapolations can be controlled and that lepton-pair production, with appropriate cuts, yields negligible strong-interaction corrections, allowing clean QED predictions. For W and Z production, NNLO calculations reduce perturbative uncertainties, though PDF normalisation and input data limit the overall precision to about ±4% at the LHC. The paper also discusses parton-parton luminosities and unintegrated/skewed distributions as tools for constraining quark and gluon fluxes, suggesting a multifaceted approach to robust luminosity determination across different collider regimes.

Abstract

We study the theoretical accuracy of various methods that have been proposed to measure the luminosity of the LHC pp collider, as well as for Run II of the Tevatron p barp collider. In particular we consider methods based on (i) the total and forward elastic data, (ii) lepton-pair production and (iii) W and Z production.

Figures (9)

• Figure 1: (a) $\Delta^+$ production mediated by photon exchange, and (b) possible rescattering corrections.
• Figure 2: (a) $\pi^0$ production mediated by photon exchanges and (b) two of the possible rescattering corrections.
• Figure 3: (a) Lepton pair production in $pp$ collisions, (b) one of the rescattering corrections, and (c) a possible contamination coming from proton dissociation into $X, Y$ systems.
• Figure 4: The predictions of the cross sections for $W$ and $Z$ production and leptonic decay at the Tevatron and the LHC obtained from parton sets of LO, NLO and NNLO global analyses of the same data set MRST. The cross sections labelled LO, NLO and NNLO are as in (\ref{['eq:F16']}) and the dashed line is the NLO$^\prime$ prediction of (\ref{['eq:F17']}). The band of the NNLO predictions allow for the ambiguity in the NNLO splitting functions VN. Also shown are measurements obtained at the Tevatron WZCDFWZD0. The figure is taken from MRST.
• Figure 5: The solid squares and triangles are the predictions of the NLO$^\prime$ cross sections of (\ref{['eq:F17']}) for $W$ and $Z$ production and leptonic decay in $p\bar{p}$ collisions at $\sqrt{s} = 1.8~{\rm TeV}$ obtained using various NLO sets of MRST99 partons MRST1. The open square and small error bar are, respectively, the NLO and NNLO predictions of (\ref{['eq:F16']}) using the MRST00 partons MRST. Also shown are the experimental measurements from CDF WZCDF and D0 WZD0. For ease of reference $\pm 5\%$ lines are shown about the MRST99 default prediction. We thank W.J. Stirling for this figure, which combines results presented in MRST1MRST.