Towards a Precise Parton Luminosity Determination at the CERN LHC

TL;DR

This work reframes LHC luminosity determination by targeting parton-parton luminosities through W and Z boson production, using lepton rapidity/pseudorapidity distributions to constrain the quark and antiquark PDFs, especially at low x and high Q^2. It demonstrates that W and Z observables are highly sensitive to the underlying $u,d,\bar{u},\bar{d}$ PDFs and that, with manageable data samples, the resulting parton luminosities can be determined with ~1% accuracy, enabling precise predictions for qq̄-initiated processes such as $W^{+}W^{-}$. The approach leverages cross-section ratios and combined W/Z measurements to mitigate luminosity and systematic uncertainties, and it outlines extending similar concepts to gluons via gluon-dominated channels to achieve a correlated, percent-level understanding of gluon luminosity. Overall, the method promises significant improvements in both luminosity calibration and the predictive power for high-energy quark- and gluon-initiated processes at the LHC.

Abstract

A new approach to determine the LHC luminosity is investigated. Instead of employing the proton-proton luminosity measurement, we suggest to measure directly the parton-parton luminosity. It is shown that the electron and muon pseudorapidity distributions, originating from the decay of W+, W- and Z0 bosons produced at 14 TeV pp collisions (LHC), constrain the x distributions of sea and valence quarks and antiquarks in the range from about 3 x 10**-4 to about 10**-1 at a Q**2 of about 10**4 GeV**2. Furthermore, it is demonstrated that, once the quark and antiquark structure functions are constrained from the W+,W- and Z0 production dynamics, other quark-antiquark related scattering processes at the LHC like q-qbar --> W+W- can be predicted accurately. Thus, the lepton pseudorapidity distributions provide the key to a precise parton luminosity monitor at the LHC, with accuracies of about +-1% compared to the so far considered goal of +-5%.

Figures (5)

• Figure 1: Expected rapidity (pseudorapidity) distribution of $W^{\pm}$ (a) and $\ell^{\pm}$ (b) originating from the reaction $q\bar{q} \rightarrow W^{\pm} \rightarrow \ell^{\pm} \nu$ at the LHC ($\sqrt{s}=14$ TeV and the MRS(A) structure functions mrsa). The assumed luminosity of 100 pb$^{-1}$ corresponds to about one day of data taking with a luminosity of $10^{33}~sec^{-1}~cm^{-2}$.
• Figure 2: The observable (a) charged lepton $p_{t}$ and (b) pseudorapidity $\eta$ distributions originating from the reaction $q\bar{q} \rightarrow W^{\pm} \rightarrow \ell^{\pm} \nu$ at the LHC ($\sqrt{s}=14$ TeV and the MRS(A) structure function mrsa) including all selection criteria discussed in the text.
• Figure 3: a) The detected charged lepton cross section ratio, $\sigma(\ell^{+} \nu)/\sigma(\ell^{-} \bar{\nu})$, originating from the reaction $q\bar{q} \rightarrow W^{\pm} \rightarrow \ell^{\pm} \nu$ as a function of the lepton pseudorapidity for the MRS(H) and MRS(A) structure function parametrisation. b) The relative changes of the charged lepton ratios of 3a) between the MRS(H) and MRS(A) parametrisations and also the cross section ratio of the $Z^{0}$ production using both parametrisations.
• Figure 4: The ratio of the accepted cross sections $\sigma(u\bar{d}\rightarrow W^{+} \rightarrow \ell^{+} \nu)$ and $\sigma(d\bar{d} \rightarrow W^{-} \rightarrow \ell^{-} \bar{\nu})$ as a function of the lepton pseudorapidity for four different structure functions mrsa.
• Figure 5: Rapidity dependence of the $\ell{^\pm}$ cross section predictions from different sets of structure functions relative to the one obtained from the MRS(A) parametrisation; a) for $\ell^{+}$, b) for $\ell^{-}$ and c) for the reconstructed $Z^{0}$.